Tactical Missile Design Presentation Fleeman

2/24/2008 ELF 1

Professional Development Short Course on

Tactical Missile Design

Professional Development Short Course on

Tactical Missile Design

Eugene L. FleemanTactical Missile DesignE-mail: [email protected] Site: http://genefleeman.home.mindspring.com

2/24/2008 ELF 2

OutlineOutlineIntroduction / Key Drivers in the Design ProcessAerodynamic Considerations in Tactical Missile DesignPropulsion Considerations in Tactical Missile DesignWeight Considerations in Tactical Missile DesignFlight Performance Considerations in Tactical Missile DesignMeasures of Merit and Launch Platform IntegrationSizing ExamplesDevelopment ProcessSummary and Lessons LearnedReferences and CommunicationAppendices ( Homework Problems / Classroom Exercises, Example of Request for Proposal, Nomenclature, Acronyms, Conversion Factors, Syllabus )

2/24/2008 ELF 3

Emphasis Is on Physics-Based, Analytical Sizing of Aerodynamic Configuration

Emphasis Is on Physics-Based, Analytical Sizing of Aerodynamic Configuration

Safe, Arm, and FuzingPower SupplySeeker, Sensors, and ElectronicsLaunch Platform IntegrationAdditional Measures of MeritCostMiss DistanceWarheadWeightStructurePropulsionAero Flight PerformanceAero Stability & ControlAero Configuration Sizing

EmphasisArea

Primary EmphasisSecondary EmphasisTertiary EmphasisNot Addressed- -

2/24/2008 ELF 4

Superior Better Comparable Inferior

Axial Acceleration AGM-88Maneuverability AA-11Speed / altitude SM-3Dynamic pressure PAC-3Size JavelinWeight FIM-92Production cost GBU-31Observables AGM-129Range AGM-86Kills per use Storm ShadowTarget acquisition LOCAAS

Tactical Missile Characteristics

Comparison With Fighter Aircraft

––

–

–

Tactical Missiles Are Different from Fighter AircraftTactical Missiles Are Different from Fighter Aircraft

Example of State-of-the-Art

2/24/2008 ELF 5

Aero Configuration Sizing ParametersEmphasized in This Course

Aero Configuration Sizing ParametersEmphasized in This Course

Nose FinenessDiameter

Propulsion Sizing / Propellant or Fuel

Wing Geometry / Size

Stabilizer Geometry / Size

Flight Control Geometry / Size

Length

ThrustProfile

Flight Conditions ( α, M, h )

2/24/2008 ELF 6

Conceptual Design Process Requires Evaluation of Alternatives and Iteration

Conceptual Design Process Requires Evaluation of Alternatives and Iteration

• Mission / Scenario Definition

• Weapon Requirements, Trade Studies and Sensitivity Analysis

• Launch Platform Integration

• Weapon Concept Design Synthesis

• Technology Assessment and Dev Roadmap

InitialTech

InitialReqs

BaselineSelected

AltConcepts

Initial Carriage /Launch

Iteration

RefineWeapons

Req

Initial Revised

Trades / Eval Effectiveness / Eval

TechTrades

InitialRoadmap

RevisedRoadmap

Alternate Concepts ⇒ Select Preferred Design ⇒Eval / Refine

Update

Note: Typical conceptual design cycle is 3 to 9 months. House of Quality may be used to translate customer requirements to engineering characteristics. DOE may be used to efficiently evaluate the broad range of design solutions.

2/24/2008 ELF 7

Missile Concept Synthesis Requires Evaluation of Alternatives and Iteration


Yes

Define Mission Requirements

Establish Baseline

Aerodynamics

Propulsion

Weight

Trajectory

MeetPerformance?

Measures of Merit and ConstraintsNo

No

Yes

Resize / Alt Config / Subsystems / Tech

Alt Mission

Alt Baseline

2/24/2008 ELF 8

Examples of Air-Launched Missile Missions / Types

Examples of Air-Launched Missile Missions / Types

Air-to-air Example SOTA

• Short range ATA. AA-11. Maneuverability

• Medium range ATA. AIM-120. Performance / weight

• Long range ATA. Meteor. Range

Air-to-surface

• Short range ATS. AGM-114. Versatility

• Medium range ATS. AGM-88. Speed

• Long range ATS. Storm Shadow. Modularity

Permission of Missile Index. Copyright 1997©Missile.Index All Rights Reserved

10 feet

2/24/2008 ELF 9

Surface-to-surface Example SOTA• Short range STS. Javelin. Size

• Medium range STS. MGM-140. Modularity

• Long range STS. BGM-109. Range

Surface-to-air• Short range STA. FIM-92. Weight

• Medium range STA. PAC-3. Accuracy

• Long range STA. SM-3. High altitude

Examples of Surface-Launched Missile Missions / Types

Examples of Surface-Launched Missile Missions / Types

Permission of Missile.Index. Copyright 1997©Missile.Index All Rights Reserved

10 feet

2/24/2008 ELF 10

Aero Configuration Range / Time to Robust- Miss Observ- LaunchSizing Parameter Weight Maneuver Target ness Lethality Distance ables Survivability Cost Platform

Nose Fineness

Diameter

Length

Wing Geometry / Size

Stabilizer Geometry / Size

Flight Control Geometry / Size

Propellant / Fuel

Thrust Profile

Flight Conditions( α, M, h )

Aero Configuration Sizing Has High Impact on Mission Requirements

Aero Configuration Sizing Has High Impact on Mission Requirements

Impact on Weapon RequirementAero Measures of Merit Other Measures of Merit Constraint

–Very Strong Strong Moderate Relatively Low

2/24/2008 ELF 11

–

Alternatives for Precision StrikeCost per

ShotFuture Systems

Standoff platforms / hypersonic missiles

Overhead loitering UCAVs / hypersonic missiles

Overhead loitering UCAVs / light weight PGMs

Current Systems

Penetrating aircraft / subsonic PGMs

Standoff platforms / subsonic missiles

Note: Superior Good Average Poor

Number ofLaunch Platforms

RequiredTCT

Effectiveness

– –

–

Example of Assessment of Alternatives to Establish Future Mission Requirements

Example of Assessment of Alternatives to Establish Future Mission Requirements

Note: C4ISR targeting state-of-the-art for year 2010 projected to provide sensor-to-shooter / weapon connectivity time of less than 2 m and target location error ( TLE ) of less than 1 m for motion suspended target.

Measures of Merit

2/24/2008 ELF 12

C4ISR Tactical Satellites and UAVs Have High Impact on Mission Capability

C4ISR Tactical Satellites and UAVs Have High Impact on Mission Capability

Launch Platforms•Fighter Aircraft•Bomber•Ship / Submarine•UCAV

Precision Strike Weapons•Hypersonic SOW•Subsonic PGM•Subsonic CM

Launch Platforms•Fighter Aircraft•Bomber•Ship / Submarine•UCAV

Precision Strike Weapons•Hypersonic SOW•Subsonic PGM•Subsonic CM

Off-board Sensors•Tactical Satellite•UAV

Off-board Sensors•Tactical Satellite•UAV

Note: C4ISR targeting state-of-the-art for year 2010 projected to provide sensor-to-shooter / weapon connectivity time of less than 2 m and target location error ( TLE ) of less than 1 m for motion suspended target.

Time Critical Targets•TBM / TEL•SAM•C3•Other Strategic

Time Critical Targets•TBM / TEL•SAM•C3•Other Strategic

2/24/2008 ELF 13

Example of System-of-Systems Analysis to Develop Future Mission Requirements

Example of System-of-Systems Analysis to Develop Future Mission Requirements

1. Compare Targeting of Subsonic Cruise MissileVersus Hypersonic Missile

t0 t1

TBMLaunch

LaunchPt Rcvd

t2 t3

Cruise Missile Launch

HM Interceptat XXX nm

Range 3 > R2

Range 2 > R1

Range 1

1000 2000 3000 4000 5000Average Speed, fps

Tim

e, Mi

n

120

020406080

100

20406080

100

020000 4000 6000

Average Speed to Survive, fps

Altit

ude –

1000

ftLe

thali

ty / C

oncr

ete

Pene

tratio

n ( f

t ) 50403020100

1000 2000 3000 40000Impact Velocity, fps

W/H W3 > W2

W/H W2 > W1

Warhead W1

0

2. Time To Target

3. Alt / Speed / RCS RequiredFor Survivability

4. Lethality

Selected For All:• Value of Speed /

Range• Time Urgent Targets• High Threat

Environments• Buried Targets• Launch Platform

Alternatives• Operating and

Attrition Cost in Campaign

• Weapon Cost in Campaign

• Mix of Weapons in Campaign

• Cost Per Target Kill• C4ISR Interface

5. Campaign Model WeaponsMix ( CM, Hypersonic

Missile ) Results( eg., Korean Scenario )

HypersonicMissile Launch

RCS1 RCS2 > RCS1

1-2 3-42-3

4-5

2/24/2008 ELF 14

Example of Technological Surprise Driving Immediate Mission Requirements

Example of Technological Surprise Driving Immediate Mission Requirements

Archer AA-11 / R-73 ( IOC 1987 )Performance

•> +/- 60 deg off boresight•20 nm range

New Technologies•TVC•Split canard•Near-neutral static margin•+/- 90 deg gimbal seeker•Helmet mounted sight

Sidewinder AIM-9L ( IOC 1977 )Performance

•+/- 25 deg off boresight•6.5 nm range

Note: AIM-9L maneuverability shortfall compared to Archer drove sudden development of AIM-9X.

2/24/2008 ELF 15



Yes

Establish Baseline

Aerodynamics

Propulsion

Weight

Trajectory

MeetPerformance?


No

Yes


Alt Mission

Alt Baseline


2/24/2008 ELF 16

Baseline Design Benefits and GuidelinesBaseline Design Benefits and Guidelines

Benefits of Baseline DesignAllows simple, conceptual design methods to be used with good accuracyWell documented benchmark / configuration control / traceabilitybetween cause and effectBalanced subsystemsGives fast startup / default values for design effortProvides sensitivity trends for changing designBaselines can cover reasonable range of starting points

Baselines can normally be extrapolated to ±50% with good accuracyGuidelines

Don’t get locked-in by baselineBe creativeProject state-of-the-art ( SOTA ) if baseline has obsolete subsystems

Sensors and electronics almost always need to be updated

2/24/2008 ELF 17

Configuration Drawing Weight / Geometry Flow Path Geometry

Aerodynamics Ramjet Propulsion Rocket Propulsion

Flight Performance House of Quality Paredo Sensitivity for DOE

InletConical forebody angle, deg 17.7Ramp wedge angle, deg 8.36Capture area, ft2 0.52Throat area, ft2 0.29

BodyLength, in 171.0Diameter, in 20.375Fineness ratio 8.39Volume, ft3 28.33Wetted area, ft2 68.81Base area, ft2 ( cruise ) 0.58Boattail fineness ratio N/ANose half angle, deg 15.0

Tail ( Exposed )Area ( 2 panels ), ft2 2.24Wetted area ( 4 panels ), ft2 8.96Aspect ratio ( exposed ) 1.64Taper ratio 0.70Root chord, in 16.5Span, in. ( exposed ) 23.0L.E. sweep, deg 37.0M.A.C., in 14.2Thickness ratio 0.04X MAC, in 150.5Y MAC, in ( from root chord ) 5.4

Reference values:Reference area, ft2 2.264Reference length, ft 1.698

•

•

•

•

•

••

••

•

M, Mach Number

I sp, S

peci

fic Im

puls

e, s

ec

1,500

1,000

500

00 1 2 3 4

Note: φ = 1

30

20

10

00 1.0 2.0 3.0 4.0

Boos

t Thr

ust ~

1000

lbs

Time ~ sec 5.0 6.0

( ISP )Booster = 250 sec

3.0

2.5

2.0Burn

out M

ach

Num

ber

h, Altitude 1,000 ft

2.0

1.0

0

ML = 0.80constant altitude flyout

Boos

t Ran

ge ~

nm

0 20 40 600 20 40 60 80h, Altitude 1,000 ft

Note: Constant altitude flyout

500

400

300

200

100

00 1 2 3 4

Ran

ge ~

nm

M, Mach Number

h = SL

20,000 ft

40,000 ft

60,000 ft

Note:• ML = 0.8, Constant Altitude FlyoutExample:• Breguet Range for Mach 3 / 60 Kft flyout: Rmax = V ISP ( L / D )Max ln [ WBC / ( WBC - Wf )] = 2901 ( 950 ) ( 3.15 ) ln ( 1739 / ( 1739 - 476 )) = 2,777,192 ft or 457 nm

Nose 15.9 15.7Forebody 42.4 33.5

Guidance 129.0 33.5Payload Bay 64.5 60.0

Warhead 510.0 60.0Midbody 95.2 101.2

Inlet 103.0 80.0Electrical 30.0 112.0Hydraulic 20.0 121.0Fuel Distribution 5.0 121.0

Aftbody 44.5 142.5Engine 33.5 142.5

Tailcone 31.6 165.0Exit Duct 31.0 165.0Controls 37.0 164.0

Fins ( 4 ) 70.0 157.2End of Cruise 1,262.6 81.8Ramjet Fuel ( 6.9 ft3 ) 476.0 87.0Start of Cruise 1,738.6 83.2

Boost Nozzle ( Ejected ) 31.0 164.0Frangible Port 11.5 126.0

End of Boost 1,781.1 84.9Boost Propellant 449.0 142.5Booster Ignition 2,230.1 96.5

Component Weight, lb CG Sta, In.

.4

.3

.2

.1

0

C D 0

M, Mach Number0 1 2 3 4

C N

δ

~ pe

r deg

0 1 2 3 4

C m

δ

~ pe

r deg

-.4

-.2

0

.10

.05

0

SRef = 2.264 ft2

LRef = DRef = 1.698 ftXcg @ Sta 82.5 in.

M, Mach Number

+ .4

0

-.4

-.8

-1.2

-1.6

Pitc

hing

Mom

ent C

oeffi

cien

t, C

m

α, Angle of Attack ~ deg0 4 8 12 16

Mach 4.0

3.0

2.0

1.5

1.2

SRef = 2.264 ft2

LRef = DRef = 1.698 ftXcg @ Sta 82.5 in.

Nor

mal

For

ce C

oeffi

cien

t, C

N


Mach 1.21.52.03.04.0

.40

.30

.20

.10

0

Axi

al F

orce

Coe

ffici

ent,

CA

0 4 8 12 16

Mach 1.2

1.5

2.0

3.04.0

SRef = 2.264 ft2

LRef = Dref = 1.698 ftXcg @ Sta 82.5 in.

4.0

3.0

2.0

1.0

0

α, Angle of Attack ~ deg

•

•

••

•

•

• •

•

• •

•• •

20,000

15,000

10,000

5,000

00 1 2 3 4

M, Mach Number

T, N

et T

hrus

t, lb

Note: φ = 1

h = SL

h = 20K ft

h = 40K ft

h = 60K ft

h = 80K ft

Example of Missile Baseline DataExample of Missile Baseline Data

Ac Inlet capture areaAIT Inlet throat areaSRef Reference areaA5 Nozzle throat areaIsp Specific impulseφ Equivalence ratio – operating fuel / air ratio divided by fuel / air ratio for stochiometric combustion

Ramjet Engine Station Identification

0Free Stream

2 3 4 5 6Subscripts0 Free stream conditions ( Ramjet Baseline A0 = 75.4 in2 at Mach 4, α = 0 deg, Note: AC = 114 in2 )1 Inlet throat ( Ramjet Baseline A1 = AIT = 41.9 in2 )2 Diffuser exit ( Ramjet Baseline A2 = 77.3 in2 )3 Flame holder plane ( Ramjet Baseline A3 = 287.1 in2 )4 Combustor exit ( Ramjet Baseline A4 = 287.1 in2 )5 Nozzle throat ( Ramjet Baseline A5 = 103.1 in2 )6 Nozzle exit ( A6 = 233.6 in2 )Ref Reference Area ( Ramjet Baseline Body Cross-sectional Area, SRef = 326 in2 )

1Inlet Throat

( CD0 )Nose Corrected = ( CD0

)Nose Uncorrected x ( 1 - Ac / SREF )

120°

Ac = 114 in2

20.375 in diameterSource: Bithell, R.A. and Stoner, R.C. “Rapid Approach for Missile Synthesis”, Vol. II, Air-breathing Synthesis Handbook, AFWAL TR 81-3022, Vol. II, March 1982.

Sta 0.

Guidance WarheadRamjet Fuel Boost Propellant

Booster, and Ramjet Engine

Boost Nozzle

Tail ConeAft-bodyMid-bodyPayload BayFore-bodyNose23.5 43.5 76.5 126.0

159.0 171.0

Sta 150.311.6

11.5

16.5

37°

Note: Dimensions are in inches

ChinInlet Transport Air Duct

20.375 dia

-1

-0.5

0

0.5

1

1.5

ISP FuelWeight

Thrust CD0, Zero-Lift Drag

Coefficient

CLA, Lift-Curve-Slope

Coefficient

InertWeight

Parameter

Nond

imen

siona

l Ran

ge S

ensit

ivity

to

Par

amet

er

Sea Level Flyout at Mach 2.3 20 Kft Flyout at Mach 2.540 Kft Flyout at Mach 2.8 60 Kft Flyout at Mach 3.0

2/24/2008 ELF 18

Baseline Design Data Allows Correction of Computed Parameters in Conceptual DesignBaseline Design Data Allows Correction of

Computed Parameters in Conceptual Design

PCD, C Parameter of conceptual design, correctedPB, C Parameter of baseline, corrected ( actual data )PB, U Parameter of baseline, uncorrected ( computed )PCD, U Parameter of conceptual design, uncorrected (computed )Example

• Ramjet Baseline with RJ-5 fuel ( heating value = 11,300,000 ft-lbf / lbm ) • Advanced Concept with slurry fuel ( 40% JP-10 / 60% boron carbide =

18,500,000 ft-lbf / lbm ) • Flight conditions: Mach 3.5 cruise, 60k ft altitude, combustion temperature

4,000 R• Calculate specific impulse ( ISP )CD,C for conceptual design, based on corrected

baseline data– ( ISP )B, C = 1,120 s– ( ISP )B, U = 1387 s– ( ISP )CD, U = 2,271 s– ( ISP )CD, C = [( ISP )B, C / ( ISP )B, U ] ( ISP )CD, U = [( 1120 ) / ( 1387 )] ( 2271 ) = 0.807 ( 2271 )

= 1,834 s

PCD, C = ( PB, C / PB, U ) PCD, U

2/24/2008 ELF 19

Summary of This ChapterSummary of This Chapter

Overview of Missile Design ProcessExamples

Tactical missile characteristicsConceptual design processSOTA of tactical missilesAerodynamic configuration sizing parametersProcesses that establish mission requirementsProcess for correcting design predictions

Discussion / Questions?Classroom Exercise

2/24/2008 ELF 20

Introduction ProblemsIntroduction Problems1. The missile design team should address the areas of mission / scenario

definition, weapon requirements, launch platform integration, design, and t_______ a_________.

2. The steps to evaluate missile flight performance require computing aerodynamics, propulsion, weight, and flight t_________.

3. Air-to-air missile characteristics include light weight, high speed, and high m______________.

4. Air-to-surface missiles are often versatile and m______.5. Four aeromechanics measures of merit are weight, range, maneuverability,

and t___ to target.6. The launch platform often constrains the missile span, length, and w_____.7. An enabling capability for hypersonic strike missiles is fast and accurate

C____.8. An enabling capability for large off boresight air-to-air missiles is a h_____

m______ sight.9. A baseline design improves the accuracy and s____ of the design process.

2/24/2008 ELF 21


2/24/2008 ELF 22



Yes

Establish Baseline

Propulsion

Weight

Trajectory

MeetPerformance?


No

Yes


Alt Mission

Alt Baseline


Aerodynamics

2/24/2008 ELF 23

Missile Diameter TradeoffMissile Diameter Tradeoff

Drivers toward Small Diameter• Decrease drag• Launch platform diameter constraint

Drivers toward Large Diameter• Increase seeker range and signal-to-noise, better resolution and tracking• Increase blast frag and shaped charge warhead effectiveness ( larger diameter

⇒ higher velocity fragments or higher velocity jet )• Increase body bending frequency• Subsystem diameter packaging • Launch platform length constraint

Typical Range in Body Fineness Ratio 5 < l / d < 25• Man-portable anti-armor missiles are low l / d ( Javelin l / d = 8.5 )• Surface-to-air and air-to-air missiles are high l / d ( AIM-120 l / d = 20.5 )

2/24/2008 ELF 24

Small Diameter Missiles Have Low DragSmall Diameter Missiles Have Low Drag

10

100

1000

10000

100000

4 8 12 16 20

d, Diameter, in

D / C

D, D

rag

/ Dra

g Co

effic

ient,

lb

Dynamic Pressure =1,000 psfDynamic Pressure =5,000 psfDynamic Pressure =10,000 psf

Example for Rocket Baseline:d = 8 in = 0.667 ftMach 2, h = 20k ft, ( CD0

)Powered = 0.95q = 1/2 ρ V2 = 1/2 ρ ( M a )2

= 1/2 ( 0.001267 ) [( 2 ) ( 1037 )]2 = 2,725 psfD0 / CD0

= 0.785 ( 2725 ) ( 0.667 )2 = 952D0 = 0.95 ( 952 ) = 900 lb

D = CD q SRef = 0.785 CD q d2

Note: D = drag in lb, CD = drag coefficient, q = dynamic pressure in psf, d = diameter ( reference length ) in ft

2/24/2008 ELF 25

Large Diameter Radar Seeker Provides Longer Detection Range and Better Resolution

Large Diameter Radar Seeker Provides Longer Detection Range and Better Resolution

1

10

100

0 5 10 15 20

d, Diameter, Inches

Example Seeker Range for Transmitted Power Pt = 100 W, nmExample Seeker Range for Transmitted Power Pt = 1,000 W, nmExample Seeker Range for Transmitted Power Pt = 10,000 W, nmExample Seeker Beam Width, deg

RD = { π σ n3/4 / [ 64 λ2 K T B F L ( S / N ) ]}1/4 Pt 1/4 d

θ3dB = 1.02 λ / d, θ3dB in rad

Assumptions: Negligible clutter, interference, and atmospheric attenuation; non-coherent radar ( only signal amplitude integrated ); uniformly illuminated circular aperture; receiver sensitivity limited by thermal noise

Symbols:

σ = Target radar cross section, m2

n = Number of pulses integratedλ = Wavelength, mK = Boltzman’s constant = 1.38 x 10-23 J / KT = Receiver temperature, K B = Receiver bandwidth, HzF = Receiver noise factorL = Transmitter loss factorS / N = Signal-to-noise ratio for target detectionPt = Transmitted power, Wd = Antenna diameterExample: Rocket Baselined = 8 in = 0.20 m, Pt = 1000 W, λ = 0.03 m ( f = 10 GHz )RD = Target detection range = { π ( 10 ) ( 100 )3/4 / [ 64 (

0.03 )2 ( 1.38 x 10-23 ) ( 290 ) ( 106 ) ( 5 ) ( 5 )( 10 )]}1/4 ( 1000 )1/4 ( 0.203 ) = 13,073 m or 7.1 nm

θ3dB = 3-dB beam width = 1.02 ( 0.03 ) / 0.203 = 0.1507 rad or 8.6 deg

Note for figure: σ = 10 m2, n = 100, λ = 0.03 m ( f = Transmitter frequency = 10 x 109 Hz ), T = 290 K, B = 106 Hz ( 10-6 s pulse ), F = 5, L = 5, S / N = 10

2/24/2008 ELF 26

Large Diameter IR Seeker Provides Longer Detection Range and Better Resolution

Large Diameter IR Seeker Provides Longer Detection Range and Better Resolution

1

10

100

0 2 4 6 8 10

do, Optics Diameter, Inches

Example Seeker Range for Exo-atmospheric, kmExample Seeker Range for Humidity at 7.5 g / m3, kmExample Seeker Range for Rain at 4 mm / hr, kmExample Seeker IFOV, 10-5 rad

RD = { ( IT )Δλ ηa Ao { D* / [( Δfp )1/2 ( Ad )1/2 ]} ( S / N )D-1 }1/2

IFOV = dp / [ ( f-number ) do ]

Example: do = 5 in = 0.127 m, exo-atmosphericLλ = 3.74 x 104 / { 45 { e{ 1.44 x 104 / [ 4 ( 300 ) ]} – 1 }} = 0.000224 W cm-2 sr-2

μm-1, ( IT )Δλ = 0.5 ( 0.000224 ) ( 4.2 – 3.8 ) 2896 = 0.1297 W / sr, Ad = 256 x 256 x ( 20 μm )2 = 0.262 cm2, f-number = 20 / [ 2.44 ( 4 ) ] = 2.05RD = { 0.1297 ( 1 ) ( 0.01267 ) { 8 x 1011 / [( 250 )1/2 ( 0.262 )1/2 ]} ( 1 )-1

}1/2 = 12, 740 mIFOV = 0.000020 / [ 2.05 ( 0.127 )] = 0.0000769 rad

Figure: dT = 2 ft ( 60.96 cm ), TT = 300 K, λ1 = 3.8 μm, λ2 = 4.2 μm, ε = 0.5, λ = 4 μm, FPA ( 256 x 256, 20 μm ), D* = 8 x 1011 cm Hz1/2 / W, ( S / N )D = 1, Δfp = 250 Hz.

RD = Target detection range, m( IT )Δλ = Target radiant intensity between λ1 and λ2= ε

Lλ ( λ2 - λ1 ) AT, W / srηa = Atmospheric transmissionAo = Optics aperture area, m2

D* = Specific detectivity, cm Hz1/2 / WΔfp = Pixel bandwidth, Hz Ad = Detectors total area, cm2

( S / N )D = Signal-to-noise ratio required for detectionε = Emissivity coefficientLλ = Spectral radiance ( Planck’s Law ) = 3.74 x 104 / {

λ5 { e[ 1.44 x 104 / ( λ TT )] – 1 }}, W cm-2 sr-2 μm-1

λ2 = Upper cutoff wavelength for detection, μmλ1 = Lower cutoff wavelength for detection, μmAT = Target planform area, cm2

λ = Average wavelength, μmTT = Target temperature, KIFOV = Instantaneous field-of-view of pixel, radf-number = dspot / ( 2.44 λ )dp = Pixel diameter, either μmdspot = Spot resolution if diffraction limited = dp, μm

2/24/2008 ELF 27

Missile Fineness Ratio May Be Limited by Impact of Body Bending on Flight ControlMissile Fineness Ratio May Be Limited by Impact of Body Bending on Flight Control

100

1000

10000

0 10 20 30l / d, length / diameter

Firs

t Mod

e Bod

y Ben

ding

Fre

quen

cy, r

ad / s

E t / W = 1,000 per inE t / W = 10,0000 per inE t / W = 100,000 per in

Derived from: AIAA Aerospace Design Engineers Guide, American Institute of Aeronautics and Astronautics, 1993.

ωBB = 18.75 { E t / [ W ( l / d ) ]}1/2

Example for Rocket Baseline:l / d = 18EAVG = 19.5 x 106 psitAVG = 0.12 inW = 500 lbE t / W = 19.5 x 106 ( 0.12 ) / 500 = 4680 per inωBB = 18.75 ( 4680 / 18 )1/2 = 302 rad / sec = 48 HzωActuator = 100 rad / sec = 16 HzωBB / ωActuator = 302 / 100 = 3.02 > 2

Assumes body cylinder structure, thin skin, high fineness ratio, uniform weight distribution, free-free motion. Neglects bulkhead, wing / tail stiffness.ωBB = First mode body bending frequency, rad / sE = Modulus of elasticity in psit = Thickness in inchesW = Weight in lbl / d = Fineness ratio

2/24/2008 ELF 28

Nose Fineness TradeoffNose Fineness Tradeoff

d

Example: lN / d = 5 tangent ogive

Example: lN / d = 0.5 ( hemisphere )

High Nose Fineness Superior Aerodynamically, Low Observables

Low Nose Fineness Ideal Electromagnetically, High Propellant Length / Volume

Moderate Nose Fineness Compromise Dome

d

Examples: lN / d = 2 tangent ogive lN / d = 2 faceted lN / d = 2 window lN / d = 2 multi-lens

dWindow

2/24/2008 ELF 29

Firestreak

Mistral

SLAM-ER

JASSM

THAAD

Faceted and Flat Window Domes Can Have Low Dome Error Slope, Low Drag, and Low RCS

Faceted and Flat Window Domes Can Have Low Dome Error Slope, Low Drag, and Low RCS

Faceted Dome ( Mistral ) Video

2/24/2008 ELF 30

Supersonic Body Drag Driven by Nose Fineness while Subsonic Drag Driven by Wetted Area

Supersonic Body Drag Driven by Nose Fineness while Subsonic Drag Driven by Wetted Area

0.01

0.1

1

10

0 1 2 3 4 5M, Mach Number

(CD0)Body,Wave;lN / d = 0.5(CD0)Body,Wave;lN / d = 1(CD0)Body,Wave;lN / d = 2(CD0)Body,Wave;lN / d = 5(CD)Base,Coast

Example for Rocket Baseline:( CD0

)Body, Wave ( CD0)Body, Friction ( CD )Base

lN / d = 2.4, Ae = 11.22 in2, SRef = 50.26 in2, M = 2, h = 20k ft, q = 2725 psf, l / d = 18, l = 12 ft

( CD0)Body, Friction = 0.053 ( 18 ) { ( 2 ) / [( 2725 )

( 12 ) ]}0.2 = 0.14( CD )Base Coast = 0.25 / 2 = 0.13( CD )Base Powered = ( 1 - 0.223 ) ( 0.25 / 2 ) = 0.10( CD0

)Body, Wave = 0.14( CD0

)Body, Coast = 0.14 + 0.13 + 0.14 = 0.41( CD0

)Body, Powered = 0.14 + 0.10 + 0.14 = 0.38

( CD0)Body = (CD0

)Body,Friction + ( CD0)Base + ( CD0

)Body, Wave

(CD0)Body,Friction = 0.053 ( l / d ) [ M / ( q l )]0.2. Based on Jerger reference, turbulent boundary layer, q in psf, l in ft.

( CD0 )Base,Coast = 0.25 / M, if M > 1 and (CD0

)Base,Coast = ( 0.12 + 0.13 M2 ), if M < 1( CD0

)Base,Powered = ( 1 – Ae / SRef ) ( 0.25 / M ), if M > 1 and ( CD0 )Base,Powered = ( 1 – Ae / SRef ) ( 0.12 + 0.13 M2 ), if M < 1

( CD0)Body, Wave = ( 1.59 + 1.83 / M2 ) { tan-1 [ 0.5 / ( lN / d )]}1.69, for M > 1. Based on Bonney reference, tan-1 in rad.

Note: ( CD0)Body,Wave = body zero-lift wave drag coefficient, ( CD0

)Base = body base drag coefficient, ( CD0)Body, Friction = body skin

friction drag coefficient, ( CD0)Body = body zero-lift drag coefficient, lN = nose length, d = missile diameter, l = missile body

length, Ae = nozzle exit area, SRef = reference area, q = dynamic pressure, tan-1 [ 0.5 / ( lN / d )] in rad.

2/24/2008 ELF 31

Moderate Nose Tip Bluntness Causes a Negligible Change in Supersonic Drag

Moderate Nose Tip Bluntness Causes a Negligible Change in Supersonic Drag

Steps to Calculate Wave Drag of a Blunted Nose1. Relate blunted nose tip geometry to pointed nose tip geometry

2. Compute (CD0)Wave,SharpNose for sharp nose, based on the body reference area

( CD0)Wave,SharpNose = ( 1.59 + 1.83 / M2 ) { tan-1 [ 0.5 / ( lN / d )]}1.69

3. Compute ( CD0)Wave,Hemi of the hemispherical nose tip ( lNoseTip / dNoseTip = 0.5 ), based on the

nose tip area( CD0

)Wave,Hemi = ( 1.59 + 1.83 / M2 ) {[ tan-1 ( 0.5 / ( 0.5 )]}1.69 = 0.665 ( 1.59 + 1.83 / M2 )

4. Finally, compute ( CD0)Wave,BluntNose of the blunt nose, based on the body reference area

( CD0)Wave,BluntNose = ( CD0

)Wave,SharpNose ( SRef - SNoseTip ) / SRef + ( CD0)Wave,Hemi SNoseTipi / SRef

Example Rocket Baseline ( dRef = 8 in ) with 10% Nose Tip Bluntness at Mach 2• ( CD0

)Wave,SharpNose = [ 1.59 + 1.83 / ( 2 )2 ] [ tan-1 ( 0.5 / 2.4)]1.69 = 0.14• dNoseTip = 0.10 ( 8 ) = 0.8 in• SNoseTip = π dNoseTip

2 / 4 = 3.1416 ( 0.8 )2 / 4 = 0.503 in2 = 0.00349 ft2

• ( CD0)Wave,Hemi = 0.665 [ 1.59 + 1.83 / ( 2 )2 ] = 1.36

• ( CD0)Wave,BluntNose = 0.14 ( 0.349 - 0.003 ) / 0.349 + ( 1.36 ) ( 0.003 ) / ( 0.349 ) = 0.14 + 0.01 = 0.15

dRefdNoseTip

lN

2/24/2008 ELF 32

Boattail Decreases Base Pressure Drag AreaBoattail Decreases Base Pressure Drag Area

Without Boattail

With Boattail

During Motor Burn After Motor Burnout

Base Pressure Drag Area

θBT

Note: Boattail angle θBT and boattail diameter dBT limited by propulsion nozzle packaging, tail flight control packaging, and flow separation

dRef

dBT

Reference: Chin, S. S., Missile Configuration Design, McGraw-Hill Book Company, New York, 1961

2/24/2008 ELF 33

Boattailing Reduces Drag for Subsonic MissilesBoattailing Reduces Drag for Subsonic Missiles0.45

0.40

0.05

0.10

0.15

0.20

0.25

0.30

0.35

C DO, E

xam

ple Z

ero-

Lift

Drag

Coe

fficie

nt

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5M∞

Note: Boatail half angle should be less than 10 deg, to avoid flow separattion.Source: Mason, L.A., Devan, L. and Moore, F.G., “Aerodynamic Design Manual for Tactical Weapons,” NSWC TR 81-156, July 1981

3.00 6.00 1.50

Center bodyNose

10.50

dBT / dRef = 1.0dBT / dRef = 0.9dBT / dRef = 0.8dBT / dRef = 0.6dBT / dRef = 0.4

Boattail

Note:dBT = Boattail DiameterdRef = Body Reference Diameter

2/24/2008 ELF 34

Note:If α negative, CN negativeBased on slender body theory ( Pitts, et al ) and cross flow theory ( Jorgensen ) referencesValid for l / d > 5Example l / d = length / diameter = 20d = 2 ( a b )1/2

φ = 0°

Lifting Body Has Higher Normal ForceLifting Body Has Higher Normal Force

CN,Example NormalForce

Coefficient for l / d = 20

150

100

50

0 0 20 40 60 80 100

α, Angle of Attack, Deg

φ2a

2b

a / b = 3

a / b = 2

a / b = 1

⏐ CN ⏐ = [⏐( a / b ) cos2 φ + ( b / a ) sin2 φ ⏐] [⏐ sin ( 2α ) cos ( α / 2 ) ⏐ + 2 ( l / d ) sin2 α ]

CN

2/24/2008 ELF 35

L / D Is Impacted by CD0, Body Fineness, and Lifting Body Cross Section Geometry

L / D Is Impacted by CD0, Body Fineness, and Lifting Body Cross Section Geometry

L / D,Lift / Drag

4

3

2

1

0 0 20 40 60 80 100α, Angle of Attack, DegNote:

• If α negative, L / D negative•d = 2 ( a b )1/2

•Launch platform span constraints ( e.g., VLS launcher ) and length constraints ( e.g., aircraft compatibility ) may limit missile aero configuration enhancements

L / D = CL / CD = ( CN cos α – CD0 sin α ) / ( CN sin α + CD0 cos α )For a lifting body, ⏐ CN ⏐ = [⏐( a / b ) cos2 ( φ ) + ( b / a ) sin2 ( φ ) ⏐] [⏐ sin ( 2α ) cos ( α / 2 ) ⏐ + 2 ( l / d ) sin2 α ]

High drag, low fineness body ( a / b = 1, l / d = 10, CDO = 0.5 )Low drag nose ( a / b = 1, l / d = 10, CDO = 0.2 )High fineness, low drag ( a / b = 1, l / d = 20, CDO = 0.2 )Lifting body, high fineness, low drag ( a / b = 2 @ φ = 0°, l / d = 20, CDO = 0.2 )

φ2a

2bCN

2/24/2008 ELF 36

Lifting Body Requires Flight at Low Dynamic Pressure to Achieve High Aero Efficiency

Lifting Body Requires Flight at Low Dynamic Pressure to Achieve High Aero Efficiency

0

1

2

3

4

100 1000 10000 100000

q, Dynamic Pressure, lb / ft2

Exam

ple

L / D

, Lift

/ Dr

ag

Circular Cross Section ( a / b = 1 ) Lifting Body ( a / b = 2 )

L / D = CL / CD = ( CN cos α – CDO sin α ) / ( CN sin α + CDO cos α )⏐ CN ⏐ = [⏐( a / b ) cos2 ( φ ) + ( b / a ) sin2 ( φ ) ⏐] [⏐ sin ( 2α ) cos ( α / 2 ) ⏐ + 2 ( l / d ) sin2 α ]

Note. Example figure based on following assumptions:Body lift only ( no surfaces ), cruise flight ( lift = weight ), W = L = 2,000 lb, d = 2 ( a b )1/2, S = 2 ft2, l / d = 10, CD0 = 0.2

Example:

q = 500 psf

•a / b = 1 ⇒ L / D = 2.40

•a / b = 2 ⇒ L / D = 3.37

q = 5,000 psf

•a / b = 1 ⇒ L / D = 0.91

•a / b = 2 ⇒ L / D = 0.96

2/24/2008 ELF 37

6

5

4

3

Body Planform Area( Body Volume )2/3

( L / D

) Max

, ( L

ift / D

rag

) Max Lower

Radar Cross

Section

TailoredWeapons

ConventionalWeapons

( circular cross section )

Trade-off of Low Observables and ( L / D )Max Versus Volumetric Efficiency

Trade-off of Low Observables and ( L / D )Max Versus Volumetric Efficiency

2 4 6 8 10

Advantages:• ( L / D )Max• Low RCS

Advantages:• Payload• Launch Platform Integration

Circular Cross Section

2/24/2008 ELF 38

Δ Cm / Δ α and Static Margin Define Static Stability

Δ Cm / Δ α and Static Margin Define Static Stability

Cm

Statically Stable: ΔCm / Δα < 0, with xac behind xcg

δ1 δ2

Cm

Statically Unstable: ΔCm / Δα > 0, with xac in front of xcg

δ1

δ2

Non-oscillatoryConvergent

OscillatoryConvergent

t

Non-oscillatoryDivergent

OscillatoryDivergent

t

α α

αα

Note: Statically unstable missile requires high bandwidth autopilot.

Autopilot negative rate feedback provides stability augmentation.

xCG

xAC

xCG

xAC

2/24/2008 ELF 39

Body Aerodynamic Center Is a Function of Angle of Attack, Nose Fineness, and Body Length

Body Aerodynamic Center Is a Function of Angle of Attack, Nose Fineness, and Body Length

0

1

2

3

4

5

0 20 40 60 80 100

Angle of Attack, Deg

Dist

ance

to B

ody A

erod

ynam

icCe

nter

/ Le

ngth

of N

ose

total length of body /length of nose = 1total length of body /length of nose = 2total length of body /length of nose = 5total length of body /length of nose = 10

( xAC )B / lN = 0.63 ( 1 - sin2 α ) + 0.5 ( lB / lN ) sin2 α

Note: Based on slender body theory ( Pitts, et al ) and cross flow theory ( Jorgensen ) references. No flare. ( xAC )B = Location of body aerodynamic center, lN = length of nose, α = angle of attack, lB = total length of body.

Example:Rocket Baseline BodylB / lN = 143.9 / 19.2 = 7.49α = 13 deg( xAC )B / lN = 0.81

19.2 143.9

2/24/2008 ELF 40

Based on Slender Body Theory:( CNα )F = 2 [( dF / d )2 – 1 ]( xac )F = xF + 0.33 lF [ 2 ( dF / d ) + 1 ] / [ ( dF / d ) + 1 ] ( CNα

)B = 2 per rad( xac )B = 0.63 lN

ΣM = 0 at Aerodynamic Center. For a Body-Flare:( CNα

)B {[ xCG – ( xAC )B ] / d } + ( CNα)F [ xCG – ( xAC )F ] / d = - [( CNα

)B + ( CNα)F ]

[( xAC – xCG ) / d ]

Static Margin for a Body-Flare( xAC – xCG ) / d = - {( CNα

)B {[ xCG – ( xAC )B ] / d } + ( CNα)F {[ xCG – ( xAC )F ] / d }} /

[( CNα)B + ( CNα

)F ]

Flare Increases Static StabilityFlare Increases Static Stability

+M+α

x = 0 ( xac )B

( CNα)B ( CNα )F

lBlN( xac )F

xFxCG

d dF

xAC

CNα= ( CNα

)B + ( CNα )F

2/24/2008 ELF 41

Example of Static Margin for THAAD ( Statically Unstable Missile )

( CNα )F = 2 [( 18.7 / 14.6 )2 – 1 ] = 2 [(1.28)2 – 1 ] = 1.28 per rad( xac )F = 230.9 + 0.33 ( 12.0 )[ 2 ( 18.7 / 14.6 ) + 1 ] / [ ( 18.7 / 14.6 ) + 1 ] = 237.1 in( xac )B = 0.63 ( 91.5 ) = 57.7 inxCGLaunch = 146.9 in( xAC – xCG )Launch / d = - { 2 {[ 146.9 – 57.7 ] / 14.6 } + 1.28 {[ 146.9 – 237.1 ] / 14.6 }} / [ 2 + 1.28 ] = - 0.41

Flare Increases Static Stability ( cont )Flare Increases Static Stability ( cont )

( CNα)B

( xac )B = 57.7 91.5 146.9

14.6 18.7 in

( xac )F = 237.1230.9 242.9

( CNα )F

xAC = 140.9

CNα= ( CNα

)B + ( CNα )F

2/24/2008 ELF 42

Tail Stabilizers Have Lower Drag While Flares Have Lower Aero Heating and Stability ChangesTail Stabilizers Have Lower Drag While Flares

Have Lower Aero Heating and Stability Changes

Type Stabilizer Drag Span Heating ΔCNαTail Control

Flare ( e.g., THAAD )

Tails ( e.g., Standard Missile )

Note: Superior Good Average Poor –

––

– –

2/24/2008 ELF 43

Wing Sizing TradesWing Sizing TradesAdvantages of Small Wing / Strake / No Wing

• Range in high supersonic flight / high dynamic pressure• Max angle of attack• Launch platform compatibility• Lower radar cross section• Volume and weight for propellant / fuel

Advantages of Larger Wing• Range in subsonic flight / low dynamic pressure• Lower guidance time constant*• Normal acceleration*• High altitude intercept*• Less body bending aeroelasticity ( wing stiffens body )• Less seeker error due to dome error slope ( lower angle of attack )• Less wipe velocity for warhead ( lower angle of attack )• Lower gimbal requirement for seeker

*Based on assumption of aerodynamic control and angle of attack below wing stall

2/24/2008 ELF 44

Stinger FIM-92 Grouse SA-18 Grison SA-19 ( two stage ) Gopher SA-13

Starburst Mistral Kegler AS-12 Archer AA-11

Gauntlet SA-15 Magic R550 Python 4 U-Darter

Python 5 Derby / R-Darter Aphid AA-8 Sidewinder AIM-9X

ASRAAM AIM-132 Grumble SA-10 / N-8 Patriot MIM-104 Starstreak

Gladiator SA-12 PAC-3 Roland ( two stage ) Crotale

Hellfire AGM-114 ATACM MGM-140 Standard Missile 3 ( three stage ) THAAD

Most Supersonic Missiles Are WinglessMost Supersonic Missiles Are Wingless


2/24/2008 ELF 45

Wings, Tails, and Canards with Large Area and at High Angle of Attack Have High Normal ForceWings, Tails, and Canards with Large Area and

at High Angle of Attack Have High Normal Force

0

1

2

3

4

0 30 60 90

M < 1.35, based on slender wing theory + Newtonian impact theoryM = 2, based on linear wing theory + Newtonian impact theoryM = 5, based on linear wing theory + Newtonian impact theory

( CN

) Win

gS RE

F/ S

W,

Win

g No

rmal

Forc

e Coe

fficie

nt

for R

ocke

t Bas

eline

α’ = αW = α + δ , Wing Effective Angle of Attack for Rocket Baseline, Deg

⏐( CN )Surface ⏐ = [ 4⏐sin α’ cos α’⏐ / ( M2 – 1 )1/2 + 2 sin2α’ ] ( SSurface / SRef ), if M > { 1 + [ 8 / ( π A )]2 }1/2

⏐( CN )Surface ⏐ = [ ( π A / 2) ⏐sin α’ cos α’⏐ + 2 sin2α’ ] ( SSurface / SRef ), if M < { 1 + [ 8 / ( π A )]2 }1/2

Note: Linear wing theory applicable if M > { 1 + [ 8 / ( π A )]2 }1/2, slender wing theory applicable if M < { 1 + [ 8 / ( π A )]2 }1/2, A = Aspect Ratio < 3, SSurface = Surface Planform Area, SRef = Reference Area

Example for Rocket Baseline Wing

AW = 2.82SW = 2.55 ft2

SRef = 0.349 ft2

δ = 13 deg, α = 9 degM = 2{ 1 +[ 8 / ( π A )]2 }1/2 = 1.35Since M > 1.35, use linear wing theory + Newtonian theory

α’ = αW = α + δ = 22°( CN )Wing SRef / SW = 4 sin 22°cos 22° / ( 22 – 1 )1/2 + 2 sin2 22°= 1.083

( CN )Wing = 1.08 ( 2.55 ) / 0.349 = 7.91

2/24/2008 ELF 46

Aerodynamic Center of a Thin Surface ( e.g., Wing, Tail, Canard ) Varies with Mach NumberAerodynamic Center of a Thin Surface ( e.g.,

Wing, Tail, Canard ) Varies with Mach Number

0

0.1

0.2

0.3

0.4

0.5


XAC

/ CMA

C, S

urfa

ce N

on-d

imen

sion

al

Aero

dyna

mic

Cen

ter

A = 1A = 2A = 3

Note: Based on linear wing theoryThin wing ⇒ M ( t / c ) << 1( xAC )Surface = Surface aerodynamic

center distance from leading edge of ( cMAC )Surface

cMAC = Mean aerodynamic chordA = Aspect ratio = b2 / S

( xAC / cMAC )Surface = [ A ( M2 – 1 )1/2 – 0.67 ] / [ 2A ( M2 –1 )1/2 – 1 ], if M > ~ 2( xAC / cMAC )Surface = 0.25, if M < ~ 0.7

Example: Rocket Baseline Wing

A = 2.82cMAC = 13.3 in( xMAC )Wing = 67.0 inM = 2( xAC / cMAC )Wing = 0.481( xAC )Wing = 6.4 in from mac leading edge = 73.4 in from nose tip

xAC

xMAC cMAC

2/24/2008 ELF 47

Hinge Moment Increases with Dynamic Pressure and Effective Angle of Attack

Hinge Moment Increases with Dynamic Pressure and Effective Angle of Attack

0

5000

10000

15000

20000

25000

30000

0 10 20 30

HM, E

xam

ple H

inge

Mom

ent, i

n - lb

q = 436 psf ( M = 0.8 ) q = 1242 psf ( M = 1.35 )q = 2725 psf ( M = 2 ) q = 17031 psf ( M = 5 )

HM = NSurface ( xAC - xHL )Surface

α’ = αW = α + δ , Wing Effective Angle of Attack of Rocket Baseline, Deg

Note: Based on linear wing theory, slender wing theory, and thin wing ( M ( t / c ) << 1 )

NSurface = Normal force on surface ( two panels )

( xAC - xHL )W = distance from surface aerodynamic center to hinge line of surface

Example for Rocket Baseline Wing Control

cmac = 13.3 inxHL = 0.25 cmac

SRef = 0.349 ft2

SW = 2.55 ft2

δ = 13 deg, α = 9 degα’ = αW = α + δ = 22°

M = 2, h = 20k ft, q = 2725 psfNW = [ CNW

( SRef / SW )] qSW = 1.083 ( 2725 ) ( 2.55 ) = 7525 lb

xAC / cmac = 0.48HM = 7525 ( 0.48 – 0.25 ) ( 13.3 ) = 23019 in – lb for two panels

NW

xHL

xAC

cmac

2/24/2008 ELF 48

Wings, Tails, and Canards Usually Have Greater Skin Friction Drag Than Shock Wave Drag

Wings, Tails, and Canards Usually Have Greater Skin Friction Drag Than Shock Wave Drag

0

0.1

0.2

0.3

0.4

0 10 20 30 40 50

M / ( q cmac ) = 0.00001 ft / lb M / ( q cmac ) = 0.0001 ft / lbM / ( q cmac ) = 0.001 ft / lb M / ( q cmac ) = 0.01 ft / lb

( CD0)Surface,Friction = nSurface { 0.0133 [ M / ( q cmac )]0.2 } ( 2 SSurface / SRef ), q in psf, cmac in ft

( CDO)Surface,Wave = nSurface ( 1.429 / MΛLE

2 ){( 1.2 MΛLE2 )3.5 [ 2.4 / ( 2.8 MΛLE

2 – 0.4 )]2.5 – 1 } sin2 δLE cos ΛLEtmac b / SRef , based on Newtonian impact theory

( CDO)Surface = ( CDO

)Surface,Wave + ( CDO)Surface,Friction

nSurfaces = number of surface planforms ( cruciform = 2 )q = dynamic pressure in psfcmac = length of mean aero chord in ftγ = Specific heat ratio = 1.4MΛLE

= M cos ΛLE = Mach number ⊥ leading edgeδLE = leading edge section total angleΛLE = leading edge sweep angletmac = max thickness of macb = span

Example for Rocket Baseline Wing:nW = 2, M = 2, h = 20k ft ( q = 2,725 psf ), cmac = 1.108 ft, SRef = 50.26 in2, SW = 367 in2, δLE = 10.01 deg, ΛLE = 45 deg, tmac = 0.585 in, b = 32.2 in, MΛLE

= 1.41 ( M = 2 )M / ( q cmac ) = 2 / [ 2725 ( 1.108 )] = 0.000662 ft / lbn SSurface / SRef = 2 ( 367 ) / 50.26 = 14.60( CDO

)Wing,Friction = 0.090( CD0

)Wing,Wave = 0.024( CDO

)Wing = 0.024 + 0.090 = 0.11

Exam

ple (

CD 0

) Surfa

ce,F

rictio

n

n SSurface / SRef

2/24/2008 ELF 49

Examples of Wing, Tail, and Canard Panel Geometry Alternatives

Examples of Wing, Tail, and Canard Panel Geometry Alternatives

ParameterVariation xAC

Bending Moment / FrictionSupersonic DragRCSSpan ConstraintStability & ControlAeroelastic Stab.λ = Taper ratio = cT / cRA = Aspect ratio = b2 / S = 2 b / [( 1 + λ ) cR ]yCP = Outboard center-of-pressure = ( b / 6 ) ( 1 + 2 λ ) / ( 1 + λ )cMAC = Mean aerodynamic chord = ( 2 / 3 ) cR ( 1 + λ + λ 2 ) / ( 1 + λ )

Note: Superior Good Average Poor

Based on equal surface area and equal span. Surface area often has more impact than geometry.

