18-1 Design of UAV Systems Propulsionc 2002 LM Corporation Lesson objective - to discuss Propulsion...

18-1

Design of UAV Systems

Propulsionc 2002 LM Corporation

Lesson objective - to discuss

Propulsion and propulsion parametrics

including …

• Rationale

• Applications

• Models

Expectations - You will understand when and how to use parametric propulsion relationships


Lesson 5a - Air vehicle parametricsc 2002 LM Corporation 18-2

Definitions

From Webster’s New Collegiate Dictionary• Parameter – any set of physical properties whose value determine the characteristics or behavior of a set of equations

Our definition• Propulsion parametric – fundamental design parameter whose value determines the design or performance characteristics of an engine• Usually (but not always) a multi-variable relationship

- e.g., SFC (WdotF/Bhp), Bypass ratio (BPR), etc.• Parametric model – Parametric based design approach to define, size, estimate performance and do trade offs on propulsion systems- Different from the traditional approach

Parametrics modelsDesign of UAV Systems

Lesson 5a - Air vehicle parametricsc 2002 LM Corporation

• Simple models that correlate thrust or power, weight, fuel flow, speed and altitude- Most based on historical and technology trend data- Others based on simple definitions- Some based on non-dimensional analysis (See

RosAP6.2.5)• Internal combustion (IC) engines are easiest to model

- Simple (and generally independent) variables- One complexity is fixed pitch propeller performance

• Jet engines are more difficult to model parametrically- Many interrelated design and operating variables

• Turboprop (TBProp) parametric models are in between

Propulsion parametrics can be used for pre-concept design but engine company models should be used as soon as they are available

18-2a

18-3



• Engine Power-to-weight ratio (HP0/Weng)- HP0 = Maximum power (hp, uninstalled, sea level static)- Weng = Engine weight (lbm, uninstalled)

• Engine thrust-to-weight ratio (T0/Weng)- T0 = Maximum thrust (lbf, uninstalled, sea level static)- Weng = Engine weight (lbm, uninstalled)

• Specific Fuel Consumption (SFC)SFC = Fuel flow/Power (WdotF/HP)SFC0 = WdotF0/ HP0 (lbm/hp-hr)

• Thrust Specific Fuel Consumption (TSFC)TSFC = Fuel flow/Thrust available(WdotF/Ta)TSFC0 = WdotF0/T0 (lbm/hp-hr)

• Specific Thrust (Fsp)- Fsp = Thrust/Airflow (T/WdotA)- Fsp0 =T0/WdotA0 (lbf-sec/lbm)

Key parametrics

or

Note - “0” postscript indicates sea level static (V=0) conditions

or

Engine sizeDesign of UAV Systems


• Any number of performance requirements can drive engine size (See RayAD 5.2)- Takeoff

- Ground roll and distance over an obstacle- And/or balanced field length (BFL)

- Time and/or distance to climb- Cruise altitude and/or speed- Acceleration and/or turn performance- Engine out performance (for multi-engine aircraft)

• Historical thrust-to-weight or power-to-weight data can be used for first pass sizing- See RayAD Tables 5.1 and 5.2

• UAV historical data is limited and we will use takeoff requirements for initial sizing - See RayAD Figure 5.4

18-4

18-5



Sizing - manned vs. unmanned

UAVs - Piston Engine

0.000

0.050

0.100

0.150

0.200

0.250

0 1000 2000 3000 4000

Gross weight (lbs)

Single

Twin

UAVs - Turboprop

0.000

0.050

0.100

0.150

0.200

0.250

0 2000 4000 6000 8000

Gross weight (lbs)

Rotary wing

Fixed wing

UAVs - Jet

0.200

0.300

0.400

0.500

0.600

0.700

0 10000 20000 30000

Gross weight (lbs)

UAV - CTOL

UAV - Boosted

Targets

UAV data from various sources including Janes, Unmanned Air Vehicles

Raymer (power-to-weight)GA Single 0.07GA Twin 0.17Twin turboprop 0.20

Raymer (thrust-to-weight)Trainer 0.4Bomber 0.25Transport 0.25

IC engines

• Engine power available (BHP)

• Output per unit size varies by type- Small piston engines run at high RPM, have higher output per unit size. Same for rotary engines

• For given engine at given altitude and RPM- Almost no variation with speed

• At given RPM, manifold pressure varies with altitude• Max power varies with air density ratio (see RayAD

Eqn13.10)- Bhp = Bhp0*(8.55*-1)/7.55 (18.1)

• Engine SFC

• Runs high for small and rotary engines • For given engine varies slightly with power available

- Typically 5-10% lower at cruise condition

• Engine power-to-weight varies with engine type



18-7



Engine size

0

250

500

750

0 100 200 300 400

Max power (HP)

Recip-air cooledRecip-liquid cooledRotary-air cooledRotary-liquid cooled

Power per unit weight

0.00

0.50

1.00

1.50

2.00

2.50

0 200 400 600 800Displacement (in3)

Recip-air cooledRecip-liquid cooledRotary-air cooledRotary-liquid cooled

Specific Fuel Consumption

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0 100 200 300Max Power(Hp)

Recip - Max PowerRecip - Cont. powerRotary - Max powerRotary - Cont. Power

IC engine parametrics

Compilation of data from various sources including: Roskam, Aerodynamics & Performance (RosAP); Janes, Aero Engines; Janes, Unmanned Air Vehicles; www.tcmlink.com/producthighlights/www.lycoming.textron.com/main

SFC Variation - Piston

0.2

0.4

0.6

0.8

0.2 0.4 0.6 0.8SFC0 (lbm/hr Hp)

18-8



IC engine size

Compilation of data from various sources including:- Roskam, Aerodynamics & Performance (RosAP)- Janes, Aero Engines- Janes, Unmanned Air Vehicles-www.tcmlink.com/producthighlights/-www.lycoming.textron.com/main

(a) (b)

(c)

Charts 18-7/8 show only contemporary IC engines • Earlier engines were

much larger

Vol vs. Weight

0.00

10.00

20.00

30.00

0 100 200 300 400 500

Weight (lb)

Vol

ume

(cuf

t)

Recip-air cooledRecip-liquid cooledRotary-air cooledRotary-liquid cooledall

Length-to-Dequiv

10

20

30

40

50

10.00 20.00 30.00 40.00

Dequiv = sqrt[wh] (in)

Leng

th (in

)


Avg=1.3

L/De=2

L/De=1

Width-to-Height

0

10

20

30

40

0 10 20 30

Height (in)


Avg=1.4w/h=2

w/h=1

= 20 pcf

= 40

= 30

PropellersDesign of UAV Systems


• Two basic types of propellers (See RayAD10.4 & 13.6)- Fixed pitch and Variable pitch

• Efficiency (p) varies with design and installation- Blockage and flow “scrubbing” generate losses

• Fixed pitch efficiency varies with advance ratio (J)- See RayADFig13.13 - Props generally designed for climb or cruise

• Variable pitch efficiency typically constant over range of design speeds- Use a nominal p = 0.8 for an initial guess

• Thrust horsepower (THP) defined by- Thp = Bhp*p =Ta*V(fps)/550=Ta*V(KTAS)/325.6

Where ……….Ta = Thrust available• Therefore……..

- Thrust available decreases with speed Ta = 325.6*BHP*p /KTAS (18.2)

18-9



Propeller size

• Key sizing constraint is tip speed (Mach number)- Linear function of engine RPM (V=R*)

• Lightest-most reliable design is direct drive- No gear reduction

• Some UAVs use high RPM engines with belt systems for speed reduction

- Manned aircraft prop sizing can be used for UAVs

- There will always be exceptions for special application aircraft (e.g.Altus)

Compilation of data from unpublished sources plus:

- Janes, Unmanned Air Vehicles

Prop Sizing

0

2

4

6

8

10

0 200 400 600

SHP

Piston UAVCessnaTurboprop UAV

Altus High Altitude

18-11



Propeller parametrics

Propeller size(All types)