–

–

–

–

–

–

Triangle

( Delta )Aft Swept LE

Trapezoid

Double

Swept LEBow Tie Rectangle–

–

2/24/2008 ELF 50

Examples of Surface Arrangement and Aerodynamic Control Alternatives

Examples of Surface Arrangement and Aerodynamic Control Alternatives

Two Panels( Mono-Wing )

Three( Tri-Tail )

Four( Cruciform ) Six* Eight*

Folded Wraparound Extended Balanced Actuation Control

Flap Control

Interdigitated In-line

Note: More than four tails are usually free-to-roll pitch / yaw stabilizers, for low induced roll.

2/24/2008 ELF 51

Control Integ Control Surfaces Example Control Effect Cost PackagingPitch / Yaw 2 Stinger FIM-92

Pitch / Roll 2 ALCM AGM-86

Pitch / Yaw / Roll 3 SRAM

Pitch / Yaw / Roll 4 Adder AA-12

Pitch + Yaw + Roll 5 Kitchen AS-4

Pitch / Yaw + Roll 6 Derby / R-Darter

Most Missiles Use Four Control Surfaces with Combined Pitch / Yaw / Roll Control IntegrationMost Missiles Use Four Control Surfaces with

Combined Pitch / Yaw / Roll Control Integration


–

––

–

–

–

–

2/24/2008 ELF 52

There Are Many Flight Control Configuration Alternatives

There Are Many Flight Control Configuration Alternatives

ControlControl Design

AlternativesTail Cruciform ( 4 )

Tri-tail ( 3 )Not CompressedFoldedWraparoundSwitchblade

Canard AboveRolling Airframe ( 2 )

Wing Tail ( 3, 4, 6, 8 )Strake / Canard & TailIn Line with ControlsInterdigitated with Controls

TVC or Reaction Jet Control

Movable NozzleJet TabJet VaneAxial PlateSecondary InjectionNormal Jet / JISpanwise Jet / JI

Fixed SurfaceAlternatives

WinglessWingStrake / CanardIn Line with ControlsInterdigitated with ControlsNumber ( 2, 3, 4 )Tail ( 3, 4, 6, 8 )Tail + WingIn Line with ControlsInterdigitated with Controls

Tail ( 3, 4, 6, 8 )Tail + Canard / StrakeTail + Wing

Above

2/24/2008 ELF 53

Tail Control Is Efficient at High Angle of Attack Tail Control Is Efficient at High Angle of Attack

α

V∞

ΔCN

CN Trim ( assumed statically stable ) CN at δ = 0

CNCNegative δ

CNC at δ = 0

☺ Efficient Packaging☺ Low Hinge Moment / Actuator

Torque☺ Low Induced Rolling Moment☺ Efficient at High α

Decreased Lift at Low α if Statically Stable

cg

2/24/2008 ELF 54

Tail Control Is More Effective Than Conventional Canard Control at High Angle of Attack

Tail Control Is More Effective Than Conventional Canard Control at High Angle of Attack

V∞

α

+ δ

• Assumed static stability• Control surface local

angle of attack α’ = α + δ• Panel stalled at high α*

Conventional Canard Control

V∞

α

– δ

• Assumed static stability• Control surface local

angle of attack α’ = α – δ• Panel not stalled at high α

Tail Control

α ~ Angle of Attack ( deg ) α ~ Angle of Attack ( deg )

C mδ

/( C

mδ

) α=

0° 1.0

0

ConvenCanardControl

TailControl☺

10 – 20° 20 – 30°C l

δ/ (

C lδ

) α=

0° 1.0

0

ConvenCanardControl

TailControl☺

10 – 15° 15 – 30°

Ø = 0°

*Note: Additional forward fixed surfaces ( such as Python 4 ) in front of movable canards alleviate stall at high α. Free-to-roll tails ( such as Python 4 ) alleviate induced roll from canard control at high α.

2/24/2008 ELF 55

JASSM AGM-158 Maverick AGM-65 CALCM JSOW AGM-154

Tomahawk BGM-109 Taurus KEPD 350 Storm Shadow / Scalp Popeye AGM-142

Exocet MIM40 TOW2-BGM71D AMRAAM AIM-120 Sunburn SS-N-22

Standard RIM-66 / 67 RBS-70 / 90 Shipwreck SS-N-19 Super 530

Sea Dart ( two stage ) FSAS Aster R-37 ( AA-X-13 ) Mica

Adder AA-12 Rapier 2000 SD-10 / PL-12 Seawolf

About 70% of Tail Control Missiles Also Have WingsAbout 70% of Tail Control Missiles Also Have Wings


2/24/2008 ELF 56

Control HingeType of Tail Control Effectiveness Drag Moment RCS

Balanced Actuation Fin ( Example: ASRAAM AIM-132 )

Flap ( Example: Hellfire AGM-114 )

Lattice Fin ( Example: Adder AA-12 / R-77 )

Tail Control Alternatives: Conventional Balanced Actuation Fin, Flap, and Lattice Fin

Tail Control Alternatives: Conventional Balanced Actuation Fin, Flap, and Lattice Fin

–

–


2/24/2008 ELF 57

Lattice Fins Have Advantages for Low Subsonic and High Supersonic Missiles

Lattice Fins Have Advantages for Low Subsonic and High Supersonic Missiles

AdvantagesHigh control effectiveness at

low subsonic and high supersonic Mach number

Low hinge momentShort chord length

DisadvantagesHigh RCS ( cavities, normal

leading edges )High drag at transonic Mach

number ( choked flow )

Low Subsonic Transonic Low Supersonic High Supersonic

☺ ☺

2/24/2008 ELF 58

Conventional Canard Control Is Efficient at Low Angle of Attack But Stalls at High Alpha

Conventional Canard Control Is Efficient at Low Angle of Attack But Stalls at High Alpha

α

V∞

δΔCN

CN Trim ( assumed statically stable )

CN at δ = 0C N C

☺ Efficient Packaging☺ Simplified

Manufacturing☺ Increased Lift at Low α

if Statically Stable

Stall at High α if Statically StableInduced Roll

Note: = CNC at δ = 0°

= CNC at δ = δ

*Note: Additional forward fixed surface in front of movable canard alleviates stall at high α. Free-to-roll tails alleviate induced roll at high α. Dedicated roll control surfaces avoid roll control saturation and simplify autopilot design.

cg

2/24/2008 ELF 59

Canard Control Missiles Are Wingless and Most Are Supersonic

Canard Control Missiles Are Wingless and Most Are Supersonic


Stinger FIM-92 Grouse SA-18 Grison SA-19 ( two-stage ) Gopher SA-13

Starburst Gauntlet SA-15 Mistral AIM-9L

Archer AA- 11 Magic R 550 Python 4 U-Darter

Python 5 Derby / R-Darter Aphid AA-8 Kegler AS-12

GBU-12 GBU-22 GBU-27 GBU-28

2/24/2008 ELF 60

Kegler AS-12 Archer AA-11 Aphid AA-8

Magic R 550 Python 4 U-Darter

Missiles with Split Canards Have Enhanced Maneuverability at High Angle of Attack

Missiles with Split Canards Have Enhanced Maneuverability at High Angle of Attack

Note: Forward fixed surface reduces local angle-of-attack for movable canard, providing higher stall angle of attack. Forward surface also provides a fixed, symmetrical location for vortex shedding from the body.Python 4 also has free-to-roll tails and separate roll control ailerons.

α’ ~ αα’ ~ δα

δΔCN

C N C

Note: α’ = Local angle of attack

2/24/2008 ELF 61

Wing Control Requires Less Body Rotation But Has High Hinge Moment, Induced Roll and StallWing Control Requires Less Body Rotation But Has High Hinge Moment, Induced Roll and Stall

δV

Δ CN ~ CN Trim

☺ Low Body α / Dome Error Slope☺ Fast Response ( if skid-to-turn )

Poor Actuator PackagingLarge Hinge MomentLarger Wing SizeInduced RollWing Stall

( α small ) cg

2/24/2008 ELF 62

Wing Control Missile Susceptible to High Vortex Shedding

Wing Control Missile Susceptible to High Vortex Shedding

Strong vortices from wing interact with tail

Source: Nielsen Engineering & Research ( NEAR ) web site: http://www.nearinc.com/near/project/MISDL.htm

Video of Vortices from Delta Wing at High Angle of Attack

Source: University of Notre Dame web site: http://www.nd.edu/~ame/facilities/SubsonicTunnels.html

2/24/2008 ELF 63

Wing Control Missiles Are Old TechnologyWing Control Missiles Are Old Technology

Sparrow AIM-7: IOC 1956

Skyflash: IOC 1978

Alamo AA-10 / R-27: IOC 1980

HARM AGM-88: IOC 1983

Aspide: IOC 1986


2/24/2008 ELF 64

TVC and Reaction Jet Flight ControlTVC and Reaction Jet Flight ControlLiquid Injection Hot Gas Injection

Axial Plate Jet Tab Movable Nozzle

± 7° ± 12°

± 7°± 15° ± 20°

Note: Jet vanes provide roll control and share actuators with aero control, but have reduced ISP

Reaction Jet

M∞ Jet Flow

Jet Vane*

± 10°

Note:•TVC and reaction jet flight control provide high maneuverability at low dynamic pressure•TVC usually has lower time constant and miss distance than aero control•Reaction jets usually have lower time constant and miss distance than TVC•Reaction jets can be either impulse jets or controlled duration jets Jet inter. Thrust Jet interaction

2/24/2008 ELF 65

Jet Vane + Aero Control:Mica Sea Sparrow RIM-7 AIM-9X

Sea Wolf GWS 26 IRIS-T A-Darter Javelin

Jet Tab + Aero Control:Archer AA-11

Reaction Jet + Aero Control:PAC-3

Movable Nozzle + Aero Control + Reaction Jet:SM-3 Standard Missile Aster FSAF 15

Movable Nozzle + Reaction Jet:THAAD

Reaction Jet:LOSAT

Most Tactical Missiles with TVC or Reaction Jet Control Also Use Aero Control

Most Tactical Missiles with TVC or Reaction Jet Control Also Use Aero Control

Example Video of TVC ( FSAF-15 and Javelin )

2/24/2008 ELF 66

Skid-to-Turn Is the Most Common Maneuver LawSkid-to-Turn Is the Most Common Maneuver LawSkid-To-Turn ( STT )

• Advantage: Fast response• Features

– Does not require roll commands from autopilot– Works best for axisymmetric cruciform missiles

Bank-To-Turn ( BTT )• Advantage: Provides higher maneuverability for planar

wing, noncircular / lifting bodies, and airbreathers• Disadvantages

– Time to roll– Requires fast roll rate– May have higher dome error slope

• Features– Roll attitude commands from autopilot– Small sideslip

Rolling Airframe ( RA )• Advantage: Requires only two sets of gyros /

accelerometers / actuators ( packaging for small missile )• Disadvantages for aero control

– Reduced maneuverability for aero control– Requires high rate gyros / actuators– Requires precision geometry and thrust alignment

• Features– Bias roll rate and roll moment– Can use impulse steering ( e.g., PAC-3, LOSAT )– Compensates for thrust offset

Step 1: Roll Until Wing ⊥ LOS

Step 2: Maneuver @ Roll Rate = 0 and Wing ⊥ LOS

Bias Roll Rate ( e.g., 3 Hz )

Maneuver w / o Roll CommandTarget

Target

Target

LOS TargetManeuver with Bias Roll

Moment

LOS

LOS

LOSSTT

BTT ( with Planar Wing )

RA

2/24/2008 ELF 67

Examples of Twin Inlet Missiles with Bank-to-Turn

Twin Side Inlets Ramjet: ASMP

Twin Cheek Inlets Ducted Rocket: HSAD

Twin Cheek Inlets Ducted Rocket: Meteor

Examples of Single Inlet Missiles with Bank-to-Turn

Chin Inlet Ramjet: ASALM

Bottom Inlet Turbojet: BGM-109 Tomahawk

Bottom Inlet Turbojet: Storm Shadow / Scalp

Top Inlet Turbofan: AGM-86 ALCM

Asymmetric Inlets Require Bank-to-Turn Maneuvering

Asymmetric Inlets Require Bank-to-Turn Maneuvering

Note: Bank-to-turn maneuvering maintains low sideslip for better inlet efficiency.

2/24/2008 ELF 68

Yaw Right

X Roll Orientation Is Usually Better Than + Roll Orientation

X Roll Orientation Is Usually Better Than + Roll Orientation

Fin 1

Fin 3

Roll Right

+ Roll Orientation with Four Tail Surfaces Control of Pitch / Yaw / Roll, Looking Forward from Base

X Roll Orientation with Four Tail Surfaces Control of Pitch / Yaw / Roll, Looking Forward from Base

Roll Right

Note: + roll orientation usually has lower trim drag, less static stability and control effectiveness in pitch and yaw, and statically unstable roll moment derivative ( Clφ > 0 ).X roll orientation has better launch platform compatibility, higher L / D, higher static stability and control effectiveness in pitch and yaw, and statically stable roll moment derivative ( Clφ < 0 ).

4 1

3 2

Pitch Up Yaw Right

Pitch Up

Fin 2Fin 4Trail

ing

edge

de

flect

ion

2/24/2008 ELF 69

Trimmed Normal Force Is Defined at Zero Pitching Moment

Trimmed Normal Force Is Defined at Zero Pitching Moment

Pitc

hing

Mom

ent,

C mNo

rmal

Forc

e, C N

Angle of Attack ( Deg )

αTrim @ Cm = 0

δ = 0

δ = δ Trim for either statically stable tail control or statically unstable canard control

δ = 0

δ = δ Max

δ = δ Trim for either statically unstable tail control or statically stable canard control

Angle of Attack ( Deg )

2/24/2008 ELF 70

Note: Rocket BaselineXCG = 75.7 in.Mach 2

( α + δ )Max = 21.8 deg, ( CNTrim)Max

α / δ = 0.75, ( Static Margin = 0.88 Diam )α / δ = 1.5, ( SM = 0.43 Diam )α / δ = ∞, ( SM = 0 )

Relaxed Static Margin Allows Higher Trim Angle of Attack and Higher Normal Force

Relaxed Static Margin Allows Higher Trim Angle of Attack and Higher Normal Force

( CN, Trim )max, Max Trimmed Normal Force Coefficient of Rocket Baseline

0 4 8 12 16 20 24

16

12

8

4

0

( αTrim )max, Μax Trim Angle of Attack, deg

2/24/2008 ELF 71

Tails Are Sized for Desired Static MarginTails Are Sized for Desired Static Margin

( CNα)B

( CNα)W

( CNα)T

( xAC )T

( xAC )B

( xAC )W

+M

+ α

x = 0xCG

x = lB

x = lN

xACΣM = 0 at aerodynamic center( CNα

)B {[ xCG – ( xAC )B ] / d } + ( CNα)W {[ xCG – ( xAC )W ] / d } SW / SRef + ( CNα

)T {[ xCG – ( xAC )T ] / d } ST / SRef

= - [( CNα)B + ( CNα

)W SW / SRef + ( CNα)T ST / SRef ] [( xAC – xCG ) / d ]

Static margin for a specified tail area is( xAC – xCG ) / d = - {( CNα

)B {[ xCG – ( xAC )B ] / d } + ( CNα)W {[ xCG – ( xAC )W ] / d } SW / SRef + ( CNα

)T {[ xCG – ( xAC )T ] / d } ( ST / SRef )} / [(CNα

)B + (CNα)W SW / SRef + ( CNα

)T ST / SRef ]

Required tail area for a specified static margin isST / SRef = ( CNα

)B {[ xCG – ( xAC )B ] / d } + ( CNα)W {[ xCG – ( xAC )W ] / d } ( SW / SRef ) + {[( CNα

)B + ( CNα)W SW / SRef ][( xAC – xCG ) / d ]}

/ {( CNα)T [( xAC )T – xCG ] / d - ( xAC – xCG ) / d }

CNα

2/24/2008 ELF 72

Larger Tail Area Is Required for Neutral Stability at High Mach Number

Larger Tail Area Is Required for Neutral Stability at High Mach Number

0

1

2

3


(ST)

Neut

ral /

SRef

, Neu

tral S

tabi

lity T

ail A

rea /

Re

fere

nce A

rea

(ST)Neutral / SRef = { (CNα)B [ xCG – (xAC)B ] / d + (CNα)W {[ xCG – (xAC)W ] / d } ( SW / SRef )} / {{[ (xAC)T – xCG ] / d } (CNα)T }

Assumptions for figure:•XCG ≈ l / 2, (XAC)B ≈ d, ( XAC )T ≈ l – d•α < 6 deg, turbulent boundary layer•(CNα)B = 2 per rad•(CNα)T = (CNα)W = 4 / [ M2 –1 ]1/2, if M > { 1 + [ 8 / ( π A )]2 }1/2

•(CNα)T = (CNα)W = π A / 2, if M < { 1 + [ 8 / ( π A )]2 }1/2

Example Rocket Baseline:l = 144 in, d = 8 in, SW = 2.55 ft2, SRef = 0.349 ft2, AW = 2.82, (cMAC)W = 13.3 in, xMAC = 67.0 in from nose tip, burnout ( xCG = 76.2 in from tip ), Mmax = 3

(xAC)W = 0.49 ( 13.3 ) = 6.5 in from leading edge of MAC

(xAC)W = 6.5 + 67.0 = 73.5 in from nose {[ xCG – (xAC)W ] / l } ( SW / SRef ) = 0.14 ( forward wing )

(ST)Neutral / SRef = 1.69 provides neutral stability

(ST)Neutral = 1.69 ( 0.349 ) = 0.59 ft2

{[ x CG– (x AC) W

] / l }( S W

/ S Ref) = 0

{[ x CG– (x AC) W

] / l } ( S W

/ S Ref) = 0.25

( forward wing )

{[ x CG– (x AC) W

] / l }( S W

/ S Ref) = - 0.25

( aft wing )

2/24/2008 ELF 73

Stability and Control Derivatives Conceptual Design Criteria

Stability and Control Derivatives Conceptual Design Criteria

z y

xClδr Clδa

z y

xCnδaCnδr

z y

xClφ Clδa

z y

xCmα

Cmδ

z y

xClβ Clδa

| Clδr / Clδa | < 0.3 ( Roll Due to Rudder Deflection ) | Clφ / Clδa | < 0.5 ( Roll Due to Roll Angle )

| Cnδa / Cnδr | < 0.2 ( Yaw Due to Aileron Deflection ) | Cmα / Cmδ | < 1 ( Pitch Due to α )

| Clβ / Clδa | < 0.3 ( Roll Due to Sideslip ) | Cnβ / Cnδr | < 1 ( Yaw Due to Sideslip )

z y

x

Cnδr

Cnβ

Note: The primary control derivative ( larger bold font ) should be larger than the undesirable stability and control derivative.

2/24/2008 ELF 74

Most of the Rocket Baseline Body Buildup Normal Force Is Provided by the Wing

Most of the Rocket Baseline Body Buildup Normal Force Is Provided by the Wing

CN, Normal ForceCoefficient of Rocket Baseline

15

10

5

00 5 10 15 20 25

α, Angle of Attack, Deg

Body + Wing + Tail

Body + Wing

Body

Note for figure: M = 2, δ = 0

( CN )Total = ( CN )Wing-Body-Tail ≅ ( CN )Body + ( CN )Wing + ( CN )Tail

Note: ( CD0 )Total = ( CD0 )Wing-Body-Tail ≅ ( CD0 )Body + ( CD0 )Wing + ( CD0 )Tail

( Cm )Total = ( Cm )Wing-Body-Tail ≅ ( Cm )Body + ( Cm )Wing + ( Cm )Tail

2/24/2008 ELF 75

Summary of AerodynamicsSummary of Aerodynamics

Conceptual Design Prediction Methods of Bodies and SurfacesNormal force coefficientDrag coefficientAerodynamic center / pitching moment coefficient / hinge moment

Design TradeoffsDiameterNose finenessBoattailLifting body versus axisymmetric bodyWings versus no wingsTails versus flaresSurface planform geometryFlight control alternativesManeuver alternativesRoll orientationStatic margin / time to converge or divergeTail sizing

2/24/2008 ELF 76

Summary of Aerodynamics ( cont )Summary of Aerodynamics ( cont )

Stability and Control Design CriteriaStatic stabilityControl effectivenessCross coupling

Body BuildupNew Aerodynamics Technologies

Faceted / window / multi-lens domesBank-to-turn maneuveringLifting body airframeForward swept surfacesNeutral static marginLattice finsSplit canard controlFree-to-roll tails

Discussion / Questions?Classroom Exercise

2/24/2008 ELF 77

Aerodynamics ProblemsAerodynamics Problems1. Missile diameter tradeoffs include consideration of seeker range, warhead

lethality, structural mode frequency, and d___.2. Benefits of a high fineness nose include lower supersonic drag and lower

r____ c____ s______.3. Three contributors to drag are base drag, wave drag, and s___ f_______

drag.4. To avoid flow separation, a boatail or flare angle should be less than __ deg.5. A lifting body is most efficient at a d______ p_______ of about 700 psf.6. At low angle of attack the aerodynamic center of the body is on the n___.7. Subsonic missiles often have w____ for enhanced range.8. The aerodynamic center of the wing is between 25% and 50% of the m___

a__________ c____.9. Hinge moment increases with the local flow angle due to control surface

deflection and the a____ o_ a_____.10. Increasing the surface area increases the s___ f_______ d___.

2/24/2008 ELF 78

Aerodynamics Problems ( cont )Aerodynamics Problems ( cont )11. Leading edge sweep reduces drag and r____ c____ s______.12. A missile with six control surfaces, four surfaces providing combined pitch /

yaw control plus two surfaces providing roll control, has an advantage of good c______ e____________.

13. A missile with two control surfaces providing only combined pitch / yaw control has advantages of lower c____ and good p________.

14. A tail control missile has larger trim normal force if it is statically u_______.15. Lattice fins have low h____ m_____.16. Split canards allow higher maximum angle of attack and higher

m______________.17. Two types of unconventional control are thrust vector control and r_______

j__ control.18. The most common type of TVC for tactical missiles is j__ v___ control.19. Three maneuver laws are skid to turn, bank to turn, and r______ a_______.20. Bank to turn maneuvering is usually required for missiles with a single wing

or with a_________ inlets.

2/24/2008 ELF 79

Aerodynamics Problems ( cont )Aerodynamics Problems ( cont )

21. A missile is statically stable if the aero center is behind the c_____ o_ g______.

22. Tail stabilizers have low drag while a f____ stabilizer has low aero heating and a relatively small shift in static stability.

23. If the moments on the missile are zero the missile is in t___.24. Total normal force on the missile is approximately the sum of the normal

forces on the surfaces ( e.g., wing, tail, canard ) plus normal force on the b___.

25. Increasing the tail area increases the s_____ m________.

2/24/2008 ELF 80


2/24/2008 ELF 81



Yes

Establish Baseline

Weight

Trajectory

MeetPerformance?


No

Yes


Alt Mission

Alt Baseline


Aerodynamics

Propulsion

2/24/2008 ELF 82

Scramjet: ISP typically constrained by thermal choking

High Specific Impulse Is Indicative of Lower Fuel / Propellant Consumption

High Specific Impulse Is Indicative of Lower Fuel / Propellant Consumption

Turbojet: ISP typically constrained by turbine temperature limit

Ramjet: ISP typically constrained by combustor insulation temperature limit

Solid Rocket: ISP typically constrained by safety

4,000

3,000

2,000

1,000

0I SP, S

pecif

ic Im

pulse

, Thr

ust /

( Fu

el or

Pro

pella

nt

Weig

ht F

low

Rate

), S

0 2 4 6 8 10 12Mach Number

Ducted Rocket

2/24/2008 ELF 83

Cruise Range Is Driven by L/D, Isp, Velocity, and Propellant or Fuel Weight Fraction

Cruise Range Is Driven by L/D, Isp, Velocity, and Propellant or Fuel Weight Fraction

Typical Value for 2,000 lb Precision Strike Missile

Note: Ramjet and Scramjet missiles booster propellant for Mach 2.5 to 4 take-over speed not included in WPfor cruise. Rockets require thrust magnitude control ( e.g., pintle, pulse, or gel motor ) for effective cruise. Max range for a rocket is usually a semi-ballistic flight profile, instead of cruise flight. Multiple stages may be required for rocket range greater than 200 nm.

R = ( L / D ) Isp V In [ WL / ( WL – WP )] , Breguet Range Equation

Parameter

L / D, Lift / DragIsp, Specific ImpulseVAVG , Average VelocityWP / WL, Cruise Propellant or Fuel Weight / Launch WeightR, Cruise Range

103,000 s1,000 ft / s0.3

1,800 nm

51,300 s3,500 ft / s0.2

830 nm

31,000 s6,000 ft / s0.1

310 nm

5250 s3,000 ft / s0.4

250 nm

Solid RocketHydrocarbon FuelScramjet Missile

Liquid FuelRamjet Missile

Subsonic TurbojetMissile

2/24/2008 ELF 84

Solid Rockets Have High Acceleration CapabilitySolid Rockets Have High Acceleration Capability

1,000

100

10

10 1 2 3 4 5

RamjetTMax = (π / 4 ) d2 ρ0 V0

2 [( Ve / V0 ) -1 ]

Solid RocketTMax = 2 Pc At = m. Ve

M, Mach Number

( T / W

) Max

, ( T

hrus

t / W

eight

) Max

Note:Pc = Chamber pressure, At = Nozzle throat area, m. = Mass flow rated = Diameter, ρ0 = Free stream density, V0 = Free stream velocity,Ve = Nozzle exit velocity ( Turbojet: Ve ~ 2,000 ft / s, Ramjet: Ve ~ 4,500 ft / s, Rocket: Ve ~ 6,000 ft / s )

TurbojetTMax = (π / 4 ) d2 ρ0 V0

2 [( Ve / V0 ) -1 ]

2/24/2008 ELF 85

Turbojet NomenclatureTurbojet Nomenclature

0

Free Stream

1

Inlet Entrance

3

Compressor Exit

2

Compressor Entrance4

Turbine Entrance

Inlet Compressor Combustor Turbine Nozzle

5

Turbine Exit

2/24/2008 ELF 86

High Temperature Compressors Are Required to Achieve High Pressure Ratio at High Speed

High Temperature Compressors Are Required to Achieve High Pressure Ratio at High Speed

0

1000

2000

3000

0 1 2 3 4

M0, Free Stream Mach Number

T3, C

ompr

esso

r Exi

t Tem

pera

ture

, Rp3 / p2 = 1p3 / p2 = 2p3 / p2 = 5p3 / p2 = 10

T3 ≈ T0 { 1 + [( γ0 - 1 ) / 2 ] M02 }( p3 / p2 )( γ3 - 1 ) / γ3

γ0 = 1.4, γ3 ≈ 1.29 + 0.16 e-0.0007 T3

Note: Ideal inlet; ideal compressor; low subsonic, isentropic flow

Example:M0 = 2, h = 60k ft ( T0 = 398 R )p3 / p2 = 5 ⇒ T3 = 1118 R, γ3 = 1.36

T3 = Compressor exit temperature in Rankine, T0 = free stream temperature in Rankine, γ = specific heat ratio, M0 = free stream Mach number, p3 = compressor exit pressure, p2 = compressor entrance pressure

T3

2/24/2008 ELF 87

High Turbine Temperature Is Required for High Speed Turbojet Missiles

High Turbine Temperature Is Required for High Speed Turbojet Missiles

0

1000

2000

3000

4000

5000

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07

f / a, Fuel-to-Air Ratio

T4,T

urbo

jet T

urbi

ne T

empe

ratu

re, R

T3 = 500 RT3 = 1000 RT3 = 2000 RT3 = 4000 R

T4 ≈ T3 + ( Hf / cp ) f / a, T in Rcp4 ≈ 0.122 T4

0.109, cp in BTU / lb / R

Example:M0 = 2, h = 60K ft ( T0 = 398 R ), p3 / p2 = 5 ⇒ T3 = 1118 R

RJ-5 fuel ( Hf = 14,525 BTU / lb ), cp = 0.302 BTU / lb / R , f / a = 0.067 ( stochiometric ) ⇒ T4 = 1118 + ( 14525 / 0.302 ) 0.067 = 4,340 R

T4 = Turbojet turbine entrance temperature in Rankine, T3 = compressor exit temperature in Rankine, Hf = heating value of fuel, cp = specific heat at constant pressure, f / a = fuel-to-air ratio

T4

2/24/2008 ELF 88

Turbine Material Temperature Limit Is a Constraint for a High Speed Turbojet Missile

Turbine Material Temperature Limit Is a Constraint for a High Speed Turbojet Missile

Slightly Constrained Turbojet

Moderately Constrained Turbojet

Moderately Constrained Turbojet

Highly Constrained Turbojet

Very Highly Constrained Turbojet, Air Turbo Rocket, Turbo Ramjet

Very Highly Constrained Turbojet, Air Turbo Rocket, Turbo Ramjet

Temperature Constrained Turbines for Mach 4 Cruise

≈ 1,500 sCeramic Matrix Composites≈ 4,000R

≈ 2,000 sRhenium Alloys≈ 4,500R

≈ 2,500 sTungsten Alloys≈ 5,000R

≈ 1,200 sSingle Crystal Nickel Aluminides

≈ 3,500R

≈ 1,000 sTitanium Aluminides ( lighter weight than nickel super alloys )

≈ 3,000R

≈ 1,000 sNickel Super Alloys≈ 3,000R

ISP for Mach 4 Cruise

Turbine MaterialMax Short Duration Temp

Note: Constrained turbojet for Mach 4 cruise imposes a limit on turbine temperature that is less than ideal. Constraints could consist of a combination of:• Constraint on compressor pressure ratio to limit turbine temperature• Constraint on fuel-to-air ratio to limit turbine temperature• Use of afterburner to limit turbine temperature

2/24/2008 ELF 89

Turbine-Based Missiles Are Capable of Subsonic to Supersonic Cruise

Turbine-Based Missiles Are Capable of Subsonic to Supersonic Cruise

Turbojet

Turbo Ramjet

Air Turbo Rocket

Regulus IIFirebee II

SS-N-19 Shipwreck

SR-71

2/24/2008 ELF 90

Compressor Pressure Ratio for Maximum Thrust Turbojet Is Limited by Turbine Temperature

Compressor Pressure Ratio for Maximum Thrust Turbojet Is Limited by Turbine Temperature

1

10

100

0 0.5 1 1.5 2 2.5 3 3.5 4M0, Mach Number

( p3 /

p2 )

@Tm

ax

T4 = 2000 R T4 = 3000 RT4 = 4000 R T4 = 5000 R

Source: Ashley, H., Engineering Analysis of Flight Vehicles, Dover Publications, Inc., New York, 1974

( p3 / p2 )@Tmax ≈ {( T4 / T0 )1/2 / { 1 + [( γ0 - 1 ) / 2 ] M02 }}γ4 / ( γ4 - 1 )

Assumptions: Ideal turbojet ( isentropic inlet, compressor, turbine, nozzle; low subsonic and constant pressure combustion; exit pressure = free stream pressure )

Example:M0 = 2.0, h = 60k ft (T0 = 390 R ) , T4 = 3,000 R, γ4 = 1.31( p3 / p2 )@Tmax = {{ ( 3000 / 390 )1/2 / { 1 + [( 1.4 -1 ) / 2 ] 2.02 }}1.31/ ( 1.31 – 1 ) = 6.31Note:T0 = Free stream temperatureT4 = Turbine entrance temperatureγ = Specific heat ratio

2/24/2008 ELF 91

Turbojet Thrust Is Limited by Turbine Maximum Allowable Temperature

Turbojet Thrust Is Limited by Turbine Maximum Allowable Temperature

0

5

10

15

20

0 1 2 3 4M0, Mach Number

Tmax

/ [(

p0 )

( A0 )

], No

ndim

ensio

nal M

axim

umTh

rust

T4 = 2000 R T4 = 3000 RT4 = 4000 R T4 = 5000 R

Ramjet

( p3

/ p2

= 1 )

Example: M0 = 2, h = 60 k ft ( T0 = 390 R, p0= 1.047 psi ), T4 = 3,000 R, γ4 = 1.31, ( p3 / p2 )@Tmax = 6.31, p2 = 8.19 psi, p3 = 51.7 psi, A0 = 114 in2, T2 = 702 R, T3 = 1133 R, γ3 = 1.36

T5t = 2569 R, γ5 = 1.32, p5t = 23.0 psi, Ve = 4524 ft / s, ( T / m. )IdealMax = 2588 ft / s, TIdealMax / p0 A0 = 7.49

TIdealMax = 7.49 ( 1.047 ) ( 114 ) = 894 lb

TIdealMax / ( p0 A0 ) = ( γ0 M0 / a0 ) ( T / m. )IdealMaxAssumption: Ideal turbojet

Note:( T / m. )IdealMax = Ve – V0

Ve = { 2 cp T5t [ 1 – ( p0 / p5t )( γ5 - 1 ) / γ5 ]}1/2

T5t ≈ T4 – T3 + T2

T3 ≈ T2 ( p3 / p2 )( γ3 - 1 ) / γ3

T2 ≈ T0 { 1 + [( γ0 - 1 ) / 2 ] M02 }

p5t ≈ p4 ( T5 / T4 )γ4 / ( γ4 - 1 )

p4 = p3

p2 ≈ p0 { 1 + [( γ0 - 1 ) / 2 ] M02 }γ0 / ( γ0 - 1 )

p0 = Free stream static pressureA0 = Free stream flow area into inletT4 = Turbine entrance temperature

2/24/2008 ELF 92

Turbojet Specific Impulse Decreases with Supersonic Mach Number

Turbojet Specific Impulse Decreases with Supersonic Mach Number

0

0.2

0.4

0.6

0.8

0 1 2 3 4M0, Mach Number

( ISP

)Ide

al ( g

c ) (

cp )

( T0)

/ [ (

a0 )

( Hf

)],

Nond

imen

siona

l Ide

al Sp

ecifi

c Im

pulse

T4 = 2000 R T4 = 3000 RT4 = 4000 R T4 = 5000 R

( ISP )Ideal@Tmax gc cp T0 / ( a0 Hf ) = TIdealMax T0 / [( p0 A0 γ0 M0 ) ( T4 – T3 )]Assumptions: Ideal turbojet ( isentropic inlet, compressor, turbine, nozzle; flow, low subsonic, constant pressure combustion;exit pressure = free stream pressure), max thrust

Example:M0 = 2, h = 60k ft ( T0 = 390 R, a0 = 968 ft / s

), RJ-5 fuel ( Hf = 14,525 BTU / lbm ), T4 = 3,000 R, cp = 0.293 BTU / lbm / R, γ0 = 1.4Calculate ( ISP )Ideal@Tmax gc cp T0 / ( a0 Hf ) = 0.559( ISP )Ideal@Tmax = 0.559 ( 968 ) ( 14525 ) / [ 32.2 ( 0.293 ) ( 390 )] = 2136 sNote:gc = Gravitational constant = 32.2cp = Specific heat at constant pressureT0 = Free stream temperaturea0 = Free stream speed of soundHf = Heating value of fuelTIdealMax = Ideal maximum thrustγ = Specific heat ratioT4 = Combustor exit temperatureT3 = Compressor exit temperature

Ramjet ( p3 / p

2 = 1 )

2/24/2008 ELF 93

Tactical Missile Ramjet Propulsion AlternativesTactical Missile Ramjet Propulsion Alternatives

Rocket Boost Inboard Profile

Ramjet Sustain Inboard Profile

Liquid Fuel Ramjet

Solid Fuel Ramjet

Solid Ducted Rocket

Boost

Sustain

Boost

Sustain

Note:Booster PropellantFuel

2/24/2008 ELF 94

High Specific Impulse for a Ramjet Occurs Using High Heating Value Fuel at Mach 3 to 4

High Specific Impulse for a Ramjet Occurs Using High Heating Value Fuel at Mach 3 to 4

0

0.2

0.4

0.6

0 1 2 3 4 5M0, Free Stream Mach Number

( ISP

)Idea

l ( gc

) ( cp

) ( T

0) / [

( a0 )

( Hf )

], No

ndim

ensio

nal Id

eal S

pecif

ic Im

pulse

T4 / T0 = 3 T4 / T0 = 5T4 / T0 = 10 T4 / T0 = 15

( ISP )Ideal gc cp T0 / ( a0 Hf ) = { M0 {{( T4 / T0 ) / { 1 + [( γ0 - 1 ) / 2 ] M02 }}1/2 - 1 } / {{ 1 + [( γ0 - 1 ) / 2 ] M0

2 } {( T4 / T0 ) / { 1 + [( γ0 - 1 ) / 2 ] M0

2 }} – 1 }Assumptions: Ideal ramjet, isentropic inlet and nozzle, low subsonic and constant pressure combustion, exit pressure = free stream pressure, φ ≤ 1

Example for Ramjet Baseline:M = 3.5, h = 60k ft ( T0 = 390 R, a0 = 968 ft / s ), RJ-5 fuel ( Hf = 14,525 BTU / lbm ), T4 = 4,000 R, cp = 0.302 BTU / lbm / R, γ0 = 1.4

Calculate ( ISP )Ideal gc cp T0 / ( a0 Hf ) = { 3.5 {{( 4000 / 390 ) / { 1 + [( 1.4 - 1 ) / 2 ] 3.52 }}1/2 - 1 } / {{ 1 + [( 1.4 - 1 ) / 2 ] 3.52 } {( 4000 / 390 ) / { 1 + [( 1.4 - 1 ) / 2 ] 3.52 }} – 1 } = 0.372

( ISP )Ideal = 0.372 ( 968 ) ( 14525 ) / [ 32.2 ( 0.302 ) ( 390 ) = 1387 s

Note:gc = Gravitational constant = 32.2cp = Specific heat at constant pressureT0 = Free stream temperaturea0 = Free stream speed of soundHf = Heating value of fuelγ = Specific heat ratioT4 = Combustor exit temperature


2/24/2008 ELF 95

High Thrust for a Ramjet Occurs from Mach 3 to 5 with High Combustion Temperature

High Thrust for a Ramjet Occurs from Mach 3 to 5 with High Combustion Temperature

0

5

10

15

20

25


T / [

PHI (

p0 ) (

A0 ) ]

, Non

dim

imen

siona

l Th

rust

T4 / T0 = 3 T4 / T0 = 5T4 / T0 = 10 T4 / T0 = 15

TIdeal / ( φ p0 A0 ) = γ0 M02 {{[ T4 / T0 ] / { 1 + [( γ0 - 1 ) / 2 ] M0

2 }}1/2 - 1 }Assumptions: Ideal ramjet, isentropic inlet and nozzle, low subsonic and constant pressure combustion, exit pressure = free stream pressure, φ ≤ 1Note: T4 and T0 in R Example for Ramjet Baseline:

M0 = 3.5, α = 0 deg, h = 60k ft ( T0 = 390 R, p0 = 1.047 psi ), T4 = 4,000 R, ( f / a ) = 0.055, φ = 0.82, A0 = 114 in2, γ0 = 1.4

TIdeal / ( φ p0 A0 ) = 1.4 ( 3.5 )2 {{[ 4000 / 390 ] / { 1 + [( 1.4 – 1 ) / 2 ] ( 3.5 )2 }}1/2 – 1 } = 12.43

TIdeal = 12.43 ( 0.82 ) ( 1.047 ) ( 114 ) = 1216 lbNote:( T )Ideal = Ideal thrustp0 = Free stream static pressureA0 = Free stream flow area into inletγ0 = Free stream specific heat ratioM0 = Free stream Mach numberT4 = Combustor exit temperatureT0 = Free stream temperatureφ = Equivalence ratio = fuel-to-air ratio / stochiometric fuel-to-air ratio


2/24/2008 ELF 96

Ramjet Combustor Temperature Increases with Mach Number and Fuel Flow

Ramjet Combustor Temperature Increases with Mach Number and Fuel Flow

0

2000

4000

6000


T4, C

ombu

stor

Exit

Tem

pera

ture

for R

J-5

Fuel,

Ran

kine

f / a = 0.01 f / a = 0.03 f / a = 0.05 f / a = 0.067

Example:•M0 = 3.5•h = 60k ft ( T0 = 390 R )•RJ-5 fuel ( Hf = 14,525 BTU / lb / R )•f / a = 0.055•γ0 = 1.4•cp = 0.122 T0.109 BTU / lbm / R.Note: cp ≈ 0.302 +/- 5% if 2500 R < T < 5000 R•Then T4 = 390 { 1 + [( 1.4 – 1 ) / 2 ] ( 3.5 )2 } + [( 14525 ) / ( 0.302 )] 0.055 = 3,991 R

Note: ( f / a )φ = 1 ≈ 0.067 for stochiometric combustion of liquid hydrocarbon fuel, e.g., RJ-5.

T4 ≈ T0 { 1 + [( γ0 - 1 ) / 2 ] M02 } + ( Hf / cp ) ( f / a )

Assumptions: Low subsonic combustion. No heat transfer through inlet ( isentropic flow ). φ ≤ 1.T4 = combustor exit temperature in Rankine, T0 = free stream temperature in Rankine, γ = specific heat ratio, M0 = free stream Mach number, Hf = heating value of fuel, cp = specific heat at constant pressure, f / a = fuel-to-air ratio.

2/24/2008 ELF 97

Ramjet Combustor Entrance Mach Number Should Be Low, to Avoid Thermal ChokingRamjet Combustor Entrance Mach Number Should Be Low, to Avoid Thermal Choking

0

0.1

0.2

0.3

0.4


( M3 )

TC, C

ombu

stor

Ent

ranc

e Mac

h Nu

mbe

r with

The

rmal

Chok

ing

T4t / T0 = 3 T4t / T0 = 5T4t / T0 = 10 T4t / T0 = 15

( M3 )TC = {{ - b + [ b2 – 4 γ32 ]1/2 } / ( 2 γ3

2 )}1/2

b = 2 γ3 + ( T4t / T0 )( 1 + γ4 )2 / {( 1 + 0.2 M02 )[ 1 + ( γ4 – 1 ) / 2 ]}

Assumptions: Constant area combustion, [( γ 3 – 1 ) / 2 ] M32 << 1, isentropic inlet

Example:M0 = 2, h = 60k ft ( T0 = 390 R ), T4t = 4,000 R, γ0 = 1.4γ4 = 1.29 + 0.16 e-0.0007 ( 4000 ) = 1.300T0t = ( 1 + 0.2 M0

2 ) T0 = 702 R γ 3 = 1.29 + 0.16 e-0.0007 ( 702 ) = 1.388b = 2 ( 1.388 ) + ( 4000 / 390 )( 1 + 1.300 )2 / {( 1 + 0.2 ( 22 )[ 1 + ( 1.300 – 1 ) / 2 ]} = - 24.211

( M3 )TC = {{ 24.211 + [( -24.211 )2 – 4 ( 1.3882 ) ]1/2 } / [ 2 ( 1.3882 )]}1/2 = 0.204

Note:( M3 )TC = Combustor entrance Mach number with thermal choking ( M4 = 1 )

γ3 = Specific heat ratio at combustor entranceM0 = Free stream Mach numberT4t = Combustor exit total temperatureT0 = Free stream static temperatureγ4 = Specific heat ratio in combustion

2/24/2008 ELF 98

A Ramjet Combustor with a Low Entrance Mach Number Requires a Small Inlet Throat Area

A Ramjet Combustor with a Low Entrance Mach Number Requires a Small Inlet Throat Area

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1( A )IT / A3, Inlet Throat Area to Combustor Area Ratio

M3,

Com

bust

or E

ntra

nce M

ach

Num

ber

AIT / A3 = [( γ + 1 ) / 2 ]( γ + 1 ) / [ 2 ( γ - 1 )] M3 {[ 1 + ( γ - 1 ) / 2 ] M32 }-( γ + 1 ) / [ 2 ( γ - 1 )] = ( 216 / 215 ) M3 ( 1 + M3

2 / 5 )-3

Assumptions: Isentropic inlet, MIT = 1, γ = 1.4

Note:AIT = Inlet throat areaA3 = Combustor entrance areaM3 = Combustor entrance Mach numberγ = Specific heat ratioExample:Ramjet BaselineAIT = 41.9 in2

A3 = 287 in2

AIT / A3 = 41.9 / 287 = 0.1459Assume sonic flow ( M = 1 ) at AIT

M3 = 0.085M3 = 0.085 < ( M3 )TC = 0.204

2/24/2008 ELF 99

Typical Ramjet Has Nearly Constant Pressure Combustion

Typical Ramjet Has Nearly Constant Pressure Combustion

Assume Rayleigh Flow, with Heat Addition atConstant AreaNegligible Friction

Pressure Loss in Combustor is Given byp4 / p3 = ( 1 + γ3 M3

2 ) / ( 1 + γ4 M42 )

Mach Number Increase in Combustor Is Given byT4t / T0 = [( 1 + γ3 M3

2 ) / ( 1 + γ4 M42 )]2 ( M4 / M3 )2 { 1 + [( γ4 – 1 ) / 2 ] M4

2 } / { 1 + [( γ3 – 1 ) / 2 ] M32 }

From Prior ExampleM0 = 2, h = 60k ft ( T0 = 390 R ), T4t = 4,000 R, γ0 = 1.4, γ4 = 1.300, and γ 3 = 1.388

Assume Ramjet Baseline with Sonic Inlet ThroatAIT / A3 = 41.9 / 287 = 0.1459 ⇒ M3 = 0.085

Solving Above EquationsM4 = 0.304p4 / p3 = 0.902

Assumption of Nearly Constant Pressure Combustion Is Reasonably Accurate10% error

2/24/2008 ELF 100

Minimum Length for the Combustor Is a Function of Combustion Velocity

Minimum Length for the Combustor Is a Function of Combustion Velocity

0.1

1

10

100 1000 10000

Vcomb, Combustion Velocity, ft / s

Mini

mum

Com

bust

or L

engt

h, ft

tcomb = 0.001 stcomb = 0.002 stcomb = 0.004 s

Example for tcomb = 0.002 s andSubsonic Combustion Ramjet:•Vcomb = 200 ft / s•( lcomb )min = 0.002 ( 200 ) = 0.4 ftExample for tcomb = 0.002 s and Scramjet:•Vcomb = 3,000 ft / s•( lcomb )min = 0.002 ( 3000 ) = 6.0 ft

( lcomb )min = tcomb Vcomb

2/24/2008 ELF 101

Ramjet Engine / Booster Integration OptionsRamjet Engine / Booster Integration Options

Integral-Rocket Ramjet ( IRR ) Aft Drop-off Booster

Podded Drop-off BoosterForward Booster

Podded Ramjet

Podded Ramjet, Aft Drop-off Booster

Podded IRR

FuelBoost Propellant

Source: Kinroth, G.D. and Anderson, W.R., “Ramjet Design Handbook,” CPIA Pub. 319, June 1980

Low Cruise Drag ( Modern Ramjets )

High Cruise Drag

2/24/2008 ELF 102

Superior Above Average Average Below average

Ramjet Engine / Booster Integration TradesRamjet Engine / Booster Integration Trades

Leng

th

Diam

eter

Weig

ht

Ejec

tabl

es

Crui

se D

rag

Carry

Dra

g

Cost

Cycle

Co

mpa

tibilit

y

Inlet

Com

patib

ilitySelection Factors


Integral Rocket – Ramjet ( IRR )

Aft Booster ( Drop-off )

Forward Booster

Podded Booster ( Drop-off )

Podded Ramjet

Podded IRR

Podded RamjetAft Booster ( Drop-off )

–

–

–

–

–

– –

–

–– – –

–

–

–

–

–

–

2/24/2008 ELF 103

Ramjets with Internal Boosters and No Wings Have Low Drag

Ramjets with Internal Boosters and No Wings Have Low Drag

1.2

0.8

0.4

02 3 4 5

M, Mach Number

CD0 = DO / ( q SREF ), Zero-Lift Drag

Coefficient

Note:Nose Fineness Ratio ≥ 2.25Nose Bluntness Ratio ≤ 0.20

• IRR• Aft Drop Off Booster• Forward Booster• Podded Drop Off Booster

With Wings

Without Wings• IRR• Aft Drop-off Booster• Forward Booster• Podded Drop-off Booster

• Podded Ramjet• Podded IRR• Podded Ramjet, Aft Drop

Off Booster


CD0

2/24/2008 ELF 104

Sketch

Ramjet Inlet OptionsRamjet Inlet Options

Nose

Source: Kinroth, G.D. and Anderson, W.R., “Ramjet Design Handbook,” CPIA Pub. 319, June 1980.

Nose-full axisymmetric

Aft-cruciform ( four ) two dimensional

Aft underside-belly mounted two dimensional

Aft underside-full axisymmetric

Aft-twin cheek-mounted two dimensional

PlacementType Inlet

Cruciform Two-dimensional

Underslung Two-dimensional

Underslung Axisymmetric

Twin Two-dimensional

Under Wing Axisymmetric

Aft Cruciform Axisymmetric

Forward Cruciform Axisymmetric

Chin

In planar wing compression field-twin axisymmetric

Aft-cruciform ( four ) axisymmetric

Forward in nose compression field-cruciform ( four ) axisymmetric

Forward underside in nose compression field-partial axisymmetric

2/24/2008 ELF 105

Ramjet Inlet Concept TradesRamjet Inlet Concept Trades

Superior Above Average Average Below average


–

Carri

age

Enve

lope

Alph

a Ca

pabi

lity

Weig

ht

Drag

War

head

Sh

roud

ing

inlet

Cos

t

Pref

erre

d St

eerin

g

Pref

erre

d Co

ntro

l

Prim

e Mi

ssio

n Su

itabi

lity

Note: BTT = Bank to TurnSTT = Skid to TurnW = Wing C = CanardT = Tail

Selection Factors

STT W, C ATS, STABTT T ATS, ATA, STA

– – STT T ATS, ATA, STASTT T ATSBTT T ATS, ATA, STA–BTT T ATS, ATA, STA

– BTT T ATS

– BTT T ATS, ATA, STA

STT T ATS

Type Inlet Pres

sure

Reco

very

––

–

–

2/24/2008 ELF 106

United KingdomSea Dart GWS-30

FranceASMP ANS

RussiaAS-17 / Kh-31 Kh-41 SS-N-22 / 3M80

SA-6 SS-N-19 SS-N-26China

C-101 C-301Taiwan

Hsiung Feng IIIIndia

BrahMos

Current Supersonic Air-breathing Missiles Have Either a Nose Inlet or Axisymmetric Aft Inlets

Current Supersonic Air-breathing Missiles Have Either a Nose Inlet or Axisymmetric Aft Inlets

• Aft inlets have lower inlet volume and do not degrade lethality of forward located warhead.• Nose Inlet may have higher flow capture, pressure recovery, smaller carriage envelope, and lower drag.

2/24/2008 ELF 107

Shock on Inlet Cowl Lip Prevents SpillageShock on Inlet Cowl Lip Prevents SpillageInlet w/o External Compression

Inlet Swallows 100% of the Free Stream Flow

External Compression Required for Efficient Pressure Recovery if Mach Number > 2 and Inlet Start at Low Supersonic Mach number

External Compression Inlet ( with Spillage )

Shocks Converge Outside Inlet Lip ( Results in Spillage Air )

External Compression Inlet ( w/o Spillage )

Inlet Swallows 100% of the Free Stream Flow

Shocks Converge at Inlet Lip ( Inlet Captures Maximum Free Stream Flow )

Shocks

Spillage

Shocks

2/24/2008 ELF 108

Shock Wave Angle Increases with Deflection Angle and Decreases with Mach Number

Shock Wave Angle Increases with Deflection Angle and Decreases with Mach Number

0

10

20

30

40

50

0 5 10 15 20Alpha + Delta, Deflection Angle, Degrees

Thet

a, 2D

Sho

ck W

ave A

ngle

@ G

amm

a =

1.4, D

egre

es

Mach 2 ( Deltamax = 23 deg ) Mach 3 ( Deltamax = 34 deg )Mach 5 ( Deltamax = 41 deg )

tan ( α + δ ) = 2 cot θ2D ( M2 sin2 θ2D – 1 ) / [ 2 + M2 ( γ + 1 – 2 sin2 θ2D )] , for 2D flow, perfect gasNote: θ2D = 2D shock wave angle, M = Mach number, α = angle of attack, δ = body deflection angle, γ = specific heat ratio, θconical ≈ 0.81 θ2D

Example for Ramjet Baseline:

δ = 17.7 deg, M = 3.5, α = 0 deg, γ = 1.4⇒ θ2D = 32 degθconical ≈ 0.81 θ2D = 0.81 ( 32 ) = 26 deg

δ

θ

α

Approximate estimate of θ:θ2D ≈ μ + α + δ = sin-1 ( 1 / M ) + α + δθconical ≈ 0.81 θ2D = 0.81 [ sin-1 ( 1 / M ) + α + δ ]

2/24/2008 ELF 109

Capture Efficiency of an Inlet Increases with Mach Number

Capture Efficiency of an Inlet Increases with Mach Number

0

0.2

0.4

0.6

0.8

1


A0 / A

c, Ba

selin

e Ram

jet In

let C

aptu

re

Effic

iency

Alpha = 0 Deg Alpha = 10 Deg

Ac

A0 streamline streamline

oblique shock

h inlet

nose bodyδ

streamlinestreamline

( A0 / Ac )conical = ( h / l ) ( 1 + δ M + αM ) / [( 1 – 0.23δM + αM )( δ + h / l )] , conical nose with forward inlet

( A0 / Ac )2D = ( h / l ) ( 1 + δ M + αM ) / [( 1 + αM )( δ + h / l )] , 2D nose with forward inletNote: A0 / Ac ≤ 1, AC = inlet capture area, A0 = free stream flow area, δ = defection angle in rad, h = inlet height, l = distance from nose tip to inlet

α

Example for baseline ramjet ( conical nose )h = 3 inl = 23.5 inh / l = 0.1277AC = 114 in2

δ = 17.7 deg ( 0.3089 rad )M = 3.5, α = 0 degA0 / Ac = 0.81 ⇒ A0 = 92 in2

Spillage = Ac - A0 = 114 - 92 = 22 in2

2/24/2008 ELF 110

Isentropic Compression Allows Inlet Start at Lower Mach Number

Isentropic Compression Allows Inlet Start at Lower Mach Number

0

1

2

3

4

0 0.2 0.4 0.6 0.8 1AIT / A0

( M )IE

, Inlet

Ent

ranc

e Sta

rt Ma

ch

Num

ber

Inlet Start for Isentropic CompressionInlet Start for Single Normal Shock

AIT / A0 = 1.728 ( MIE )start [ 1 + 0.2 ( MIE )start2 )-3, Assumptions: 2-D inlet, Isentropic flow through inlet ( n = ∞ ), γ = 1.4

AIT / A0 = ( MIE )start {[ 0.4 ( MIE )start2 + 2 ] / [ 2.4 ( MIE )start

2 ]3.5 }{[2.8 ( MIE )start2 – 0.4 ] / 2.4 }2.5 {[ 1.2 / ( 1 + 0.2 (

MIE )start2 ]}3, Assumptions: 2-D inlet, single normal shock ( n = 1 ), γ = 1.4

Note: AIT = inlet throat area, A0 = free stream flow area, ( MIE )start = inlet entrance start Mach number, γ = specific heat ratio, n = number of shocks

Example for ramjet baselineAIT = 0.29 ft2

Ac = 114 in2 = 0.79 ft2 ⇒ AIT / Ac = 0.367Process:1. Assume ( MIE )start

2. Compute capture efficiency AIT / A0

3. Compute ( MIE )start and compare with assumed ( MIE )start

4. Iterate until convergence Limit for isentropic compression- From Prior Figure, A0 / Ac = 0.53- Compute AIT / A0 = ( AIT / Ac ) / ( A0 / Ac ) =

0.367 / 0.53 = 0.69 ⇒ ( MIE )start = 1.8Ramjet baseline has mixed compression

with n = 5. Actual inlet start Mach number is ( MIE )start > 1.8

n = 1n = ∞

2/24/2008 ELF 111

Forebody Shock Compression Reduces the Inlet Entrance Mach Number

Forebody Shock Compression Reduces the Inlet Entrance Mach Number

0

1

2

3

4

0 10 20 30 40

Alpha + Delta, Local Angle of Attack at Inlet Entrance, Deg

( M )IE

, Inlet

Ent

ranc

e Mac

h Nu

mbe

r

M0 = 2 M0 = 3 M0 = 5

( MIE )2D = {{ 36 M04 sin2 θ2D - 5 [ M0

2 sin2 θ2D - 1 ][ 7 M02 sin2 θ2D + 5 ]} / {[ 7 M0

2 sin2 θ2D - 1 ][ M02 sin2 θ2D + 5 ]}}1/2

tan ( α + δ ) = 2 cot θ2D ( M02 sin2 θ2D – 1 ) / [ 2 + M0

2 ( 2.4 – 2 sin2 θ2D )]Assumptions: 2D flow, perfect gas, γ = specific heat ratio = 1.4 Note: MIEt= inlet entrance Mach number, M0 = free stream Mach number, θ = oblique shock angle, α = angle of attack, δ = body deflection angle

Example for ramjet baseline

δ = 17.7 deg( MIE )start = 1.8 ( from prior example )Compute M0 = 2.55Note: Ramjet baseline forebody is conical, not 2D

2/24/2008 ELF 112

Optimum Forebody Deflection Angle(s) for Best Pressure Recovery Increases with Mach NumberOptimum Forebody Deflection Angle(s) for Best Pressure Recovery Increases with Mach Number

0

20

40

60

0 1 2 3 4M0, Free Stream Mach Number

Optim

um T

otal

Defle

ctio

n An

gle,

Deg

n = 1 n = 2 n = 3 n = 4 Isentropic Compression

δ1

First External ShockSecond External Shock

δ2

Note: δTotal = Total deflection angle, δ1 = 1st deflection angle, δ2 = 2nd

deflection, δ3 = 3rd deflection.Optimum deflection angle provides

equal loss in total pressure across each shock wave.

Optimum deflection angles are nearly equal for M > 4.

Reference: “Technical Aerodynamics Manual,” North American Rockwell Corporation, DTIC AD 723823, June 1970.

Example: Optimum forebody deflection angles for double wedge ( n = 3 ) at Mach 2: δ1 = 10.4 deg, δ2= 11.2 deg ⇒ δtotal = 10.4 + 11.2 = 21.6 deg

δTotal

10.4, 11.2

15.0, 18.816.1, 22.1

7.6, 8.2, 8.2

11.1, 13.0, 15.5

12.1, 15.2, 19.4

2/24/2008 ELF 113

Oblique Shocks Prior to the Inlet Normal Shock Are Required to Satisfy MIL-E-5008B

Oblique Shocks Prior to the Inlet Normal Shock Are Required to Satisfy MIL-E-5008B

0.01

0.1

1

0 1 2 3 4 5

M, Mach Number

PtIn

let /

pt0

, Inl

et T

otal

Pre

ssur

e R

atio

n = 1 ( Normal Shock )

n = 2 ( 1 Optimum ObliqueShock + Normal Shock )n = 3 ( 2 Opt ObliqueShocks + Normal Shock )n = 4 ( 3 Opt ObliqueShocks + Normal ShockIdeal Isentropic Inlet

MIL-E-5008B

Source for Optimum 2D Shocks: Oswatitsch, K.L., “Pressure Recovery for Missiles with Reaction Propulsion at High Supersonic Speeds”, NACA TM - 1140, 1947.

Example: MIL-E-5008B requirement for Mach 3.5 ( ptInlet/ pt0

= ηinlet = 0.74 ) can be satisfied only if there are more than three oblique shocks prior to inlet normal shock.

Note: 2D flow assumedptInlet

= Inlet total pressurept0

= Free stream total pressure

MIL-E-5008B Requirement: ptInlet/ pt0

= 1 – 0.075 ( M – 1 )1.35

2/24/2008 ELF 114

Turbine ( JP-4, JP-5, JP-7, JP-8, JP-10 ) ~ 0.028 559

Liquid Ramjet ( RJ-4, RJ-5, RJ-6, RJ-7 ) ~ 0.040 581

HTPB ~ 0.034 606

Slurry ( 40% JP-10 / 60% carbon ) ~ 0.049 801

Solid Carbon ( graphite ) ~ 0.075 1132

Slurry ( 40% JP-10 / 60% aluminum ) ~ 0.072 866

Slurry ( 40% JP-10 / 60% boron carbide ) ~ 0.050 1191

Solid Mg ~ 0.068 1200

Solid Al ~ 0.101 1300

Solid Boron ~ 0.082 2040

High Density Fuels Provide Higher Volumetric Performance but Have Higher Observables

High Density Fuels Provide Higher Volumetric Performance but Have Higher Observables

–

Type Fuel

VolumetricPerformance,

BTU / in3

Superior Above average Average Below average

LowObservables

–

–

–

–

–

Density,lb / in3

–

2/24/2008 ELF 115

Ducted Rocket Design ImplicationsDucted Rocket Design ImplicationsExcess Fuel from Gas Generator

~ 30 % ⇒ Behaves more like a rocket ( higher burn rate, higher burn temperature, lower ISP )~ 70 % ⇒ Behaves more like a ramjet ( higher ISP, lower burn rate, lower burn temperature )

Choice of FuelMetal ( e.g., B, Al, Mg ) ⇒ Higher ISP, higher density, deposits, higher observablesCarbon based ( e.g., C, HTPB ) ⇒ Lower observables, higher reliability, lower ISP

Choice of OxidizerAP ⇒ Higher burn rate, lower hazard, HCl contrailMin Smoke ( e.g., HMX, RDX ) ⇒ Lower Observables, lower heating value, lower burn rate, hazardous

Thrust Magnitude Control ApproachesPintle or valve in gas generator throatRetractable wires in grain

2/24/2008 ELF 116

0

High Propellant Fraction Increases Burnout Velocity

High Propellant Fraction Increases Burnout Velocity

5000

4000

3000

2000

1000

0 0.1 0.2 0.3 0.4 0.5

Example: Rocket BaselineWi,boost = WL = 500 lb, Wp, boost = 84.8 lbISP, boost = 250 sWP, boost / Wi = 84.8 / 500 = 0.1696ΔV = -32.2 ( 250 ) ln ( 1 - 0.1696 ) = 1496 ft / s

ΔV, Missile Incremental

Burnout Velocity,ft / s

WP / Wi, Propellant Weight / Initial Missile Weight

Isp = 250 s

Isp = 200 s

Assumption: T >> D, T >> W sin γ, γ = const

ΔV = -gc Isp ln (1 - Wp / Wi)

2/24/2008 ELF 117

High Specific Impulse Requires High Chamber Pressure and Optimum Nozzle Expansion

High Specific Impulse Requires High Chamber Pressure and Optimum Nozzle Expansion

200

250

300

0 10 20 30Nozzle Expansion Ratio

Isp, S

pecif

ic Im

pulse

of R

ocke

t Bas

eline

, s

pc = 300 psi pc = 1000 psipc = 2000 psi pc = 3000 psi

Note:ε = nozzle expansion ratiope = exit pressurepc = chamber pressurep0 = atmospheric pressurew.

P = propellant weight flow rateAt = nozzle throat area ( minimum, sonic, choked ) γ = specific heat ratio = 1.18 in figurecd = discharge coefficient = 0.96 in figurec* = characteristic velocity = 5,200 ft / s in figureh = 20k ft, p0 = 6.75 psi in figure

Example for Rocket Baseline:ε = Ae / At = 6.2 ⇒ pe / pc = 0.02488, At = 1.81 in2

( pc )boost = 1769 psi, pe = 44 psi, ( ISP )boost = 257 s( ISP )ε = 6.2 / ( ISP )ε = 1 = 257 / 200 = 1.29( T )boost = ( 32.2 / 5200 ) ( 1769 ) (1.81 )( 257 ) = 5096 lb( pc )sustain = 301 psi, pe = 7.49 psi, ( ISP )sustain = 239 s( ISP )ε = 6.2 / ( ISP )ε = 1 = 240 / 200 = 1.20( T )sustain = ( 32.2 / 5200 ) ( 301 ) (1.81 )( 240 ) = 810 lb

ISP = cd {{[ 2 γ2 / ( γ - 1 )] [ 2 / ( γ + 1 )] ( γ + 1 ) / ( γ - 1 ) [ 1 – ( pe / pc ) ( γ - 1 ) / γ ]}1/2 + ( pe / pc ) ε - ( p0 / pc ) ε } c* / gc

T = w.p ISP = ( gc / c* ) pc At ISP

ε = {[ 2 / ( γ + 1 )]1 / ( γ - 1 ) [( γ -1 ) / ( γ + 1 )]1/2 } / {( pe / pc )1 / γ [ 1 - ( pe / pc ) ( γ - 1 ) / γ ]1/2 }

2/24/2008 ELF 118

High Propellant Weight Flow Rate Requires High Chamber Pressure and Large Nozzle Throat

High Propellant Weight Flow Rate Requires High Chamber Pressure and Large Nozzle Throat

100

1000

10000

100000

1 10 100Propellant Weight Flow Rate, lb / s

(pc)

At, C

ham

ber P

ress

ure x

Noz

zle

Thro

at A

rea,

lb

c* = 4800 ft / sc* = 5200 ft / sc* = 5600 ft / s

w.p = gc pc At / c*

Rocket Baseline At for Boost:c* = 5200 ft / s( pc )boost = 1,769 psiw.

p = Wp / tb = 84.8 / 3.69 = 23.0 lb / spc At = c* w.

p / gc = 5200 ( 23.0 ) / 32.2 = 3,714 lb

At = 3714 / 1769 = 2.10 in2

Note: At = nozzle throat area, c* = characteristic velocity, w.p = propellant weight flow rate, gc = gravitational constant,

pc = chamber pressure

2/24/2008 ELF 119

High Chamber Pressure Requires Large Propellant Burn Area and Small Nozzle Throat

High Chamber Pressure Requires Large Propellant Burn Area and Small Nozzle Throat

0

200

400

600

0 500 1000 1500 2000Pc, Rocket Baseline Motor Chamber Pressure, psi

Ab, R

ocke

t Bas

eline

Pro

pella

nt B

urn

Area

, in2

Ab = gc pcAt / ( ρc*r )r = rpc=1000 psi ( pc / 1000 )n

Example Ab for Rocket Baseline:At= 1.81 in2

ρ = 0.065 lb / in3

n = 0.3rpc = 1000 psi = 0.5 in / sc* = 5,200 ft / sTatmosphere = 70 °FFor sustain ( pc = 301 psi ):•r = 0.5 ( 301 / 1000 )0.3 = 0.35 in / s•Ab = 149 in2

For boost ( pc = 1,769 psi )•r = 0.59 in / s•Ab = 514 in2

Note: Ab = propellant burn area, gc = gravitation constant, At = nozzle throat area, ρ = density of propellant, c* = characteristic velocity, r = propellant burn rate, rpc=1000 psi = propellant burn rate at pc = 1,000 psi, pc = chamber pressure, n = burn rate exponent

2/24/2008 ELF 120

Conceptual Design Sizing Process for a Rocket Motor

Conceptual Design Sizing Process for a Rocket Motor

Yes

1. Define Altitude and Required Thrust-time

4. Compute Propellant Weight Flow Rate and Propellant Used

No

NoYes

5. Determine Diameter and Length to Satisfy wp and Ae

OK?

OK?

OK?

Yes

New Value ( s )

New Value ( s )

No

2. Assume Propellant ( Characteristic Velocity, Nominal Burn Rate, Burn Rate Exponent ), Chamber Pressure, Burn

Area, and Nozzle Geometry ( Expansion Ratio, Throat Area )

3. Compute ISP and Thrust

2/24/2008 ELF 121

Example Web Cross Section / Volumetric Loading

~ 82% ~95% ~90%

End Burner Radial Slotted Tube~ 79%

~ 87%

~ 85%

~ 85%

Conventional Solid Rocket Thrust-Time Design Alternatives with Propellant Cross-Section

Conventional Solid Rocket Thrust-Time Design Alternatives with Propellant Cross-Section

Thru

st ( lb

)Burning Time ( s )

ConstantThrust

RegressiveThrust

ProgressiveThrust

Boost-Sustain

Boost-Sustain-Boost

Burning Time ( s )

Burning Time ( s )

Burning Time ( s )

Burning Time ( s )

Thru

st ( lb

)Th

rust

( lb )

Thru

st ( lb

)Th

rust

( lb )

Medium Burn Rate Propellant

High Burn Rate PropellantNote: High thrust and chamber pressure require large surface burn area.

Example Mission•≈ Cruise

•Dive at ≈constant dynamic pressure

•Climb at ≈constant dynamic pressure

•Fast launch –≈ cruise

•Fast launch –≈ cruise – high speed terminal

Thrust Profile

Production of Star Web Propellant. Photo Courtesy of BAE

2/24/2008 ELF 122

Conventional Rocket Has Fixed Burn while Thrust Magnitude Control Can Vary Burn Interval

Conventional Rocket Has Fixed Burn while Thrust Magnitude Control Can Vary Burn Interval

End Burning

Conventional Fixed Burn Interval ( Boost )

Conventional Fixed Burn Interval ( Boost – Sustain )

Radial BoostEnd Burning Sustain

Simultaneous Burning

1st Pulse: Radial Boost2nd Pulse: End Burning Sustain

Separate Burning ( Pulsed Motor )

1st Pulse: Radial Boost2nd Pulse: Radial Sustain / Boost

Separate Burning ( Pulsed Motor )

Concentric Radial BurningHigh Burn Rate BoostLow Burn Rate Sustain

Radial Burning

Boost PropellantSustain Propellant

Pulse Motor TMC Variable Burn Interval ( Boost – Coast – Boost / Sustain - Coast )

Note: Each pulse increases motor cost approximately 40%.

2/24/2008 ELF 123

Tactical Rocket Motor Thrust Magnitude Control Alternatives

Tactical Rocket Motor Thrust Magnitude Control Alternatives

Solid Pulse Motor☺ High ISP

Limited Pulses

Solid Pintle Motor☺ Continuously Select Up to

40:1 Variation in Thrust

☺ Reduce MEOP on Hot Day

Good ISP Only If Burn Rate Exponent n → 1

Bi-propellant Gel Motor☺ High ISP

☺ Duty Cycle Thrust

☺ Insensitive Munition

Lower Max Thrust

Toxicity

Thermal or Mechanical Barriers

Pintle

Pressurization Gelled Oxidizer Gelled Fuel Combustion Chamber

2/24/2008 ELF 124

250 - 260 0.062 0.1 - 1.5

Solid Rocket Propellant AlternativesSolid Rocket Propellant Alternatives

Superior Above Average Average Below Average

• Min Smoke. No Al fuel or AP oxidizer. Either Composite with Nitramine Oxidizer ( CL-20, ADN, HMX, RDX ) or Double Base. Very low contrail (H2O).

• Reduced Smoke. No Al ( binder fuel ). AP oxidizer. Low contrail ( HCl ).

• High Smoke. Al fuel. AP oxidizer. High smoke ( Al2O3 ).

–

ISP, Specific

Impulse, s

ρ, Density,lb / in3

BurnRate @

1,000 psi, in / s Safety Observables

– – –

–

Type

220 - 255 0.055 - 0.062 0.25 - 2.0

260 - 265 0.065 0.1 - 3.0

2/24/2008 ELF 125

Steel is the Most Common Motor Case MaterialSteel is the Most Common Motor Case Material


Steel

Aluminum

Strip Steel / Epoxy Laminate

Composite

Titanium

–

VolumetricEfficiency Weight

Airframe / Launcher

Attachment Cost

–

Type

–

–

– –

– –

Temper-ature

–

IM

2/24/2008 ELF 126

Heat Transfer Drives Rocket Nozzle Materials, Weight, and Cost

Heat Transfer Drives Rocket Nozzle Materials, Weight, and Cost

HousingThroat

Exit ConeDome Closeout

Rocket Nozzle Element High Heating ( High Chamber Pressure or Long Burn ) ⇒ High Cost / Heavy Nozzle

Low Heating ( Low Chamber Pressure or Short Burn ) ⇒ Low Cost / Light Weight Nozzle

♦ Housing Material Alternatives

♦ Steel ♦ Cellulose / Phenolic ♦ Aluminum

♦ Throat Material Alternatives

♦ Tungsten Insert ♦ Rhenium Insert ♦ Molybdenum Insert

♦ Cellulose / Phenolic Insert ♦ Silica / Phenolic Insert ♦ Graphite Insert ♦ Carbon – Carbon Insert

♦ Exit Cone, Dome Closeout, and Blast Tube Material Alternatives

♦ Silica / Phenolic Insert ♦ Graphite / Phenolic Insert ♦ Silicone Elastomer Insert

♦ No Insert ♦ Glass / Phenolic Insert

2/24/2008 ELF 127

Summary of PropulsionSummary of PropulsionEmphasis

Turbojet propulsionRamjet propulsionRocket propulsion

Conceptual Design Prediction MethodsThrustSpecific impulse

Design TradesTurbojet turbine material, compressor ratio, and cycleRamjet engine / booster / inlet integrationRamjet fuelPropellant burn area requirementNozzle throat areaNozzle expansion ratioRocket motor grainThrust magnitude control

2/24/2008 ELF 128

Summary of Propulsion ( cont )Summary of Propulsion ( cont )Design Trades ( cont )

Solid propellant alternativesMotor case material alternativesNozzle materials

New Propulsion TechnologiesHypersonic turbojetRamjet / ducted rocketScramjetCombined cycle propulsionHigh temperature turbine materialsHigh temperature combustorOblique shock airframe compressionMixed compression inletLow drag inletHigh density fuel / propellantEndothermic fuel

2/24/2008 ELF 129

Summary of Propulsion ( cont )Summary of Propulsion ( cont )New Propulsion Technologies ( cont )

Solid rocket thrust magnitude controlHigh burn exponent propellantLow observable fuel / propellant

Discussion / Questions?Classroom Exercise ( Appendix A )

2/24/2008 ELF 130

Propulsion ProblemsPropulsion Problems1. An advantage of turbojets compared to ramjets is s_____ thrust.2. The specific impulse of a turbojet is often limited by the maximum

allowable temperature of the t______.3. The specific impulse of a ramjet is often limited by the maximum allowable

temperature of the c________.4. Ducted rockets are based on a fuel-rich g__ g________.5. A safety advantage of solid rocket propulsion over liquid propulsion is less

t_______.6. A rocket boost to a take-over Mach number is required by ramjets and

s________.7. Parameters that enable the long range of subsonic cruise turbojet missiles

are high lift, low drag, available fuel volume, and high s_______ i______.8. High thrust and high acceleration are achievable with s____ r_____

propulsion.9. In a turbojet the power to drive the compressor is provided by the t______.

2/24/2008 ELF 131

Propulsion Problems ( cont )Propulsion Problems ( cont )10. The compressor exit temperature is a function of the flight Mach number

and the compressor p_______ r____.11. Compressor exit temperature, fuel heating value, and fuel-to-air ratio

determine the turbojet t______ temperature.12. Three types of turbine based propulsion are turbojet, turbo ramjet, and a__

t____ r_____.13. Mach number and fuel-to-air ratio determine the ramjet c________

temperature.14. An example of a ramjet with low drag and light weight is an i_______ r_____

ramjet.15. Russia, France, China, United Kingdom, Taiwan, and India are the only

countries with currently operational r_____ missiles.16. 100% inlet capture efficiency occurs when the forebody shock waves

intercept the i____ l__.17. Excess air that does not flow into the inlet is called s_______ air.

2/24/2008 ELF 132

Propulsion Problems ( cont )Propulsion Problems ( cont )18. Starting a ramjet inlet at lower supersonic Mach number requires a larger

area of the inlet t_____.19. Optimum pressure recovery across shock waves is achieved when the total

pressure loss across each shock wave is e____.20. The specific impulse and thrust of a ramjet are a function of the efficiency

of the combustor, nozzle, and i____.21. High density fuels have high payoff for v_____ limited missiles.22. The specific impulse of a ducted rocket with large excess fuel from the gas

generator can approach that of a r_____.23. High speed rockets require large p_________ weight.24. At the throat, the flow area is minimum, sonic, and c_____ .25. For an optimum nozzle expansion the nozzle exit pressure is equal to the

a__________ pressure.26. High thrust and chamber pressure are achievable through a large propellant

b___ area.

2/24/2008 ELF 133

Propulsion Problems ( cont )Propulsion Problems ( cont )27. Three approaches to solid rocket thrust magnitude control are pulse motor,

pintle motor, and g__ motor.28. A high burn exponent propellant allows a large change in thrust with only a

small change in chamber p_______.29. Three tradeoffs in selecting a solid propellant are safety, observables, and

s_______ i______.30. A low cost motor case is usually based on steel or aluminum material while

a light weight motor case is usually based on c________ material.31. Rockets with high chamber pressure or long burn time may require a

t_______ throat insert.

2/24/2008 ELF 134

OutlineOutline

Introduction / Key Drivers in the Design ProcessAerodynamic Considerations in Tactical Missile DesignPropulsion Considerations in Tactical Missile DesignWeight Considerations in Tactical Missile DesignFlight Performance Considerations in Tactical Missile DesignMeasures of Merit and Launch Platform IntegrationSizing ExamplesDevelopment ProcessSummary and Lessons LearnedReferences and CommunicationAppendices ( Homework Problems / Classroom Exercises, Example of Request for Proposal, Nomenclature, Acronyms, Conversion Factors, Syllabus )

2/24/2008 ELF 135



Yes

Establish Baseline

Trajectory

MeetPerformance?


No

Yes


Alt Mission

Alt Baseline


Aerodynamics

Propulsion

Weight

2/24/2008 ELF 136

Designing Light Weight Missile Has High PayoffDesigning Light Weight Missile Has High Payoff

Production cost

Logistics cost

Size

Firepower

Observables

Mission flexibility

Expeditionary warfare

2/24/2008 ELF 137

Flight Performance ( Range, Speed, Maneuverability ) Sensitive to Subsystem Weight

Flight Performance ( Range, Speed, Maneuverability ) Sensitive to Subsystem Weight

High Sensitivity Low Sensitivity - Minor Sensitivity

Dome - Seeker - Guidance andControl -

Propulsion Wings Stabilizers

Warhead Insulation FlightControl

PowerSupply

Structure Data Link -

2/24/2008 ELF 138

Missile Range is a Function of Launch Weight, Propellant Weight, and Specific Impulse

Missile Range is a Function of Launch Weight, Propellant Weight, and Specific Impulse

10

100

1000

100 1000 10000Wi, Example Initial Launch Weight, lb

Rmax

, Max

imum

Ran

ge, n

m

Single-Stage Missile Two-Stage Missile

ΔV ≈ -gc Isp ln ( 1 - WPropellant / Wi )

R ≈ V2 sin ( 2θi ) / gc

Assumptions:

θI = Launch Incidence Angle = 45 deg for max range

Thrust Greater Than Drag and Weight

Flat, Non-rotating Earth

For Two-Stage Missile with ( Wi )Min : ΔV1 = ΔV2

Example: Two-Stage Missile with Minimum Weight and Rmax = 200 nm = 1.216 x 106 ft

Assume ISP = 250 sec, WPayload = 500 lb, WInert = 0.2 WPropellant

V = [( 32.2 ) ( 1.216 x 106 )]1/2 = 6251 ft / s

ΔV1 = ΔV2 = V / 2 = 3125 ft / s

Wi,SecondStage = WPayload + WInert + WPropellant = 814 lb

Wi, FirstStage = WInert + WPropellant = 85 + 427 = 512 lb

Wi = Wi,FirstStage + Wi,SecondStage = 1326 lb

Compare: Single-Stage Missile, R = 200 nm

ΔV = 6251 = - 32.2 ( 250 ) ln [ 1 – WPropellant / ( WPropellant + 0.2 WPropellant + 500 )] ⇒ Wp = 767 ⇒Wi = 1420 lb

2/24/2008 ELF 139

Missile Weight Is a Function of Diameter and Length

Missile Weight Is a Function of Diameter and Length

10

100

1000

10000

100 1000 10000 100000 1000000ld2, Missile Length x Diameter2, in3

WL,

Mis

sile

Lau

nch

Wei

ght,

lb

FIM-92 SA-14 Javelin RBS-70 Starstreak Mistral HOT Trigat LRLOCAAS AGM-114 Roland RIM-116 Crotale AIM-132 AIM-9M Magic 2Mica AA-11 Python 3 AIM-120C AA-12 Skyflash Aspide AIM-9PSuper 530F Super 530D AGM-65G PAC-3 AS-12 AGM-88 Penguin III AIM-54CArmat Sea Dart Sea Eagle Kormoran II AS34 AGM-84H MIM-23F ANSMM40 AGM-142 AGM-86C SA-10 BGM-109C MGM-140 SSN-22 Kh-41

WL = 0.04 l d2

Units: WL( lb ), l ( in ), d ( in )

2/24/2008 ELF 140

Most Subsystems for Tactical Missiles Have a Density of about 0.05 lb / in3

Most Subsystems for Tactical Missiles Have a Density of about 0.05 lb / in3

Guidance:0.04 lb / in3

Flight Control:0.04 lb / in3

Warhead:0.07 lb / in3

Propellant:0.06 lb / in3

Structure and Motor Case:0.10 ( Al ) to 0.27 ( steel ) lb / in3

Aero Surfaces:0.05 ( built-up Al ) to 0.27 ( solid steel ) lb / in3

Data Link:0.04 lb / in3

Dome Material:0.1 lb / in3

2/24/2008 ELF 141

Modeling Weight, Balance, and Moment-of-Inertia Is Based on a Build-up of Subsystems

Modeling Weight, Balance, and Moment-of-Inertia Is Based on a Build-up of Subsystems

Example Missile Configuration

Model

Structure and Subsystems Engine Structure and Subsystems

Warhead and Structure Fuel

Inlet Structure and Subsystems Aero Surfaces

LegendAssume Uniform Weight Distribution For a Given Segment

+x

Inlet

EngineInlet SectionWith Fuel

Wing SectionWith Fuel

FuelPlug

+z

Nose G&C Warhead

xCG = Σ ( xsubsystem1 Wsubsystem1 + xsubsystem2 Wsubsystem2 + … ) / Wtotal

IY = Σ [ ( Iy,subsystem1 )local + Wsubsystem1 ( xsubsystem1 - xCG )2 / gc + ( Iy,subsystem2 )local + Wsubsystem2 ( xsubsystem2 - xCG )2 / gc + … ]

2/24/2008 ELF 142

Moment-of-Inertia Is Higher for High Fineness Ratio Body

Moment-of-Inertia Is Higher for High Fineness Ratio Body

0.01

0.1

1

10

100

0 10 20 30

l / d, Length / Diameter

( Iy,l

ocal

) g /

( W d

2 ), N

ondi

men

siona

l Yaw

Loc

al Mo

men

of In

ertia

Example for Ramjet Baseline at Launch ( xcg = 8.04 ft )Assume missile can be approximated as a conical nose-cylinderFor the cone, d = 1.25 ft, l / d = 1.57, Wcone = 15.9 lb, xcg,cone = 1.308 ft For the cylinder, l / d = 7.22, d = 1.698 ft, Wcylinder = 2214 lb, xcg,cylinder = 8.09 ftIy = ( Iy,cone )local + Wcone ( xcg,cone - xCG )2 / gc + ( Iy,cylinder )local + Wcylinder ( xcg,cylinder -xCG )2 / gc

( Iy,cone )local = [ 15.9 ( 1.25 )2 / 32.2 ] [ 0.0375 + 0.0375 ( 1.57 )2 ] = 0.10 slug-ft2

( Iy,cylinder )local = [ 2214 ( 1.698 )2 / 32.2 ] [ 0.0625 + 0.0833 ( 7.22 )2 ] = 872 slug-ft2

Iy = 0.10 + 22.4 + 872 + 0.16 = 895 slug-ft2

CylinderCone

( Iy,cylinder )local = [ W d2 / gc ] [( 1 / 16 ) + ( 1 / 12 ) ( l / d )2 ]( Iy,cone )local = [ W d2 / gc ] [ ( 3 / 80 ) + ( 3 / 80 ) ( l / d )2 ]

2/24/2008 ELF 143

Structure Design Factor of Safety Is Greater for Hazardous Subsystems / Flight Conditions

Structure Design Factor of Safety Is Greater for Hazardous Subsystems / Flight Conditions

3.0

2.0

1.0

0

FOS,Factor of Safety

( Ultimate / Yield )

Note:• MIL STDs include environmental ( HDBK-310, NATO STANAG 4370, 810F, 1670A ), strength and rigidity ( 8856 ), and captive carriage ( 8591 ).•The entire environment ( e.g., manufacturing, transportation, storage, ground handling, captive carriage, launch separation, post-launch maneuvering, terminal maneuvering ) must be examined for driving conditions in structure design.•FOS Δ for castings is expected to be reduced in future as casting technology matures.•Reduction in required factor of safety is expected as analysis accuracy improves will result in reduced missile weight / cost.

Pressure Bottle ( 2.50 / 1.50 )Ground Handling Loads ( 1.50 / 1.15 )

Captive Carriage and Separation Flight Loads ( 1.50 / 1.15 )Motor Case ( MEOP ) ( 1.50 / 1.10 )

Free Flight Loads ( 1.25 / 1.10 )Δ Castings ( 1.25 / 1.25 )

Δ Fittings ( 1.15 / 1.15 )Thermal Loads ( 1.00 / 1.00 )

2/24/2008 ELF 144

Structure Concepts and Manufacturing Processes for Low Parts Count

Structure Concepts and Manufacturing Processes for Low Parts Count

Structure Manufacturing Process AlternativesComposites Metals

GeometryAlternatives

VacuumAssistRTM

VacuumBag /

Autoclave

HighSpeed

MachineCompression

MoldFilament

Wind PultrusionThermal

Form FormingCastMonocoqueIntegrally HoopStiffened

IntegrallyLongitudinalStiffened

Solid

Sandwich

AxisymmetricAirframe

Surface

Lifting BodyAirframe

StructureConcept

Alternatives

MonocoqueIntegrally HoopStiffened

IntegrallyLongitudinalStiffened

Strip Laminate

Note: Manufacturing process cost is a function of recurring cost ( unit material, unit labor ) and non-recurring cost ( tooling ).Note: Very Low Parts Count Low Parts Count Moderate Parts Count High Parts Count–

–

–

2/24/2008 ELF 145

Low Parts Count Manufacturing Processes for Complex Airframes

Low Parts Count Manufacturing Processes for Complex Airframes

Vacuum Assisted RTM

Filament Wind

Pultrusion ………………………………….

Metal CastingMold Cavity

Riser

Pour Cup Vent

Parting Line

Resin Pump3D Fiber Orientation

2D Fiber Orientation ( 0-±45-90 deg )Helical wind versus radial wind

2/24/2008 ELF 146

Tactical Missile Airframe Material AlternativesTactical Missile Airframe Material Alternatives

Superior Above Average Average Below Average–Note:

Tension( σTU / ρ )

Aluminum 2219

Steel PH 15-7Mo

Titanium 6Al-4V

S994 Glass /Epoxy and S994Glass / Polyimide

Glass orGraphite ReinforceMolding

Graphite / Epoxyand GraphitePolyimide

MaterialTypeBucklingStability

( σBuckling / ρ )

MaxShort – Life

Temp

ThermalStress Joining Cost Weight

MetallicIncreasing Cost

Composite Increasing Cost

–

–– –

– –

–

–

2/24/2008 ELF 147

Strength – Elasticity of Airframe Material AlternativesStrength – Elasticity of Airframe Material Alternatives

Aluminum Alloy ( 2219-T81 )

400

300

200

100

0

σt, Tensile Stress,103 psi

0 1 2 3 4 5ε, Strain, 10-2 in / in

Titanium Alloy ( Ti-6Al-4V )

Very High Strength Stainless Steel( PH 15-7 Mo, CH 900 )

Glass Fiberw / o Matrix

Kevlar Fiberw / o Matrix

Graphite Fiberw / o Matrix( 400 – 800 Kpsi )

E, Young’s modulus of elasticity, psiP, Load, lbε, Strain, in / inA, Area, in2

Room temperature

Note:• High strength fibers are:

– Very small diameter– Unidirectional– High modulus of

elasticity– Very elastic– No yield before failure– Non forgiving failure

• Metals:– Ductile,– Yield before failure– Allow adjacent structure

to absorb load– Resist crack formation– Resist impact loads– More forgiving failure

σt = P / A = E ε

High Strength Stainless Steel( PH 15-7 Mo, TH 1050 )

2/24/2008 ELF 148

Structural Efficiency at High Temperature of Short Duration Airframe Material AlternativesStructural Efficiency at High Temperature of Short Duration Airframe Material Alternatives

200 400 600 800 1,0000Short Duration Temperature, ° F

8.0

10.0

12.0

6.0

4.0

2.0

0

σ TU/ ρ

, Ulti

mat

e Ten

sile S

treng

th /

Dens

ity, 1

05In

.

Graphite / Epoxy( ρ = 0.065 lb / in3 )0-±45-90 Laminate

Graphite / Polyimide ( ρ = 0.057 lb / in3 ), 0-±45-90 Laminate

Ti-6Al-4V Annealed Titanium ( ρ = 0.160 lb / in3 )PH15-7 Mo Stainless Steel ( ρ = 0.277 lb / in3 ). Note: Thin wall steel susceptible to buckling.

Graphite

Glass

2219-T81Aluminum( ρ = 0.101 lb / in3 )

Chopped Epoxy Composites, Random Orientation( ρ = 0.094 lb / in3 )

Ti3Al ( ρ = 0.15 lb / in3 )

2/24/2008 ELF 149

Hypersonic Missiles without External Insulation Require High Temperature Structure

Hypersonic Missiles without External Insulation Require High Temperature Structure

M, Mach Number

T r, Rec

over

y Tem

pera

ture

, °F

•••

••

•

2,000

1,500

1,000

500

0 10 2 3 4 5 6r =

1

r = 0.