5

8

11

14

0 2000 4000 6000 8000

HP or ESHP

2 Blades3 Blades4 Blades5 Blades8 Blade10 Blade

Propeller size< 1000 HP

4

6

8

10

0 250 500 750 1000

HP or ESHP

2 Blades3 Blades4 Blades5 Blades8 Blade10 Blade

Propeller weight

y = 0.8x + 4.9

0

100

200

300

400

500

0 100 200 300 400 500

Nb*Rp (in)

Nb = Number of blades

Rp = Prop radius (in)

Weight/Total blade length(in) ≈ 0.8 lb/in

Raw data from Janes All the Worlds Aircraft

Turboprop enginesDesign of UAV Systems


• Have typical prop characteristics (and constraints) plus jet exhaust for thrust augmentation• Thrust component is added for equivalent shaft HP, the

difference between Shp and EShp (see RayAD 13.7)• Power available decreases with altitude

• Decreases with pressure (see RayAD Table E.3)• SFC variation with altitude less severe than jet

• Typical Lth/Dia = 2 - 3

• Typical density = 22 pcf

• Typical diameter = [4*Vol/(*L/D)]^1/3- From Vol(cyl) = [/4][D^2]L[D/D]

18-12

18-13



Turboprop SFC

0.4

0.5

0.6

0.7

0.8

0 1000 2000 3000 4000 5000

Shaft HP

Max RPM SLSCruise RPM SLS

Turboprop Power/Weight

0.75

1.25

1.75

2.25

2.75

0 1000 2000 3000 4000 5000

Shaft HP

Max RPM SLSCruise RPM SLSSLS

Turboprop engines

Turboprop Size

0

10

20

30

40

50

25 50 75 100 125

Length (in)

Max widthMax hieght

TBP density

0

50

100

150

0 1000 2000 3000

Weight (lbm)

Data compiled from RosAP and Janes Aero Engines

Typical TBProp parametrics

18-14



Jet engines

• Includes turbojet (TBJet) and turbofan (TBFan) engines• Thrust, weight, airflow and TSFC depend on design and

technology content and operating conditions• Difficult to capture in general purpose parametrics

• Thrust available decreases with altitude - all engines• TSFC decreases with altitude - all engines• Effect of speed on thrust varies with bypass ratio (BPR)

• Low BPR - thrust generally increases with speed• High BPR - thrust decreases with speed• See RayAD Appendix E for specific examples

• Thrust-to-weight varies with engine size, BPR and advanced technology content

• Physical geometry primarily a function of design BPR• Physical installation reduces thrust by 5-20%

18-15



Generic jet engine

Gas Generator (GG)

GG thrust

Fan

Fan thrustFanAirflow

GGAirflow

V

Bypass ratio (BPR) = Fan airflow/total airflow

WdotAgg WdotA*1/(BPR+1)WdotAfn WdotA*BPR/(BPR+1)

Turbojet (TBJ) BPR = 0, Turbofan (TBFan) BPR < 10; TBProp BPR >> 10

18-16



Typical TBJet parametrics

Specific thrust

55.00

60.00

65.00

70.00

75.00

0 5000 10000 15000 20000T0 (lbf)

Thrust-to-weight

2.00

4.00

6.00

8.00

10.00

12.00

0 5000 10000 15000 20000T0 (lbf)

SFC0 - Small turbojets

0.5

1

1.5

0 1000 2000 3000T0 (lbf)

Engine diameter

0

30

60

90

120

150

0 30 60 90 120 150

Raymer parametric (in)

D^2 (ft) = WdotA/26

All engines (more later)

Data from Roskam, Aerodynamics & Performance (RosA)P and Janes, Aero Engines

18-17



Specific thrust

10.00

30.00

50.00

70.00

90.00

0 2 4 6 8 10

BPR

TSFC

0

0.25

0.5

0.75

1

0 2 4 6 8 10

BPR

Geometry

0

2

4

6

8

10

1 2 3 4 5L/D

Typical TBFan parametrics

Thrust-to-weight

4.00

4.50

5.00

5.50

6.00

6.50

7.00

0 1 2 3 4 5 6 7 8 9BPR


(lbm

/hr-

lbf)