8

r = 0.

9

Tr = T0 ( 1 + 0.2 r M2 )

Note:

• γ = 1.4

• Tr = Recovery Temperature, R

• T0 = Free stream temperature, R

• Tmax = Max temperature capability

• No external insulation assumed

• r is recovery factor• h = 40k ft ( TFree Stream = 390 R )• Stagnation r = 1• Turbulent boundary layer r = 0.9• Laminar boundary layer r = 0.8• Short-duration flight ( less than

30 m ), but with thermal soak

( Tmax )Graphite Polyimide

( Tmax )Al Alloy

( Tmax )Steel

( Tmax )Nickel Alloys ( e.g., Inconel, Rene, Hastelloy, Haynes )

( Tmax )Ti Alloy•

( Tmax )Graphite Epoxy

( Tmax )Titanium Aluminide ≈ 2,500 °F )( Tmax )Single Crystal Nickel Aluminides ≈ 3,000 °F( Tmax )Ceramic Matrix Composite ≈ 3,500 °F

2/24/2008 ELF 150

Structure / Insulation Trades for Short Duration FlightStructure / Insulation Trades for Short Duration FlightExample Structure / Insulation Concepts Mach Tmax k c ρ α

Increasing

Hot Metal Structure ( e.g., Al ) withoutInsulation 600 0.027 0.22 0.101 0.000722

Hot Metal Structure ( e.g., Al ) 600 0.027 0.22 0.101 0.000722

Cold Metal Structure ( e.g., Al ) 600 0.027 0.22 0.101 0.000722Internal Insulation ( e.g., Min-K ) 2000 0.0000051 0.24 0.012 0.00000106

Note:• Tactical missiles use passive thermal protection ( no active cooling )• Small thickness allows more propellant / fuel for diameter constrained missiles ( e.g., VLS launcher )• Weight and cost are application specific• Tmax = max temp capability, ° F; k = thermal conductivity, BTU / s / ft2 / ° F / ft; c = specific heat or thermal

capacity, BTU / lbm / ° F; ρ = density, lbm / in3; α = thermal diffusivity = k / ( ρ c ), ft2 / s

Self-insulating Composite Structure( e.g., Graphite Polyimide ) 1100 0.000109 0.27 0.057 0.00000410

Ext Insulation ( e.g., Micro-Quartz Paint ) 1200 0.0000131 0.28 0.012 0.00000226

Internal Insulation ( e.g., Min-K ) 2000 0.0000051 0.24 0.012 0.00000106

2/24/2008 ELF 151

External Insulation Has High Payoff for Short Duration Flight

External Insulation Has High Payoff for Short Duration Flight

1,000

900

800

700

600

500

400

300

200

100

0

Exam

ple T

empe

ratu

re °

F

0 2 4 6 8 10 12 14

1.0

2.0

3.0

4.0

Mach Number

Time After Launch ~ s

Example Airframe Temperature with No External Insulator – Steel Airframe Selected.

Mach

Note: Short Range Air-to-Air MissileLaunch ~ 0.9 Mach at 10k ft AltitudeAtmosphere ~ Hot Day ( 1% Risk ) Mil-HDBK-310

Example Airframe Temperature with 0.012 in Insulator –Aluminum Airframe Acceptable for Short Duration.

2/24/2008 ELF 152

Bulk Ceramics• Melt• ρ ~ 0.20 lb / in3

• Zirconium Ceramic, Hafnium Ceramic

Graphites• Burn• ρ ~ 0.08 lb / in3

• Carbon / Carbon

Tmax, MaxTemperatureCapability,

R

4,000

3,000

2,000

00 1 2 3 4

Insulation Efficiency, Minutes To Reach 300° F at Back Wall

1,000

6,000

5,000

Note: Assumed Weight Per Unit Area of Insulator / Ablator = 1 lb / ft2

Porous Ceramics• Melt• Resin Impregnated• ρ ~ 0.12 lb / in3

• Carbon-Silicon Carbide

Medium Density PhenolicComposites

• Char• ρ ~ 0.06 lb / in3

• Nylon Phenolic, Silica Phenolic, Glass Phenolic, Carbon Phenolic, Graphite Phenolic

Low DensityComposites• Char• ρ ~ 0.03 lb / in3

• Micro-Quartz Paint, Glass-Cork-Epoxy, Silicone Rubber

Plastics• Sublime• Depolymerizing• ρ ~ 0.06 lb / in3

• Teflon

Phenolic Composites Are Good Insulators for High Temperature Structure and Propulsion

Phenolic Composites Are Good Insulators for High Temperature Structure and Propulsion

2/24/2008 ELF 153

A “Thermally Thin” Surface ( e.g., Metal Airframe ) Has Uniform Internal Temperature

A “Thermally Thin” Surface ( e.g., Metal Airframe ) Has Uniform Internal Temperature

1

10

100

1000

0 1 2 3 4 5 6M, Mach Number

dT / d

t, Ini

tial S

kin T

empe

ratu

re R

ate f

or

Rock

et B

aseli

ne, D

eg F

/ sec

h = sea level h = 20K ft h = 50K ft h = 80K ft

( dT / dt )t = 0 = ( Tr - Tinitial ) h / ( c ρ z )T = Tr – ( Tr – Tinitial ) e – h t / ( c ρ z )

h = k NNU / xThermally thin ⇒ h ( z / k )surface < 0.1

Note: No external insulation; thermally thin structure ( uniform internal temperature ); “Perfect” insulation behind airframe; 1-D heat transfer; Turbulent boundary layer; Radiation neglected; dT / dt = Temperature rate, R / s; Tr = Recovery ( max ) temperature, R; h = Convection heat transfer coefficient, BTU / s / ft2 / R; c = Specific heat, BTU / lb / R; ρ = Density, lb / ft3; z = Thickness, ft; k = Conductivity, BTU / s / ft2 / R / ft; Re = Reynolds number; NNU = Nusselt number

Example for Rocket Baseline Airframe:Aluminum skin w/o external insulationc = 0.215 BTU / lb / R, ρ = 0.10 lb / in3 = 172.8 lb / ft3, z = 0.16 in = 0.0133 ft, k = 0.027 BTU / s / ft2 / R / ft

Assume Mach 2 sustain flight, 20k ft altitude ( T0 = 447 R , k = 3.31 x 10-6 BTU / s / ft2 / R / ft ), Turbulent boundary layer, x = 1.6 ft

Rex = ρ0 M a0 x / μ0 = 12.56 x 106

NNU = 0.0271 Re0.8 = 12947h = k NNU / x = 0.0268 BTU / s / ft2 / RTest: h ( z / k )surface = 0.0132 < 0.1 ⇒ thermally thinCalculate Tr = T0 [ 1 + 0.2 r M2 ] = 447 [ 1 + 0.2 ( 0.9 ) ( 2 )2 ] = 769 R

At t = 0, Assume Tinitial = 460 R, or 0° F( dT / dt )t = 0 = ( 769 - 460 ) ( 0.0268 ) / [( 0.215 ) (172.8 ) ( 0.01333 )] = 17°F / s

At a sustain time t = 10 s, T = 769 - ( 769 – 460 ) e –0.0268 ( 10 ) / [ 0.215 ( 172.8 ) ( 0.0133 )] = 589 R, or 129° F

Reference: Jerger, J.J., Systems Preliminary Design Principles of Guided Missile Design, D. Van Nostrand Company, Inc., Princeton, New Jersey, 1960

x = 1.6 ft

2/24/2008 ELF 154

A “Thermally Thick” Surface ( e.g., Radome ) Has a Large Internal Temperature Gradient

A “Thermally Thick” Surface ( e.g., Radome ) Has a Large Internal Temperature Gradient

0

0.5

1

0.1 1 10 100

[ T ( z, t ) - Tinitial ] / [ Tr – Tinitial ] = erfc { z / [ 2 ( α t )1/2 ]} – e( h z / k ) + h2 α t / k2 erfc { z / [ 2 ( α t )1/2 ] + h ( α t )1/2 / k }[ T ( 0, t ) - Tinitial ] / [ Tr – Tinitial ] = 1 - eh2 α t / k2 erfc [ h ( α t )1/2 / k ]Applicable for thermally thick surface: z / [ 2 ( α t )1/2 ] > 1

Note: T ( z,t ) ∼ ( T )initial; 1-D heat transfer; Radiation neglected; Turbulent boundary layer; Tr = Recovery temperature, R; h = Heat transfer coefficient, BTU / ft2 / s / R; k = Thermal conductivity of material, BTU / s / ft2 / R / ft; α = Diffusivity of material, ft2 / s; zmax = Thickness of material, ft; erfc = Complementary error function

Example: Rocket Baseline Radomez = 0.25 in = 0.0208 ft, k = 5.96 x 10-4 BTU / s / ft / R,α = 1.499 x 10-5 ft2 / sMach 2, 20k ft alt ( T0 = 447 R ), Turbulent boundary layer, x = 19.2 in = 1.6 ft, t = 10 s, Tr = 769 R, Tinitial = 460 R⇒ h = 0.0268 BTU / s / ft ⇒ ( h / k )( α t )1/2 = 0.491Test: z / [ 2 ( α t )1/2 ] = 0.0208 / { 2 [ 1.499x10-5 ( 10 )]1/2 } = 0.849 < 1 ⇒ not quite thermally thickInner wall ⇒ h z / k = 0.935[ T ( 0.0208, 10 ) - Tinitial ] / [ Tr – Tinitial ] = 0.0608T ( 0.0208, 10 ) = 479 R ( Note: Tinner ≈ Tinitial )Surface ⇒ h z / k = 0[ T ( 0, 10 ) - Tinitial ] / [ Tr – Tinitial ] = 0.372T ( 0, 10 ) = 575 R


( h / k )( α t )1/2

h z / k

= 10

0

h z / k

10

h z / k

= 1

h z / k

= 0.1

[ T (

z, t )

-( T

) initi

al] /

[( T

) r–( T

) initi

al] X = 1.6 ft

h z / k =

0

2/24/2008 ELF 155

Internal Insulation Temperature Can Be Predicted Assuming Constant Flux Conduction

Internal Insulation Temperature Can Be Predicted Assuming Constant Flux Conduction

0

0.5

1

0.1 1 10 100

[ T ( z, t ) – Tinitial ] / [ T ( 0, t ) – Tinitial ] = e- z2 / ( 4 α t ) – ( π / α t )1 / 2 ( z / 2 ) erfc { z / [ 2 ( α t )1/2 ]}Applicable for thermally thick surface: z / [ 2 ( α t )1/2 ] > 1

Note: 1-D conduction heat transfer, Radiation neglected, Constant heat flux input, T ( z,t ) = Inner temperature of insulation at time t, Tinitial = Initial temperature, T ( 0, t ) = Outer temperature of insulation at time t, α = Diffusivity of insulation material, ft2 / s; zmax = Thickness of insulation material, ft; erfc = Complementary error function

Example for Rocket Baseline Airframe Insulation:0.10 in Min-K Internal Insulation behind 0.16 in aluminum Skin

Assume M = 2, 20k ft alt, x = 1.6 ft, Tinitial = 460 R, t = 10 s, zMin-K = 0.10 in = 0.00833 ft, αMin-K = 0.00000106 ft2 / s, k = 5.96 x 10-4 BTU / s / ft, h = 0.0268 BTU / s / ftTest: z / [ 2 ( α t )1/2 ] = 0.00833 / {2 [ 0.00000106 ( 10 )]1/2} = 1.279 > 1 ⇒ thermally thick( α t )1/2 / z = [ 0.00000106 ( 10 ) ]1/2 / 0.00833 = 0.3907[ TMin-K ( 0.0217, 10 ) – 460 ] / [ TMin-K ( 0, 10 ) – 460 ] = 0.0359Assume ( Tinner )aluminum = ( Touter )Min-K

From prior example, ( Tinner )aluminum = 569 R at = 10 sThen, ( Touter )Min-K = 569 R at t = 10 sCompute, ( Tinner )Min-K = 460 + ( 569 – 460 ) 0.0338 = 460 + 4 = 464 R

Reference: Carslaw, H. S. and Jaeger, J. C., Conduction of Heat in Solids, Clarendon Press, 1989

X = 1.6 ft

( α t )1/2 / z

[ T (

z, t )

–T in

itial

] / [

T ( 0

, t )

–Tin

itial

] Aluminum

Min-K

0.16 in

0.10 inz

2/24/2008 ELF 156

A Sharp Nose Tip / Leading Edge Has High Aerodynamic Heating

A Sharp Nose Tip / Leading Edge Has High Aerodynamic Heating

0

0.1

0.2

0.3

0.4

0.5

0.6

0 1 2 3 4 5 6M, Mach Number

hr, S

tagn

atio

n He

at T

rans

fer C

oeff

for

Rock

et B

aseli

ne at

h =

20k f

t, BT

U / f

t2 / s

/ R

1% Bluntness 2% Bluntness5% Bluntness 10% Bluntness

hr = NNUr kr / dNoseTip

NNUr = 1.321 RedNoseTip0.5 Pr

0.4

Note: 1-D conduction heat transfer; Laminar boundary layer; Stagnation heating; Radiation neglected; hr = Convection heat transfer coefficient for stagnation recovery, BTU / s / ft2 / R; NNUr = Nusselt number for stagnation recovery; kr = Air thermal conductivity at stagnation recovery ( total ) temperature, BTU / s / ft / R; dNoseTip = Nose tip diameter, ft; RedNoseTip = Reynolds number based on nose tip diameter, Pr = Prandtl number

Example for Rocket Baseline Nose Tip:Assume M = 2, 20k ft alt, stagnation ( Tr = 805 R ) for a sharp nose tip ( e.g., 1% blunt )

dNoseTip / dRef = 0.01 ⇒ dNoseTip = 0.01 ( 8 in ) = 0.08 in = 0.00557 ft

RedNoseTip = ρ0 V0 dNoseTip / μr = 3.39 x 104

NNUr = 223hr = 0.1745 BTU / ft2 / s / ROuter surface temperature after 10 s heating in sustain flight ( M = const, Tr = const ):

[ T ( 0, t ) - Tinitial ] / [ Tr – Tinitial ] = 1 – e h2αt / k2

erfc { h ( α t )1/2 / k }[ T ( 0, 10 ) - 460 ] / [ 805 – 460 ] = 1 – e [( 0.1745 )2

( 1.499 x 10-5 ) ( 10 ) / ( 5.96 x 10-4 )2 ] erfc { ( 0.1745 ) [ 1.499 x 10-5 ( 10 )]1/2 / ( 5.96 x 10-4 )]} = 0.845

T ( 0, 10 ) = 460 + 345 ( 0.845 ) = 752 R

Reference: Allen, J. and Eggers, A. J., “A Study of the Motion and Aerodynamic Heating of Ballistic Missiles Entering the Earth’s Atmosphere at High Supersonic Speeds”, NACA Report 1381, April 1953.

2/24/2008 ELF 157

Tactical Missile Radiation Heat Loss Is Usually Small Compared to Convective Heat Input

Tactical Missile Radiation Heat Loss Is Usually Small Compared to Convective Heat Input

0.01

0.1

1

10

100

0 1 2 3 4 5 6Cruise Mach Number

Radiation Heat Flux at

Equilibrium Temperature, BTU / ft2 / s

Emissivity = 0.1 Emissivity = 1

QRad = 4.76 x 10-13 ε T4

QRad in BTU / ft2 / s, T in RExample: Ramjet BaselineAssume:•Titanium skin with emissivity ε = 0.3•Long duration ( equilibrium ) heating at Mach 4•h = 80k ft, T0 = 398 R•Turbulent boundary layer ( r = 0.9 ) ⇒ T = Tr = T0 ( 1 + 0.2 r M2 ) = 1513 RCalculate:QRad = 4.76 x 10-13 ( 0.3 ) ( 1513 )4

= 0.748 BTU / ft2 / s

2/24/2008 ELF 158

Design Concerns for Localized Aerodynamic Heating and Thermal Stress

Design Concerns for Localized Aerodynamic Heating and Thermal Stress

Body JointsHot missile shellCold frames or bulkheadsCauses premature buckling

IR Domes / RF RadomesLarge temp gradients due to low thermal conductionThermal stress at attachmentLow tensile strengthDome fails in tension

Leading EdgesHot stagnation temperature on leading edgeSmall radius prevents use of external insulationCold heat sink material as chord increases in thickness leads to leading edge warpShock wave interaction with adjacent body structure

Flare / Wedge Corner FlowShock wave – boundary layer interactionSeparated FlowHigh heating at reattachment

Note: σTS = Thermal stress from restraint in compression or tension = α E ΔTα = coefficient of thermal expansion, E = modulus of elasticity, ΔT = T2 – T1 = temperature difference.Example: Thermal Stress for Rocket Baseline Pyroceram Dome, α = 3 x 10-6, E = 13.3 x 106 psiAssume M = 2, h = 20k ft alt, t = 10 s. Based on prior figure, ΔT = TOuterWall – TInnerWall = 102 RThen σTS = 3 x 10-6 ( 13.3 x 106 ) ( 102 ) = 4,070 psi

2/24/2008 ELF 159

Examples of Aerodynamic Hot SpotsExamples of Aerodynamic Hot Spots

Nose Tip

Leading Edge

Flare

2/24/2008 ELF 160

Tactical Missile Body Structure Weight Is about 22% of the Launch Weight

Tactical Missile Body Structure Weight Is about 22% of the Launch Weight

10

100

1000

100 1000 10000WL, Launch Weight, lb

WBS

,Bod

y Stru

ctur

e Weig

ht, l

b Hellfire ( 0.22 )Sidewinder ( 0.23 )Sparrow ( 0.18 )Phoenix ( 0.19 )Harpoon ( 0.29 )SM 2 ( 0.20 ) SRAM ( 0.21 )ASALM ( 0.13 )SETE ( 0.267 )Tomahawk ( 0.24 )TALOS ( 0.28 )

WBS / WL ≈ 0.22

Example for 500 lb missile

WL = 500 lb

WBS = 0.22 ( 500 ) = 110 lb

Note: WBS includes all load carrying body structure. If motor case, engine, or warhead case carry external loads then they are included in WBS. WBS does not include tail, wing, or other surface weight.

2/24/2008 ELF 161

Body Structure Thickness Is Based on Considering Many Design Conditions

Body Structure Thickness Is Based on Considering Many Design Conditions

Structure Design Conditions That May Drive Airframe ThicknessManufacturingTransportationCarriageLaunchFly-outManeuvering

Contributors to Required Thickness for Cylindrical Body StructureMinimum Gage for Manufacturing: t = 0.7 d [( pext / E ) l / d ]0.4. t ≈ 0.06 in if pext ≈ 10 psiLocalized Buckling in Bending: t = 2.9 r σ / ELocalized Buckling in Axial Compression: t = 4.0 r σ / EThrust Force: t = T / ( 2 π σ r )Bending Moment: t = M / ( π σ r2 )Internal Pressure: t = p r / σ

High Risk ( 1 ), Moderate Risk ( 2 ), and Low Risk ( 3 ) Estimates of Required Thickness1. t = FOS x Max ( tMinGage , tBuckling,Bending , tBuckling,AxialCompression , tAxialLoad , tBending , tInternalPressure )2. t = FOS x ( t2

MinGage + t2Buckling,Bending + t2

Buckling,AxialCompression + t2AxialLoad + t2

Bending + t2InternalPressure )1/2

3. t = FOS x ( tMinGage + tBuckling,Bending + tBuckling,AxialCompression + tAxialLoad + tBending + tInternalPressure )

2/24/2008 ELF 162

Localized Buckling May Be A Concern forThin Wall Structure

Localized Buckling May Be A Concern forThin Wall Structure

0.0001

0.001

0.01

0.1

0.001 0.01 0.1t / r, thickness / radius

Nond

imen

siona

l Buc

kling

Stre

ssBendingAxial Compression

σBuckling,Bending / E ≈ 0.35 ( t / r )σBuckling,AaxialCcompression / E ≈ 0.25 ( t / r )

Note: Thin wall cylinder with local bucklingσBuckling / E = Nondimensional buckling stressσBucklingBending = Buckling stress in bendingσBucklingAxialCompression = Buckling stress in axial compressionE = Young’s modulus of elasticityt = Airframe thicknessr = Airframe radiusMin thickness for fab and handling ≈ 0.06 in

Example for Rocket Baseline in Bending:4130 steel motor case, E = 29.5 x 106 psiσyield = 170,000 psit = 0.074 in, r = 4 int / r = 0.0185σBuckling,Bending / E ≈ 0.35 ( 0.0185 ) = 0.006475σbuckling,Bending ≈ 191,000 psiσbuckling,Bending ~ σyield

rt

Note: Actual buckling stress can vary +/- 50%, depending upon typical imperfections in geometry and the loading.

2/24/2008 ELF 163

Process for Captive and Free Flight Loads Calculation

Process for Captive and Free Flight Loads Calculation

Free Flight

Maneuver PerDesign Requirements

Weight load of bulkhead

section

Air LoadObtainedBy WindTunnel

Air Load

Captive Flight

Max Aircraft ManeuverPer MIL-A-8591

Weight load of bulkhead

sectionAir Load

Note: MIL-A-8591 Procedure A assumes max air loads combine with max g forces regardless of angle of attack.

Carriage Load

Example of αmax Calculated by MIL-A-8591 Using Procedure A for F-18 Aircraft Carriage:αmax = 1.5 nz,max Wmax / ( CLα

q SRef )aircraftαmax = 1.5 ( 5 ) ( 49200 ) / [ 0.05 ( 1481 ) ( 400 )] = 12.5 deg

2/24/2008 ELF 164

Maximum Bending Moment Depends Upon Load Distribution

Maximum Bending Moment Depends Upon Load Distribution

Example for Rocket Baseline:c = 4, ejection loadl = 144 in

⇒N = 10,000 lb ( 20 g )

⇒ MB = 360,000 in-lbMax Bending Moment MB

MB = N l / c

C = 8 for uniform loading

C = 7.8 for linear loading

C = 6 for linear loading to center

C = 4 for load at center ( e.g., ejection load )

6440,000

30,00020,000

4 1 3

2 5

100

200

1,000,000

2,000,000

5,0004,0003,0002,000

1,000

500400300200

100500,000400,000300,000200,000

100,000

TotalLoad

N

Coefficient C Length l8 7.8

100,000

50,000

10,000

50,00040,00030,00020,000

10,0005,0004,0003,0002,0001,000

500400300200

100

w = load per unit length

0 l = length

w

0 l

w

0 l

l0

N = Normal Forcel / 2

10

C = 1 for load at end ( e.g., control force )N = Normal Force

l0

l

1

2/24/2008 ELF 165

Bending Moment May Drive Body Structure Weight

Bending Moment May Drive Body Structure Weight

Example for Rocket Baseline:• Body has circular cross section• 2219-T81 aluminum skin ( σult = 65,000 psi )• r = 4 in• Ejection load = 10,000 lb ( 20 g )• MB = 360,000 in ⋅ lb• FOS = 1.5• t = 360,000 ( 1.5 ) / [ π ( 4 )2 ( 65,000 )] = 0.16 in

t = MB ( FOS ) / [ π r2 σMax ]

A = 2 π r tIz = IY = π r3 t

rtt

MB

Note / Assumptions:Thin cylinderCircular cross sectionSolid skinLongitudinal strengthAxial load stress and thermal

stress assumed small compared to bending moment stress

σ = MB r / IZ = MB r / (π r3 t )= MB / (π r2 t )

2/24/2008 ELF 166

Tactical Missile Propellant Weight Is about 72% of Rocket Motor Weight

Tactical Missile Propellant Weight Is about 72% of Rocket Motor Weight

10

100

1000

10000

10 100 1000 10000

WM, Total Motor Weight, lb

WP,

Pro

pella

nt W

eight

, lb Hellfire ( 0.69 )

Sidewinder ( 0.61 )Sparrow ( 0.64 )Phoenix ( 0.83 )ASALM ( 0.86 ) SM-2 ( 0.76 )SRAM ( 0.71 )TALOS ( 0.66 )

WP / WM ≈ 0.72

Example for Rocket Baseline

WM = 209 lb

WP = 0.72 ( 209 ) = 150 lb

Note: WM includes propellant, motor case, nozzle, and insulation.

Increased propellant fraction if:High volumetric loadingComposite caseLow chamber pressureLow flight loadsShort burn time

2/24/2008 ELF 167

Motor Case Weight Is Usually Driven By Stress from Internal Pressure

Motor Case Weight Is Usually Driven By Stress from Internal Pressure

Assume motor case is axisymmetric, with a front ellipsoid dome and an aft cylinder body

With metals – the material also reacts body bendingIn composite motor designs, extra ( longitudinal ) fibers must usually be added to accommodate body bending

Motor CaseCylinderHoopStress

Motor DomeEllipsoid LongitudinalStress

p p

( σt )Longitudinal Stress= [ 2 + ( a / b )2 ] p ( a b )1/2 / ( 6 t )

If a = b ( hemi dome of radius r ), then ( σt )Longitudinal Stress = p r / ( 2 t )

σt t = - 0∫π/2p r sinθ dθ

( σt )Hoop Stress = p r / t

Case Dome Nozzle

Case Cylinder

2 a

b

2/24/2008 ELF 168

A Composite Motor Case Is Usually Lighter Weight

A Composite Motor Case Is Usually Lighter Weight

Calculate Maximum Effective Operating Pressure ( Burst Pressure )pburst = pBoost, Room Temp x eπk Δ T x ( Design Margin for Ignition Spikes, Welds, Other Design Uncertainty )Assume Rocket Motor Baseline: diameter = 8 in., length = 55 in, ellipsoid dome a / b = 2, pBoost,RoomTemp = 1769 psi, πk = ( Δp / ΔT ) / pc = 0.14% / °F

Assume Hot day T = 160° F ⇒ eπk ΔT = e0.0014 ( 160 - 70 ) = 1.134. Uncertainty factor is 1.134, 1σ

Assume a 3σ uncertainty design margin is provided by, pburst ≈ 1769 x ( 1.134 )3 = 2,582 psiAssume Ultimate Factor of Safety FOS = 1.5Rocket Baseline Steel Case ( σt )ult = 190,000 psi

tHoop = ( FOS ) x pburst x r / σt = 1.5 x 2582 x 4.0 / 190,000 = 0.082 intDome = ( FOS ) x pburst x ( a b )1/2 x [ 2 + ( a / b )2 ] / ( 6 σt ) = 1.5 x 2582 x [ 4 x 2 ]1/2 x [ 2 + ( 2 )2 ] / [ 6 x 190,000 ] = 0.058 in

Weight = WCylinder + WDome = ρ π d tHoop l + ρ ( 2 π a b ) tDome = 30.8 + 0.8 = 31.6 lb for steel case

Try Graphite Fiber at σt = 450,000 psi Ultimate, Assume 60% Fiber / 40% Epoxy CompositetHoop = 1.5 x 2582 x 4.0 / [ 450,000 ( 0.60 )] = 0.057 in radial fibers for internal pressure loadtDome = 0.041 in, for internal pressure loadWeight = 11.1 lb for composite case ( w/o insulation, attachment, aft dome, and body bending fiber )Must also add about 0.015 in of either longitudinal fibers or helical wind to counteract body bending load

2/24/2008 ELF 169

A Low Aspect Ratio Delta Wing Allows Lighter Weight Structure

A Low Aspect Ratio Delta Wing Allows Lighter Weight Structure

0

1

2

3

0 1 2 3 A, Aspect Ratio

Taper Ratio = 0 Taper ratio = 0.5 Taper Ratio = 1

WSurface σmax1/2 / [ ρ S Nmax

1/2 ] = [ A ( 1 + 2 λ )]1/2

WSurface = ρ S tmac

troot = [ FOS Nmax A ( 1 + 2 λ ) / σmax,]1/2

Assumption: Uniform loading

Note:Surface is 2 panels ( Cruciform wing has 4 panels )WSurface = Surface weight sized by bending momentρ = Densityσmax = Maximum allowable ( ultimate ) stresstmac = Thickness of mean aero chord cmac

troot = Thickness of root chord croot

Nmax = Maximum loadA = Aspect ratioλ = Taper ratioExample for Rocket Baseline Wing ( 2219-T81 Aluminum ): A = 2.82, λ = 0.175, cr = 19.4 in, σmax = σult = 65k psi

Assume M = 2, h = 20k ft, α + δ = 22 degFrom prior example, Nmax = 7525 lbCalculate troot = [ 1.5 ( 7525 ) ( 2.82 ) [ 1 + 2 ( 0.175 ) / 65000 ]1/2 = 0.813 in

troot / croot = 0.813 / 19.4 = 0.0419 = tmac / cmac

tmac = 0.0419 ( 13.3 ) = 0.557 inWwing σmax

1/2 / [ ρ S Nmax1/2 ] = [ A ( 1 + 2 λ )]1/2.= 1.95

Wwing = 20.6 lb for 1 wing ( 2 panels )

WSu

rface

σ max

1/2/ (

ρS

N max

1/2),

Non-

dim

ensio

nal W

eight

2/24/2008 ELF 170

Seeker Dome

Material

Density ( g / cm3 )

Dielectric Constant

MWIR / LWIR

Bandpass

Transverse Strength ( 103 psi )

Thermal Expansion ( 10-6 / ο F )

Erosion, Knoop ( kg

/ mm2 )

Max Short-Duration

Temp ( ο F )

RF-IR Seeker Zinc Sulfide ( ZnS )

4.05 8.4 18 4 350 700

Zinc Selenide ( ZnSe )

5.16 9.0 8 4 150 600

Sapphire / Spinel

3.68 8.5 28 3 1650 1800

Quartz / Fused Silica ( SiO2 )

2.20 3.7 8 0.3 600 2000

Silicon Nitride ( Si3N4 )

3.18 6.1 90 2 2200 2700

Diamond ( C ) 3.52 5.6 400 1 8800 3500 RF Seeker Pyroceram 2.55 5.8 25 3 700 2200 Polyimide 1.54 3.2 17 40 70 400 IR Seeker Mag. Fluoride ( MgF2 )

3.18 5.5 7 6 420 1000

Alon ( Al23O27N5 )

3.67 9.3 44 3 1900 1800

Germanium ( Ge )

5.33 16.2 15 4 780 200

Dome Material Is Driven by the Type of Seeker and Flight Environment

Dome Material Is Driven by the Type of Seeker and Flight Environment

Superior Above Average Average Below Average - Poor

---

---

--

2/24/2008 ELF 171

Radome Weight May Be Driven by Optimum Thickness Required for Efficient Transmission

Radome Weight May Be Driven by Optimum Thickness Required for Efficient Transmission

0.1

1

1 10

Incidence Angle = 0 deg Incidence Angle = 40 degIncidence Angle = 80 deg

t opt/

( N λ

0),

Non-

dim

ensio

nal O

ptim

um T

hick

ness

ε, Dielectric Constant

WOptTrans = ρ Swet tOptTrans

tOptTrans = 0.5 n λ0 / ( ε - sin2 θi )1/2

Note:

WOptTrans = Weight at Optimum Transmission

ρ = Density

Swet = Surface wetted area

tOptTrans = Optimum thickness for 100% transmission

n = Integer ( 1, 2, … )

λ0 = Wavelength in air

ε = Dielectric constant

θi = Radar signal incidence angle = 90 deg - δ - θ

θ = Surface local angle

δ = Seeker look angle

Example for Rocket Baseline Pyroceram Radome:

ε = 5.8, ρ = 0.092 lb / in3, λ0 = 1.1 in, n = 1, tangent ogive, l = 19.2 in, d = 8 in, Swet = 326 in2

δ = 0 deg ⇒ ( θI )avg ≈ 90 – 0 - 11.8 = 78.2 deg

tOptYtans = 0.5 ( 1 ) ( 1.1 ) / ( 5.8 – 0.96 )1/2 = 0.25 in

WOptTrans = 0.092 ( 326 ) ( 0.25 ) = 7.5 lb

90 degδ

θi

l

dθ

2/24/2008 ELF 172

Missile Electrical Power Supply AlternativesMissile Electrical Power Supply Alternatives

Power SupplyMeasure of Merit

Voltage Stability

0.31.51.4WP, Weight / Power ( kg / kW )

0.01250.00120.0007WE, Weight / Energy

( kg / kW-s )

CostStorage Life

Thermal BatteryLithium BatteryGenerator


W = WE E + WP P

Example for Thermal battery: If E = 900 kW–s, P = 3 kW ⇒ W = WEE + WPP = 0.0125 ( 900 ) + 0.3 ( 3 ) = 12.2 kgNote: Generator provides highest energy with light weight for long time of flight ( e.g., cruise missile ).Lithium battery provides nearly constant voltage suitable for electronics. Relatively high energy with light weight.Thermal battery provides highest power with light weight ( may be required for actuators ).

2/24/2008 ELF 173


Electromechanical Actuators Are Light Weight and Reliable

Electromechanical Actuators Are Light Weight and Reliable

HydraulicCold Gas PneumaticEMMeasure of Merit

ReliabilityCost

Up to 60Up to 20Up to 40Bandwidth ( Hz )

Up to 1000Up to 600 Up to 800Rate ( deg / s )

0.00340.00500.0025WT, Weight / Stall Torque ( lb / in-lb )

Note:•Actuation system weight based on four actuators.•Cold gas pneumatic actuation weight includes actuators, gas bottle, valves, regulator, and supply lines.•Hydraulic actuation weight includes actuators, gas generator or gas bottle, hydraulic reservoir, valves, and supply lines.•Stall torque ≈ 1.5 maximum hinge moment of single panel.

W = WT TS

Example weight for rocket baseline hydraulic actuation at Mach 2, 20k ft alt, α = 9 deg, with max control deflection of wing ( δ= 13 deg ) ⇒ Hinge moment of one panel = 11,500 in-lb. TS = 1.5 ( 11500 ) = 17,250 in-lb ⇒ W = WTTS = 0.0034 ( 17250 ) = 59 lb

Schematic of Cold Gas Pneumatic Actuation

2/24/2008 ELF 174

Examples of Electromechanical Actuator Packaging

Examples of Electromechanical Actuator Packaging

Canard ( Stinger ) ……………

Tail ( AMRAAM ) …………………………………………………………………

Jet Vane / Tail ( Javelin ) ……

Movable Nozzle ( THAAD ) ……………………………………………………………

2/24/2008 ELF 175

Summary of WeightSummary of WeightConceptual Design Weight Prediction Methods and Weight Considerations

Missile system weight, cg, moment of inertiaFactors of safetyAerodynamic heatingStructureDomePropulsionInsulationPower supplyActuator

Manufacturing Processes for Low Parts Count, Low CostPrecision castingsVacuum assisted RTMPultrusion / ExtrusionFilament winding

2/24/2008 ELF 176

Summary of Weight ( cont )Summary of Weight ( cont )Design Considerations

Airframe materialsInsulation materialsSeeker dome materialsThermal stressAerodynamic heating

TechnologiesMEMSCompositesTitanium alloysHigh density insulationHigh energy and power density power supplyHigh torque density actuators


2/24/2008 ELF 177

Weight ProblemsWeight Problems1. Propulsion system and structure weight are driven by f_____ o_ s_____

requirements.2. For a ballistic range greater than about 200 nautical miles, a t__ s____ missile

is lighter weight.3. Tactical missile weight is proportional to v_____.4. Subsystem d______ for tactical missiles is about 0.05 lb / in3

5. Modeling weight, balance, and moment-of-inertia is based on a build-up of s_________.

6. Missile structure factor of safety for free flight is usually about 1.25 for ultimate loads and about 1.10 for y____ loads.

7. Manufacturing processes that can allow low parts count include vacuum assisted resin transfer molding of composites and c______ of metals.

8. Low cost airframe materials are usually based on aluminum and steel while light weight airframe materials are usually based c________ materials.

9. Graphite fiber has high strength and high m______ o_ e_________.

2/24/2008 ELF 178

Weight Problems ( cont )Weight Problems ( cont )10. The recovery factors of stagnation, turbulent boundary layer, and laminar

boundary layer are 1.0, 0.9, and ___ respectively.11. The most popular types of insulation for temperatures greater than 4,000 R

are charring insulators based on p_______ composites.12. Tactical missiles experience transient heating, and with increasing time

the temperature approaches the r_______ temperature.13. The inner wall temperature is nearly the same as the surface temperature

for a t________ t___ structure.14. A thermally thick surface is a good i________.15. A low conductivity structure is susceptible to thermal s_____.16. The minimum gauge thickness is often set by the m____________ process.17. A very thin wall structure is susceptible to localized b_______.18. Ejection loads and flight control loads often result in large b______

moment.19. An approach to increase the tactical missile propellant / motor weight

fraction over the typical value of 72% would be c________ motor case.

2/24/2008 ELF 179

Weight Problems ( cont )Weight Problems ( cont )

20. The required rocket motor case thickness is often driven by the combustion chamber p_______.

21. A low aspect ratio delta wing has reduced w_____.22. For low speed missiles, a popular infrared dome material is z___ s______.23. A thermal battery provides high p____.24. The most popular type of actuator for tactical missiles is an

e________________ actuator.

2/24/2008 ELF 180


2/24/2008 ELF 181



Yes

Establish Baseline

MeetPerformance?


No

Yes


Alt Mission

Alt Baseline


Aerodynamics

Propulsion

Weight

Trajectory

2/24/2008 ELF 182

Flight Envelope Should Have Large Max Range, Small Min Range, and Large Off Boresight

Off Boresight Flyout Envelope / Range•Max•Min

Forward Flyout Envelope / Range•Max•Min

Examples of Max / Min Range Limitations:

Fire Control System Range and Off Boresight

Seeker Range, Gimbal Angle, and Tracking Rate

Maneuver Capability

Time of Flight

Closing Velocity

2/24/2008 ELF 183

Conceptual Design Modeling Versus Preliminary Design Modeling

Conceptual Design Modeling Versus Preliminary Design Modeling

Conceptual Design Modeling

1 DOF [ Axial force ( CDO ), thrust, weight ]

2 DOF [ Normal force ( CN ), axial force, thrust, weight ]

3 DOF point mass [ 3 aero forces ( normal, axial, side ), thrust, weight ]

3 DOF pitching [ 2 aero forces ( normal, axial ), 1 aero moment ( pitching ), thrust, weight ]

4 DOF [ 2 aero forces ( normal, axial ), 2 aero moments ( pitching, rolling ), thrust, weight ]

Preliminary Design Modeling

6 DOF [ 3 aero forces ( normal, axial, side ), 3 aero moments ( pitching, rolling, yawing ), thrust, weight ]

CDO

CN

CN

CN Cm

CA

CA

CA

CA

CA

Cl

ClCN Cm

CN Cm

CnCY

CY

2/24/2008 ELF 184

1-DOF Coast Equation May Have Good Accuracy Near Zero Angle of Attack

1-DOF Coast Equation May Have Good Accuracy Near Zero Angle of Attack

( V )2-DOF / ( V )1-DOF, Predicted Deceleration Comparison for Rocket Baseline

•

2.0

1.5

1.0

0.5

00 2 4 6 8 10

αTrim, Trim Angle of Attack, DegNote:

– ( V )2-DOF = Two-degrees-of-freedom deceleration– ( V )1-DOF = One-degree-of-freedom deceleration– Rocket baseline during coast– Mach 2, h = 20,000 ft– αTrim ≈ 0.3 deg for 1-g flyout

.

.

•

2/24/2008 ELF 185

3-DOF Simplified Equations of Motion Show Drivers for Configuration Sizing

3-DOF Simplified Equations of Motion Show Drivers for Configuration Sizing

Configuration Sizing ImplicationΙy θ

.. ≈ Ιy α.. ≈ q SRef d Cmα

α + q SRef d Cmδδ High Control Effectiveness ⇒ Cmδ

> Cmα

, Iy small ( W small ), q large( W / gc ) V γ. ≈ q SRef CNα

α + q SRef CNδδ - W cos γ Large / Fast Heading Change ⇒ CN

large, W small, q large

( W / gc ) V.

≈ T - CA SRef q - CNαα2 SRef q - W sin γ High Speed / Long Range ⇒ Total

Impulse large, CA small, q small

+ Normal Force

α << 1 rad

γθ

δW

+ Moment V

+ Thrust

+ Axial Force

Note: Based on aerodynamic control

2/24/2008 ELF 186

1.00E+05

1.00E+06

1.00E+07

1.00E+08

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

WP / WBC, Propellant or Fuel Weight / Weight at Begin of Cruise

R, C

ruise

Ran

ge, ft

( V ISP )( L / D ) = 2,000,000 ft ( V ISP )( L / D ) = 10,000,000 ft( V ISP )( L / D ) = 25,000,000 ft

For Long Range Cruise, Maximize V Isp, L / D, and Weight Fraction of Fuel / Propellant

For Long Range Cruise, Maximize V Isp, L / D, and Weight Fraction of Fuel / Propellant

Example: Ramjet Baseline at Mach 3 / 60k ft altR = 2901 ( 1040 ) ( 3.15 ) ln [ 1739 / ( 1739 - 476 )]= ( 9,503,676 ) ln [ 1 / ( 1 - 0.2737 )] = 3,039,469 ft = 500 nm

R = ( V Isp ) ( L / D ) ln [ WBC / ( WBC - WP )] , Breguet Range Equation

Note: R = cruise range, V = cruise velocity, ISP = specific impulse, L = lift, D = drag, WBC = weight at begin of cruise, WP = weight of propellant or fuel

Typical Rocket with Axisymmetric AirframeTypical Ramjet with Axisymmetric AirframeTypical Subsonic Turbojet with Wing

2/24/2008 ELF 187

Efficient Steady Flight Is Enhanced by High L / D and Light Weight

Efficient Steady Flight Is Enhanced by High L / D and Light Weight

Steady Level Flight Steady Climb Steady Descent ( Glide )

T = DL = W

L

D T

W

γC

SIN γD = ( D – T ) / W = VD / V∞VD = ( D – T ) V∞/ WRD = Δh / tan γD = Δh ( L / D )

T – DL

DT

W

V∞γC VC

D – TL

DT

WγDVD

γD

• Small Angle of Attack• Equilibrium Flight• VC = Velocity of Climb• VD = Velocity of Descent• γC = Flight Path Angle During Climb• γD = Flight Path Angle During Descent• V∞ = Total Velocity• Δh = Incremental Altitude• RC = Horizontal Range in Steady Climb• RD = Horizontal Range in Steady Dive ( Glide )

Note:

Reference: Chin, S.S., “Missile Configuration Design,”McGraw Hill Book Company, New York, 1961

V∞T = W / ( L / D ) SIN γc = ( T – D ) / W = Vc / V∞

Vc = ( T – D ) V∞ / WRC = Δh / tan γC = Δh ( L / D )

2/24/2008 ELF 188

Flight Trajectory Lofting / Shaping Provides Extended Range

Flight Trajectory Lofting / Shaping Provides Extended Range

Altitude

RangeRMAX

Apogee or Cruise

GlideClimb

Rapid Pitch Up

Line-Of-Sight Trajectory

RMAX

Lofted Trajectory Design Guidelines for Horizontal Launch:– High thrust-to-weight ≈ 10 for safe separation– Rapid pitch up minimizes time / propellant to reach efficient altitude– Climb at α ≈ 0 deg with thrust-to-weight T / W ≈ 2 and q ≈ 700 psf to minimize drag /

propellant– Apogee at q ≈ 700 psf, followed by either ( L / D )MAX cruise or ( L / D )MAX glide

2/24/2008 ELF 189

Small Turn Radius Using Aero Control Requires High Angle of Attack and Low Altitude Flight

Small Turn Radius Using Aero Control Requires High Angle of Attack and Low Altitude Flight

1000

10000

100000

1000000

0 5 10 15 20Delta Alpha, Deg

RT, E

xam

ple I

nsta

ntan

eous

Tur

n Ra

dius

, ft

h = sea level h = 20k ft h = 40k fth = 60k ft h = 80k ft

RT = V / γ. ≈ 2 W / ( gc CN SRef ρ ) Assumption: Horizontal Turn

Note for Example Figure:W = Weight = 2,000 lba / b = 1 ( circular cross section ), No wingsCN = sin 2 α cos ( α / 2 ) + 2 ( l / d ) sin2 αl / d = Length / Diameter = 10SRef = 2 ft2

CDO = 0.2( L / D )Max = 2.5q( L / D )Max

≈ 700 psfα( L / D )Max

= 15 degT( L / D )Max

= 740 lb

Example:Δ α = 10 degCN = 0.94h = 40k ft ( ρ = 0.000585 slug / ft3 )RT = 2 ( 2,000 ) / [( 32.2 ) ( 0.94 ) ( 2 ) ( 0.000585 )] = 112,000 ft

Note: Require ( RT )Missile ≤ ( RT )Target, for small miss distance

2/24/2008 ELF 190

High Turn Rate Using Aero Control Requires High Angle of Attack and High Velocity

High Turn Rate Using Aero Control Requires High Angle of Attack and High Velocity

0

5

10

15

20

0 1000 2000 3000Velocity, ft / s

Exam

ple G

amm

a Dot

, Tur

n Ra

te, d

eg / s

Alpha = 15 deg Alpha = 30 degAlpha = 90 deg

γ. = gc CN ρ V SRef / ( 2 W ), rad / sAssumption: Horizontal Turn

Example for Lifting Body at Altitude h = 20,000 ft:Assume:• W = Weight = 2,000 lb• a / b = 1 ( circular cross section )• No wings• Negligible tail lift• Neutral static stabilityCN = sin 2 α cos ( α / 2 ) + 2 ( l / d ) sin2 α• SRef = 2 ft2

• l / d = Length / Diameter = 10• α = 15 deg• V = 2000 ft / sThen:• N = Normal Force = CN q SRefCN = sin [ 2 ( 15 )] cos ( 15 / 2 ) + 2 ( 10 ) sin2 ( 15 ) =

0.50 + 1.34 = 1.835q = Dynamic Pressure = 0.5 ρ V2 = 0.5 ( 0.001267 ) (

2000 )2 = 2534 psfN = 1.835 ( 2534 ) ( 2 ) = 9,300 lbN / W = 9300 / 2000 = 4.65 gγ. = 32.2 ( 1.835 ) ( 0..001267 ) ( 2000 ) ( 2 ) / [ 2 ( 2000 )]

= 0.0749 rad / s = 4.29 deg / s

n = 100 g

2/24/2008 ELF 191

For Long Range Coast, Maximize Initial Velocity and Altitude and Minimize Drag Coefficient

For Long Range Coast, Maximize Initial Velocity and Altitude and Minimize Drag Coefficient

0

0.2

0.4

0.6

0.8

1

0 0.5 1 1.5 2

Example for Rocket Baseline:•W = WBO = 367 lb, SRef = 0.349 ft2, Vi = 2,151 ft / s, γ = 0 deg, ( CD0

)AVG = 0.9, h = 20,000 ft ( ρ = 0.00127 slug / ft3 ), t = 10 s

•[( gc ρ SRef ( CD0 )AVG Vi ) / ( 2 W )] t = {[ 32.2 ( 0.00127 ) ( 0.349 ) ( 0.9 ) ( 2151 )] / [ 2 ( 367 ) ]} 10 = 0.376

•V / Vi = 0.727 ⇒ V = 0.727 x 2151 = 1564 ft / s, {[( gc ρ SRef ( CD 0 )AVG )] / ( 2 W )} R = 0.319 ⇒ Rcoast = 18,300 ft or 3.0 nm

[( gc ρ SRef CD0 Vi ) / ( 2W )] t, Non-dimensional Coast Time

V / Vi = { 1 – [( gc sin γ ) / Vi ] t } / { 1 + {[ gc ρAVG SRef ( CD0 )AVG Vi ] / ( 2 W )} t }

{[ gc ρAVG SRef ( CD0 )AVG ] / ( 2 W )} R = ln { 1 – [ gc

2 ρAVG SRef ( CD0 )AVG / ( 2 W )] [ sin γ ] t2

+ {[ gc ρAVG SRef ( CD0 )AVG Vi ] / ( 2 W )} t }

Note: Based on 1 DOF coast

dV / dt = - gc CD0 SRef q / W – gc sin γ

Assumptions:

• γ = constant

• α ≈ 0 deg

• D > W sin γ

V = velocity during coast

Vi = initial velocity ( begin coast )

R = coast range

Vx = V cos γ, Vy = V sin γ

Rx = R cos γ, Ry = R sin γ

V / Vi @ γ = 0 deg

{[ gc ρAVG SRef (CD0 )AVG ] / ( 2 W )} R

@ γ = 0 deg

2/24/2008 ELF 192

For Ballistic Range, Maximize Initial Velocity, Optimize Launch Angle, and Minimize Drag

For Ballistic Range, Maximize Initial Velocity, Optimize Launch Angle, and Minimize Drag

0

0.2

0.4

0.6

0.8

1

1.2

0 0.5 1 1.5 2

Example for Rocket Baseline:

•W = 367 lb, SRef = 0.349 ft2, Vi = VBO = 2,151 ft / s, γi = 0 deg, ( CD0)AVG = 0.9, hi = 20,000 ft, ρAVG = 0.00182 slug / ft3, t = 35 s

•[ gc ρ SRef ( CD0 )AVG Vi / ( 2 W )] t = { 32.2 ( 0.00182 ) ( 0.349 ) ( 0.9 ) ( 2151 ) / [ 2 ( 367 ) ]} 35 = 1.821

•Vx / Vi = 0.354 ⇒ Vx = 762 ft / s, ( Vy + 32.2 t ) / Vi = 0.354 ⇒ Vy = - 1127 ft / s, {[ gc ρ SRef ( CD 0 )] / ( 2 W cos γi )} Rx = 1.037 ⇒

Rx = 42,900 ft or 7.06 nm, {[ gc ρAVG SRef ( CD 0 )AVG ] / ( 2 W sin γi )} ( h – hi + 16.1 t2 ) = 1.037 ⇒ h = 0 ft

{[ gc ρAVG SRef ( CD0 )AVG Vi ] / ( 2 W )} t, Non-dimensional Time

Vx / Vi = cos γi / { 1 + {[ gc ρAVG SRef ( CD0 )AVG Vi ] / ( 2 W )} t }

( Vy + gc t ) / Vi = sin γi / { 1 + {[ gc ρAVG SRef ( CD0 )AVG Vi ] / ( 2 W )} t }

Assumptions: Thrust = 0, α = 0 deg, D > W sin γ, flat earth

Nomenclature: V = velocity during ballistic flight, Vi = initial velocity, Rx = horizontal range, h = altitude, hi = initial altitude, Vx = horizontal velocity, Vy = vertical velocity

{[ gc ρAVG SRef (CD0 )AVG ] / ( 2 W cos γi )} Rx

= ln { 1 + [ gc ( ρ )AVG SRef ( CD0 )AVG Vi ] / ( 2 W )} t }

{[ gc ρAVG SRef (CD0 )AVG ] / ( 2 W sin γi )} ( h – hi + gc t2 / 2 )

= ln { 1 + {[ gc ρAVG SRef ( CD0 )AVG Vi ] / ( 2 W ) t }

2/24/2008 ELF 193

High Propellant Weight, High Thrust, and Low Drag Provide High Burnout Velocity

High Propellant Weight, High Thrust, and Low Drag Provide High Burnout Velocity

00.10.20.30.40.50.60.7

0 0.1 0.2 0.3 0.4 0.5Wp / Wi, Propellant Fraction

Delta

V /

( g IS

P ),

Nond

imen

sion

al

Incr

emen

tal V

eloc

ity

DAVG / T = 0 DAVG / T = 0.5 DAVG / T = 1.0

ΔV / ( gc ISP ) = - [ 1 – ( DAVG / T ) – ( WAVG sin γ / T )] ln ( 1 - Wp / Wi )Example for Rocket Baseline:Assume γ = 0 degAssume Mi = 0.8, h = 20k ftWi = WL = 500 lbFor boost, WP = 84.8 lbWP / WL = 0.1696ISP = 250 sTB = 5750 lbAssume D = DAVG = 635 lbDAVG / T = 0.110ΔV / [( 32.2 ) ( 250 )] = - ( 1 - 0.110 ) ln ( 1 - 0.1696 ) = 0.1654

ΔV = ( 0.1654 ) ( 32.2 ) ( 250 ) = 1331 ft / s

Note: 1 DOF Equation of Motion with α ≈ 0 deg, γ = constant, Wi = initial weight, WAVG = average weight, WP = propellant weight, ISP = specific impulse, T = thrust, Mi = initial Mach number, h = altitude, DAVG = average drag, ΔV = incremental velocity, gc = gravitation constant, Vx = V cos γ, Vy = V sin γ, Rx = R cos γ, Ry = R sin γNote: R = ( Vi + ΔV / 2 ) tB, where R = boost range, Vi = initial velocity, tB = boost time

2/24/2008 ELF 194

High Missile Velocity and Lead Are Required to Intercept High Speed Crossing Targets

High Missile Velocity and Lead Are Required to Intercept High Speed Crossing Targets

VM / VT

4

3

2

00 10 20 30 40 50

L, Lead Angle, Deg

1

A = 90°

A = 45°

Note:Proportional GuidanceVM = Missile VelocityVT = Target VelocityA = Target AspectL = Missile Lead Angle

≈Seeker Gimbal

VM VTL A

VM sin L = VT sin A, Proportional Guidance Trajectory

Example:L = 30 degA = 45 degVM / VT = sin ( 45° ) / sin ( 30° ) = 1.42

2/24/2008 ELF 195



Yes

Establish Baseline

MeetPerformance?