18-18



TBJet and TBFan size

• Despite its apparent simplicity, Raymer’s engine size parametric correlates well with our database- One difference is that Raymer bases his correlation on

engine inlet diameter- Our data shows that it correlates with overall engine

diameter• Parametrics are for

uninstalled engine weight- Nominal TBFan

T0/Weng = 5.5- An installation factor

of 1.3 is applied to estimate installed engine weight

Engine diameter

0

30

60

90

120

150

0 30 60 90 120 150

Raymer parametric (in)

Dat

abas

e D

(in)

D^2 (ft) = WdotA/26

18-19



Thrust-to-weight

4.00

4.50

5.00

5.50

6.00

6.50

7.00

0 10 20 30 40 50 60 70 80 90TO(Klb)


Size

0

10

2030

40

50

60

0 100 200 300 400 500

Airflow (pps)

TBFan parametrics – cont’d

18-20



Afterburning

• Way to augment jet engine performance to meet peak thrust requirements such as…..

Takeoff….combat maneuvers….supersonic flight• Works by injecting fuel into engine exhaust to react

residual oxygen and increase temperature/jet velocity• Inefficient turbojet engines and turbofans can achieve high augmentation ratios - lots of air to “burn”

• Efficient turbojets achieve low augmentation ratios- Most of the air already “burned”

• Essentially a ramjet on the rear of the engine • Only works for low-to-moderate BPR turbofans

- High BPR fans have insufficient overall pressure ratio• Relatively light weight but very fuel inefficient• High noise levels limit civil applications

18-21



A/B parametric data

SFC Comparison

0.5

1

1.5

2

0.25 0.5 0.75 1 1.25SFC0-Dry

Turbojet

Turbofan

Thrust Augmentation

0

10000

20000

30000

0 5000 10000 15000 20000T0-Dry (lbf)

Turbojet

Turbofan

Data from Roskam, Aerodynamics & Performance (RosAP) and Janes, Aero Engines

18-22



TBProp baseline

ground roll = 220 or: 220 = [W0/Sref]/[Clto*T0/W0] • For Clto = Clmax/(Vto/Vs^2)

= 1.49 and W0 = 1918 lbmBHp0/W0 = 0.092BHp0 = 176.5 BHp

• BHp0/W0 correlates well with our parametric data

• We will use parametric data to make a first pass engine size estimate for our example UAV (see chart 15-40)• We assume a nominal TBProp UAV wing loading (W0/Sref) = 30 psf, a typical plan flap Clmax =1.8 (See RayAD Fig 5.3) and a standard Vto/Vs = 1.1

• From RayAD Figure 5.4, required takeoff parameter (TOP) for a 1500 ft takeoff

UAV sizing parametric

0

0.1

0.2

0.3

0.4

0.5

0.00 20.00 40.00 60.00

Wing loading (psf)

HP

/W0

or T

0/W

0 (S

LS) Piston

TurbopropJet

18-23



Turboprop SFC

0.4

0.5

0.6

0.7

0.8

0 1000 2000 3000 4000 5000

Shaft HP

Max RPM SLSCruise RPM SLS

Turboprop Power/Weight

0.75

1.25

1.75

2.25

2.75

0 1000 2000 3000 4000 5000

Shaft HP

Max RPM SLSCruise RPM SLSSLS

Chart 18-13 shows turboprops of this small size class should be available at 2.25 Shp/lb- Nominal weight would be 78.4 lbm- At a density of 22 lb/cuft, volume would be 3.6 cuft- At nominal Lth/Diam = 2.5, engine diameter (Deng) = [4*Vol/(*Lth/Deng)]^1/3 ≈ 1.22ft and length (Leng) = 3ft

- SFC0 would about 0.65 lbm/hr-BhpIn reality, however, there are no TBProps this small

Application – TBProp

18-24



TBFan alternative

ground roll = 100 or: 100 = [W0/Sref]/[Clto*T0/W0] • For Clto = Clmax/(Vto/Vs^2)

= 1.49 and W0 = 2939 lbmT0/W0 = 0.269T0 = 790 Lbf

• T0/W0 correlates well with our parametric data

• We will also use parametric data to make a first pass engine sizing for the TBFan alternative• We assume a nominal TBFan UAV wing loading (W0/Sref) = 40 psf, a typical plan flap Clmax =1.8 (See Raymer AD Fig 5.3) and a standard Vto/Vs = 1.1

• From RayAD Figure 5.4, required takeoff parameter (TOP) for a 1500 ft takeoff

UAV sizing parametric

0

0.1

0.2

0.3

0.4

0.5

0.00 20.00 40.00 60.00

Wing loading (psf)

HP

/W0

or T

0/W

0 (S

LS) Piston

TurbopropJet

18-25



Specific thrust

10.00

30.00

50.00

70.00

90.00

0 2 4 6 8 10

BPR

Thrust-to-weight

4.00

4.50

5.00

5.50

6.00

6.50

7.00

0 10 20 30 40 50 60 70 80 90TO(Klb)

TBFan

From charts 18-16/17 we estimate T0/Weng ≈ 5.5- Our TBFan would weigh 144 lbm - At BPR = 5, WdotAmax = 790/30 = 26.3 pps- From charts 18-16/17 Deng ≈ 12 in, Leng ≈ 24 in

From charts 18-17/19 TSFC0 ≈ 0.4 and TSFCcr ≈ 0.65- But unfortunately, there are no BPR = 5 turbofans of size class (see ASE261.Engine database.xls)- However, there might be some under development

18-26



Overall results

The TBProp parametrics show the SFC0 value assumed in the Lesson 15 example is low (0.4 vs 0.65) - Small engines are less efficient than larger ones

- The performance impact will significant but it will make make the results fit better with our sizing parametrics

- And there are no engines available at the size requiredThe TBFan parametrics show that Raymer’s values of cruise TSFC are optimistic (which we already knew) and that there are also no small BPR = 5 TBFan engines- Size effects are likely to reduce TSFC also

However, we will continue our study as if engines were available since we really don’t know yet what size air vehicle we will end up with- We will, however, note these issues as development risk items and consider the implications when we select our final configurations

18-27



Next subject

From Webster’s New Collegiate Dictionary• Parameter – any set of physical properties whose value determine the characteristics or behavior of a set of equations

Our definition• Propulsion parametric – fundamental design parameter whose value determines the design or performance characteristics of an engine• Usually (but not always) a multi-variable relationship

- e.g., wing loading (W0/Sref), Swet/Sref, etc.• Parametric model – Parametric based design approach to define, size, estimate performance and do trade offs on propulsion systems- Different from the traditional approach

18-28



Parametric models

In the absence of real data, engine parametric models can be used to provide reasonable trends for use in pre-concept and conceptual design

- For example, Equation 5.4 (RayAD Eq. 13.10) captures IC engine altitude effects and is useful for initial design

- No similar effects are captured in traditional jet engine parametric models such as RayAD Eq. 10.5-10.15- Mach and altitude effects are absent - More general purpose thrust and fuel flow models are

needed and none existTherefore, we will have to develop our own jet engine models (both TBJet and TBFan)

- We will use the engine performance charts in RayAD, Appendix E as the basis for these models

18-29



IC parametric model

• Use Equation 18.1 (RayAD Eq. 13.10) to calculate maximum power as a function of altitude

• BHP = BHP0*(8.55* -1)/7.55 (18.1)where

• BHP0 = maximum power, SLS (sea level static) = air density ratio

• Calculate cruise performance at 75% takeoff power• Assume nominal 80% propulsion efficiency (p)• Estimate thrust available from

• Ta = 325.6*BHP*p/KTAS (18.2)• Estimate fuel flow from

• WdotF = SFC*BHPwhere

• SFC assumed constant (use SFC0 from chart 18-7)• Estimate engine weight from chart 18-7• For supercharged engine, assume pressure ratio/stage = 2

• See Raymer Figure 13.10 (page 394)• Adjust engine weight as appropriate

18-30



Jet parametric model

Assumptions

GG Fsp = constant = Fsp-ggFan Fsp = (V0/V)*Fsp-fn(SLS)BPR = Constant

Gas Generator (GG)