No

Yes


Alt Mission

Alt Baseline


Aerodynamics

Propulsion

Weight

Trajectory

2/24/2008 ELF 196

Summary of Flight PerformanceSummary of Flight PerformanceFlight Performance Activity in Missile Design

Compute range, velocity, time-to-target, off boresightCompare with requirements

Discussed in This ChapterEquations of motionFlight performance driversPropulsion alternatives range comparisonSteady level flight required thrustSteady climb and steady dive range predictionCruise predictionBoost predictionCoast predictionBallistic flight predictionTurn radius and turn rate predictionTarget lead for proportional homing guidance

2/24/2008 ELF 197

Summary of Flight Performance ( cont )Summary of Flight Performance ( cont )

Flight Performance Strongly Impacted byAerodynamicsPropulsionWeight


2/24/2008 ELF 198

Flight Performance ProblemsFlight Performance Problems1. Flight trajectory calculation requires input from aero, propulsion, and w_____.2. Missile flight envelope can be characterized by the maximum effective range,

minimum effective range, and o__ b________.3. Limitations to the missile effective range include the fire control system,

seeker, time of flight, closing velocity, and m_______ capability.4. 1 DOF simulation requires modeling only the thrust, weight, and a____ f____.5. A 3 DOF simulation that models 3 aero forces is called p____ m___ simulation.6. A simulation that includes 3 aero forces ( normal, axial, side ), 3 aero moments

( pitch, roll, yaw ), thrust, and weight is called a _ DOF simulation.7. The pitch angular acceleration θ

..is approximately equal to the second time

derivative of the a____ o_ a_____.8. Cruise range is a function of velocity, specific impulse, L / D, and f___ fraction.9. If thrust is equal to drag and lift is equal to weight, the missile is in s_____

l____ flight.10. Turn rate is a function of normal force, weight, and v_______.

2/24/2008 ELF 199

Flight Performance Problems ( cont )Flight Performance Problems ( cont )11. Coast range is a function of initial velocity, weight, drag, and the t___ of flight.12. Incremental velocity due to boost is a function of ISP, drag, and p_________

weight fraction.13. To intercept a high speed crossing target requires a high speed missile with a

high g_____ angle seeker.14. An analytical model of a rocket in co-altitude, non-maneuvering flight can be

developed by patching together the flight phases of boost and c____.15. An analytical model of a rocket in a short range, off-boresight intercept can be

developed by patching the flight phases of boost and t___.16. An analytical model of a guided bomb in non-maneuvering flight can be

developed from the flight phase of a steady d___.17. An analytical model of an unguided weapon can be developed from the

b________ flight phase. 18. An analytical model of a ramjet in co-altitude, non-maneuvering flight can be

developed by patching the flight phases of boost and c_____.

2/24/2008 ELF 200


2/24/2008 ELF 201



Yes

Establish Baseline

MeetPerformance?

No

No

Yes


Alt Mission

Alt Baseline


Aerodynamics

Propulsion

Weight

Trajectory

Measures of Merit and Constraints

2/24/2008 ELF 202

Measures of Merit and Launch Platform Integration Should Be Harmonized

Measures of Merit and Launch Platform Integration Should Be Harmonized

Robustness

Lethality

Miss Distance

Carriage and Launch

Observables

Other Survivability

Considerations

Reliability

Cost

Launch Platform Integration / Firepower

Balanced Design

2/24/2008 ELF 203

Tactical Missiles Must Be RobustTactical Missiles Must Be RobustRobustnessTactical Missiles Must Have Robust Capability to

HandleAdverse WeatherClutterLocal ClimateFlight Environment VariationUncertaintyCountermeasuresEMI / EMP

This Section Provides Examples of Requirements for Robustness

Robustness

Lethality

Miss Distance

Carriage and Launch

Observables

Other Survivability

Considerations

Reliability

Cost


2/24/2008 ELF 204

Adverse Weather and Cloud Cover Are PervasiveAdverse Weather and Cloud Cover Are Pervasive

0.0

0.2

0.4

0.6

0.8

1.0

85°N 65°N 45°N 25°N 5°N 0° 5°S 25°S 45°S 65°S 85°S

Cloud CoverOver Ocean

CloudCoverOver Land

Annual AverageFraction of

Cloud Cover

Note: Annual Average Cloud CoverGlobal Average = 61%Global Average Over Land = 52%Global Average Over Ocean = 65%

Latitude Zone

North Atlantic

Deserts ( Sahara,Gobi, Mojave )

DescendingAir

Rising Air Rising Air

Argentina, SouthernAfrica and Australia

DescendingAir

South PoleRegion

Reference: Schneider, Stephen H. Encyclopedia of Climate and Weather. Oxford University Press, 1996.

NOAA satellite image of earth cloud cover

North PoleRegion

2/24/2008 ELF 205

Radar Seekers Are Robust in Adverse WeatherRadar Seekers Are Robust in Adverse Weather

3 cm 3 mm 0.3 mm 30 µm 3.0 µm

Increasing WavelengthIncreasing Frequency

Source: Klein, L.A., Millimeter-Wave and Infrared Multisensor Design and Signal Processing, Artech House, Boston, 1997

0.3 µm

Note:EO attenuation through cloud at 0.1 g / m3 and 100 m visibilityEO attenuation through rain at 4 mm / hHumidity at 7.5 g / m3

Millimeter wave and microwave attenuation through cloud at 0.1 gm / m3 or rain at 4 mm / h

1000

100

10

1

0.1

0.01

ATTE

NU

ATIO

N (d

B / k

m)

100 1 THz 10 100 1000INFRAREDSUBMILLIMETER

10 GHz MILLIMETER VISIBLE

H2O

O2, H2O

H2O

H2O

O2

O2

CO2

CO2

H2O

H2O, CO2

20° C1 ATM

EO sensors are ineffective through cloud coverRadar sensors have good to superior performance through cloud cover and rain

RADARX Ku K Ka Q V W Very Long Long Mid Short

H2O

O3

2/24/2008 ELF 206

Radar Seekers Are Desirable for Robust Operation within the Troposphere Cloud Cover

Radar Seekers Are Desirable for Robust Operation within the Troposphere Cloud Cover

40

30

20

10

0

h,Altitude,

103 ft

Note:•IR seeker may be able to operate “Under the Weather” at elevations less than 2,000 ft using GPS / INS midcourse guidance•IR attenuation through cloud cover greater than 100 dB per km. Cloud droplet size ( 0.1 to 50 μm ) causes resonance.•mmW has ~ 2 dB / km attenuation through rain. Typical rain drop size ( ∼ 4 mm ) is comparable to mmW wavelength.

Fog

Cirrus ( 16 – 32k ft )Cumulonimbus ( 2 – 36k ft )

Altocumulus ( 9 – 19k ft )

Cumulus ( 2 – 9k ft )Stratus ( 1 – 7k ft )

Altostratus ( 8 – 18k ft )

2/24/2008 ELF 207

Note: Superior Good Below Average Poor

Sensor Adverse Weather Impact

ATR / ATA in Clutter

Range Moving Target

Volume Search Time

Hypersonic Dome

Compat.

Diameter Required

Weight and Cost

Maturity

• SAR

• Active Imaging mmW

• Passive Imaging mmW

• Active Imaging IR (LADAR)

• Active Non-image IR (LADAR)

• Active Non-image mmW

• Passive Imaging IR

• Acoustic

• GPS / INS / Data Link

-

-

-

-

-

-

---

--

-

-

Precision Strike Missile Target Sensors Are Complemented by GPS / INS / Data Link Sensors

--

- -

-

2/24/2008 ELF 208

Imaging Sensors Enhance Target Acquisition / Discrimination

Imaging Sensors Enhance Target Acquisition / Discrimination

Imaging LADAR Imaging Infrared SAR

Passive Imaging mmW Video of Imaging Infrared Video of SAR Physics

2/24/2008 ELF 209

Example of Mid Wave – Long Wave IR Seeker Comparison

Example of Mid Wave – Long Wave IR Seeker Comparison

Assume Exo-atmospheric Intercept withTarget diameter DT = 2 ft ( AT = 2919 cm2 ), temperature TT = 300 K, emissivity ε = 0.5Diameter of seeker aperture do = 5 in ( Ao = 0.01267 m2 )Diameter of pixel detector dp = 40 μmSpot resolution if diffraction limited = dspot = dp = 40 μmTemperature of pixel detector Td = 77 KFocal plane array size 256x256 FPA ( Ad = 1.049 cm2 )Pixel detector bandwidth Δfp = 50 Hz ( tinteg = 0.00318 s )Required signal-to-nose ratio for detection ( S / N )D = 5

First Calculate MWIR Seeker Detection RangeRD = { ( IT )Δλ ηa Ao { D* / [( Δfp )1/2 ( Ad )1/2 ]} ( S / N )D

-1 }1/2, m

Radiant intensity of target within seeker bandwidth ( IT )Δλ = ε Lλ ( λ2 - λ1 ) AT, W sr-1

Spectral radiance of target Lλ = 3.74 x 104 / { λ5 { e[ 1.44 x 104 / ( λ TT )] – 1 }}, W cm-2 sr-2 μm-1

Assume λ = 4 μm, λ2 = 5 μm, λ1 = 3 μm, then Lλ = 0.000224 W cm-2 sr-2 μm-1, ( IT )Δλ = 0.643 W sr-1

Assume Hg0.67Cd0.33Te detector at λ = 4 μm and 77 K ⇒ D* = 8 x 1011 cm Hz1/2 W-1

RD = { ( 0.643 ) ( 1 ) ( 0.01267 ) {( 8 x 1011 ) / [( 50 )1/2 ( 1.049 )1/2 ]} ( 5 )-1 }1/2 = 13,480 m

2/24/2008 ELF 210

Example of Mid Wave – Long Wave IR Seeker Comparison ( cont )

Example of Mid Wave – Long Wave IR Seeker Comparison ( cont )

Next, Calculate LWIR Seeker Detection RangeRD = { ( IT )Δλ ηa Ao { D* / [( Δfp )1/2 ( Ad )1/2 ]} ( S / N )D

-1 }1/2, m( IT )Δλ = ε Lλ ( λ2 - λ1 ) AT, W sr-1

Lλ = 3.74 x 104 / { λ5 { e[ 1.44 x 104 / ( λ TT )] – 1 }}, W cm-2 sr-2 μm-1

Assume λ = 10 μm, λ2 = 13 μm, λ1 = 7 μm, thenLλ = 0.00310 W cm-2 sr-2 μm-1, ( IT )Δλ = 26.7 W sr-1

Assume Hg0.80Cd0.20Te detector at λ = 10 μm and 77 K ⇒ D* = 5 x 1010 cm1/2 Hz1/2 W-1

RD = { ( 26.7 ) ( 1 ) ( 0.01267 ) {( 5 x 1010 ) / [( 50 )1/2 ( 1.049 )1/2 ]} ( 5 )-1 }1/2 = 21,600 mMWIR Seeker Versus LWIR Seeker Selection Depends Upon Target Temperature

0

5

10

15

0 500 1000 1500 2000

TT, Target Temperature, K

Wav

eleng

th fo

r Max

Spe

ctral

Radi

ance

, Micr

ons Subsonic Airframe

Mach 4 AirframeJet EngineRocket PlumeFlare

( λ )( Lλ )max = 2898 / TT, Wein’s Displacement Law, TT in K

MWIR

LWIR

Example: TT = 300 K

( λ )( Lλ )max = 2898 / TT

= 2898 / 300 = 10.0 μm

2/24/2008 ELF 211

GPS / INS Provides Robust Seeker Lock-on in Adverse Weather and Clutter

GPS / INS Provides Robust Seeker Lock-on in Adverse Weather and Clutter

• 48

0 Pixe

ls

640 Pixels ( 300 m )

Target Image

175 m

44 m88 m

Note: = Target Aim Point and Seeker Tracking Gate, GPS / INS Accuracy = 3 m, Seeker 640 x 480 Image, Seeker FOV = 20 deg, Proportional Guidance Navigation Ratio = 4, Velocity = 300 m / s, G&C Time Constant = 0.2 s.

Seeker Lock-on @ 250 m to go ( 1 pixel = 0.14 m )3 m GPS / INS error ⇒ nMreq

= 1.76 g, σ = 0.9 m

Seeker Lock-on @ 850 m to go ( 1 pixel = 0.47 m )3 m GPS / INS error ⇒ nMreq

= 0.15 g, σ < 0.1 mSeeker Lock-on @ 500 m to go ( 1 pixel = 0.27 m )3 m GPS / INS error ⇒ nMreq

= 0.44 g, σ < 0.1 m

Seeker Lock-on @ 125 m to go ( 1 pixel = 0.07 m ) 3 m GPS / INS error ⇒ nMreq

= 7.04 g, σ = 2.2 m

2/24/2008 ELF 212

Data Link Update at Seeker Lock-on Reduces Moving Target Error

Data Link Update at Seeker Lock-on Reduces Moving Target Error

10

100

1000

0.1 1 10 100 1000

Target Latency at Seeker Lock-on, s

Targ

et E

rror a

t See

ker L

ock-

on, m

VT = 1 m / sVT = 10 m / sVT = 100 m / sVT = 1000 m / s

Note: tSeekerLock-on = Seeker Lock-on time, tUdate = Data Link Update Time, VT = Target Velocity, TLE = Target Location Error at Update = 10 m

Example:TLE = 10 mtSeekerLock-on = 100 stUdate = 90 sVT = 10 m / stLatency = tSeeker- tUdate = 100 – 90 = 10 s TESeekerLock-on = [ TLE2 + ( VT tLatency )2 ]1/2

= { 102 + [ 10 ( 10 )]2 ]1/2

= 100.5 m

TESeekerLock-on = [ TLE2 + ( VT tLatency )2 ]1/2

2/24/2008 ELF 213

Optimum Cruise Is a Function of Mach Number, Altitude, and Planform Geometry

Optimum Cruise Is a Function of Mach Number, Altitude, and Planform Geometry

0

20

40

60

80

100

120

0 1 2 3 4 5 6 7

M, Mach number

h, A

ltitu

de, k

ft

q = 200 psfq = 500 psfq = 1,000 psfq = 2,000 psfq = 5,000 psfq = 10,000 psfq = 20,000 psf

Note:• U.S. 1976 Standard Atmosphere• For Efficient Cruise, ( L / D )Max for Cruising Lifting Body Typically Occurs for 500 < q < 1,000 psf• ( L / D )Max for Cruise Missile with Low Aspect Ratio Wing Typically Occurs for 200 < q < 500 psf• q ≈ 200 psf lower limit for aero control

Note: q = 1 / 2 ( ρ V2 )

Ramjet

Scramjet

Wingless Subsonic Turbojet

Subsonic Turbojet with Low Aspect Ratio Wing

2/24/2008 ELF 214

Engine ShutdownTransient

Missile Guidance and Control Must Be Robust for Changing Events and Flight Environment

Missile Guidance and Control Must Be Robust for Changing Events and Flight Environment

Air Launch at Low Mach ( high α ) / Deploy Compressed Carriage Surfaces

Booster Ignition

Pitch-Up at High AlphaClimb

Booster ShutdownTransient at High Mach

Engine Start TransientPitch-Over at High Alpha

Terminal at HighDynamic Pressure

Example High Performance Missile Has• Low-to-High Dynamic Pressure• Negative-to-Positive Static Margin• Thrust / Weight / cg Transients• High Temperature• High Thermal Load• High Vibration• High Acoustics

Dive

Precision Impact at α ≈ 0 Deg

Level Out

Cruise

Vertical Launch in Cross Wind ( high α ) / Deploy Compressed Carriage Surfaces

Pitch-Over at High Alpha

2/24/2008 ELF 215

Design Robustness Requires Consideration of Flight Altitude

Design Robustness Requires Consideration of Flight Altitude

0.01

0.1

10 20 40 60 80 100

h, Geometric Altitude, kft

Char

acte

ristic

at A

ltitu

de /

Char

acte

ristic

at S

ea L

evel

Temperature RatioPressure RatioDensity RatioSpeed of Sound Ratio

Note: TSL = Temperature at sea level, pSL = pressure at sea level, ρSL = density at sea level, cSL = speed of sound at sea level, h = altitude in ft.

U.S. Standard Atmosphere, 1976– TSL = 519 R– pSL = 2116 lb / ft2

– ρSL = 0.00238 slug / ft3

– cSL = 1116 ft / s

Troposphere Stratosphere

Troposphere ( h < 36,089 ft )T / TSL = 1 – 6.875 x 10-6 h, h in ftp / pSL = ( T / TSL )5.2561

ρ / ρSL = ( T / TSL )4.2561

Stratosphere ( h > 36089 ft )T = constant = 390 Rp / pSL = 0.2234 e - ( h – 36089 ) / 20807

ρ / ρSL = 0.2971 e - ( h – 36089 ) / 20807

2/24/2008 ELF 216

0

0.5

1

1.5

Temp Density Speed ofSound

Varia

tion

from

Sta

ndar

d At

mos

pher

e Ratio: Cold-to-StandardAtmosphereRatio: Hot-to-StandardAtmosphereRatio: Polar-to-StandardAtmosphereRatio: Tropic-to-StandardAtmosphere

Note:

• Based on properties at sea level

•U. S. 1976 Standard Atmosphere: Temperature = 519 R, Density = 0.002377 slug / ft3, Speed of sound = 1116 ft / s

( + 30 % )

( - 23% )

Design Robustness Requires Consideration of Cold and Hot Atmospheres

Design Robustness Requires Consideration of Cold and Hot Atmospheres

2/24/2008 ELF 217

Design Robustness Is Required to Handle UncertaintyDesign Robustness Is Required to Handle Uncertainty

0

0.5

1

-20 -10 0 10 20Typical % Error from Forecast Value

Exam

ple N

orm

alize

d PD

FNarrow Uncertainty ( e.g.,SDD Flight Performance )

Broad Uncertainty ( e.g.,Conceptual Design FlightPerformance )Skewed Uncertainty ( e.g.,Cost, Weight, MissDistance )Bimodal Uncertainty ( e.g.,Multi-mode Seeker TargetLocation )Uniform Bias Uncertainty ( e.g., Seeker Aim PointBias )

Note for normal distribution: PDF = { 1 / [ σ ( 2 π )1/2 ]} e {[( x - μ ) / σ ]2 / 2 }

2/24/2008 ELF 218

Counter-Countermeasures by Missile Enhance Design Robustness

Counter-Countermeasures by Missile Enhance Design Robustness

Examples of CM ( Threat )EOCM

directed laserflaresmoke

RFCMactive radarjammerchaff

DecoyLow ObservablesSpeedAltitudeManeuverabilityLethal Defense

Examples of CCM ( Missile )Imaging SeekerMulti-spectral / Multi-mode SeekerTemporal ProcessingHardened GPS / INS

standoff acquisitionIntegrated GPS / INSdirectional antennapseudolite / differential GPS

ATR / ATASpeedAltitudeManeuverabilityLow ObservablesSaturation

2/24/2008 ELF 219

IIR ( I2R AGM-130 ) ………………………………………………

Two Color IIR ( Python 5 )

Acoustic - IIR ( BAT ) …………………………………………..

IIR – LADAR ( LOCAAS ) ………………………………………

ARH – mmW ( AARGM )

ARH - IIR ( Armiger ) …………………………………………….

Examples of Countermeasure-Resistant SeekersExamples of Countermeasure-Resistant Seekers

2/24/2008 ELF 220

TBM / TELs

OilRefineries

Naval

Armor

Transportation ChokePoints ( Bridges,Railroad Yards, TruckParks )

Counter AirAircraft

C3II

Artillery

Air Defense ( SAMs,AAA )

A Target Set Varies in Size and Hardness

Examples of Targets where Size and Hardness Drive Warhead Design / Technology

•Small Size, Hard Target: Tank ⇒ Small Shaped Charge, EFP, or KE Warhead

•Deeply Buried Hard Target: Bunker ⇒ KE / Blast Frag Warhead

•Large Size Target: Building ⇒ Large Blast Frag Warhead

LethalityRobustness

Lethality

Miss Distance

Carriage and Launch

Observables

Other Survivability

Considerations

Reliability

Cost


Video Example of Precision Strike Targets

Example of Precision Strike Target Set

2/24/2008 ELF 221

76% of Baghdad Targets Struck First Night of Desert Storm Were C3 Time Critical Targets

76% of Baghdad Targets Struck First Night of Desert Storm Were C3 Time Critical Targets

Targets: 1. Directorate of Military Intelligence; 2, 5, 8, 13, 34. Telephone switching stations; 3. Ministry of Defense national computer complex; 4. Electrical transfer station; 6. Ministry of Defense headquarters; 7. Ashudadhighway bridge; 9. Railroad yard; 10. Muthena airfield ( military section ); 11. Air Force headquarters; 12. Iraqi Intelligence Service; 14. Secret Police complex; 15. Army storage depot;16. Republican Guard headquarters; 17. New presidential palace; 18. Electrical power station; 19. SRBM assembly factory ( Scud ); 20. Baath Party headquarters; 21. Government conference center; 22. Ministry of Industry and Military Production; 23. Ministry of Propaganda; 24. TV transmitter; 25, 31. Communications relay stations; 26. Jumhuriya highway bridge; 27. Government Control Center South; 28. Karada highway bridge ( 14th July Bridge ); 29. Presidential palace command center; 30. Presidential palace command bunker; 32. Secret Police headquarters;33. Iraqi Intelligence Service regional headquarters; 35. National Air Defense Operations Center; 36. Ad Dawrah oil refinery; 37. Electrical power plantSource: AIR FORCE Magazine, 1 April 1998

1

23

4

567

891011

1213 1415 16

17

1819

20

2122

232425

2627

28

2930

3132

33

3435

36

37

2/24/2008 ELF 222

Anti-Fixed Surface Target Missiles ( large size, wings, subsonic, blast frag warhead )

AGM-154 Storm Shadow / Scalp KEPD-350 BGM-109 AGM-142

Anti-Radar Site Missiles ( ARH seeker, high speed or duration, blast frag warhead )

AGM-88 AS-11 / Kh-58 ARMAT Armiger ALARM

Anti-Ship Missiles ( large size, KE / blast frag warhead, and high speed or low altitude )

MM40 AS-34 Kormoran AS-17 / Kh-31 BrahMos SS-N-22 / 3M80

Anti-Armor Missiles ( small size, hit-to-kill, low cost, shape charge, EFP, or KE warhead )

Hellfire LOCAAS MGM140 AGM-65 LOSAT

Anti-Buried Target Missiles ( large size, high fineness, KE / blast frag warhead )

CALCM GBU-28 GBU-31 Storm Shadow MGM-140

Type of Target Drives Precision Strike Missile Size, Speed, Cost, Seeker, and Warhead

Type of Target Drives Precision Strike Missile Size, Speed, Cost, Seeker, and Warhead

Permission of Missile Index.

2/24/2008 ELF 223

Examples of Light Weight Air Launched Multi-Purpose Precision Strike Weapons

Examples of Light Weight Air Launched Multi-Purpose Precision Strike Weapons

Weapon Fixed Surface Targets(1)

Moving Targets(2)

Time Critical Targets(3)

Buried Targets(4)

Adverse Weather(5)

Firepower(6)

Example New Missile

AGM-65

Small Diameter Bomb

AGM-88

Hellfire / Brimstone / Longbow

LOCAAS

–

– –

– ––

–

–

Note:SuperiorGoodAveragePoor–

(1) – Multi-mode warhead desired. GPS / INS provides precision ( 3 m ) accuracy.

(2) - Seeker or high bandwidth data link required for terminal homing.

(3) - High speed with duration required ⇒ High payoff of high speed / loiter and powered submunition.

(4) - KE penetration warhead required ⇒ High impact speed, low drag, high density, long length.

(5) - GPS / INS, SAR seeker, imaging mmW seeker, and data link have high payoff.

(6) - Light weight required. Light weight also provides low cost

2/24/2008 ELF 224

Blast Is Effective at Small Miss DistanceBlast Is Effective at Small Miss Distance

1

10

100

1000

0 2 4 6 8 10

z ( p0 )1/3

Delta

p /

p0, O

verp

ress

ure R

atio

to U

ndist

urbe

d Pr

essu

reΔ p / p0 = 37.95 / ( z p0

1/3 ) + 154.9 / ( z p01/3 )2 + 203.4 / ( z p0

1/3 )3 + 403.9 / ( z p01/3 )4

z = r / c1/3

Note:Based on bare sphere of pentolite ( Ec

1/2 = 8,500 ft / s )Δp = overpressure at distance r from explosionp0 = undisturbed atmospheric pressure, psiz = scaling parameter = r / c1/3

r = distance from center of explosion, ftc = explosive weight, lb

Reference: US Army Ordnance Pamphlet ORDP-2—290-Warheads, 1980

Example for Rocket Baseline Warhead:c = 38.8 lbh = 20k feet, p0 = 6.8 psir = 10 ftz = 10 / ( 38.8 )1/3 = 2.95z p0

1/3 = 5.58Δp / p0 = 13.36Δp = 90 psi

2/24/2008 ELF 225

Guidance Accuracy Enhances LethalityGuidance Accuracy Enhances LethalityRocket Baseline Warhead Against Typical Aircraft TargetPK > 0.5 if σ < 5 ft ( Δ p > 330 psi, fragments impact energy > 130k ft-lb / ft2 )

PK > 0.1 if σ < 25 ft ( Δp > 24 psi, fragments impact energy > 5k ft-lb / ft2 )

Note: Rocket Baseline 77.7 lb warheadC / M = 1, spherical blast, h = 20k ft.

Video of AIM-9X Flight Test Missile Impact on Target ( No Warhead )

2/24/2008 ELF 226

Warhead Blast and Fragments Are Effective at Small Miss Distance

Warhead Blast and Fragments Are Effective at Small Miss Distance

Hellfire 24 lb shaped charge warhead fragments are from natural fragmenting case

2.4 m witness

plate

Roland 9 kg explosively formed warhead multi-projectiles are from preformed case

Video of Guided MLRS 180 lb blast fragmentation warhead

2/24/2008 ELF 227

Maximum Total Fragment Kinetic Energy Requires High Charge-to-Metal Ratio

Maximum Total Fragment Kinetic Energy Requires High Charge-to-Metal Ratio

0

0.1

0.2

0.3

0.4

0 0.5 1 1.5 2 2.5 3Mc / Mm, Charge-to-Metal Ratio

( KE

/ Mwh

) / E

c, No

n-di

men

siona

l Kin

etic

Ener

gyKE = ( 1 / 2 ) Mm Vf

2 = Ec Mc / ( 1 + 0.5 Mc / Mm )

Note:Based on Gurney EquationCylindrical WarheadKE = Total Kinetic EnergyMm = Total Mass Metal FragmentsVf = Fragment VelocityEc = Energy Per Unit Mass ChargeMc = Mass of ChargeMwh = Mass of Warhead = Mm + Mc

Reference: Carleone, Joseph (Editor), Tactical Missile Warheads (Progress in Astronautics and Aeronautics, Vol 155), AIAA, 1993.

Low KE High KE

Example:Rocket Baseline WarheadMc = 1.207 slugMm = 1.207 slugMc / Mm = 1Ec Mc = 52,300,000 ( 1.207 ) = 63,100,000 ft-lbKE = 63100000 / [1 + 0.5 ( 1 )] = 42,100,000 ft-lb

2/24/2008 ELF 228

Multiple Impacts Are Effective Against Threat Vulnerable Area Subsystems

Multiple Impacts Are Effective Against Threat Vulnerable Area Subsystems

00.10.20.30.40.50.60.70.80.9

1

0 5 10 15 20 25 30

nhits, Number of Impacts on Target

Pk, P

roba

bilit

y of

Kil

Av / Atp = 0.1Av / Atp = 0.5Av / Atp = 0.9

PK = 1 - ( 1 - Av / Atp )nhits

Note:• Av = Target vulnerable area• Atp = Target presented area

Example:If Av / Ap = 0.1, nhits = 22 gives PK = 0.9If Av / Ap = 0.9, nhits = 1 gives PK = 0.9

2/24/2008 ELF 229

Small Miss Distance Improves Number of Warhead Fragment Hits

Small Miss Distance Improves Number of Warhead Fragment Hits

0

20

40

60

80

100

0 20 40 60 80 100

Sigma, Miss Distance, ft

Num

ber o

f Fra

gmen

t Hits

Wwh = 5 lbWwh = 50 lbWwh = 500 lb

Example for Rocket Baseline:WWH = 77.7 lbMc / Mm = 1, Wm = 38.8 lb = 17,615 gAverage fragment weight = 3.2 gnfragments = 17615 / 3.2 = 5505AP = Target presented area = 20 ft2

σ = Miss distance = 25 ft

nhits = 5505 { 20 / [( 4 π ) ( 25 )2 ]} = 14Kinetic energy per square foot. = KE / ( 4 π σ2 ) = 42100000 / [ 4 π ( 25 )2 ] = 5,360 ft-lb / ft2

Note:• Spherical blast with uniformly distributed fragments• nhits = nfragments [ AP / ( 4 π σ2 )]• Warhead charge / metal weight = 1• Average fragment weight = 50 grains ( 3.2 g )• AP = Target presented area = 20 ft2

nhits = nfragments [ AP / ( 4 π σ2 )]

2/24/2008 ELF 230

High Fragment Velocity Requires High Charge-to-Metal Ratio

High Fragment Velocity Requires High Charge-to-Metal Ratio

0

2000

4000

6000

8000

10000

0 1 2 3

Mc / Mm, Charge-to-Metal Ratio

Vf, F

ragm

ent V

elocit

y, ft

/ sHMX ExplosiveTNT Explosive

Note: Based on the Gurney equation for a cylindrical warheadHMX Explosive ( 2 EC )1/2 = 10,230 ft / sTNT Explosive ( 2 EC )1/2 = 7,600 ft / sVf = Fragment initial velocity, ft / sEc = Energy per unit mass of charge, ft2 / s2

Mc = Mass of chargeMm = Total mass of all metal fragmentsMwh = Mass of warhead = Mm + Mc

Vf = ( 2 Ec )1/2 [ ( Mc / Mm ) / ( 1 + 0.5 Mc / Mm )]1/2

Example:Baseline Rocket WarheadHMX ExplosiveMC / Mm = 1Vf = 8,353 ft / s

2/24/2008 ELF 231

Note: Typical air-to-air missile warhead• Fragments initial velocity 5,000 ft / s• Sea level• Average fragment weight 3.2 g• Fewer than 0.3% of the fragments weigh more than 9.7 g for nominal 3.2 g preformed warhead fragments• Small miss distance gives less reduction in fragment velocity, enhancing penetration

2010 30 40 50 60 70 80 90 100 110 120

Stee

l Per

fora

tion

by F

ragm

ent

( in

)

50 Grains ( 3.2 g )

150 Grains ( 9.7 g )

.5

.375

.25

.125

Small Miss Distance Improves Fragment Penetration

Small Miss Distance Improves Fragment Penetration

Miss Distance ( ft )

2/24/2008 ELF 232

Hypersonic Hit-to-Kill Enhances Energy on Target for Missiles with Small Warheads

Hypersonic Hit-to-Kill Enhances Energy on Target for Missiles with Small Warheads

0123456789

0 1000 2000 3000 4000 5000 6000Missile Closing Velocity, ft / s

ET /

EC, T

otal

Ene

rgy

on T

arge

t / W

arhe

ad

Char

ge E

nerg

yWeight ofmissile /Weight ofcharge = 20

Weight ofmissile /Weight ofcharge = 10



Note: Warhead explosive charge energy based on HMX, ( 2 EC )1/2 = 10,230 ft / s.

1 kg weight at Mach 3 closing velocity has kinetic energy of 391,000 J ⇒ equivalent chemical energy of 0.4 lb TNT.

ET / EC = [( 1 / 2 ) ( WMissile / gc ) V2 + EC ( WC / gc )] / [ EC ( WC / gc )]

Example for Rocket Baseline:WMissile = 367 lbWC = 38.8 lbWMissile / WC = 9.46V = 2,000 ft / s( 1 / 2 ) ( WMissile / gc ) V2 = 22.8 x 106 ft-lb )EC ( WC / gc ) = 63.1 x 106 ft-lbET / EC = 1.36

2/24/2008 ELF 233

Kinetic Energy Warhead Density, Length, and Velocity Provide Enhanced Penetration

Kinetic Energy Warhead Density, Length, and Velocity Provide Enhanced Penetration

0

10

20

30

40

50

60

0 1000 2000 3000 4000

V, Velocity, ft / s

P / d

, Tar

get P

enetr

ation

/ Pe

netra

tor D

iamete

r for

St

eel o

n Co

ncre

te

l / d = 2 l / d = 5 l / d = 10

Note:V > 1,000 ft / sl / d > 2Non-deforming ( high strength, sharp nose )

penetratorl = Penetrator lengthd = Penetrator diameterV = Impact velocityρP= Penetrator densityρT= Target densityσT= Target ultimate stress

Example for 250 lb Steel Penetratorl / d = 10l = 48 in ( 4 ft )d = 4.8 in ( 0.4 ft )Concrete targetρP = 0.283 lb / in3 ( 15.19 slug / ft3 )ρT = 0.075 lb / in3 ( 4.02 slug / ft3 )V = 4,000 ft / sσT = 5,000 psi ( 720,000 psf )P / d = [ 10 – 1 }( 15.19 / 4.02 )1/2 + 3.67 ( 15.19 / 4.02 )2/3 [ 4.02 ( 4000 )2 / 720000 ]1/3 = 57.3P = ( 57.3 ) ( 0.4 ) = 22.9 ft

P / d = [( l / d ) – 1 ] ( ρP / ρT )1/2 + 3.67 ( ρP / ρT )2/3 [( ρT V2 ) / σT ]1/3

Source: Christman, D.R., et al, “Analysis of High-Velocity Projectile Penetration,” Journal of Applied Physics, Vol 37, 1966

2/24/2008 ELF 234

Standard Missile 3 ( NTW ) PAC-3 THAAD

LOSAT LOSAT Video

Examples of Kinetic-Kill MissilesExamples of Kinetic-Kill Missiles

2/24/2008 ELF 235

CEP Approximately Equal to 1σ Miss DistanceCEP Approximately Equal to 1σ Miss Distance

Median Trajectory

Extreme MissileTrajectory

Extreme Missile Trajectory

Hypothetical Plane Through Target

Missile Circular Error Probable ( 50% of shots within circle )

Missile 1σ Miss Distance ( 68% of shots within circle for a normal distribution of error )

Target

Presented Target Area

For a normal distribution of error:

Probability < 1σ miss distance = 0.68



Source: Heaston, R.J. and Smoots, C.W., “Introduction to Precision Guided Munitions,” GACIAC HB-83-01, May 1983.

Miss DistanceRobustness

Lethality

Miss Distance

ObservablesSurvivability

Reliability

Cost


2/24/2008 ELF 236

A Collision Intercept Has Constant Bearing for a Constant Velocity, Non-maneuvering Target

A Collision Intercept Has Constant Bearing for a Constant Velocity, Non-maneuvering Target

Example of Miss( Line-of-Sight Angle Diverging )

( Line-of-Sight Angle Rate L.≠ 0 )

Example of Collision Intercept( Line-of-Sight Angle Constant )

( Line-of-Sight Angle Rate L. = 0 )

Overshoot Miss

Missile Target

Seeker Line-of-Sight

( LOS )1 > ( LOS )0 ( LOS )1 = ( LOS )0

Missile Target

t0

t1

t2

t0

t1

Seeker Line-of-Sight

Note: L = Missile LeadA = Target Aspect

AL L A

2/24/2008 ELF 237

A Maneuvering Target and Initial Heading Error Cause Miss

A Maneuvering Target and Initial Heading Error Cause Miss

Target

MissileCollision

Point

+Z

γM0

L

ManeuveringTarget

: τ d2Zdt2

+ dZdt

+ N’ Zto – t

= – N’to – t

cos Acos L

12

aT t2

Initial HeadingError

: τ d2Zdt2

+ dZdt

+ N’ Zto – t

= – VM γM0

A

Note: to - t = 0 at intercept, causing discontinuity in above equations.N’ = Effective navigation ratio = N [ VM / ( VM - VT cos A )]N = Navigation ratio = ( dγ / dt ) / ( dL / dt )τ = Missile time constant, VM= Velocity of missile, γM0

= Initial flight path angle error of missile, to = Total time of flight, aT = Acceleration of target, VT = Velocity of target


2/24/2008 ELF 238

Missile Time Constant Causes Miss DistanceMissile Time Constant Causes Miss Distance

τ is a measure of missile ability to respond to target condition changesτ equals elapsed time from input of target return until missile hascompleted 63% or ( 1 – e-1 ) of corrective maneuver ( t = τ )τ also called “rise time”Contributions to time constant τ

Control effectiveness ( τδ )Control dynamics ( e.g., actuator rate ) ( τδ

. )Dome error slope ( τDome )Guidance and control filters ( τFilter )Other G&C dynamics ( gyro dynamics, accelerometer, processor latency, etc )Seeker errors ( resolution, latency, blind range, tracking, noise, glint, amplitude )

Approach to estimate ττ = τδ + τδ

. + τDome

Input

Output

ti

Time

Timeti

63%

τ

Acceleration AchievedAcceleration Commanded = 1 – e- t / τ

Example for Rocket Baseline:M = 2, h = 20k ft, coastτ = τδ + τδ

. + τDome

= 0.096 + 0.070 + 0.043 = 0.209 s

2/24/2008 ELF 239

Time Constant τδ for Control Effectiveness Is Driven by Static Margin

Time Constant τδ for Control Effectiveness Is Driven by Static Margin

Assumptions for τδ

Control surface deflection limitedNear neutral stability

Equation of motion isα

.. = [ ρ V2 S d Cmδ/ ( 2 Iy ) ] δMax

Integrate to solve for αMaxαMax= [ ρ V2 S d Cmδ

/ ( 8 Iy ) ] δMax τδ2

τδ is given byτδ = [ 8 Iy ( αMax / δMax ) / ( ρ V2 SRef d Cmδ

)]1/2

Contributors to small τδ

Low fineness ( small Iy / ( SRef d ))High dynamic pressure ( low altitude / high speed )Large Cmδ

αMax, δMax

– δMax

αMax

τδ / 2 τδ

Example for Rocket Baseline:W = 367 lb, d = 0.667 ft, SRef = 0.349 ft2, Iy = 94.0 slug-ft2,M = 2, h = 20k ft ( ρ = 0.001267 slug / ft3 ),αMax = 9.4 deg, δMax = 12.6 deg, Cmδ = 51.6 per rad,τδ = { 8 ( 94.0 ) ( 9.4 / 12.6 ) / [ 0.001267 ( 2074 )2 ( 0.349 ) ( 0.667 ) ( 51.6 ) ]}1/2 = 0.096 s

2/24/2008 ELF 240

Time Constant τδ. for Flight Control System Is

Driven by Actuator Rate DynamicsTime Constant τδ

. for Flight Control System Is Driven by Actuator Rate Dynamics

Assumptions for τδ.

Control surface rate limited ( δ.= δ

.Max )

Near neutral stabilityEquation of motion for δ

.= +/- δ

.Max

α... = [ ρ V2 S d Cmδ / ( 2 Iy ) ] δ

.Max

Equation of motion for “perfect” response δ

.= ∞, δ = δMax

α.. = [ ρ V2 S d Cmδ / ( 2 Iy ) ] δMax

τδ. is difference between actual response

to αMax and “perfect” ( τδ ) response

Thenτδ

. = 2 δMax / δ.Max

α Max, δ Max α Max α Max

- δ Max

δ.

1

Note:Response for control rate limitResponse for no control rate limit

Example for Rocket Baseline• δ

.Max = 360 deg / s, δMax = 12.6 deg

• τδ. = 2 ( 12.6 / 360 ) = 0. 070 s

τδ.τδ

2/24/2008 ELF 241

| R | = 0.05 ( lN / d – 0.5 ) [ 1 + 15 ( Δ f / f ) ] / ( d / λ )

τDome = N’ ( VC / VM ) | R | ( α / γ. )

α / γ. = α ( W / gc ) VM / { q SRef [ CNα+ CNδ

/ ( α / δ )]}

Substituting gives τDome = N’ W VC | R | / { gc q SRef [ CNα+ CNδ

/ ( α / δ )]}

Time Constant τDome for Radome Is Driven by Dome Error Slope

Time Constant τDome for Radome Is Driven by Dome Error Slope

0.03

0.02

0.01

0

|R| @

d/ λ

= 10

, Rad

ome E

rror S

lope

,De

g / D

eg

0 1 2 3lN / d, Nose Fineness

TangentOgiveDome

Faceted or WindowDome

Multi-lensDome

Δ f / f = 0.05Δ f / f = 0.02Δ f / f = 0

Example for Rocket Baseline at M = 2, h = 20k ft, q = 2725 psf

Assume VT = 1,000 ft / s, giving VC = 3,074 ft / sAssume N’ = 4, f = 10 GHz or λ = 1.18 in, Δ f / f = 0.02Configuration data are lN / d = 2.4, d = 8 in, SRef = 0.349 ft2, W = 367 lb, CNα

= 40 per rad, CNδ= 15.5 per rad, α / δ

= 0.75Compute | R | = 0.05 ( 2.4 – 0.5 ) [ 1 + 15 ( 0.02 )] / ( 8 / 1.18 ) = 0.0182 deg / degτDome = 4 ( 367 ) ( 3074 ) ( 0.0182 ) / [ 32.2 ( 2725 ) ( 0.349 ) ( 40 + 15.5 / 0.75 )] = 0.043 s

2/24/2008 ELF 242

High Initial Acceleration Is Required to Eliminate a Heading Error

High Initial Acceleration Is Required to Eliminate a Heading ErroraM t0 / ( VM γM ) = N’ ( 1 – t / t0 ) N’ – 2

aM t0 / ( VM γM ), Non-dimensional

Acceleration

2

00 0.2 0.4 0.6 0.8

t / t0, Non-dimensional Time

6

4

1.0

N’ = 22.53

4

6

Note: Proportional Guidanceτ = 0t0 = Total Time to Correct Heading ErroraM = Acceleration of MissileVM = Velocity of MissileγM = Initial Heading Error of MissileN’ = Effective Navigation Ratio

Example: Exoatmospheric Head-on Intercept, N’ = 4Midcourse lateral error at t = 0 ( seeker lock-on ) = 200 m, 1 σRlock-on = 20000 m ⇒ γM = 200 / 20000 = 0.0100 radVM = 5000 m / s, VT = 5000 ⇒ t0 = Rlock-on / ( VM + VT ) = 20000 / ( 5000 + 5000 ) = 2.00 saM t0 / ( VM γM ) = 4aM = 4 ( 5000 ) ( 0.0100 ) / 2.00 ) = 100 m / s2

nM = 100 / 9.81 = 10.2 g

2/24/2008 ELF 243

Missile Minimum Range May Be Driven By 4 to 8 Time Constants to Correct Initial Heading Error

Missile Minimum Range May Be Driven By 4 to 8 Time Constants to Correct Initial Heading Error

0.1

00 2 4 6 8tO / τ

0.3

0.2

10

N’ = 3

N’ = 4

N’ = 6

Note: Proportional Guidance( σHE )Max shown in figure is the envelope of adjoint solution( σHE )Max = Max miss distance ( 1 σ ) from heading error, ftVM = Velocity of missile, ft / sγM = Initial heading error, radt0 = Total time to correct heading error, s τ = Missile time constant, s N’ = Effective navigation ratio

References:•Donatelli, G.A., et al, “Methodology for Predicting Miss Distance for Air Launched Missiles,” AIAA-82-0364, January 1982•Bennett, R.R., et al, “Analytical Determination of Miss Distances for Linear Homing Navigation,” Hughes Memo 260, March 1952

Example: Ground Target, N’ = 4, τ = 0.2, GPS / INS error = 3 m, Rlock-on = 125 m, γM = 3 / 125 = 0.024 rad, VM = 300 m / s, t0 = 125 / 300 = 0.42 st0 / τ = 0.42 / 0.2 = 2.1, (σHE )Max / ( VM γM to ) = 0.12( σHE )Max = 0.12 ( 300 ) ( 0.024 ) ( 0.42 ) = 2.2 m

| ( σHE )Max / ( VM γM to ) |

σHE = VM γM t0 e-( t0 / τ )j = 1∑N’ – 1 {( N’ - 2 )! [ - ( t0 / τ )]j / [( j – 1 )! ( N’ – j – 1 )! j! ]}

If N’ = 3, σHE = VM γM t0 e-( t0 / τ ) [ ( t0 / τ ) - ( t0 / τ )2 / 2 ]If N’ = 4, σHE = VM γM t0 e-( t0 / τ ) [( t0 / τ ) - ( t0 / τ )2 + ( t0 / τ )3 / 6 ]If N’ = 5, σHE = VM γM t0 e-( t0/ τ ) [( t0 / τ ) – ( 3 / 2 ) ( t0 / τ )2 + ( t0 / τ )3 / 2 – ( t0 / τ )4 / 24 ]If N’ = 6, σHE = VM γM t0 e-( t0 / τ ) [( t0 / τ ) - 2 ( t0 / τ )2 + ( t0 / τ )3 - ( t0 / τ )4 / 6 + ( t0 / τ )5 / 120 ]

2/24/2008 ELF 244

Required Maneuverability Is about 3x the Target Maneuverability for an Ideal ( τ = 0 ) Missile

Required Maneuverability Is about 3x the Target Maneuverability for an Ideal ( τ = 0 ) Missile

4

2

00 0.2 0.4 0.6 0.8 1.0

t / t0, Non-Dimensional Time

Assumptions:τ = 0VM > VT

6

3

46

N’ = 2.5

N’ = 2 ∞↑

Wheret = Elapsed Timet0 = Time to TargetN’ = Effective Navigation Ratio

Missile-to-TargetAcceleration

Ratio

nMnT

,

nM / nT = [ N’ / ( N’ – 2 )] [ 1 – ( 1 – t / t0 )N’ – 2 ]

Example:τ = 0, N’ = 3, t / t0 = 1⇒ nM / nT = 3

2/24/2008 ELF 245

Target Maneuvers Require 6 to 10 Time Constants to Settle Out Miss Distance

Target Maneuvers Require 6 to 10 Time Constants to Settle Out Miss Distance

0.1

00 2 4 6 8tO / τ

0.3

0.2

10

( σMAN )Maxgc nT τ2

N’ = 3

N’ = 4

N’ = 6

Note: Proportional Guidance( σMAN )Max is the envelope of adjoint solution( σMAN )Max = Max miss ( 1 σ ) from target accel, ftnT = Target acceleration, ggc = Gravitation constant, 32.2τ = Missile time constant, sN’ = Effective navigation ratioτ0 = Time of flight, s

References:•Donatelli, G.A., et al, “Methodology for Predicting Miss Distance for Air Launched Missiles,” AIAA-82-0364, January 1982•Bennett, R.R., et al, “Analytical Determination of Miss Distances for Linear Homing Navigation,” Hughes Memo 260, March 1952

σMAN = gc nT τ2 e-( t0 / τ )j = 2∑N’ – 1 {( N’ - 3 )! [ - ( t0 / τ )]j / [( j – 2 )!

( N’ – j – 1 )! j! ]}If N’ = 3, σMAN = gc nT τ2 e-( t0 / τ ) [ ( t0 / τ )2 / 2 ] If N’ = 4, σMAN = gc nT τ2 e-( t0 / τ ) [ ( t0 / τ )2 / 2 - ( t0 / τ )3 / 6 ]If N’ = 5, σMAN = gc nT τ2 e-( t0 / τ ) [ ( t0 / τ )2 / 2 - ( t0 / τ )3 / 3 + ( t0 / τ )4 / 24 ]If N’ = 6, σMAN = gc nT τ2 e-( t0 / τ ) [ ( t0 / τ )2 / 2 - ( t0 / τ )3 / 2 + ( t0 / τ )4 / 8 - ( t0 / τ )5 / 120 ]

2/24/2008 ELF 246

An Aero Control Missile Has Reduced Miss Distance at Low Altitude / High Dynamic Pressure

An Aero Control Missile Has Reduced Miss Distance at Low Altitude / High Dynamic Pressure

0.1

1

10

100

0 2 4 6 8 10Target Maneuverability, g

Rock

et B

aseli

ne M

axim

um M

iss D

ue to

Man

euve

ring

Targ

et, f

t

h = SLh = 20k fth = 40k fth = 60k fth = 80k ft

( σMan )Max = 0.13 gc nT τ2 @ N’ = 4, t0 / τ = 2 Note: Proportional guidanceTarget maneuver initiated for max miss ( t0 / τ = 2 )( σMan )Max in figure = Envelope of adjoint miss distanceτ = Missile time constant, sN’ = Effective navigation ratio = 4nT = Target acceleration, ggc = Gravitation constant = 32.2

Example for Rocket Baseline at Mach 2, coastingAssume:• nT = 5g, VT = 1,000 ft / s, head-on intercept•h = 20k ft ⇒ τ = 0.209 s

( σMan )Max = 0.13 ( 32.2 )( 5 )( 0.209 )2 = 0.9 ft•h = 80k ft ⇒ τ = 1.17 s

( σMan )Max = 0.13 ( 32.2 )( 5 )( 1.17 )2 = 28.7 ft

2/24/2008 ELF 247

Glint Miss Distance Driven by Seeker Resolution, Missile Time Constant, and Navigation Ratio

Glint Miss Distance Driven by Seeker Resolution, Missile Time Constant, and Navigation Ratio

0

0.2

0.4

0.6

0.8

0 0.2 0.4 0.6 0.8 1Tau, Missile Time Constant, s

Sigm

a / (

bT )R

es, N

ondi

men

siona

l Miss

Dist

ance

fro

m G

lint @

2 Hz

Ban

dwid

th

N' = 3 N' = 4 N' = 6

σGlint = KN’ ( W / τ )1/2

KN’ = 0.5 ( 2 KN’ = 4 )N’ / 4

KN’ = 4 = 1.206W = ( bT )Res

2 / ( 3 π2 B )

Note:Proportional guidanceAdjoint miss distanceσGlint = Miss distance due to glint noise, ftW = Glint noise spectral density, ft2 / Hzτ = Missile time constant, sN’ = Effective navigation ratio( bT )Res = Target span resolution at seeker blind range, ftB = Noise bandwidth, Hz ( 1 < B < 5 Hz )

Example: Rocket Baseline at Mach 2, h = 20k ft altitude ⇒ τ = 0.209 sAssume:•N’ = 4•B = 2 Hz•( bT )Res = bt = 40 ft ( radar seeker beam width resolution of target wing span )Calculate:W = ( 40 )2 / [ 3 π2 ( 2 )] = 27.0 ft2 / HzσGlint / ( bT )Res = KN’ ( W / τ )1/2 / ( bt )Res

= 1.206 ( 27.0 / 0.209 )1/2 / 40 = 0.343σGlint = 0.343 ( 40 ) = 13.7 ftReference:

Bennett, R.R., et al, “Analytical Determination of Miss Distances for Linear Homing Navigation,” Hughes Memo 260, March 1952

2/24/2008 ELF 248

Minimizing Miss Distance with Glint Requires Optimum Time Constant and Navigation RatioMinimizing Miss Distance with Glint Requires Optimum Time Constant and Navigation Ratio

0

10

20

30

40

50

0 0.2 0.4 0.6 0.8 1Tau, Missile Time Constant, s

Rock

et B

aseli

ne M

iss D

istan

ce, ft

N' = 3 N' = 4 N' = 6

σ = [( σMAN )Max2 + ( σGlint )2 ]1/2

Note:Proportional guidanceAdjoint miss distance( σMAN )Max = Max miss distance from target maneuver, ft

σGlint = Miss distance from glint noise, ftτ = Missile time constant, sN’ = Effective navigation ratio

Example for Rocket Baseline at Mach 2, h = 20k ft altitude ⇒ τ = 0.209 sAssume:N’ = 4•B = 2 Hz•( bT )Res = 40 ft•nT = 5g, VT = 1,000 ft / s, Head-onFrom prior figures:( σMAN )Max = 0.9 ft, σGlint = 13.7 ftCalculate:σ = [( σMAN )Max

2 + ( σGlint )2 ]1/2 = 13.7 ftReference:Bennett, R.R., et al, “Analytical Determination of Miss Distances for Linear Homing Navigation,” Hughes Memo 260, March 1952

2/24/2008 ELF 249

Missile Carriage RCS and Launch Plume Are Considerations in Launch Platform Observables

Missile Carriage RCS and Launch Plume Are Considerations in Launch Platform Observables

Missile Carriage AlternativesInternal Carriage: Lowest Carriage RCSConformal Carriage: Low Carriage RCSConventional External Pylon or External Rail Carriage: High Carriage RCS

Plume AlternativesMin Smoke: Lowest Launch Observables ( H2O Contrail )Reduced Smoke: Reduced Launch Observables ( e.g., HCl Contrail from AP Oxidizer )High Smoke: High Launch Observables ( e.g., Al2O3 Smoke from Al Fuel )

Carriage andLaunch Observables

Robustness

Lethality

Miss Distance


Reliability

Cost


2/24/2008 ELF 250

Center Weapon Bay Best for Ejection Launchers

F-22 Bay Loadout: 3 AIM-120C, 1 GBU-32 F-117 Bay Loadout: 1 GBU-27, 1 GBU-10 B-1 Bay Loadout: 8 AGM-69

Video Side Weapon Bay Best for Rail Launchers

AMRAAM Loading in F-22 Bay F-22 Side Bay: 1 AIM-9 Each Side Bay RAH-66 Side Bay: 1 AGM-114, 2 FIM-92, 4 Hydra 70 Each Side Bay

Examples of Weapon Bay Internal Carriage and Load-out

Examples of Weapon Bay Internal Carriage and Load-out

2/24/2008 ELF 251

Minimum Smoke Propellant Has Low ObservablesMinimum Smoke Propellant Has Low Observables

High Smoke Example: AIM-7Particles ( e.g., metal fuel ) at all atmosphere temperature.

Reduced Smoke Example: AIM-120Contrail ( HCl from AP oxidizer ) at T < -10° F atmospheric temperature.

Minimum Smoke Example: JavelinContrail (H2O ) at T < -35º F atmospheric temperature.

High Smoke Motor

Reduced Smoke Motor

Minimum Smoke Motor

2/24/2008 ELF 252

High Altitude Flight and Low RCS Enhance Survivability

High Altitude Flight and Low RCS Enhance Survivability

100

1000

10000

100000

1000000

10000000

0 20 40 60 80 100

h, Geometric Altitude, kft

Pt, R

adar

Tra

nsm

itted

Pow

erRe

quire

d fo

r Det

ectio

n, W

RCS = 0.1 m2 RCS = 0.01 m2 RCS = 0.001 m2

Note:Range Slant Angle = 20 deg, Gt = Transmitter Gain = 40 dB, Gr = Receiver Gain = 40 dB, λ = Wavelength = 0.03 m, Pr = Receiver Sensitivity = 10-14 W, σ = radar cross section ( RCS )Based on Radar Range Equation with ( S / N )Detect = 1 and Unobstructed Line-of-Sight

Example for Pt = 50,000 W:

Not detected if:

h > 25k ft for σ = 0.001 m2

h > 77k ft for σ = 0.1 m2

Pt = ( 4 π )3 Pr R4 / ( Gt Gr σ λ2 ) Other Survivability Considerations

Robustness

Lethality

Miss Distance


Reliability

Cost


2/24/2008 ELF 253

Mission Planning and High Speed Enhance Survivability

Mission Planning and High Speed Enhance Survivability

0

1

2

0 0.2 0.4 0.6 0.8 1yoffset / Rmax, Non-dimensional Offset Distance from

Threat

texp

( V / R

max

), No

n-di

men

siona

l Thr

eat

Expo

sure

Tim

e

treact ( V / Rmax ) = 0 treact ( V / Rmax ) = 1.0

texp = 2 ( Rmax / V ) cos [ sin-1 ( yoffset / Rmax )] – treact

Note: Based on assumption of constant altitude, constant heading flyby of threat SAM site with an unobstructed line-of-sight. texp = exposure time to SAM threat, Rmax = max detection range by SAM threat, V = flyby velocity, yoffset = flyby offset, treact = SAM site reaction time from detection to launch

Example:

yoffset = 7 nm, Rmax = 10 nm = 60750 ft, yoffset / Rmax = 0.7, treact = 15 s

If V = 1000 ft / s, treact ( V / Rmax ) = 0.247

•texp ( V / Rmax ) = 2 cos [ sin-1 ( 7 / 10 )] –15 ( 1000 / 60746 ) = 1.428 – 0.247 = 1.181

•texp = 1.181 ( 60746 / 1000 ) = 71.7 s

If V = 4000 ft / s, treact ( V / Rmax ) = 0.988

•texp ( V / Rmax ) = 0.440

•texp = 0.440 ( 60746 / 4000 ) = 6.7 s

R max treact V

texp V

Flyby

SAMSite yoffset

2/24/2008 ELF 254

Low Altitude Flight and Terrain Obstacles Provide Masking from Threat

Low Altitude Flight and Terrain Obstacles Provide Masking from Threat

0

500

1000

1500

2000

0 10 20 30 40

Rlos, Line-of-Sight Range to Surface Threat, nm

hmas

k, A

ltitu

de th

at M

asks

Lin

e-of

-Sig

ht

Expo

sure

to S

urfa

ce T

hrea

t, ft

Rlos ( hobstacle / Robstacle ) = 100 ftRlos ( hobstacle / Robstacle ) = 200 ftRlos ( hobstacle / Robstacle ) = 500 ftRlos ( hobstacle / Robstacle ) = 1000 ft

hmask = ( hmask )obstacle + ( hmask )earth = hobstacle ( Rlos / Robstacle ) + ( Rlos / 7113 )2

Example:

hobstacle = 200 ft

Robstaacle = 5.0 nm = 30395 ft

Rlos = 10.0 nm = 60790 ft

Rlos ( hobstacle / Robstaacle ) = 60790 ( 200 / 30395 ) = 400 ft

hmask = 200 ( 60790 / 30395 ) + ( 60790 / 7113 )2 = 400 + 73 = 473 ft above terrain

hmask = altitude that allows obstacle and earth curvature to mask exposure to surface threat LOS, ft

hobstacle = height of obstacle above terrain, ft

Rlos = line-of-sight range to surface threat, ft

Robstacle = range from surface threat to obstacle, ft

Height of low hill or tall tree ≈ 100 ft

Height of moderate hill ≈ 200 ft

Height of high hill ≈ 500 ft

Height of low mountain ≈ 1000 ft

2/24/2008 ELF 255

Insensitive Munitions Improve Launch Platform Survivability

Insensitive Munitions Improve Launch Platform Survivability

Critical Subsystems Rocket motor or fuel tankWarhead

Severity Concerns Ranking of Power Output - Type1. Detonation ( ~ 0.000002 s rise time )2. Partial detonation ( ~ 0.0001 s rise time )3. Explosion ( ~ 0.001 s rise time )4. Deflagration or propulsion rise time ( ~ 0.1 s rise time ) 5. Burning ( > 1 s )Design and test considerations ( MIL STD 2105C )

Fragment / bullet impact or blastSympathetic detonationFast / slow cook-off fireDropTemperatureVibrationCarrier landing ( 18 ft / s sink rate )

2/24/2008 ELF 256

Robustness

Lethality

Miss Distance


Reliability

Cost


High System Reliability Is Provided by High Subsystem Reliability and Low Parts CountHigh System Reliability Is Provided by High Subsystem Reliability and Low Parts Count

Typical Event / Subsystem

Rsystem ≈ 0.94 = RArm X RLaunch X RStruct X RAuto X RAct X RSeeker X RIn Guid X RPS X RProp X RFuze X RW/H

Arm ( 0.995 – 0.999 )

Launch ( 0.990 – 0.995 )

Structure ( 0.997 – 0.999 )Autopilot ( 0.993 – 0.995 )

Actuators ( 0.990 – 0.995 )

Seeker ( 0.985 – 0.990 )

Inertial Guidance ( 0.995 – 0.999 )

Power Supply ( 0.995 – 0.999 )

Propulsion ( 0.995 – 0.999 )

Fuze ( 0.987 – 0.995 )

Warhead ( 0.995 – 0.999 )

0.90 0.92 0.94 0.96 0.98 1.00Typical Reliability

ReliabilityTypical System Reliability

2/24/2008 ELF 257

Sensors, Electronics and Propulsion Drive Missile Production Cost

Sensors, Electronics and Propulsion Drive Missile Production Cost

Very High( > 25% Production Cost )

–High( > 10% )

Moderate( > 5% )

Relatively Low( < 5% )

Dome Seeker Guidance andControl

Propulsion•Rocket•Airbreather

Wings

Stabilizers

Warheadand Fuzing

AerothermalInsulation

FlightControl

PowerSupply

Structure•Rocket•Airbreather

–

–

––––

Note:System assembly and test ~ 10% production costPropulsion and structure parts count / cost of airbreathing missiles are higher than that of rockets

CostRobustness

Lethality

Miss Distance


Reliability

Cost


Data Link

2/24/2008 ELF 258

Sensors and Electronics Occupy a Large Portion of a High Performance / High Cost Missile.

Sensors and Electronics Occupy a Large Portion of a High Performance / High Cost Missile.

Example: Derby / R-Darter Missile

Source: http://www.israeli-weapons.com/weapons/missile_systems/air_missiles/derby/Derby.html

2/24/2008 ELF 259

Cost ConsiderationsCost ConsiderationsLife Cycle

System Development and Demonstration ( SDD )

Production

Logistics

Culture / processes

Relative Emphasis of Cost, Performance, Reliability, Organization Structure

Relaxed Mil STDs

IPPD

Profit

Competition

2/24/2008 ELF 260

SDD Cost Is Driven by Schedule Duration and Risk

SDD Cost Is Driven by Schedule Duration and Risk

10

100

1000

10000

0 2 4 6 8 10 12 14

tSDD, SDD Schedule Duration in Years

CSD

D, S

DD

Cos

t in

Mill

ions

AGM-142 TOW 2 SLAM-ER MLRS LB Hellfire JASSM Hellfire IISLAM JDAM AGM-130 Harpoon ATACMS Tomahawk ESSMAIM-120A JSOW HARM Javelin BAT PAC-3 Patriot

Note: SDD required schedule duration depends upon risk. Should not ignore risk in shorter schedule.-- Source of data: Nicholas, T. and Rossi, R., “U.S. Missile Data Book, 1999,” Data Search Associates, 1999– SDD cost based on 1999 US$

CSDD = $20,000,000 tSDD1.90, ( tSDD in years )

Example:5 year ( medium risk ) SDD programCSDD = $20,000,000 tSDD

1.90

= ( 20,000,000 ) ( 5 )1.90

= $426,000,000

LowRiskSDD

HighRiskSDD

ModerateRiskSDD

2/24/2008 ELF 261

Light Weight Missiles Have Low Unit Production Cost

Light Weight Missiles Have Low Unit Production Cost

10000

100000

1000000

10000000

10 100 1000 10000

JavelinLongbow HellfireAMRAAMMLRSHARMJSOWTomahawk

Example:2,000 unit buy of 100 lb missile:C1000th ≈ $6,100 WL

0.758 = 6100 ( 100 )0.758 = $200,000Cost of 2,000 missiles = 2000 ( $200000 ) = $400,000,000

Note:-- Source of data: Nicholas, T. and Rossi, R., “U.S. Missile Data Book, 1999,” Data Search Associates, 1999– Unit production cost based on 1999 US$

C1000th ≈ $6,100 WL0.758, ( WL in lb )

C 100

0th,

Cost

of M

issile

Num

ber 1

000,

U.S.

$

WL , Launch Weight, lb

2/24/2008 ELF 262

Learning Curve and Large Production Reduce Unit Production Cost

Learning Curve and Large Production Reduce Unit Production Cost

0.01

0.1

1

1 10 100 1000 10000 100000 1E+06x, Number of Units Produced

Cx /

C1st

, Cos

t of U

nit x

/ Co

st o

f Firs

t Uni

t

Javelin ( L = 0.764, C1st = $3.15M,Y1 = 1994 )Longbow HF ( L = 0.761, C1st =$4.31M, Y1 = 1996 )AMRAAM ( L = 0.738, C1st =$30.5M, Y1 = 1987 )MLRS ( L = 0.811, C1st = $0.139M,Y1 = 1980 )HARM ( L = 0.786, C1st = $9.73M,Y1 = 1981 )JSOW ( L = 0.812, C1st = $2.98M,Y1 = 1997 )Tomahawk ( L = 0.817, C1st =$13.0M, Y1 = 1980 )

Cx = C1st Llog2x, C2x = L Cx , where C in U.S. 99$

Source of data: Nicholas, T. and Rossi, R., “U.S. Missile Data Book, 1999,” Data Search Associates, 1999

Labor intensive learning curve: L < 0.8Machine intensive learning curve: L > 0.8 )Contributors to the learning curve include:

• More efficient labor• Reduced scrap• Improved processes

Example:For a learning curve coefficient of L = 80%, cost of unit #1000 is 11% the cost of the first unit

L = 1.0

L = 0.9

L = 0.8

L = 0.7

2/24/2008 ELF 263

Low Parts Count Reduces Missile Unit Production Cost

Low Parts Count Reduces Missile Unit Production Cost

10

100

1000

10000

100000

1000000

Parts Fasteners Circuit Cards Connectors Assembly /Test Hours

UnitProduction

Cost ( US$ )

Parts

Cou

nt, H

ours

, or C

ost (

US$

)

Current Tomahawk Tactical Tomahawk

Note: Tactical Tomahawk has superior flexibility ( e.g., shorter mission planning, in-flight retargeting, BDI / BDA, modular payload ) at lower parts count / cost and higher reliability. Enabling technologies for low parts count include: casting, pultrusion / extrusion, centralized electronics, and COTS.

2/24/2008 ELF 264

Copperhead Seeker and Electronics Production Patriot Control Section Production

Video of Hellfire Seeker and Electronics Production

Tactical Missile Culture Is Driven by Rate Production of Sensors and Electronics

Tactical Missile Culture Is Driven by Rate Production of Sensors and Electronics

2/24/2008 ELF 265

Peacetime Logistics Activity

•Contractor Post-production Engineering•Training Manuals / Tech Data Package•Simulation and Software Maintenance•Configuration Management•Engineering Support•System Analysis•Launch Platform Integration•Requirements Documents•Coordinate Suppliers

•Storage Alternatives•Wooden Round ( Protected )•Open Round ( Humidity, Temp, Corrosion, Shock )

•Reliability Maintenance•Surveillance•Testing

•Maintenance Alternatives•First level ( depot )•Two level ( depot, field )

•Disposal

Logistics Cost ConsiderationsLogistics Cost ConsiderationsWartime Logistics Activity

•Deployment Alternatives•Airlift•Sealift

•Combat Logistics•Launch Platform Integration•Mission Planning•Field Tests•Reliability Data•Maintainability Data•Effectiveness Data•Safety Data

2/24/2008 ELF 266

Simple: Stinger More Sophisticated: Hawk and SLAMRAAM Complex: PAC-3

Very Complex: THAAD Video of Logistics Alternatives

Logistics Cost Lower for Simple Missile SystemsLogistics Cost Lower for Simple Missile Systems

2/24/2008 ELF 267

Logistics Is Simpler for Light Weight MissilesLogistics Is Simpler for Light Weight Missiles

0

2

4

6

10 100 1000 10000Missile Weight, lb

Supp

ort P

erso

nnel

requ

ired

for I

nsta

llatio

nSupport personnel for installation with 50 lb lift limit per personSupport personnel for installation with 100 lb lift limit per personMachine lift for installation

Predator ( 21 lb ) Sidewinder ( 190 lb ) Sparrow ( 500 lb ) Laser Guided Bomb ( 2,500 lb )

Video of Simple Logistics for a Light weight Missile

2/24/2008 ELF 268

Small MEMS Sensors Can Provide Health Monitoring, Reducing Cost and Weight

Small MEMS Sensors Can Provide Health Monitoring, Reducing Cost and Weight

Micro-machined Electro-Mechanical Systems ( MEMS )Small size / low cost semiconductor manufacturing process2,000 to 5,000 sensors on a 5 in silicon wafer

Wireless ( RF ) Data Collection and Health MonitoringDistributed Sensors Over Missile

Stress / strainVibrationAcousticsTemperaturePressure

Reduced Logistics Cost and Improved ReliabilityHealth monitoring

Reduced Weight and Production CostMore Efficient Design

2/24/2008 ELF 269

Missile Carriage Size, Shape, and Weight Are Driven by Launch Platform Compatibility

Missile Carriage Size, Shape, and Weight Are Driven by Launch Platform Compatibility

Surface Ships

CLS

~24” x 24”

263”

263”

~168”

3400 lb

3400 lb

~500 lb to 3000 lb

~ 22” ~ 22”Fighters /Bombers / UCAVs

Rail /Ejection

VLS

Submarines


Robustness

Lethality

Miss Distance


Reliability

Cost


22”

Ground

Vehicles158” 3700 lb

Helos

Launch Pods

Rail

US Launch Platform Launcher Carriage Span / Shape Length Weight

∼13” x 13” 70” 120 lb

~ 28” ~ 28”

2/24/2008 ELF 270

Light Weight Missiles Enhance FirepowerLight Weight Missiles Enhance Firepower

E, carry 1

C, carry 3

C, carry 1

E, carry 2C, carry 2E, carry 3

E, carry 1

C, carry 1E, carry 2

C, carry 2

5,000 lb

4,000 lb

3,000 lb

2,000 lb

1,000 lb

Max S

trike

Wea

pon

Weig

ht

Clea

n+

CL T

ank

+ 2 I

nbd

Tank

s+

CL T

k + 2

AIM-

9+

CL T

k + 2

AGM-

88+

2 Inb

d Tk

+ 2

AIM-

9Configuration for Day Operation

with Bring-Back Load

Clea

n+

CL T

ank

+ 2 I

nbd

Tank

s+

CL T

k + 2

AIM-

9+

CL T

k + 2

AGM-

88+

2 Inb

d Tk

+ 2

AIM-

9

Configuration for Night Operationwith Bring-Back Load

F-18 C / E

Inboard AsymmetricBring-Back Load Limit

Outboard AsymmetricBring-Back Load Limit

2/24/2008 ELF 271

Launch Envelope Limitations in Missile / Launch Platform Physical Integration

Launch Envelope Limitations in Missile / Launch Platform Physical Integration

Off BoresightSeeker field of regard ⇒ potential obscuring from launch platform

Minimum RangeLauncher rail clearance and aeroelasticity ⇒ miss at min rangeHelo rotor downwash ⇒ miss at min range

SafetyLauncher retention ⇒ potential inadvertent release, potential hang-fireLaunch platform local flow field α, β ⇒ potential unsafe separationLaunch platform maneuvering ⇒ potential unsafe separationHandling qualities with stores ⇒ potential unsafe handling qualitiesLaunch platform bay / canister acoustics ⇒ missile factor of safetyLaunch platform bay / canister vibration ⇒ missile factor of safety

2/24/2008 ELF 272

Store Separation Wind Tunnel Tests Are Required for Missile / Aircraft Compatibility

Store Separation Wind Tunnel Tests Are Required for Missile / Aircraft Compatibility

F-18 Store Compatibility Test in AEDC 16T AV-8 Store Compatibility Test in AEDC 4T

Types of Wind Tunnel Testing for Store Compatibility- Flow field mapping with probe- Flow field mapping with store- Captive trajectory simulation- Drop testing

Example Stores with Flow Field Interaction: Kh-41 + AA-10

2/24/2008 ELF 273

Examples of Rail Launched and Ejection Launched Missiles

Examples of Rail Launched and Ejection Launched Missiles

Example Rail Launcher: Hellfire / Brimstone Example Ejection Launcher: AGM-86 ALCM

Video of Hellfire / Brimstone Carriage / Launch Video of AGM-86 Carriage / Launch

2/24/2008 ELF 274

Examples of Safe Store SeparationExamples of Safe Store Separation

AMRAAM Rail Launch from F-16 Video of Rapid Drop ( 16 Bombs ) from B-2

Laser Guided Bombs Drop from F-117

2/24/2008 ELF 275

Examples of Store Compatibility ProblemsExamples of Store Compatibility Problems

Unsafe Separation Hang-Fire Store Aeroelastic Instability

2/24/2008 ELF 276

MIL-STD-8591 Aircraft Store Suspension and Ejection Launcher Requirements

MIL-STD-8591 Aircraft Store Suspension and Ejection Launcher Requirements

Store Weight / Parameter

30 Inch Suspension

14 Inch Suspension

♦ Weight Up to 100 lb

Not Applicable

Yes

• Lug height ( in ) 0.75 • Min ejector area ( in x in )

4.0 x 26.0

♦ Weight 101 to 1,450 lb Yes Yes • Lug height ( in ) 1.35 1.00 • Min lug well ( in ) 0.515 0.515 • Min ejector area ( in x in ) 4. 0 x 36.0 4.0 x 26.0

♦ Weight Over 1,451 lb Yes Not Applicable • Lug height ( in ) 1.35 • Min lug well ( in ) 1.080 • Min ejector area ( in x in ) 4.0 x 36.0

Ejection Stroke

2/24/2008 ELF 277

Rail Launcher Forward Hanger Aft HangerLAU-7 Sidewinder Launcher 2.260 2.260

LAU 117 Maverick Launcher 1.14 7.23

MIL-STD-8591 Aircraft Store Rail Launcher Examples

MIL-STD-8591 Aircraft Store Rail Launcher Examples

Note: Dimensions in inches.• LAU 7 rail launched store weight and diameter limits are ≤ 300 lb, ≤ 7 in•LAU 117 rail launched store weight and diameter limits are ≤ 600 lb, ≤ 10 in

2/24/2008 ELF 278

Baseline AIM-120B AMRAAM

Compressed Carriage AIM-120C AMRAAM ( Reduced Span Wing / Tail )

Compressed Carriage Missiles Provide Higher Firepower

Compressed Carriage Missiles Provide Higher Firepower

17.5 in 17.5 in

12.5 in 12.5 in 12.5 in

Baseline AMRAAM: Loadout of 2 AMRAAM per F-22 Semi-Bay

Compressed Carriage AMRAAM: Loadout of 3 AMRAAM per F-22 Semi-Bay

Note: Alternative approaches to compressed carriage include surfaces with small span, folded surfaces, wrap around surfaces, and planar surfaces that extend ( e.g., switch blade, Diamond Back, Longshot ).

Video of Longshot Kit on CBU-97

2/24/2008 ELF 279

Example of Aircraft Carriage and Fire Control Interfaces

Example of Aircraft Carriage and Fire Control Interfaces

WingWing DeploySafety Pin

FoldingSuspensionLug

Fire Control /Avionics UmbilicalConnector

Flight ControlAccess Cover Electrical

Safety Pin

FoldingSuspensionLug

Example: ADM-141 TALD ( Tactical Air-Launched Decoy ) Carriage and Fire Control Interfaces

2/24/2008 ELF 280

Example of Ship Weapon Carriage and Launcher, Mk41 VLS

Example of Ship Weapon Carriage and Launcher, Mk41 VLS

8 Modules / Magazine Module Gas Management

Tomahawk Launch 8 Canister Cells / Module Standard Missile Launch

Canister Cell Hatch

Cell Before Firing

Cell After Firing

Ship DeckExhaust Hatch

Missile Cover

Plenum

2/24/2008 ELF 281

Robustness Is Required for Carriage, Shipping, and Storage Environment

Robustness Is Required for Carriage, Shipping, and Storage Environment

Environmental Parameter Typical Requirement Video: Ground / Sea EnvironmentSurface Temperature -60° F* to 160° FSurface Humidity 5% to 100%Rain Rate 120 mm / h**Surface Wind 100 km / h steady***

150 km / h gusts****Salt fog 3 g / mm2 deposited per yearVibration 10 g rms at 1,000 Hz: MIL STD 810, 648, 1670A Shock Drop height 0.5 m, half sine wave 100 g / 10 ms: MIL STD 810, 1670AAcoustic 160 dB

Note: MIL-HDBK-310 and earlier MIL-STD-210B suggest 1% world-wide climatic extreme typical requirement.

* Lowest recorded temperature = -90° F. 20% probability temperature lower than -60° F during worst month of worst location.

** Highest recorded rain rate = 436 mm / h. 0.5% probability greater than 120 mm / h during worst month of worst location.

*** Highest recorded steady wind = 342 km / h. 1% probability greater than 100 km / h during worst month of worst location.

**** Highest recorded gust = 378 km / h. 1% probability greater than 150 km / h during worst month of worst location.

2/24/2008 ELF 282

Summary of Measures of Merit and Launch Platform Integration

Summary of Measures of Merit and Launch Platform Integration

Measures of MeritRobustnessWarhead lethalityMiss distanceCarriage and launch observablesOther survivability considerationsReliabilityCost

Launch Platform IntegrationFirepower, weight, fitmentStore separationLaunch platform handling qualities, aeroelasticityHang-fireVibrationStandard launchersCarriage and storage environment


2/24/2008 ELF 283

Measures of Merit and Launch Platform Integration Problems

Measures of Merit and Launch Platform Integration Problems

1. IR signal attenuation is greater than 100 dB per km through a c____.2. GPS / INS enhances seeker lock-on in adverse weather and ground c______.3. A data link can enhance missile seeker lock-on against a m_____ target.4. An example of a missile counter-counter measure to flares is an i______

i_____ seeker.5. Compared to a mid-wave IR seeker, a long wave IR seeker receives more

energy from a c___ target.6. High fineness kinetic energy penetrators are required to defeat b_____

targets.7. For the same lethality with a blast fragmentation warhead, a small decrease in

miss distance allows a large decrease in the required weight of the w______.8. For a blast / frag warhead, a charge-to-metal ratio of about one is required to

achieve a high total fragment k______ e_____.9. A blast fragmentation warhead tradeoff is the number of fragments versus the

individual fragment w_____.

2/24/2008 ELF 284

Measures of Merit and Launch Platform Integration Problems ( cont )


10. Kinetic energy penetration is a function of the penetrator diameter, length, density, and v_______.

11. In proportional homing guidance, the objective is to make the line-of-sight angle rate equal to z___.

12. Aeromechanics contributors to missile time constant are flight control effectiveness, flight control system dynamics, and dome e____ s____.

13. Miss distance due to heading error is a function of missile navigation ratio, velocity, time to correct the heading error, and the missile t___ c_______.

14. A missile must have about t_____ times the maneuverability of the target.15. Minimizing the miss distance due to radar glint requires a high resolution

seeker, an optimum missile time constant and an optimum n_________ r____.16. Weapons on low observable launch platforms use i_______ carriage.17. Weapons on low observable launch platforms use m______ smoke propellant.18. For an insensitive munition, burning is preferable to detonation because it

releases less p____.

2/24/2008 ELF 285



19. Missile system reliability is enhanced by subsystem reliability and low p____ count.

20. High cost subsystems of missiles are sensors, electronics, and p_________. 21. Missile SDD cost is driven by the program duration and r___.22. Missile unit production cost is driven by the number of units produced,

learning curve, and w_____.23. First level maintenance is conducted at a d____.24. A standard launch system for U.S. Navy ships is the V_______ L_____ S_____.25. Most light weight missiles use rail launchers while most heavy weight missiles

use e_______ launchers.26. Higher firepower is provided by c_________ carriage.27. The typical environmental requirement from MIL-HDBK-310 is the _% world-

wide climatic extreme.

2/24/2008 ELF 286


2/24/2008 ELF 287

Sizing ExamplesSizing ExamplesRocket Baseline Missile

Standoff range requirement

Wing sizing requirement

Multi-parameter harmonization

Lofted range comparison

Ramjet Baseline Missile

Range robustness

Propulsion and fuel alternatives

Velocity control

Computer Aided Conceptual Design Sizing Tools

Soda Straw Rocket Design, Build, and Fly

2/24/2008 ELF 288

Air-to-Air Engagement Analysis Process and Assumptions

Air-to-Air Engagement Analysis Process and Assumptions

F-pole range provides kill of head-on threat outside of threat weapon launch rangeAircraft contrast for typical engagement

C = 0.18Typical visual detection range by target ( Required F-pole range )

RD = 3.3 nmTypical altitude and speed of launch aircraft, target aircraft, and missile

h = 20k ft altitudeVL = Mach 0.8 = 820 ft / sVT = Mach 0.8 = 820 ft / sVM = 2 VT = 1,640 ft / s

2/24/2008 ELF 289

Assumed Air-to-Air Engagement Scenario for Head-on Intercept

Assumed Air-to-Air Engagement Scenario for Head-on Intercept

t = 0 s (Launch Missile)

RL= Launch Range = 10.0 nm

Red Aircraft( 820 ft / s )

Blue Aircraft( 820 ft / s )

t = tf = 24.4 s ( Missile Impacts Target )

R F-pole = 3.3 nm

Red AircraftDestroyed

Blue Aircraft( 820 ft / s )

Blue Missile( 1640 ft / s )

RL= VM tf + VT tf

RF-Pole = VM tf - VL tf

RF = Missile Flight Range = 6.7 nm

2/24/2008 ELF 290

0

2

4

6

8

0.01 0.1 1C, Contrast

R, V

isibl

e Ran

ge fo

r 50 f

t2 T

arge

t, nm

Visual Detection Range,nmVisual RecognitionRange, nm

Target Contrast and Size Drive Visual Detection and Recognition Range

Target Contrast and Size Drive Visual Detection and Recognition Range

Note:RD = Visual detection range for probability of detection PD = 0.5C = ContrastCT = Visual threshold contrast = 0.02Atp = Target presented area = 50 ft2

RR = Visual recognition range θF = Pilot visual fovial angle = 0.8 degClear weatherPilot search glimpse time = 1 / 3 s

Example:If C = 0.18RD = 3.3 nmRR = 1.0 nm

RD = 1.15 [ Atp ( C – CT )]1/2, RD in nm, Atp in ft2

RR = 0.29 RD

C = 0.01 C = 0.02 C = 0.05 C = 0.1 C = 0.2 C = 0.5 C = 1.0

2/24/2008 ELF 291

High Missile Velocity Improves Standoff RangeHigh Missile Velocity Improves Standoff Range

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

Target Velocity / Missile Velocity

F-Po

le R

ange

/ La

unch

Ran

ge

VL / VM = 0VL / VM = 0.2VL / VM = 0.5VL / VM = 1.0

Example:• VL = VT• VM = 2 VT• Then VT / VM = VL / VM = 0.5• RF-Pole / RL = 0.33• RF-Pole = RD = 3.3 nm• RL = 3.3 / 0.33 = 10.0 nm

RF-Pole / RL = 1 – ( VT + VL ) / ( VM + VT ) Note: Head-on interceptRF-Pole = Standoff range at interceptRL= Launch rangeVM = Missile average velocityVT = Target velocityVL = Launch velocity

2/24/2008 ELF 292

Missile Flight Range Requirement Is Greatest for a Tail Chase Intercept

Missile Flight Range Requirement Is Greatest for a Tail Chase Intercept

0

0.5

1

1.5

2

2.5

3

0 1 2 3 4 5VM / VT, Missile Velocity / Target Velocity

RF /

RL, M

issi

le F

light

Ran

ge /

Laun

ch R

ange

( RF / RL ) Head-on( RF / RL ) Tail Chase

Examples:•Head-on Intercept

• VM = 1,640 ft / s, VT = 820 ft / s• VM / VT = 1640 / 820 = 2• RF / RL = 2 / ( 2 + 1 ) = 0.667• RL = 10.0 nm• RF = 0.667 ( 10.0 ) = 6.67 nm

•Tail Intercept at same conditions• RF / RL = 2 / ( 2 – 1 ) = 2.0• RF = 2.0 ( 10.0 ) = 20.0 nm

( RF / RL )Head-on = ( VM / VT ) / [(VM / VT ) + 1 ]( RF / RL )TailChase = ( VM / VT ) / [(VM / VT ) - 1 ]

2/24/2008 ELF 293

Drawing of Rocket Baseline Missile ConfigurationDrawing of Rocket Baseline Missile Configuration

STA 60.819.4

3.4 18.5

STA 125.4

LEmac at STA 67.0BL 10.2

Λ = 45°

40.2STA 0 19.2 46.1 62.6 84.5 138.6

Note: Dimensions in inches

Source: Bithell, R.A. and Stoner, R.C., “Rapid Approach for Missile Synthesis, Vol. 1, Rocket Synthesis Handbook,” AFWAL-TR-81-3022, Vol. 1, March 1982.

Nose Forebody PayloadBay

Midbody Aftbody Tailcone

Rocket MotorΛ = 57°

12.0

LEmac at STA 131.6

BL 8.016.18.0 d

cgBO cgLaunch

143.9

2/24/2008 ELF 294

Mass Properties of Rocket Baseline MissileMass Properties of Rocket Baseline Missile

1 Nose ( Radome ) 4.1 12.03 Forebody structure 12.4 30.5

Guidance 46.6 32.62 Payload Bay Structure 7.6 54.3

Warhead 77.7 54.34 Midbody Structure 10.2 73.5

Control Actuation System 61.0 75.55 Aftbody Structure 0.0 –

Rocket Motor Case 47.3 107.5Insulation ( EDPM – Silica ) 23.0 117.2

6 Tailcone Structure 6.5 141.2Nozzle 5.8 141.2

Fixed Surfaces 26.2 137.8Movable Surfaces 38.6 75.5Burnout Total 367.0 76.2Propellant 133.0 107.8Launch Total 500.0 84.6

Component Weight, lb. C.G. STA, in.

2/24/2008 ELF 295

Rocket Baseline Missile DefinitionRocket Baseline Missile DefinitionBody

Dome Material PyroceramAirframe Material Aluminum 2219-T81Length, in 143.9Diameter, in 8.0Airframe thickness, in 0.16Fineness ratio 17.99Volume, ft3 3.82Wetted area, ft2 24.06Nozzle exit area, ft2 0.078Boattail fineness ratio 0.38Nose fineness ratio 2.40Nose bluntness 0.0Boattail angle, deg 7.5

Movable surfaces ( forward )Material Aluminum 2219-T81Planform area, ft2 ( 2 panels exposed ) 2.55Wetted area, ft2 ( 4 panels ) 10.20Aspect ratio ( 2 panels exposed ) 2.82Taper ratio 0.175Root chord, in 19.4Tip chord, in 3.4Span, in ( 2 panels exposed ) 32.2Leading edge sweep, deg 45.0

2/24/2008 ELF 296

Rocket Baseline Missile Definition ( cont )Rocket Baseline Missile Definition ( cont )Movable surfaces ( continued )

Mean aerodynamic chord, in 13.3Thickness ratio 0.044Section type Modified double wedgeSection leading edge total angle, deg 10.01xmac, in 67.0ymac, in ( from root chord ) 6.2Actuator rate limit, deg / s 360.0

Fixed surfaces ( aft )Material Aluminum 2219-T81Modulus of elasticity, 106 psi 10.5Planform area, ft2 ( 2 panels exposed ) 1.54Wetted area, ft2 ( 4 panels ) 6.17Aspect ratio ( 2 panels exposed ) 2.59Taper ratio 0.0Root chord, in 18.5Tip chord, in 0.0Span, in ( 2 panels exposed ) 24.0Leading edge sweep, deg 57.0Mean aerodynamic chord, in 12.3Thickness ratio 0.027Section type Modified double wedgeSection leading edge total angle, deg 6.17xmac, in 131.6ymac, in ( from root chord ) 4.0

2/24/2008 ELF 297

Rocket Baseline Missile Definition ( cont )Rocket Baseline Missile Definition ( cont )References values

Reference area, ft2 0.349Reference length, ft 0.667Pitch / Yaw Moment of inertia at launch, slug-ft2 117.0Pitch / Yaw Moment of inertia at burnout, slug-ft2 94.0

Rocket Motor Performance ( altitude = 20k ft, temp = 70° F )Burning time, sec ( boost / sustain ) 3.69 / 10.86Maximum pressure, psi 2042Average pressure, psi ( boost / sustain ) 1769 / 301Average thrust, lbf ( boost / sustain ) 5750 / 1018Total impulse, lbf-s ( boost / sustain ) 21217 / 11055Specific impulse, lbf-s / lbm ( boost / sustain ) 250 / 230.4

PropellantWeight, lbm ( boost / sustain ) 84.8 / 48.2Flame temperature @ 1,000 psi, °F 5282 / 5228Propellant density, lbm / in3 0.065Characteristic velocity, ft / s 5200Burn rate @ 1000 psi, in / s 0.5Burn rate pressure exponent 0.3

2/24/2008 ELF 298

Rocket Baseline Missile Definition ( cont )Rocket Baseline Missile Definition ( cont )Propellant ( continued )

Burn rate sensitivity with temperature, % / °F 0.10Pressure sensitivity with temperature, % / °F 0.14

Rocket Motor CaseYield / ultimate strength, psi 170,000 / 190,000Material 4130 SteelModulus of elasticity, psi 29.5 x 106 psiLength, in 59.4Outside diameter, in 8.00Thickness, in (minimum) 0.074Burst pressure, psi 3140Volumetric efficiency 0.76Grain configuration Three slots + webDome ellipse ratio 2.0

NozzleHousing material 4130 SteelExit geometry Contoured ( equiv. 15° )Throat area, in2 1.81Expansion ratio 6.2Length, in 4.9Exit diameter, in 3.78

2/24/2008 ELF 299

Rocket Baseline Missile Has Boost-Sustain Thrust - Time History

Rocket Baseline Missile Has Boost-Sustain Thrust - Time History

Time – seconds0 4 8 12 16

0

2

4

6

8

Thrust – 1,000 lb

Note: Altitude = 20k ft, Temperature = 70° FTotal impulse drives velocity change

Boost Total Impulse = ∫Tdt = 5750 ( 3.69 ) = 21217 lb-s

Sustain Total Impulse = ∫Tdt = 1018 ( 10.86 ) = 11055 lb-s

2/24/2008 ELF 300

Rocket Baseline Missile Aerodynamic Characteristics

Rocket Baseline Missile Aerodynamic Characteristics

4

00 4 8 12 16

α, Angle of Attack – Deg

12

8

20

Norm

al Fo

rce ~

CN

Pitc

hing

Mom

ent –

C m

20

16

24

-16.0

-8.0

-12.0

0

-4.0

1.20.6

M1.52.02.352.873.954.60

2.352.0

M = 1.2 and 1.54.600.6

3.95

SRef = 0.349 ft2, lRef = d = 0.667 ft, CG at STA 75.7, δ = 0 deg

2/24/2008 ELF 301

Rocket Baseline Missile Aerodynamic Characteristics ( cont )

Rocket Baseline Missile Aerodynamic Characteristics ( cont )

0.4

00 1 2 3 4

M, Mach Number

1.2

0.8

5

C A at

α= 0

deg

0.1

0

Power Off

Power On

0.2

0.3C N

δat

α=

0 deg

,Per

Deg

0.4

0

1.2

0.8

.002

0

.004

.006K2

K1

CA = CAα = 0 + K1 δ2 + K2 α δ

C mδ

at α

= 0 d

eg,P

er D

egK 1

, K2

~ Pe

r Deg

2

0 1 2 3 4M, Mach Number

5

2/24/2008 ELF 302

High Altitude Launch Enhances Rocket Baseline Range

High Altitude Launch Enhances Rocket Baseline Range

Range ~ nm0 5 10 15 20

0

10

20

30

40Al

titud

e ~ 10

3ft

Burnout

25

Boost /Sustain

TerminationMach = 1.5

Coast

Vmax = 2147 ft / s

Vmax = 1916 ft / s

Vmax = 2524 ft / s

ML = 0.7CDAVG

= 0.65Constant Altitude Flight

2/24/2008 ELF 303

Low Altitude Launch and High Alpha Maneuvers Enhance Rocket Baseline Turn Performance

Low Altitude Launch and High Alpha Maneuvers Enhance Rocket Baseline Turn Performance

Cros

s Ran

ge 1,

000 f

t.

25

20

15

10

5

0-10 -5 0 5 10

Down Range 1,000 ft.

Termination at M = 1.0Marks at 2 s intervals

Alt.10k ft10k ft40k ft40k ft

α

15°10°15°10°

1

2

3

4

1234

Note: Off boresight envelope that is shown does not include the rocket baseline seeker field-of-regard limit ( 30 deg ).

2/24/2008 ELF 304

Paredo Shows Range of Rocket Baseline Driven by ISP, Propellant Weight, Drag, and Static MarginParedo Shows Range of Rocket Baseline Driven

by ISP, Propellant Weight, Drag, and Static Margin

-1

-0.5

0

0.5

1

1.5

Isp Prop.Weight

CD0 Drag-Due-to-

Lift

StaticMargin

Thrust InertWeight

Parameter

Nondimensional Range

Sensitivity to Parameter

Note: Rocket baseline:hL = 20k ft, ML = 0.7, MEC = 1.5R@ ML = 0.7, hL = 20k ft = 9.5 nm

Example: 10% increase in propellant weight ⇒ 8.8% increase in flight range

2/24/2008 ELF 305

Boost - Sustain Trajectory AssumptionsBoost - Sustain Trajectory Assumptions

Assumptions1 degree of freedomConstant altitude

Simplified equation for axial acceleration based on thrust, drag, and weight

nX = ( T – D ) / W

Missile weight varies with burn rate and timeW = WL – WP t / tB

Drag is approximated byD = CDO

q S

2/24/2008 ELF 306

-5

0

5

10

15

0 5 10 15 20 25

t, Time, s

nx, A

xial A

ccel

erat

ion,

g

Example of Rocket Baseline Axial Acceleration Example of Rocket Baseline Axial Acceleration

Note:tf = 24.4 sML = 0.8hL = 20,000 ftTB = 5750 lbtB = 3.69 sTS = 1018 lbtS = 10.86 sD = 99 lb at Mach 0.8D = 1020 lb at Mach 2.1WL = 500 lbWP = 133 lb

nX = ( T - D ) / W

Boost

Sustain

Coast

2/24/2008 ELF 307

0

1000

2000

3000

0 5 10 15 20 25

t, Time, s

V, V

elocit

y, ft

/ s

Example of Rocket Baseline Missile Velocity vs Time

Example of Rocket Baseline Missile Velocity vs Time

Boost

Sustain

Coast

ΔV / ( gc ISP ) = - ( 1 - DAVG / T ) ln ( 1 - Wp / Wi ), During Boost-SustainV / VBO = 1 / { 1 + t / { 2 WBO / [ gc ρAVG SRef ( CD0

)AVG VBO ]}}, During Coast

Note:ML = 0.8hL = 20k feet

2/24/2008 ELF 308

Range and Time-to-Target of Rocket Baseline Missile Meet Requirements

Range and Time-to-Target of Rocket Baseline Missile Meet Requirements

0

2

4

6

8

10

0 5 10 15 20 25

t, Time, s

R, F

light

Ran

ge, n

m

Boost

Sustain

Coast

(RF)Req = 6.7 nm @ t =24.4 s

R = Δ Rboost + Δ Rsustain + Δ Rcoast

Note:ML = 0.8hL = 20k ft

2/24/2008 ELF 309







Range robustness


Velocity control



2/24/2008 ELF 310

Example of Wing Sizing to Satisfy Required Maneuver Acceleration

Example of Wing Sizing to Satisfy Required Maneuver Acceleration

Size Wing for the Assumptions( nZ )Required = 30 g to counter 9 g maneuvering target )

( nZ ) = Δ ( nZ )Wing + Δ ( nZ )Body + Δ ( nZ )Tail

Rocket Baseline @Mach 220,000 ft altitude367 lb weight ( burnout )

From Prior Example, ComputeαWing = α’Max = ( α + δ )Max = 22 deg for rocket baseline

α = 0.75δ, αBody = αTail = 9.4 deg

Δ ( nZ )Body = q SRef ( CN )Body / W = 2725 ( 0.349 ) ( 1.28 ) / 367 = 3.3 g ( from body )

Δ ( nZ )Tail = q STail [( CN )Tail ( SRef / STail )] / W = 2725 ( 1.54 ) ( 0.425 ) / 367 = 4.9 g ( from tail )

Δ ( nZ )Wing = ( nZ )Required - Δ ( nZ )Body - Δ ( nZ )Tail = 30 – 3.3 – 4.9 = 21.8 g

( SW )Required = Δ ( nZ )Wing W / { q [( CN )Wing (SRef / SWing )]} = 21.8 ( 367 ) / {( 2725 ) ( 1.08 )} = 2.72 ft2

Note: ( SW )RocketBaseline = 2.55 ft2

Video of Intercept of Maneuvering Target

2/24/2008 ELF 311

Wing Sizing to Satisfy Required Turn RateWing Sizing to Satisfy Required Turn Rate

Assume( γ. )Required > 18 deg / s to counter 18 deg / s maneuvering aircraft

Rocket Baseline @ Mach 220,000 ft altitude367 lb weight ( burnout )γi = 0 deg

Computeγ. = gc n / V = [ q SRef CNα α + q SRef CNδ δ - W cos ( γ ) ] / [( W / gc ) V ]α / δ = 0.75α’ = α + δ = 22 deg ⇒ δ = 12.6 deg, α = 9.4 degγ. = [ 2725 ( 0.349 )( 0.60 )( 9.4 ) +2725 ( 0.349 )( 0.19 )( 12.6 ) – 367 ( 1 )] / ( 367 / 32.2 )( 2074 ) = 0.31

rad / s or 18 deg / sNote: ( SW )RocketBaseline ⇒ 18 deg / s Turn Rate

2/24/2008 ELF 312

Wing Sizing to Satisfy Required Turn RadiusWing Sizing to Satisfy Required Turn RadiusAssume Maneuvering Aircraft Target with

γ. = 18 deg / s = 0.314 rad / sV = 1000 ft / s( RT )Target = V / γ. = 1000 / 0.314 = 3183 ft

Assume Rocket Baseline @Mach 220,000 ft altitude367 lb weight ( burnout )

Computeγ. = 18 deg / s ( prior figure )( RT )RocketBaselinet = V / γ. = 2074 / 0.314 = 6602 ft

Note: ( RT )RocketBaselinet > ( RT )Target ⇒ Rocket Baseline Can Be Counter-measured by Target in a Tight TurnCounter-Countermeasure Alternatives

Larger WingHigher Angle of AttackLonger Burn Motor with TVC

2/24/2008 ELF 313

Sizing ExamplesSizing Examples

Rocket Baseline Missile






Range robustness


Velocity control



2/24/2008 ELF 314

Combined Weight / Miss Distance Drivers: Nozzle Expansion and Motor Volumetric Efficiency

Combined Weight / Miss Distance Drivers: Nozzle Expansion and Motor Volumetric Efficiency

Fixed surface number of panels 4 3 +0.054 +0.100Movable surface number of panels 4 2 +0.071 +0.106Design static margin at launch 0.40 0.30 +0.095 +0.167Wing movable surface sweep ( deg ) 45.0 49.5 -0.205 +0.015Tail fixed surface sweep ( deg ) 57.0 60.0 +0.027 +0.039Wing movable surface thickness ratio 0.044 0.034 +0.041 +0.005Nose fineness ratio 2.4 2.6 -0.016 -0.745Rocket chamber sustain pressure ( psi ) 301 330 -0.076 -0.045Boattail fineness ratio ( length / diameter ) 0.38 0.342 +0.096 +0.140Nozzle expansion ratio 6.2 6.82 -0.114 -0.181Motor volumetric efficiency 0.76 0.84 -0.136 -0.453Propellant density ( lb / in3 ) 0.065 0.084 -0.062 +0.012Boost thrust ( lb ) 5,750 6,325 +0.014 -0.018Sustain thrust ( lb ) 1,018 1,119 +0.088 +0.246Characteristic velocity ( ft / s ) 5,200 5,720 -0.063 -0.077Wing location ( percent total length ) 47.5 42.75 +0.181 -0.036

Parameter Baseline W* σ*SensitivityVariation

Note: Strong impact with synergyStrong impactModerate impact with synergyModerate impact

Baseline: Weight = 500 lb, Miss distance = 62.3 ftW* = weight sensitivity for parameter variation = ΔW / Wσ* = miss distance sensitivity for parameter variation = Δ σ / σ

2/24/2008 ELF 315

A Harmonized Missile Can Have Smaller Miss Distance and Lighter Weight

A Harmonized Missile Can Have Smaller Miss Distance and Lighter Weight

Judicious changesBoost thrust ( lb ) 5,750 3,382 3,382 3,382Wing location ( percent missile length to 1/4 mac ) 47.5 47 44 46Wing taper ratio 0.18 0.2 0.2 0.2Nose fineness ratio 2.4 3.2 2.55 2.6Nose blunting ratio 0.0 0.05 0.05 0.05Nozzle expansion ratio 6.2 15 15 15Sustain chamber pressure ( psi ) 301 1,000 1,000 1,000Boattail fineness ratio 0.38 0.21 0.21 0.21Tail leading edge sweep ( deg ) 57 50 50 50

Technology limited changesNo. wing panels 4 2 2 2No. tail panels 4 3 3 3Wing thickness ratio 0.044 0.030 0.030 0.030Wing leading edge sweep ( deg ) 45 55 55 55Static margin at launch ( diam ) 0.4 0.0 0.0 0.0Propellant density ( lb / in3 ) 0.065 0.084 0.084 0.084Motor volumetric efficiency 0.76 0.84 0.84 0.84

Measures of MeritTotal weight ( lb ) 500 385.9 395.0 390.1Miss distance ( ft ) 62.3 63.1 16.2 16.6Time to target ( s ) 21.6 23.8 23.6 23.8Length ( in ) 144 112.7 114.7 114.9Mach No. at burnout 2.20 2.08 2.09 2.07Weight of propellant ( lb ) 133 78.3 85.4 85.9Wing area ( in2 ) 368.6 175.5 150.7 173.8Tail area ( in2 ) 221.8 109.1 134.5 112.0

Parameter Baseline Value Weight Miss Distance Harmonized

Missile Configured for Minimum:

*Note: Value of driving parameter

2/24/2008 ELF 316

Baseline Missile vs Harmonized MissileBaseline Missile vs Harmonized Missile

144”

57°45°

Propellant Density ( lb / in3 );

0.0650.084

50°55°115”

NoseFineness;

2.42.6

Surfaces; { 4 wings / 4 tails

2 wings / 3 tailsWeight ( lb ); 500

390

2/24/2008 ELF 317








Range robustness


Velocity control



2/24/2008 ELF 318

Lofted Glide Trajectory Provides Extended RangeLofted Glide Trajectory Provides Extended Range

Using Rocket Baseline, CompareLofted Launch-Coast-Glide TrajectoryLofted Launch-Ballistic TrajectoryConstant Altitude Trajectory

Assume for Lofted Launch-Coast-Glide Trajectory:γi = 45 degγ = 45 deg during boost and sustainγ = 45 deg coastSwitch to ( L / D )max glide at optimum altitude( L / D )maxg glide trajectory after apogeehi = hf = 0 ft

Velocity, Horizontal Range, and Altitude During Initial Boost @ γ = 45 degΔV = - gc ISP [ 1 – ( DAVG / T ) - ( WAVG sin γ ) / T ] ln ( 1 - Wp / Wi ) = -32.2 ( 250 ) [ 1 - ( 419 /

5750 ) – 458 ( 0.707 ) / 5750 ] ln ( 1 - 84.8 / 500 ) = 1,303 ft / sΔR = ( Vi + ΔV / 2 ) tB = ( 0 + 1303 / 2 ) 3.69 = 2,404 ftΔRx = ΔR cos γi = 2404 ( 0.707 ) = 1,700 ftΔRy = ΔR sin γi = 2404 ( 0.707 ) = 1,700 fth = hi + ΔRy = 0 + 1700 = 1,700 ft

2/24/2008 ELF 319

Lofted Glide Trajectory Provides Extended Range ( cont )


Velocity, Horizontal Range, and Altitude During Sustain @ γ = 45 degΔV = - gc ISP [ 1 – ( DAVG / T ) – ( WAVG sin γ ) / T ] ln ( 1 - Wp / Wi ) = -32.2 ( 230.4 ) [ 1 – ( 650 /

1018 ) – 391 ( 0.707 ) / 1018 ] ln ( 1 - 48.2 / 415.2 ) = 81 ft / secVBO = 1303 + 81 = 1,384 ft / sΔR = ( Vi + ΔV / 2 ) tB = ( 1303 + 81 / 2 ) 10.86 = 14,590 ftΔRx = ΔR cos γi = 14590 ( 0.707 ) = 10,315 ftΔRy = ΔR sin γi = 14,590 ( 0.707 ) = 10,315 fth = hi + ΔRy = 1700 + 10315 = 12,015 ft

Velocity, Horizontal Range, and Altitude During Coast @ γ = 45 deg to h@( L / D )max

Vcoast = Vi { 1 – [( gc sin γ ) / Vi ] t } / { 1 + {[ gc ρAVG SRef ( CD0 )AVG Vi ] / ( 2 W )} t } = 1384 { 1 –

[( 32.2 ( 0.707 )) / 1384 ] 21 } / { 1 + {[ 32.2 ( 0.001338 ) ( 0.349 ) ( 0.7 ) ( 1384 )] / ( 2 ( 367 ))} 21 } = 674 ft / s

Rcoast = { 2 W / [ gc ρAVG SRef ( CD0 )AVG )]} ln { 1 – [ gc

2 ρAVG SRef ( CD0 )AVG / ( 2 W )] [ sin γ ] t2 +

{[ gc ρAVG SRef ( CD0 )AVG Vi ] / ( 2 W )} t } = { 2 ( 367 ) / [ 32.2 ( 0.001338 ) ( 0.349 ) ( 0.7 )] ln

{ 1 – [ (32.2)2 ( 0.001338 ) ( 0.349 ) ( 0.7 ) / (( 2 ( 367 ))] [ 0.707 ] ( 21 )2 + {[ 32.2 ( 0.001338 ) ( 0.349 ) ( 0.7 ) ( 1384 )] / ( 2 ( 367 ))} 21 } = 17148 ft

( Rx )coast = ( Ry )coast = Rcoast sinγ = 17148 ( 0.707 ) = 12124 ft

2/24/2008 ELF 320

Lofted Glide Trajectory Provides Extended Range( cont )

Lofted Glide Trajectory Provides Extended Range( cont )

Flight Conditions At End-of-Coast Are:t = 35 sV = 674 ft / sh = 24,189 ftq = 251 psfM = 0.66( L / D )max = 5.22α( L / D )max = 5.5 deg

Initiate α = α( L / D )max = 5.5 deg at h = 24,189 ftIncremental Horizontal Range During ( L / D )max Glide Is

ΔRx = ( L / D ) Δh = 5.22 ( 24189 ) = 126,267 ftTotal Horizontal Range for Elevated Launch-Coast-Glide Trajectory Is

Rx = ΣΔRx = ΔRx,Boost + ΔRx,Sustain + ΔRx,Coast + ΔRx,Glide = 1700 + 10315 + 12124 + 126267 = 150406 ft = 24.8 nm

2/24/2008 ELF 321



0

10

20

30

0 10 20 30R, Range, nm

h, A

ltitu

de, k

ft

Susta

in

Ballis

tic

Ballistic

Glide @ ( L / D )max

Co-altitude

Note: Rocket Baseline

End of boost

End of sustain

Lofted ballistic apogee, t = 35 s, V = 667 ft / s, h = 21,590 ft

Lofted coast apogee, t = 35 s, V = 674 ft / s, h = 24,189 ft

Lofted ballistic impact, t = 68 s, γ = - 71 deg, V = 1368 ft / s

Lofted glide impact, t = 298 s, γ = - 10.8 deg, V = 459 ft / s

Co-altitude flight impact, t = 115 s, V = 500 ft / sCoas

t @ γ

= 45 d

eg

2/24/2008 ELF 322







Range robustness


Velocity control



2/24/2008 ELF 323

Ramjet Baseline Is a Chin Inlet Integral Rocket Ramjet ( IRR )

Ramjet Baseline Is a Chin Inlet Integral Rocket Ramjet ( IRR )

Source: Bithell, R.A. and Stoner, R.C. “Rapid Approach for Missile Synthesis”, Vol. II, Air-breathing Synthesis Handbook, AFWAL TR 81-3022, Vol. II, March 1982.

Sta 0.

Guidance WarheadRamjet Fuel Boost Propellant

Booster, and Ramjet Engine

Boost Nozzle

Tail ConeAft-bodyMid-bodyPayload BayForebody23.5 43.5 76.5 126.0

159.0 171.0

Sta 150.311.6

11.5

16.5

37°

Note: Dimensions are in inches

ChinInlet Transport Air Duct

20.375 dia

Nose

2/24/2008 ELF 324

Component Weight, lb CG Sta, inNose 15.9 15.7Forebody Structure 42.4 33.5

Guidance 129.0 33.5Payload Bay Structure 64.5 60.0

Warhead 510.0 60.0Midbody Structure 95.2 101.2

Inlet 103.0 80.0Electrical 30.0 112.0Hydraulic System for Control Actuation 20.0 121.0Fuel Distribution 5.0 121.0

Aftbody Structure 44.5 142.5Engine 33.5 142.5

Tailcone Structure 31.6 165.0Ramjet Nozzle 31.0 165.0Flight Control Actuators 37.0 164.0

Fins ( 4 ) 70.0 157.2End of Cruise 1,262.6 81.8Ramjet Fuel ( 11900 in3 ) 476.0 87.0Start of Cruise 1,738.6 83.2

Boost Nozzle ( Ejected ) 31.0 164.0Frangible Port 11.5 126.0

End of Boost 1,781.1 84.9Boost Propellant 449.0 142.5Booster Ignition 2,230.1 96.5

Mass Properties of Ramjet Baseline MissileMass Properties of Ramjet Baseline Missile

2/24/2008 ELF 325

Ramjet Baseline Missile DefinitionRamjet Baseline Missile Definition

InletType Mixed compressionMaterial TitaniumConical forebody half angle, deg 17.7Ramp wedge angle, deg 8.36Cowl angle, deg 8.24Internal contraction ratio 12.2 PercentCapture area, ft2 0.79Throat area, ft2 0.29

BodyDome Material Silicon nitrideAirframe Material TitaniumCombustor Material Insulated InconelLength, in 171.0Diameter, in 20.375Fineness ratio 8.39Volume, ft3 28.33Wetted area, ft2 68.81Base area, ft2 ( cruise ) 0.58Boattail fineness ratio N/ANose half angle, deg 17.7Nose length, in 23.5

2/24/2008 ELF 326

Ramjet Baseline Missile Definition ( cont )Ramjet Baseline Missile Definition ( cont )

Tail ( Exposed )Material TitaniumPlanform area ( 2 panels ), ft2 2.24Wetted area ( 4 panels ), ft2 8.96Aspect ratio ( 2 panels exposed ) 1.64Taper ratio 0.70Root chord, in 16.5Span, in. ( 2 panels exposed ) 23.0Leading edge sweep, deg 37.0Mean aerodynamic chord, in 14.2Thickness ratio 0.04Section type Modified double wedgeSection leading edge total angle, deg 9.1xmac, in 150.3ymac, in ( from root chord ) 5.4

Reference valuesReference area, ft2 2.264Reference length, ft 1.698

2/24/2008 ELF 327

0 1 2 3 4 5 6Subscripts0 Free stream flow into inlet ( Example, Ramjet Baseline at Mach 4, α = 0 deg ⇒ A0 = 104 in2. Note: AC = 114 in2 )1 Inlet throat ( Ramjet Baseline A1 = AIT = 41.9 in2 )2 Diffuser exit ( Ramjet Baseline A2 = 77.3 in2 )3 Flame holder plane ( Ramjet Baseline A3 = 287.1 in2 )4 Combustor exit ( Ramjet Baseline A4 = 287.1 in2 )5 Nozzle throat ( Ramjet Baseline A5 = 103.1 in2 )6 Nozzle exit ( Ramjet Baseline A6 = 233.6 in2 )Ref Reference Area ( Ramjet Baseline Body Cross-sectional Area, SRef = 326 in2 )

Ac = Inlet capture areaSRef = Reference area

Engine Nomenclature and Flowpath Geometry for Ramjet Baseline

Engine Nomenclature and Flowpath Geometry for Ramjet Baseline

Ramjet Engine Station Identification

( CD0 )Nose Corrected = ( CD0

)Nose Uncorrected x ( 1 - Ac / SREF )

120°

Ac = 114 in2

20.375 in

SRef

2/24/2008 ELF 328

Norm

al Fo

rce C

oeffi

cient

, CN


Mach 1.21.52.03.04.0

.40

.30

.20

.10

0

Axial

For

ce C

oeffi

cient

, CA

0 4 8 12 16

Mach 1.2

1.5

2.0

3.04.0

SRef = 2.264 ft2

lRef = dRef = 1.698 ftXcg @ Sta 82.5 inδ = 0 deg

4.0

3.0

2.0

1.0

0

α, Angle of Attack ~ deg

Aerodynamic Characteristics of Ramjet BaselineAerodynamic Characteristics of Ramjet Baseline

Source: Reference 27, based on year 1974 computer program from Reference 32.

2/24/2008 ELF 329

+ .4

0

-.4

-.8

-1.2

-1.6

Aerodynamic Characteristics of Ramjet Baseline ( cont )


Pitc

hing

Mom

ent C

oeffi

cient

, Cm


Mach 4.0

3.0

2.0

1.5

1.2

SRef = 2.264 ft2

lRef = dRef = 1.698 ftXcg @ Sta 82.5 inδ = 0 deg


2/24/2008 ELF 330



.4

.3

.2

.1

0C D

0M, Mach Number

0 1 2 3 4

CN δ

~ per

deg

0 1 2 3 4

Cm δ

~ per

deg

.10

.05

0

SRef = 2.264 ft2

lRef = dRef = 1.698 ftXcg @ Sta 82.5 inδ= 0 degα = 0 deg.

M, Mach Number

-.4

0

-.2


2/24/2008 ELF 331

100

1000

10000

100000

0 1 2 3 4

M, Mach Number

Tmax

, Max

Thr

ust,

lb

h = Sea Levelh = 20k fth = 40k fth = 60k fth = 80k ft

Thrust Modeling of Ramjet BaselineThrust Modeling of Ramjet Baseline

Note:Standard atmosphereT = Tmax ϕ

φ = 1 if stochiometric ( f / a = 0.0667 )α = 0 deg

Example: M = 3.5, h = 60k ft, ϕ= 1 ⇒ Max Thrust = 1,750 lb

Figure based on Reference 27 prediction

2/24/2008 ELF 332

Specific Impulse Modeling of Ramjet BaselineSpecific Impulse Modeling of Ramjet Baseline

•

•

•

•

•

••

••

•

M, Mach Number

I SP,

Spe

cific

Impu

lse,

s1,500

1,000

500

00 1 2 3 4

Note:Standard atmosphereϕ ≤ 1ISP based on Reference 27 computer prediction.

Example: M = 3.5 ⇒ ISP = 1,120 s

2/24/2008 ELF 333

Rocket Booster Acceleration / Performance of Ramjet Baseline

Rocket Booster Acceleration / Performance of Ramjet Baseline

30

20

10

00 1.0 2.0 3.0 4.0

Boos

t Thr

ust ~

1000

lb

Time ~ s 5.0 6.0

( ISP )Booster = 250 s

3.0

2.5

2.0Burn

out M

ach

Num

ber

h, Altitude 1,000 ft

2.0

1.0

0

Standard atmosphereML = 0.80Constant altitude flyout

Boos

t Ran

ge ~

nm

0 20 40 600 20 40 60 80h, Altitude 1,000 ft

2/24/2008 ELF 334

Ramjet Baseline Has Best Performance at High Altitude

Ramjet Baseline Has Best Performance at High Altitude

500

400

300

200

100

00 1 2 3 4

Rang

e ~ n

m

M, Mach Number

h = SL

20,000 ft

40,000 ft

60,000 ft

Example, Mach 3 / 60k ft flyout ⇒ 445 nm. Breguet Range Prediction is R = V ISP ( L / D ) ln [ WBC / ( WBC - Wf )] = 2901 ( 1040 ) ( 3.15 ) ln ( 1739 / ( 1739 - 476 )) = 3,039,469 ft or 500 nm. Predicted range is 10% greater than baseline missile data.

Note: ML = 0.8, Constant Altitude Fly-out

2/24/2008 ELF 335

From Paredo Sensitivity, Ramjet Baseline Range Driven by ISP, Fuel Weight, Thrust, and CD0

From Paredo Sensitivity, Ramjet Baseline Range Driven by ISP, Fuel Weight, Thrust, and CD0

-1

-0.5

0

0.5

1

1.5

ISP FuelWeight

Thrust CD0, Zero-Lift Drag

Coefficient

CLA, Lift-Curve-Slope

Coefficient

InertWeight

Parameter

Nond

imen

siona

l Ran

ge S

ensit

ivity

to

Par

amet

er

Sea Level Flyout at Mach 2.3 20k ft Flyout at Mach 2.540k ft Flyout at Mach 2.8 60k ft Flyout at Mach 3.0

Example: At Mach 3.0 / 60k ft altitude cruise, 10% increase in fuel weight ⇒ 9.6% increase in flight range

2/24/2008 ELF 336

Ramjet Baseline Flight Range Uncertainty Is +/- 7%, 1 σRamjet Baseline Flight Range Uncertainty Is +/- 7%, 1 σParameter Baseline Value at Mach 3.0 / 60k ft

Uncertainty in Parameter ΔR / R from Uncertainty

1. Specific Impulse 1040 s +/- 5%, 1σ +/- 5%, 1σ

2. Ramjet Fuel Weight 476 lb +/- 1%, 1σ +/- 0.9%, 1σ

3. Cruise Thrust ( φ = 0.39 ) 458 lb +/- 5%, 1σ +/- 2%, 1σ

4. Zero-Lift Drag Coefficient 0.17 +/- 5%, 1σ +/- 4%, 1σ

5. Lift Curve Slope Coefficient 0.13 / deg +/- 3%, 1σ +/- 1%, 1σ

6. inert Weight 1205 lb +/- 2%, 1σ +/- 0.8%, 1σ

Level of Maturity Based on Flight Demo of Prototype, Subsystem Tests, and IntegrationWind tunnel testsDirect connect, freejet, and booster firing propulsion testsStructure testMock-upHardware-in-loop simulationFlight Test

Total Flight Range Uncertainty at Mach 3.0 / 60k ft FlyoutΔR / R = [ (ΔR / R )1

2 + (ΔR / R )22 + (ΔR / R )3

2 + (ΔR / R )42 + (ΔR / R )5

2 + (ΔR / R )62 ]1/2 = +/- 6.9%, 1σ

R = 445 nm +/- 31 nm, 1σ

2/24/2008 ELF 337








Range robustness


Velocity control



2/24/2008 ELF 338

Slurry Fuel and Efficient Packaging Provide Extended Range Ramjet

Slurry Fuel and Efficient Packaging Provide Extended Range Ramjet

Propulsion / Configuration

Fuel Type / Volumetric Performance (BTU / in3) / Density (lb / in3)

Fuel Volume (in3) / Fuel Weight (lb)

ISP (s) / Cruise Range at Mach 3.5, 60k ft (nm)

Liquid Fuel Ramjet

RJ-5 / 581 / 0.040 11900 / 476 1120 / 390

Ducted Rocket ( Low Smoke )

Solid Hydrocarbon / 1132 / 0.075

7922 / 594 677 / 294

Ducted Rocket ( High Performance )

Boron / 2040 / 0.082 7922 / 649 769 / 366

Solid Fuel Ramjet

Boron / 2040 / 0.082 7056 / 579 1170 / 496

Slurry Fuel Ramjet 40% JP-10, 60% boron carbide / 1191 / 0.050

11900 / 595 1835 / 770

Note: Flow Path Available Fuel Rcruise = V ISP ( L / D ) ln [ WBC / ( WBC - Wf )]

2/24/2008 ELF 339








Range robustness


Velocity control


Soda Straw Rocket, Design, Build, and Fly

2/24/2008 ELF 340

Example of Ramjet Velocity Control Through Fuel Control

Example of Ramjet Velocity Control Through Fuel Control

0.1

1

10

0 1 2 3 4Mi, Impact Mach Number at Sea Level

Ramjet BaselineEquivalence RatioRamjet Baseline FuelFlow Rate, lb / s

T

W

D

Note: Ramjet baseline, vertical impact at sea level, steady state velocity at impact, T = thrust, W = weight, D = drag, WBO = burnout weight, CD0

= zero-lift drag coefficient, Mi= impact Mach number, Trequired = required thrust for steady state flight, wf

. = fuel flow rate, ISP = specific impulse, φ = equivalence ratio ( φ = 1 stochiometric )

Example for Ramjet Baseline:Mi = 4, h = sea level, T0 = 519RT + W - D = 0W = WBO = 1263 lbD = CD0

q SRef = 3353 CD0MI

2 = 3353 ( 0.14 ) ( 4 )2 = 7511 lb

Trequired = D - W = 7511 - 1263 = 6248 lbwf

. = T / ISP = 6248 / 1000 = 6.25 lb / sφ = Trequired / Tφ = 1 = 6248 / 25000 = 0.25Note: Excess air provides cooling of combustor

2/24/2008 ELF 341







Range robustness


Surface impact velocity



2/24/2008 ELF 342

Computer Sizing Code Should Have Fast Turnaround and Be Easy to Use

Computer Sizing Code Should Have Fast Turnaround and Be Easy to Use

Objective of Conceptual DesignSearch Broad Solution SpaceIterate to Design Convergence

Characteristics of Good Conceptual Design Sizing CodeFast Turnaround TimeEasy to UseDirectly Connect Predictions of Aeromechanics and Physical Parameters to Trajectory CodeSimple, Physics Based MethodsIncludes Most Important, Driving ParametersProvides Insight into Relationships of Design ParametersStable ComputationImbedded Baseline Missile DataHuman Designer Makes the Creative Decisions

2/24/2008 ELF 343

Example of DOS-Based Conceptual Sizing Computer Code – ADAM

Example of DOS-Based Conceptual Sizing Computer Code – ADAM

Conceptual Sizing Computer ProgramAdvanced Design of Aerodynamic Missiles ( ADAM )PC compatibleWritten in DOS

Aerodynamic Module Based on NACA 1307 CalculatesStatic and dynamic stability derivativesControl effectiveness and trim conditions

3, 4, 5, and 6-DOF Simulation ModulesProportional guidanceInput provided automatically by aerodynamic module

Configurations Benchmarked with Wind Tunnel DataGreater than 50 Input Parameters Available

Defaults to benchmark configuration ( s )

2/24/2008 ELF 344

Example of Spreadsheet Based Conceptual Sizing Computer Code - TMD Spreadsheet

Example of Spreadsheet Based Conceptual Sizing Computer Code - TMD Spreadsheet

Conceptual Sizing Computer CodeTactical Missile Design ( TMD ) SpreadsheetPC compatibleWindows Excel spreadsheet

Based on Tactical Missile Design Short Course and TextbookAerodynamicsPropulsionWeightFlight trajectoryMeasures of merit

2/24/2008 ELF 345

Example of Spreadsheet Based Conceptual Sizing Computer Code, TMD Spreadsheet

Example of Spreadsheet Based Conceptual Sizing Computer Code, TMD Spreadsheet

Define Mission Requirements [ Flight Performance ( RMax, RMin, VAVG ) , MOM, Constraints ]

Establish Baseline ( Rocket , Ramjet )

Aerodynamics Input ( d, l, lN, A, c, t, xcg ) Aerodynamics Output [ CD0

, CN, xac, Cmδ, L / D, ST ]

Propulsion Input ( pc, ε, c*, Ab, At, A0, Hf, ϕ, T4, Inlet Type ) Propulsion Output [ Isp, Tcruise, pt2

/ pt0, w., Tboost, Tsustain, ΔVBoost ]

Weight Input ( WL, WP, ρ, σmax )Weight Output [ WL, WP, h, dT / dt, T, t, σbuckling, MB, σ, Wsubsystems, xcg, Iy ]

Trajectory Input ( hi, Vi, Type ( cruise, boost, coast, ballistic, turn, glide )Trajectory Output ( R, h, V, and γ versus time )

MeetPerformance?


No [ pBlast, PK, nHit, Vfragments, PKE, KEWarhead, τTotal,σHE, σMAN, Rdetect, CSDD, C1000th, Cunit x ]

No [ RMax, RMin, VAVG ]

Yes

Yes

Alt Mission

Alt Baseline


2/24/2008 ELF 346

Example of TMD Spreadsheet Sizing Code Verification: Air-to-Air Range RequirementExample of TMD Spreadsheet Sizing Code Verification: Air-to-Air Range RequirementExample Launch Conditions

hL = 20k ftML = 0.8

Example RequirementRF = 6.7 nm with tf < 24.4 s

Solutions for Rocket BaselineADAM: RF = 6.7 nm at tf = 18 sTMD Spreadsheet: RF = 6.7 nm at tf = 19 s3 DOF using wind tunnel aero data: RF = 6.7 nm at tf = 21 s

Differences in Flight Time to 6.7 nm Mostly Due to Zero-Lift Drag Coefficient. For Example:

ADAM prediction at Mach 2.0: ( CD0 )coast = 0.53

TMD Spreadsheet prediction at Mach 2.0: ( CD0 )coast = 0.57

Wind tunnel aero data at Mach 2.0: ( CD0 )coast = 1.05

Wind Tunnel Data / Baseline Missile Data Correction Required to Reduce Uncertainty in CD0

2/24/2008 ELF 347







Range robustness


Surface impact velocity



2/24/2008 ELF 348

Example of Design, Build, and Fly Customer Requirements

Example of Design, Build, and Fly Customer Requirements

Objective – Design, Build, and Fly Soda Straw Rocket with:Flight Range Greater Than 90 ftWeight Less Than 2 g

Furnished PropertyLaunch SystemDistance Measuring WheelWeight ScaleMicrometer ScaleEngineer’s ScaleScissors

Furnished Material1 “Giant” Soda Straw: 0.28 in Diameter by 7.75 in Length, Weight = 0.6 g1 Strip Tabbing: ½ in by 6 in, Weight = 1.4 g1 Ear Plug: 0.33 – 0.45 in Diameter by 0.90 in Length, Weight = 0.6 g1 “Super Jumbo” Soda Straw: 0.25 in Diameter by 7.75 in Length

2/24/2008 ELF 349

Example of Design, Build, and Fly Customer Requirements ( cont )

Example of Design, Build, and Fly Customer Requirements ( cont )

Furnished Property Launch System with Specified Launch ConditionsLaunch Tube Diameter: 0.25 inLaunch Tube Length ( e.g., 6 in )Launch Pressure ( e.g., 30 psi )Launch Elevation Angle ( e.g., 40 deg )

Predict Flight Trajectory Range and Compare with Test

2/24/2008 ELF 350

Soda Straw Rocket Launcher and TargetingSoda Straw Rocket Launcher and Targeting9. Rocket on Launcher8. Launch Tube7. Inclinometer6b. Manual Valve Launcher ( 0.1 s average response )6a. Solenoid Valve Launcher ( 0.025 s average response )5. Launch Switch4. Pressure Gauge3. Air Hose

2. Pressure Tank

1. Pump11. Rockets with Various Length, Tail Geometry, Nose Geometry, and Other Surfaces10. Laser Pointer Targeting Device

2/24/2008 ELF 351

It Is Easy to Make a Soda Straw RocketIt Is Easy to Make a Soda Straw Rocket

1. Cut Large Diameter “Giant” Soda Straw to Desired Length

3. Slide Ear Plug Inside Soda Straw

5. Apply Adhesive Tabs to Soda Straw

4. Cut Adhesive Tabs to Desired Height and Width of Surfaces

7. Slide Giant Soda Straw Rocket Over Smaller Diameter “Super Jumbo” Soda Straw Launch Tube

2. Twist and Squeeze Ear Plug to Fit Inside Soda Straw

6. Wrap Front of Ear Plug and Straw with Tape

2/24/2008 ELF 352

Soda Straw Rocket Baseline ConfigurationSoda Straw Rocket Baseline Configuration

llcc = 6.0 in= 6.0 in

l = 7.0 inl = 7.0 in

Ear Plug Soda Straw Strip Tabbing

0.28 in0.25 in

0.5 in

2/24/2008 ELF 353

Soda Straw Rocket Baseline Weight and BalanceSoda Straw Rocket Baseline Weight and Balance

Component Weight, g cg Station, inNose ( Plug ) 0.6 0.5Body ( Soda Straw ) 0.5 3.5Fins ( Four ) 0.5 6.75 Total 1.6 3.39

2/24/2008 ELF 354

Soda Straw Rocket Baseline DefinitionSoda Straw Rocket Baseline DefinitionBody

Material Type HDPE PlasticMaterial density, lb / in3 0.043Material strength, psi 4,600Thickness, in 0.004Length, in 7.0Diameter, in 0.28Fineness ratio 25.0Nose fineness ratio 0.5

FinsMaterial PlasticPlanform area, in2 ( 2 panels exposed ) 0.25Wetted area, in2 ( 4 panels ) 1.00Aspect ratio ( 2 panels exposed ) 1.00Taper ratio 1.0Chord, in 0.5Span ( exposed ), in 0.5Span ( total including body ), in 0.78Leading edge sweep, deg 0xmac, in 6.625

2/24/2008 ELF 355

Soda Straw Rocket Baseline Definition ( cont )Soda Straw Rocket Baseline Definition ( cont )

NoseMaterial Type FoamMaterial density, lb / in3 0.012Average diameter 0.39 inLength 0.90 in

Reference ValuesReference area, in2 0.0616Reference length, in 0.28

Thrust PerformanceInside cavity length, in 6.0Typical Pressure, psi 30Maximum thrust @ 30 psi pressure, lb 1.47Time constant, s ( standard temperature ) 0.025

2/24/2008 ELF 356

For body-tail geometry, static margin given by( xAC – xCG ) / d = - {( CN α )B {[ xCG – ( xAC )B ] / d } + ( CNα )T {[ xCG – ( xAC )T ] / d }( ST /

SRef )} / [( CNα )B + ( CNα )T ST / SRef ]For baseline soda straw configuration

xCG = 3.39 in, d = 0.28 in, ( CNα )B = 2 per rad, ST = 0.25 in2, SRef = 0.0616 in2

( xAC )B = [( xAC )B / lN ] lN = 0.63 ( 0.14 ) = 0.09 in( CNα )T = π AT / 2 = π ( 1 ) / 2 = 1.57( xAC )T = 6.5 + 0.25 ( cmac )T = 6.63

Substituting( xAC - xCG ) / d = - { 2 ( 3.39 – 0.09 ) / 0.28 + [ 1.57 ( 3.39 – 6.63 ) / 0.28 ] [( 0.25 ) /

0.0616 ]} / [ 2 + 1.57 ( 0.25 ) / 0.0616 ] = 6.00 ( statically stable )xAC = 6.00 ( 0.28 ) + 3.39 = 5.07 in from nose

Soda Straw Rocket Baseline Static MarginSoda Straw Rocket Baseline Static Margin

( ( xxAC )Tl

( xAC )B

xxACAC

xxCGCGd

2/24/2008 ELF 357

Soda Straw Rocket Has High Acceleration Boost Performance

Soda Straw Rocket Has High Acceleration Boost Performance

0

20

40

60

80

100

0 2 4 6 8 10s, Distance Traveled During Launch, Inches

V, V

elocit

y, fp

s

pgauge = 15 psi pgauge = 30 psipgauge = 60 psi

T = ( p – p0 ) A = pgauge ( 1 – e – t / τ ) Aa ≈ 32.2 T / W, V = ∫ a dt, s = ∫ V dt Thrust ( T ) from Pressurized Tube of Area A

T = ( p – p0 ) A = pgauge ( 1 – e – t / τ ) AA = ( π / 4 ) ( 0.25 )2 = 0.0491 in2, τ = Valve Rise Time Example:Assume pgauge = 30 psi, lt = 6 in, τ = 0.025 s ( Average

for Solenoid Valve ), s = lc = 6 inThrust Equation Is:T = 30 ( 1 - e – t / 0.025 ) ( 0.0491 ) = 1.4726 ( 1 - e – 40.00 t )Note: Actual Boost Thrust Lower ( Pressure Loss,

Boundary Layer, Launch Tube Leakage, Launch Tube Friction )

Equations for Acceleration ( a ), Velocity ( V ), and Distance ( s ) During Boost Are:

a ≈ 32.2 T / W = 32.2 ( 1.4726 ) ( 1 - e – 40.00 t ) / 0.00352 = 13471.1 ( 1 - e – 40.00 t )

V = ∫ a dt = 13471.1 t + 336.78 e – 40.00 t – 336.78s = ∫ V dt = 6735.57 t2 – 8.419 e – 40.00 t – 336.78 t +

8.419End of Boost Conditions Are:s = lc = 6 in = 0.500 ft ⇒ t = 0.0188 sa = 7123 ft / s2 = 221 gV = 75.2 ft / sq = ½ ρ V2 = ½ ( 0.002378 ) ( 75.2 )2 = 6.72 psfM = V / c = 75.2 / 1116 = 0.0674

Note: Time Tics Every 0.01 s

2/24/2008 ELF 358

Most of the Soda Straw Rocket Drag Coefficient Is from Body Skin Friction

Most of the Soda Straw Rocket Drag Coefficient Is from Body Skin Friction

0

0.5

1

1.5

0 2 4 6 8 10

ST / SRef, Tail Planform Area / Reference Area

CD0,

Zero

-Lift

Dra

g Co

effic

ient

V = 40 fps V = 80 fps

Example: V = 75.2 fps, ST = 0.00174 ft2, SRef = 0.000428 ft2 ⇒ ST / SRef = 4.07

Compute:CD0 = 0.053 ( 25.0 ){ 0.0674 / [( 6.72 ) ( 0. 583 )]}0.2 +

0.12 + 2 { 0.0133 { 0.0674 / [( 6.72 ) ( 0.0417 )]}0.2 }[ 2 ( 4.07 )] = 0.58 + 0.12 + 0.16 = 0.86

Note:• Above Drag Coefficient Not Exact• Based on Assumption of Turbulent Boundary

Layer• Soda Straw Rocket Small Size and Low Velocity ⇒

Laminar Boundary Layer ⇒ Large Boundary Layer Thickness on Aft Body at Tails

Compute Drag Force:Dmax = CD qmax SRef = 0.86 ( 6.72 ) ( 0.000428 ) =

0.00247 lbCompare Drag Force to Weight:Dmax / W = 0.00247 / 0.00352 = 0.70Note: Drag Force Smaller Than Weight

CD0 = ( CD0 )Body,Friction + ( CD0 )Base,Coast + ( CD0 )Tail,Friction= 0.053 ( l / d ) [ M / ( q l )]0.2 + 0.12 + nT { 0.0133 [ M / ( q cmac )]0.2 } ( 2 ST / SRef )

2/24/2008 ELF 359

0

10

20

30

40

0 20 40 60 80 100

Rx, Horizontal Range, ft

h - h

i, He

ight

abov

e Ini

tial L

aunc

hHe

ight

, ft

Gamma = 10 Deg Gamma = 30 Deg Gamma = 50 Deg

Soda Straw Rocket Baseline Has a Ballistic Flight Range Greater Than 90 Feet

Soda Straw Rocket Baseline Has a Ballistic Flight Range Greater Than 90 Feet

Rx = { 2 W cos γi / [ gc ρ SRef CD0]} ln { 1 + t / { 2

W / [ gc ρ SRef CD0Vi ]}}

h = { 2 W sin γi / [ gc ρ SRef CD0]} ln { 1 + t / { 2

W / [ gc ρ SRef CD0 Vi ]}} + hi - gc t2 / 2

Note: Time Tics every 0.5 s

Example, Assume lt = 6 in, pgauge = 30 psi, γi= 30 deg, τ = 0.025 sec, Soda Straw Baseline, t = timpact = 1.8 s

Horizontal Range At Impact = Rx = { 2 ( 0.00352 ) cos γi / [ 32.2 ( 0.002378 ) ( 0.000428 ) ( 0.86 )]} ln { 1 + t / { 2 ( 0.00352 ) / [ 32.2 ( 0.002378 ) ( 0.000428 ) ( 0.86 ) ( 75.2 )]}}

= 249.8 cos γi ln ( 1 + 0.301 t )= 249.8 ( 0.866 ) ln [ 1 + 0.301 ( 1.8 )] = 93.7 ft

Height At Impact = h = { 2 ( 0.00352 ) sin γi / [ 32.2 ( 0.002378 ) ( 0.000428 ) ( 0.86 )} ln { 1 + t / { 2 ( 0.00352 ) / [ 32.2 ( 0.002378 ) ( 0.000428 ) ( 0.86 ) ( 75.2 )]}} + hi – 32.2 t2 / 2

= 249.8 sin γi ln ( 1 + 0.301 t ) + hi –32.2 t2 / 2 = 249.8 ( 0.5 ) ln [ 1 + 0.301 ( 1.8 )] + hi – 32.2 ( 1.2 )2 / 2

= hi + 1.9 ft

2/24/2008 ELF 360

Soda Straw Rocket Range Driven by Inside Chamber Length and Launch Angle

Soda Straw Rocket Range Driven by Inside Chamber Length and Launch Angle

-0.2

0

0.2

0.4

0.6

0.8

lc Gamma pgauge W tau CD0

Nondimensional Range

Sensitivity to Parameter

Note: Decreased chamber length ⇒shorter duration thrust ( decreased total impulse ) ⇒ decreased end-of-boost velocitySoda Straw Rocket Baseline:

W = Weight = 0.00423 lblc = inside chamber length = 6 inτ = Time constant to open solenoid valve = 0.025 spgauge = gauge pressure = 30 psiγi = Initial / launch angle angle = 30 deglt = 7 inV = Launch velocity = 75.2 fpsCD0 = Zero-lift drag coefficient = 0.86timpact = Time from launch to impact = 1.8 sRx = Horizontal range = 94 ft

Example: 10% decrease in inside chamber length ⇒7.7% decrease in range at t = 1.8 s. Note: Result is nonlinear because inside chamber length = launcher length. Increase in lc also leads to decrease in range.

2/24/2008 ELF 361

Soda Straw Rocket Baseline Flight Range Uncertainty Is +/- 2.4%, 1 σ

Soda Straw Rocket Baseline Flight Range Uncertainty Is +/- 2.4%, 1 σ

Estimate of Level of Maturity / Uncertainty of Soda Straw Rocket Baseline Parameters Based onWind tunnel testThrust static testWeight measurementPrediction methods

Total Flight Range Uncertainty for 30 psi launch at 30 degΔR / R = [ (ΔR / R )1

2 + (ΔR / R )22 + (ΔR / R )3

2 + (ΔR / R )42 + (ΔR / R )5

2 + (ΔR / R )62 ]1/2 = +/- 2.4%, 1σ

R = 94 ft +/- 2.3 ft, 1σ

+/- 0.2%, 1σ+/- 20%, 1σ0.866. Zero-Lift Drag Coefficient

+/- 0.2%, 1σ+/- 20%, 1σ0.025 s5. Solenoid Time Constant+/- 0.4%, 1σ+/- 6%, 1σ1.6 g4. Weight+/- 0.5%, 1σ+/- 3%, 1σ30 psi3. Gauge Pressure+/- 1.7%, 1σ+/- 3%, 1σ30 deg2. Launch Angle

+/- 1.5%, 1σ+/- 2%, 1 σ6 in1. Inside Chamber Length

ΔR / R Due to Uncertainty

Uncertainty in Parameter

Baseline ValueParameter

2/24/2008 ELF 362

1 - Customer Requirements2 – Customer Importance Rating ( Total = 10 )3 – Design Characteristics4 – Design Characteristics Importance Rating ( Total = 10 )5 – Design Characteristics Sensitivity Matrix 6 – Design Characteristics Weighted Importance7 – Design Characteristics Relative Importance

House of Quality Translates Customer Requirements into Engineering Emphasis

House of Quality Translates Customer Requirements into Engineering Emphasis

WeightFlight Range

37

Tail Planform AreaChamber Length

4628

26 = ( 7x2 + 3x4 )74 = ( 7x8 + 3x6 )

21

0

Note on Design Characteristics Sensitivity Matrix: ( Room 5 ):++ Strong Synergy+ Synergy0 Near Neutral Synergy- Anti-Synergy- - Strong Anti-Synergy

Note: Based on House of Quality, inside chamber length most important design parameter.

2/24/2008 ELF 363

DOE Explores the Broad Possible Design Space with a Reasonably Small Set of Alternatives

DOE Explores the Broad Possible Design Space with a Reasonably Small Set of Alternatives

0.1254Lower Value0.256Upper Value

ST, Tail Planform Area, in2

lc, Inside Chamber Length, in

Engineering Characteristics Range

“Petite”“Stiletto”“Shorty”

“Big Kahuna”

Concept Sketch

0.12540.12560.2540.256

ST, Tail Planform Area, in2

lc, Inside Chamber Length, in

Full Factorial DOE Based on Upper / Lower Values of k = 2 Parameters: Number of Combinations = 2k = 22 = 4

Design Space for Design of Experiments ( DOE )

Note: DOE concepts should emphasize customer driving requirements and the driving engineering characteristics.

2/24/2008 ELF 364

Engineering Experience Should Guide the DOE Set of Alternatives and the Preferred Design

Engineering Experience Should Guide the DOE Set of Alternatives and the Preferred Design

As an Example, for the Soda Straw Rocket, from Experience We Know That

Soda Straw Rocket Must Fit on LauncherMaximum Boost Velocity Occurs When Chamber Length = Launch Tube LengthThree or Four Tails Best for StabilityTails That Are Too Small May Result in an Unstable FlightTails That Are Too Large Add Weight and Cause Trajectory DispersalCanards Require Larger Tails for Stability, Add Weight, and Cause Trajectory DispersalWings Add Weight, Add Drag, and Cause Trajectory Dispersal

2/24/2008 ELF 365

Engineering Experience Should Guide the DOE Set of Alternatives and Preferred Design ( cont )Engineering Experience Should Guide the DOE Set of Alternatives and Preferred Design ( cont )

As an Example, Soda Straw Rocket Geometry Should Be Comparable to an Operational Rocket with Near-Neutral Static Stability ( e.g., Hydra70 )

2.661.891.892.792.79

b / d,Total Tail Span /

Diameter

217.9“Petite”Hydra 70

“Stiletto”“Shorty”

“Big Kahuna”

Concept Sketch

115.1

225217.9225

c / d,Tail Chord /

Diameter

l / d,Total Length /

Diameter

Note: For a subsonic rocket with the center-of-gravity in the center of the rocket, slender body theory and slender surface theory give total tail span and chord for neutral stability of bNeutralStability ≈ 2 d and cNeutralStability > ≈ d respectively.

2/24/2008 ELF 366

Optimum Design Should Have Balanced Engineering Characteristics

Optimum Design Should Have Balanced Engineering Characteristics

As an Example, for the Soda Straw Rocket Design We Should

Reflect Customer Emphasis of Requirements forRangeWeight

Provide Balanced Emphasis of Most Important Engineering Characteristics

Chamber LengthTail Size / Span

2/24/2008 ELF 367

Summary of Sizing ExamplesSummary of Sizing Examples

Rocket Powered Missile ( Sparrow Derived Baseline )Standoff range requirementWing area sizing requirements for maneuverability, turn rate, and turn radiusMulti-parameter harmonizationBallistic versus lofted glide flight range

Ramjet Powered Missile ( ASALM Derived Baseline )Robustness in range uncertaintyPropulsion and fuel alternativesSurface target impact velocity

Computer Aided Sizing Tools for Conceptual DesignADAM

Analytical prediction of aerodynamicsNumerical solution of equations of motion

2/24/2008 ELF 368

Summary of Sizing Examples ( cont )Summary of Sizing Examples ( cont )

Computer Aided Sizing Tools for Conceptual Design ( cont )TMD analytical sizing spreadsheet ( based on this text )

Analytical prediction of aero, propulsion, and weightClosed form analytical solution of simplified equations of motion

Soda Straw Rocket Design, Build, and FlyStatic marginDragPerformanceSensitivity studyHouse of QualityDesign of Experiment ( DOE )


2/24/2008 ELF 369

Sizing Examples ProblemsSizing Examples Problems1. Required flight range is shorter for a head-on intercept and it is longer

for a t___ c____ intercept.2. The rocket baseline center-of-gravity moves f______ with motor burn.3. The rocket baseline is an a_______ airframe.4. The rocket baseline thrust profile is b____ s______.5. The rocket baseline motor case and nozzle are made of s____.6. The rocket baseline flight range is driven by ISP, propellant weight

fraction, drag, and s_____ m_____.7. Contributors to the maneuverability of the rocket baseline are its body,

tail, and w___.8. Although the rocket baseline has sufficient g’s and turn rate to

intercept a maneuvering aircraft, it needs a smaller turn r_____.9. Compared to a co-altitude trajectory, the rocket baseline has extended

range with a l_____ glide trajectory.10. The ramjet baseline has a c___ inlet.11. The Mach 4 ramjet baseline has a t_______ airframe.

2/24/2008 ELF 370

Sizing Examples Problems ( cont )Sizing Examples Problems ( cont )12. Although the ramjet baseline combustor is a nickel-based super alloy, it

requires insulation, due high temperature. The super alloy is i______.13. The flight range of the ramjet baseline is driven by ISP, weight, thrust,

zero-lift coefficient, and the weight fraction of f___.14. Extended range for the ramjet baseline would be provided by more

efficient packaging of subsystems and the use of s_____ fuels.15. A conceptual design sizing code should be based on the simplicity,

speed, and robustness of p______ based methods.16. The House of Quality room for design characteristics weighted

importance indicates which engineering design characteristics are most important in meeting the c_______ r___________.

17. Paredo sensitivity identifies the design parameters that are most i________.

18. DOE concepts should emphasize the customer driving requirements and the driving e__________ characteristics

19. If the total tail span ( including body diameter ) is twice the body diameter, the missile is approximately n________ s_____.

2/24/2008 ELF 371


2/24/2008 ELF 372

Relationship of Technology Assessment / Roadmap to the Development Process

Relationship of Technology Assessment / Roadmap to the Development Process

Technology Roadmap Establishes Time-phased Interrelationships for

Technology development and validation tasksTechnology optionsTechnology goalsTechnology transition ( ATD, ACTD, DemVal, PDRR, SDD )

Technology Roadmap IdentifiesKey, enabling, high payoff technologiesTechnology driversKey decision pointsCritical pathsFacility requirementsResource needs

2/24/2008 ELF 373

Research Technology Acquisition

Relationship of Design Maturity to the US Research, Technology, and Acquisition Process

Relationship of Design Maturity to the US Research, Technology, and Acquisition Process

BasicResearch

ExploratoryDevelopment

AdvancedDevelopment

Demonstration & Validation

System Development

and Demonstration

Production

~ $0.1B ~ $0.9B~ $0.3B ~ $0.5B ~ $1.0B ~ $6.1B ~ $1.2B

6.1 6.2 6.3 6.4 6.5

SystemUpgrades

TechnologyDevelopment

~ 10 Years

TechnologyDemonstration

~ 8 Years

PrototypeDemonstration

~ 4 Years

Full ScaleDevelopment

~ 5 Years

Limited~ 2 Years

1-3 BlockUpgrades

~ 5-15 Years

First Block

~ 5 Years

ProductionNote:Total US DoD Research and Technology for Tactical Missiles ≈ $1.8 Billion per yearTotal US DoD Acquisition ( SDD + Production + Upgrades ) for Tactical Missiles ≈ $8.3 Billion per yearTactical Missiles ≈ 11% of U.S. DoD RT&A budgetUS Industry IR&D typically similar to US DoD 6.2 and 6.3A

Maturity Level Conceptual Design Preliminary Design Detail Design Production DesignDrawings ( type ) < 10 ( subsystems ) < 100 ( components ) > 100 ( parts ) > 1000 ( parts )

2/24/2008 ELF 374

Technology Readiness Level ( TRL ) Indicates the Maturity of Technology

Technology Readiness Level ( TRL ) Indicates the Maturity of Technology

TRL 1- 3Category 6.1

Basic research

TRL 4Category 6.2A

Exploratory development of a component, conceptual design studies, and prediction methods

TRL 5Category 6.2B

Exploratory development of a subsystem

TRL 6Category 6.3

Advanced tech demo of a subsystem

TRL 7Category 6.4

Prototype demonstration

Initial assessment ⇒⇒ component test ⇒⇒ subsystem test ⇒⇒ integrated subsystems ⇒⇒ integrated missile

2/24/2008 ELF 375

Conceptual Design Has Broad Alternatives While Detail Design Has High Definition

Conceptual Design Has Broad Alternatives While Detail Design Has High Definition

1

10

100

1000

0 5 10 15Time ( Years )

Typi

cal N

umbe

r of A

ltern

ative

Con

cept

s or

Num

ber o

f Des

ign

Draw

ings

Number of ConceptsNumber of Drawings

Conceptual Prelim. Detail ProductionDesign Design Design Design

2/24/2008 ELF 376

US Tactical Missile Follow-On Programs Occur about Every 24 Years

US Tactical Missile Follow-On Programs Occur about Every 24 Years

Year Entering SDD

AIM-9X ( maneuverability ), 1996 - Hughes

AIM-120 ( autonomous, speed, range, weight ), 1981 - Hughes

Long Range ATS, AGM-86, 1973 - Boeing AGM-129 ( RCS ), 1983 - General Dynamics

PAC-3 (accuracy), 1992 - Lockheed MartinLong Range STA, MIM-104, 1966 - Raytheon

1950 1965 1970 1975 1980 1985 1990 1995 > 2000

AGM-88 ( speed, range ), 1983 - TI

Man-portable STS, M-47, 1970 - McDonnell Douglas

Anti-radar ATS, AGM-45, 1961 - TI

Short Range ATA, AIM-9, 1949 - Raytheon

Javelin ( gunner survivability, lethality, weight ), 1989 - TI

Medium Range ATA, AIM-7,1951 - Raytheon

Medium Range ATS, AGM-130, 1983 - Rockwell JASSM ( cost, range, observables ), 1999 - LM

Hypersonic Missile, > 2007

Hypersonic Missile > 2007

Long Range STS, BGM-109, 1972 - General Dynamics Hypersonic Missile > 2007

2/24/2008 ELF 377

Missile Design Validation / Technology Development Is an Integrated ProcessMissile Design Validation / Technology Development Is an Integrated Process

•Rocket Static•Turbojet Static•Ramjet Tests-Direct Connect-Freejet

StructureTest

HardwareIn-Loop

Simulation

Ballistic Tests

Lab Tests

Seeker

Actuators / Initiators

Sensors

Propulsion Model

Aero Model

Model Digital Simulation

Wind TunnelTests

Propulsion

Airframe

Guidanceand Control

Power Supply

Warhead

EnvironmentTests•Vibration•Temperature

Sled Tests

IM Tests

IM Tests

Flight Test Progression ( Captive Carry,Jettison, Separation, Unpowered Guided Flights, Powered Guided Flights, Live Warhead Flights )Lab Tests

TowerTests

Autopilot / Electronics

Witness / Arena Tests

2/24/2008 ELF 378

Airframe Wind Tunnel Test ………………………………………………………

Propulsion Static Firing with TVC ……..

Propulsion Direct Connect Test …………………………………….

Propulsion Freejet Test …………

Examples of Missile Development Tests and Facilities

Examples of Missile Development Tests and Facilities

2/24/2008 ELF 379

Examples of Missile Development Tests and Facilities ( cont )


Warhead Arena Test ……………………………………………………….

Warhead Sled Test ………………………

Insensitive Munition Test ……………………………………………..

Structure Test …………………………………………..

2/24/2008 ELF 380



Seeker Test ……………………………………………………….

Hardware-In-Loop ………

Environmental Test ……………………………………………..

Submunition Dispenser Sled Test ……………………

2/24/2008 ELF 381

RCS Test ……………………………………………………………….

Store / Avionics Test

Flight Test ……………………………………………………………………….

Video of Facilities and Tests



2/24/2008 ELF 382

Missile Flight Test Should Cover Extremes of Flight Envelope

Missile Flight Test Should Cover Extremes of Flight Envelope

Flight 7

Flight 7

Flight 3

Flight 7

Flight 1

Flight 3

Flight 7

Flight 3

Flight 7

High Dynamic Pressure

High Aero Heating

High L / D Cruise

Low Dynamic Pressure

Boos

ter

Tran

sitio

n:

Thru

st -

Drag

Note: Seven Flights from Oct 1979 to May 1980.Flight 1 failure of fuel control. As a result of the high thrust, the flight Mach number exceeded the design Mach number.

Example: Ramjet Baseline Propulsion Test Validation ( PTV )

2/24/2008 ELF 383

Example of Aero Technology DevelopmentExample of Aero Technology Development

Conceptual Design ( 5 to 50 input parameters ) PredictionPreliminary Design ( 50 to 200 input parameters ) Prediction

Missile DATCOM. Contact: AFRL. Attributes include: Low costMISL3. Contact: NEAR. Attributes include: Modeling vortex sheddingSUPL. Contact: NEAR. Attributes include: Paneling complex geometryAP02. Contact: NSWC. Attributes include: Periodic updatesCFD. Contact: Georgia Tech. Attributes include: Model runs on Parallel Processing PCs

Preliminary Design OptimizationResponse Surface Model: Contact: Georgia Tech. Attributes include 10x more rapid computationProbabilistic Analysis: Contact: Georgia Tech. Attributes include an evaluation of design robustness

2/24/2008 ELF 384

Example of Aero Technology Development( cont )

Example of Aero Technology Development( cont )

Wind Tunnel Test VerificationBody buildup force and momentControl effectiveness and hinge momentStore carriage and separationFlow field ( may be required )Pressure distribution ( may be required )Plume, heat transfer, and dynamic stability ( usually not required )Inlet ( if applicable )

3 to 6-DOF Digital SimulationHardware-in-loop SimulationDetail Design ( over 200 input parameters )Flight Test Validation

2/24/2008 ELF 385

Example of Missile Technology State-of-the-Art Advancement: Air-to-Air Missile ManeuverabilityExample of Missile Technology State-of-the-Art Advancement: Air-to-Air Missile Maneuverability

0

10

20

30

40

50

60

1950 1960 1970 1980 1990 2000 2010

Year IOC

Oper

atio

nal A

ngle

of A

ttack

, Deg

AIM-7AAM-9BR530AA-8AIM-54R550SkyflashPython 3AA-10AspideSuper 530DAA-11AIM-120Python 4AA-12MICAAIM-132AIM-9X

Controls Augmentedwith Propulsion Devices ( TVC, Reaction Jet )

2/24/2008 ELF 386

Example of Missile Technology State-of-the-Art Advancement: Ramjet Propulsion

Example of Missile Technology State-of-the-Art Advancement: Ramjet Propulsion

01234567

1950 1960 1970 1980 1990 2000 2010Year Flight Demonstration

Mcru

ise, C

ruise

Mac

h Nu

mbe

r

Cobra X-7 Vandal/Talos St-450 SE 4400RARE Bloodhound BOMARC Typhon STATEXD-21 CROW SA-6 Sea Dart LASRMALVRJ 3M80 ASALM AS-17 / Kh-31 ASMPANS Kh-41 SLAT BrahMos MeteorHyFly SED

ScramjetRamjet

2/24/2008 ELF 387

Enabling Technologies for Tactical MissilesEnabling Technologies for Tactical MissilesDome

Faceted / WindowMulti-modeMulti-spectralMulti-lens

SeekerMulti-modeMulti-spectralSARStrapdownUncooled ImagingHigh Gimbal

G & CGPS / INSIn-flight Optimizeα, β FeedbackATR

PropulsionHypersonic Turbine-BasedLiquid / Solid Fuel RamjetVariable Flow Ducted RocketScramjetCombined Cycle PropulsionHigh Temperature TurbineHigh Temperature CombustorHigh Density Fuel / PropellantHigh Throttle Fuel ControlEndothermic FuelComposite CasePintle / Pulsed / Gel MotorHigh Burn Rate Exponent PropellantLow Observable

WarheadHigh Energy DensityMulti-modeHigh Density PenetratorBoosted PenetratorSmart DispenserPowered Submunition

InsulationHypersonicHigh Density

Flight ControlEM and

PiezoelectricTVC / Reaction JetDedicated RollPower

MEMS

AirframeLifting BodyNeutral Static MarginLattice FinsSplit CanardLow ΔxAC Wing / Low Hinge Moment Control Free-to-Roll TailsCompressed CarriageLow Drag InletMixed Compression InletSingle Cast StructureVARTM, Pultrusion, Extrusion, Filament WindHigh Temperature CompositesTitanium AlloyMEMS Data CollectionLow Observable Shaping and Materials

ElectronicsCOTSCentral

Data LinkBDI / BDAIn-flight RetargetMoving TargetPhased Array

2/24/2008 ELF 388

Summary of Development ProcessSummary of Development ProcessDevelopment Process

Technology roadmapDevelopment activitiesTime frame

Level of Design Maturity Related to Stage of DevelopmentMissile Follow-on ProgramsSubsystems Development ActivitiesSubsystems Integration and Missile System DevelopmentFlight Test ActivitiesMissile Development Tests and FacilitiesState-of-the-Art Advancement in Tactical MissilesNew Technologies for Tactical MissilesDiscussion / Questions?Classroom Exercise ( Appendix A )

2/24/2008 ELF 389

Development Process ProblemsDevelopment Process Problems1. A technology roadmap establishes the high payoff technologies g____.2. The levels of design maturity from the most mature to least mature are

production, detail, preliminary, and c_________ design.3. Technology transitions occur from basic research to exploratory

development, to advanced development, to d____________ and v_________.4. Approximately 11% of the U.S. RT&A budget is allocated to t_______

m_______.5. In the U.S., a tactical missile has a follow-on program about every __ years.6. Compared to the AIM-9L, the AIM-9X has enhanced m______________.7. Compared to the AIM-7, the AIM-120 has autonomous guidance, lighter

weight, higher speed, and longer r____.8. Compared to the PAC-2, the PAC-3 has h__ t_ k___ accuracy.9. Guidance & control is verified in the h_______ in l___ simulation.10. Airbreathing propulsion ground tests include direct connect tests and

f______ tests.11. Aerodynamic force and moment data are acquired in w___ t_____ tests.

2/24/2008 ELF 390


2/24/2008 ELF 391

Evaluate Alternatives and Iterate the System-of-Systems Design

Evaluate Alternatives and Iterate the System-of-Systems Design

• Mission / Scenario Definition

• Weapon Requirements, Trade Studies and Sensitivity Analysis

• Launch Platform Integration

• Weapon Concept Design Synthesis

• Technology Assessment and Dev Roadmap

InitialTech

InitialReqs

BaselineSelected

AltConcepts

Initial Carriage /Launch

Iteration

RefineWeapons

Req

Initial Revised

Trades / Eval Effectiveness / Eval

TechTrades

InitialRoadmap

RevisedRoadmap

Update

Note: Typical design cycle for conceptual design is usually 3 to 9 months

Alternate Concepts ⇒ Select Preferred Design ⇒Eval / Refine

2/24/2008 ELF 392

Exploit Diverse Skills for a Balanced DesignExploit Diverse Skills for a Balanced Design

Customer ( requirements pull )⇒ mission / MIR weighting

Operations analysts⇒ system-of-systems analysis

System integration engineers⇒ launch platform integration

Missile design engineers⇒ missile concept synthesis

Technical specialists ( technology push )⇒ technology assessment / roadmap

2/24/2008 ELF 393

Utilize Creative SkillsUtilize Creative Skills

Use Creative Skills to Consider Broad Range of AlternativesAsk Why? of Requirements / ConstraintsProject into Future ( e.g., 5 – 15 years )

State-of-the-art ( SOTA )ThreatScenario / Tactics / DoctrineConceptsTechnology Impact Forecast

Recognize and Distill the Most Important, Key DriversDevelop Missile Concept that is Synergistic within a System-of-SystemsDevelop Synergistic / Balanced Combination of High Leverage Subsystems / Technologies

2/24/2008 ELF 394

Identify and Quantify the High Payoff Measures of Merit

Identify and Quantify the High Payoff Measures of Merit

Max / MinRange

Time toTarget Robustness

WeightSurvivability

Lethality Miss Distance

Observables

Reliability

2/24/2008 ELF 395

Start with a Good BaselineStart with a Good Baseline

I would haveused the wheelas a baseline.

2/24/2008 ELF 396

Conduct Balanced, Unbiased TradeoffsConduct Balanced, Unbiased Tradeoffs

Aerodynamics

Propulsion

Structures

Seeker

Guidance andControl

Warhead – Fuze

Production

2/24/2008 ELF 397

AA- 8 / R-60 Python 4 Magic 550 U-Darter

Python 5 Derby / R-Darter AIM-9L Aspide

AA-10 / R-27 Skyflash AIM-7 R-37

AA-12 / R-77 AIM-9x Super 530D AIM-132

AA-11 / R-73 AIM-54 AIM-120 Mica

IRIS-T Meteor A-Darter Taildog

Evaluate Many AlternativesEvaluate Many Alternatives

Note: Although all of the above are supersonic air-to-air missiles, they have different configuration geometry

2/24/2008 ELF 398

Search a Broad Design Solution Space ( Global Optimization vs Local Optimization )

Search a Broad Design Solution Space ( Global Optimization vs Local Optimization )

Local Optimum ( e.g., Lowest Cost Only in Local Solution Space )

Local Optimum ( e.g., Lowest Cost Only in Local Solution Space )

Global Optimum ( e.g., Lowest Cost in Global Solution Space ) within Constraints

2/24/2008 ELF 399

Evaluate and Refine as Often as PossibleEvaluate and Refine as Often as Possible

2/24/2008 ELF 400

Provide Balanced Emphasis of Analytical vs Experimental

Provide Balanced Emphasis of Analytical vs Experimental

Thomas Edison: "Genius is 1% inspiration and 99% perspiration."

Albert Einstein: "The only real valuable thing is intuition."

2/24/2008 ELF 401

Use Design, Build, and Fly Process, for Feedback That Leads to Broader Knowledge

Use Design, Build, and Fly Process, for Feedback That Leads to Broader Knowledge

Design

Build

Fly ( Test )

Prediction Satisfies Customer

Requirements?

Test Results Satisfy Customer Requirements

and Consistent with Prediction?

Is it Producible?

No

Yes

Clim

b La

dder

of K

nowl

edge

Data

Failure / Success

Information

Understanding

Wisdom

No

No

Where is the wisdom we have lost in knowledge? Where is the knowledge we have lost in information?--T. S. Eliot ( The Rock )Knowledge comes by taking things apart: analysis. But wisdom comes by putting things together.--John A. MorrisonWe are drowning in information but starved for knowledge.--John Naisbitt( Megatrends: Ten New Directions Transforming Our Lives )We learn wisdom from failure much more than from success. We often discover what will do, by finding out what will not do; and probably he who never made a mistake never made a discovery.--Samuel Smiles ( Self Help )

Knowledge

2/24/2008 ELF 402

Evaluate Technology RiskEvaluate Technology Risk

2/24/2008 ELF 403

Keep Track of Assumptions and Develop Real-Time Documentation

Keep Track of Assumptions and Develop Real-Time Documentation

It’s finallyfinished ! . . .

2/24/2008 ELF 404

Develop Good DocumentationDevelop Good Documentation

MIRs Weighting

Sketches of alternative

concepts

Justification of recommended concept(s)

Aero and propulsion characteristics

Mission flight profiles of preferred concept( s )

Sensitivity of system / subsystem parameters

Traceability of system driving MIRs

Three-view drawing of preferred concept( s )

Weight and balance

Unit production cost and development cost

Technology Roadmap

2/24/2008 ELF 405

Utilize Group SkillsUtilize Group Skills

Source: Nicolai, L.M., “Designing a Better Engineer,” AIAA Aerospace America, April 1992

Detail / Production Design –

30%

Other Than Design –

60%

Preliminary Design – 8%Conceptual Design – 2%

(Test, Analysis, Configuration

Management, Software, Program Management,

Integration, Requirements,

etc.)

2/24/2008 ELF 406

Balance the Tradeoff of Importance vs Priority Balance the Tradeoff of Importance vs Priority

Advanced Programs /

Conceptual DesignSDD Programs /

Preliminary Design

Production Programs / Detail Design

2/24/2008 ELF 407

Evaluate Alternatives and Iterate the Configuration Design

Evaluate Alternatives and Iterate the Configuration Design

Yes

Establish Baseline

MeetPerformance?

No

No

Yes


Alt Mission

Alt Baseline


Aerodynamics

Propulsion

Weight

Trajectory


2/24/2008 ELF 408

Configuration Sizing Conceptual Design Guidelines: Aeromechanics

Configuration Sizing Conceptual Design Guidelines: Aeromechanics

Configuration Sizing Parameter Aeromechanics Design GuidelineBody fineness ratio 5 < l / d < 25Nose fineness ratio lN / d ≈ 2 if M > 1Boattail or flare angle < 10 degEfficient cruise dynamic pressure q < 1,000 psfMissile homing velocity VM / VT > 1.5Ramjet combustion temperature > 4,000° FOblique shocks prior to inlet normal > 2 oblique shocks / compressions if M > shock to satisfy MIL-E-5008B 3.0, > 3 shocks / compressions if M > 3.5Inlet flow capture Shock on cowl lip at Mmax cruiseRamjet Minimum cruise Mach number M > 1.2 x MInletStart , M > 1.2 MMaxThrust = DragSubsystems packaging Maximize available volume for fuel /

propellant

2/24/2008 ELF 409

Configuration Sizing Conceptual Design Guidelines: Guidance & Control

Configuration Sizing Conceptual Design Guidelines: Guidance & Control

Configuration Sizing Parameter G&C Design GuidelineBody bending frequency ωBB > 2 ωACTTrim control power α / δ > 1Neutral stability tail-body If low aspect ratio, b / d ≈ 2, c / d > ≈ 1Stability & control cross coupling < 30%Airframe time constant τ < 0.2 sMissile maneuverability nM / nT > 3Proportional guidance ratio 3 < N’ < 5Target span resolution by seeker < btargetMissile heading rate γ.

M > γ.T

Missile turn radius RTM < RTT

2/24/2008 ELF 410

Wrap Up ( Part 1 of 2 )Wrap Up ( Part 1 of 2 )

Missile design is a creative and iterative process that includesSystem considerationsMissile concepts and sizingFlight trajectory evaluation

Cost / performance drivers may be “locked in” during conceptual designMissile design is an opportunity for a diverse group to work together for a better product

Military customer ⇒ mission / scenario definitionOperations analysts ⇒ system-of-systems modelingSystem integration engineers ⇒ launch platform integrationMissile design engineers ⇒ missile concept synthesisTechnical specialists ⇒ technology assessment / technology roadmap

2/24/2008 ELF 411

Wrap Up ( Part 2 )Wrap Up ( Part 2 )

The missile conceptual design philosophy requiresIteration, iteration, iteration Evaluation of a broad range of alternativesTraceable flow-down allocation of requirementsStarting with a good baselineParedo sensitivity analysis to determine the most important, driving parametersSynergistic compromise / balanced subsystems and technologies that are high leverageAwareness of technology SOTA / technology assessmentTechnology impact forecastRobust designCreative design decisions made by the designer ( not the computer )Fast, simple, robust, physics-based prediction methods

2/24/2008 ELF 412


2/24/2008 ELF 413

ReferencesReferences1. “Missile.index,” http://missile.index.ne.jp/en/2. AIAA Aerospace Design Engineers Guide, American Institute of Aeronautics and Astronautics, 19933. Bonney, E.A., et al, Aerodynamics, Propulsion, Structures, and Design Practice, “Principles of Guided Missile Design”,

D. Van Nostrand Company, Inc., 19564. Jerger, J.J., Systems Preliminary Design Principles of Guided Missile Design, “Principles of Guided Missile Design”, D.

Van Nostrand Company, Inc., 19605. Chin, S.S., Missile Configuration Design, McGraw-Hill Book Company, 19616. Mason, L.A., Devan, L., and Moore, F.G., “Aerodynamic Design Manual for Tactical Weapons,” NSWCTR 81-156, 19817. Pitts, W.C., Nielsen, J.N., and Kaattari, G.E., “Lift and Center of Pressure of Wing-Body-Tail Combinations at Subsonic,

Transonic, and Supersonic Speeds,” NACA Report 1307, 19578. Jorgensen, L.H., “Prediction of Static Aerodynamic Characteristics for Space-Shuttle-Like, and Other Bodies at Angles

of Attack From 0° to 180°,” NASA TND 6996, January 19739. Hoak, D.E., et al., “USAF Stability and Control DATCOM,” AFWAL TR-83-3048, Global Engineering, 197810. “Nielsen Engineering & Research (NEAR) Aerodynamic Software Products,” http://www.nearinc.com/near/software.htm11. Ashley, H., Engineering Analysis of Flight Vehicles, Dover Publications, Inc., 197412. Anderson, John D. Jr., “Modern Compressible Flow,” Second Edition, McGraw Hill, 199013. Kinroth, G.D. and Anderson, W.R., “Ramjet Design Handbook,” CPIA Pub. 319 and AFWAL TR 80-2003, June 198014. “Technical Aerodynamics Manual,” North American Rockwell Corporation, DTIC AD 723823, June 197015. Oswatitsch, K.L., “Pressure Recovery for Missiles with Reaction Propulsion at High Supersonic Speeds”, NACA TM -

1140, 194716. Carslaw, H.S. and Jaeger, J. C., Conduction of Heat in Solids, Clarendon Press, 1988

2/24/2008 ELF 414

References ( cont )References ( cont )17. Allen, J. and Eggers, A.J., “A Study of the Motion and Aerodynamic Heating of Ballistic Missiles Entering the Earth’s

Atmosphere at High Supersonic Speeds”, NACA Report 1381, April 1953.18. Schneider, S.H., Encyclopedia of Climate and Weather, Oxford University Press, 199619. Klein, L.A., Millimeter-Wave and Infrared Multisensor Design and Signal Processing, Artech House, Boston, 199720. US Army Ordnance Pamphlet ORDP-20-290-Warheads, 198021. Carleone, J. (Editor), Tactical Missile Warheads, “AIAA Vol. 155 Progress in Astronautics and Aeronautics,” American

Institute of Aeronautics and Astronautics, 1993 22. Christman, D.R. and Gehring, J.W., “Analysis of High-Velocity Projectile Penetration Mechanics,” Journal of Applied

Physics, Vol. 37, 196623. Heaston, R.J. and Smoots, C.W., “Precision Guided Munitions,” GACIAC Report HB-83-01, May 198324. Donatelli, G.A. and Fleeman, E.L., “Methodology for Predicting Miss Distance for Air Launched Missiles,” AIAA-82-

0364, January 198225. Bennett, R.R. and Mathews, W.E., “Analytical Determination of Miss Distances for Linear Homing Navigation

Systems,” Hughes Tech Memo 260, 31 March 195226. Nicholas, T. and Rossi, R., “US Missile Data Book, 1996,” Data Search Associates, 199627. Bithell, R.A. and Stoner, R.C., “Rapid Approach for Missile Synthesis,” AFWAL TR 81-3022, March 198228. Fleeman, E.L. and Donatelli, G.A., “Conceptual Design Procedure Applied to a Typical Air-Launched Missile,” AIAA 81-

1688, August 198129. Hindes, J.W., “Advanced Design of Aerodynamic Missiles ( ADAM ),” October 199330. Frits, A.P., et al, “A Conceptual Sizing Tool for Tactical Missiles, “ AIAA Missile Sciences Conference, November 200231. Bruns, K.D., Moore, M.E., Stoy, S.L., Vukelich, S.R., and Blake, W.B., “Missile DATCOM,” AFWAL-TR-91-3039, April

1991

2/24/2008 ELF 415

References ( cont )References ( cont )32. Moore, F.G., et al, “The 2002 Version of the Aeroprediction Code”, Naval Surface Warfare Warfare Center, March 200233. Nicolai, L.M., “Designing a Better Engineer,” AIAA Aerospace America, April 1992

2/24/2008 ELF 416

Bibliography of Other Reports and Web SitesBibliography of Other Reports and Web SitesSystem Design

Fleeman, E.L., “Tactical Missile Design,” American Institute of Aeronautics and Astronautics, 2006“DoD Index of Specifications and Standards,” http://stinet.dtic.mil/str/dodiss.html“Periscope,” http://www.periscope1.com/Defense Technical Information Center, http://www.dtic.mil/NATO Research & Technology Organisation, http://www.rta.nato.int/“Missile System Flight Mechanics,” AGARD CP270, May 1979Hogan, J.C., et al., “Missile Automated Design ( MAD ) Computer Program,” AFRPL TR 80-21, March 1980Rapp, G.H., “Performance Improvements With Sidewinder Missile Airframe,” AIAA Paper 79-0091, January 1979Nicolai, L.M., Fundamentals of Aircraft Design, METS, Inc., 1984Lindsey, G.H. and Redman, D.R., “Tactical Missile Design,” Naval Postgraduate School, 1986Lee, R.G., et al, Guided Weapons, Third Edition, Brassey’s, 1998Giragosian, P.A., “Rapid Synthesis for Evaluating Missile Maneuverability Parameters,” 10th AIAA Applied Aerodynamics Conference, June 1992Fleeman, E.L. “Aeromechanics Technologies for Tactical and Strategic Guided Missiles,” AGARD Paper presented at FMP Meeting in London, England, May 1979Raymer, D.P., Aircraft Design, A Conceptual Approach, American Institute of Aeronautics and Astronautics, 1989Ball, R.E., The Fundamentals of Aircraft Combat Survivability Analysis and Design, American Institute of Aeronautics and Astronautics, 1985“National Defense Preparedness Association Conference Presentations,” http://www.dtic.mil/ndia

2/24/2008 ELF 417

Bibliography of Other Reports and Web Sites ( cont )Bibliography of Other Reports and Web Sites ( cont )System Design ( continued )

Eichblatt, E.J., Test and Evaluation of the Tactical Missile, American Institute of Aeronautics and Astronautics, 1989“Aircraft Stores Interface Manual (ASIM),” http://akss.dau.mil/software/1.jsp“Advanced Sidewinder Missile AIM-9X Cost Analysis Requirements Description (CARD),”http://deskbook.dau.mil/jsp/default.jspWertz, J.R and Larson W.J., Space Mission Analysis and Design, Microprism Press and Kluwer Academic Publishers, 1999 “Directory of U.S. Military Rockets and Missiles”, http://www.designation-systems.net/Fleeman, E.L., et al, “Technologies for Future Precision Strike Missile Systems,” NATO RTO EN-018, July 2001“The Ordnance Shop”, http://www.ordnance.org/portal/“Conversion Factors by Sandelius Instruments”, http://www.sandelius.com/reference/conversions.htm“Defense Acquisition Guidebook”, http://akss.dau.mil/dag/

Aerodynamics“A Digital Library for NACA,” http://naca.larc.nasa.gov/Briggs, M.M., Systematic Tactical Missile Design, Tactical Missile Aerodynamics: General Topics, “AIAA Vol. 141 Progress in Astronautics and Aeronautics,” American Institute of Aeronautics, 1992Briggs, M.M., et al., “Aeromechanics Survey and Evaluation, Vol. 1-3,” NSWC/DL TR-3772, October 1977“Missile Aerodynamics,” NATO AGARD LS-98, February 1979“Missile Aerodynamics,” NATO AGARD CP-336, February 1983“Missile Aerodynamics,” NATO AGARD CP-493, April 1990“Missile Aerodynamics,” NATO RTO-MP-5, November 1998Nielsen, J.N., Missile Aerodynamics, McGraw-Hill Book Company, 1960

2/24/2008 ELF 418

Bibliography of Other Reports and Web Sites ( cont )Bibliography of Other Reports and Web Sites ( cont )Aerodynamics ( continued )

Mendenhall, M.R. et al, “Proceedings of NEAR Conference on Missile Aerodynamics,” NEAR, 1989Nielsen, J.N., “Missile Aerodynamics – Past, Present, Future,” AIAA Paper 79-1818, 1979Dillenius, M.F.E., et al, “Engineering-, Intermediate-, and High-Level Aerodynamic Prediction Methods and Applications,” Journal of Spacecraft and Rockets, Vol. 36, No. 5, September-October, 1999Nielsen, J.N., and Pitts, W.C., “Wing-Body Interference at Supersonic Speeds with an Application to Combinations with Rectangular Wings,” NACA Tech. Note 2677, 1952Spreiter, J.R., “The Aerodynamic Forces on Slender Plane-and Cruciform-Wing and Body Combinations”, NACA Report 962, 1950Simon, J.M., et al, “Missile DATCOM: High Angle of Attack Capabilities, AIAA-99-4258Burns, K.A., et al, “Viscous Effects on Complex Configurations,” WL-TR-95-3060, 1995 Lesieutre, D., et al, “Recent Applications and Improvements to the Engineering-Level Aerodynamic Prediction Software MISL3,’’ AIAA-2002-0274Moore, F.G., Approximate Methods for Weapon Aerodynamics, American Institute of Aeronautics and Astronautics, 2000“1976 Standard Atmosphere Calculator”, http://www.digitaldutch.com/atmoscalc/“Compressible Aerodynamics Calculator”, http://www.aoe.vt.edu/~devenpor/aoe3114/calc.htmlAshley, H. and Landahl, M., Aerodynamics of Wings and Bodies, Dover Publications, 1965John, James E.A., Gas Dynamics, Second Edition, Prentice Hall, 1984Zucker, Robert D., Fundamentals of Gas Dynamics, Matrix Publishers, 1977

PropulsionChemical Information Propulsion Agency, http://www.cpia.jhu.edu/St. Peter, J., The History of Aircraft Gas Turbine Engine Development in the United States: A Tradition of Excellence, ASME International Gas Turbine Institute, 1999

2/24/2008 ELF 419

Bibliography of Other Reports and Web Sites ( cont )Bibliography of Other Reports and Web Sites ( cont )

Propulsion ( continued )Mahoney, J.J., Inlets for Supersonic Missiles, American Institute of Aeronautics and Astronautics, 1990Sutton, G.P., Rocket Propulsion Elements, John Wiley & Sons, 1986“Tri-Service Rocket Motor Trade-off Study, Missile Designer’s Rocket Motor handbook,” CPIA 322, May 1980Humble, R.W., Henry, G.N., and Larson, W.J., Space Propulsion Analysis and Design, McGraw-Hill, 1995Jenson, G.E. and Netzer, D.W., Tactical Missile Propulsion, American Institute of Aeronautics and Astronautics, 1996Durham, F.P., Aircraft Jet Powerplants, Prentice-Hall, 1961Bathie, W.W., Fundamentals of Gas Turbines, John Wiley and Sons, 1996Hill, P.G. and Peterson, C.R., Mechanics and Thermodynamics of Propulsion, Addison-Weshley Publishing Company, 1970Mattingly, J.D., et al, Aircraft Engine Design, American Institute of Aeronautics and Astronautics, 1987

Materials and Heat TransferBudinski, K.G. and Budinski, M.K., Engineering Materials Properties and Selection, Prentice Hall, 1999“Matweb’s Material Properties Index Page,” http://www.matweb.com“NASA Ames Research Center Thermal Protection Systems Expert (TPSX) and Material Properties Database”, http://tpsx.arc.nasa.gov/tpsxhome.shtmlHarris, D.C., Materials for Infrared Windows and Domes, SPIE Optical Engineering Press, 1999Kalpakjian, S., Manufacturing Processes for Engineering Materials, Addison Wesley, 1997MIL-HDBK-5J, “Metallic Materials and Elements for Aerospace Vehicle Structures”, Jan 2003“Metallic Material Properties Development and Standardization ( MMPDS )”, http://www.mmpds.org

2/24/2008 ELF 420

Bibliography of Other Reports and Web Sites ( cont )Bibliography of Other Reports and Web Sites ( cont )

Materials and Heat Transfer ( continued )Mallick, P.K., Fiber-Reinforced Composites: Materials, Manufacturing, and Design, Second Edition, MaecelDekker, 1993Chapman, A.J., Heat Transfer, Third Edition, Macmillan Publishing Company, 1974Incropera, F.P. and DeWitt, D.P., Fundamentals of Heat and Mass Transfer, Fourth Edition, John Wiley and Sons, 1996

Guidance, Navigation, Control, and SensorsZarchan, P., Tactical and Strategic Missile Guidance, “AIAA Vol. 124 Progress in Astronautics and Aeronautics,” American Institute of Aeronautics and Astronautics, 1990“Proceedings of AGARD G&C Conference on Guidance & Control of Tactical Missiles,” AGARD LS-52, May 1972Garnell, P., Guided Weapon Control Systems, Pergamon Press, 1980Locke, A. S., Guidance, “Principles of Guided Missile Design”, D. Van Nostrand, 1955Blakelock, J. H., Automatic Control of Aircraft and Missiles, John Wiley & Sons, 1965Lawrence, A.L., Modern Inertial Technology, Springer, 1998Siouris, G.M., Aerospace Avionics Systems, Academic Press, 1993Stimson, G.W., Introduction to Airborne Radar, SciTech Publishing, 1998Lecomme, P., Hardange, J.P., Marchais, J.C., and Normant, E., Air and Spaceborne Radar Systems, SciTech Publishing and William Andrew Publishing, 2001Wehner, D.R., High-Resolution Radar, Artech House, Norwood, MA, 1995Donati, S., Photodetectors, Prentice-Hall, 2000Jha, A.R., Infrared Technology, John Wiley and Sons, 2000Schlessinger, M., Infrared Technology Fundamentals, Marcel Decker, 1995

2/24/2008 ELF 421

Follow-up CommunicationFollow-up Communication

I would appreciate receiving your comments and corrections on this text, as well as any data, examples, or references that you may offer.

Thank you,Gene FleemanTactical Missile DesignE-mail: [email protected] Site: http://genefleeman.home.mindspring.com

2/24/2008 ELF 422


Date post:	12-Nov-2014
Category:	Documents
Upload:	farhadi
View:	5,997 times
Download:	165 times