GG thrust

Fan

Fan thrustFanAirflow

GGAirflow

V

Bypass ratio (BPR)

WdotAgg WdotA*1/(BPR+1)WdotAfn WdotA*BPR/(BPR+1)

Turbojet BPR = 0, Turbofan BPR < 10; Propfan BPR >> 10

18-31



Jet parametric model

• Assume jet engine thrust (subsonic) can be modeled as the sum two (2) simplified components

- “Gas generator”(gg) - the core engine of a turbofan or turboprop

- “Fan” (fn) - the fan or propeller• Assume core engine thrust varies with core airflow

(constant core engine Fsp - a very simple approximation)• Assume fan Fsp varies inversely with speed ratio (V0/V)

- Like a propeller- Select non-zero V0 to fit data as appropriate

• Assume fan bypass ratio remains constant• Assume all other engine parameters follow “corrected”

performance relationships (See P&W handbook, page 129)- Ta = Ta0* (18.3) - WdotF = WdotF0**sqrt(^k) (18.4) - SFC = SFC0*sqrt( ^k) (18.5) - WdotA = WdotA0* /sqrt()

(18.6) - f/a = (f/a0)*sqrt()*sqrt( ^k) ≈ (f/a0)* ^.75 (18.7)

k = f(cycle) but ≈ 0.5

18-32



Jet parametric model (cont’d)

• Using these simplifying assumptions, thrust available can be estimated from:Ta = WdotA*Fsp = WdotA*[Fsp-gg/(1+BPR) +

Fsp-fn*(V0/V)*(BPR/(1+BPR)] (18.8)

where• WdotA = Total airflow (note :WdotA-gg = gg

airflow) • Fsp-gg = Core engine Fsp • Fsp-fn = Fan Fsp (varies with number of fan stages)• V0 = Non-zero reference speed (select to fit data)• BPR - Fan bypass ratio (given by design)

• Estimate installation losses at 5-20% (more to follow)• Estimate airflow from

WdotA = WdotA0*delta/sqrt() (18.9)

where = ( @h)*(1+.2M^2)^3.5 (18.10) = (@h)*(1+.2M^2)

(18.11) • Estimate fuel flow from WdotA-gg*corrected fuel/air ratio

= WdotA/(1+BPR)*(f/a0)* ^.75

18-33



RayAD model matching

RayAD Appendix E engines (Table E.1 - Low BPR, Table E.2 - High BPR and Table E.3 - TBP) were modeled parametrically using the following values:

Core Fsp (sec)

Fan Fsp (sec)

V0 (KTAS)

BPR

Fuel/air ratio

LBPR HBPR TBP

90 90 90

66 25 5

100 100 50

0.4 8 133

0.0292 0.0292 0.0292

Even though our parametric model is unique to this course, engine companies often provide generic “cycle decks” which produce similar (but more accurate) results

18-34



Model input rationale

Core engine Fsp

Fan Fsp

V0

BPR

Fuel/air ratio

- Value (90 sec) selected from chart 18-17 for BPR = 0

- LBPR value selected to match data, HBPR Fsp scaled based on fan pressure ratio differences (1.6 vs. 4.3), TBP Fsp estimated at 20% HBPR Fsp.

- Values selected to match data

- Given values used except for TBP which was selected to match data

- Value selected to match data

18-35



Model correlation - LBPR

Low Bypass Ratio Turbofan Airflow Correlation

0

100

200

300

400

0 100 200 300 400

Table E.1 airflow (pps)

Low Bypass Ratio Turbofan Thrust Correlation

0

5000

10000

15000

20000

25000

0 5000 10000 15000 20000 25000

Table E.1 thrust (Lbf)

Low Bypass Ratio Turbofan SFC Correlation

0.7

0.8

0.9

1.0

1.1

1.2

0.7 0.8 0.9 1.0 1.1 1.2

Table E.1 SFC (sec)

Para

metr

ic m

odel S

FC

(s

ec)

Low Bypass Ratio Turbofan Fuel Flow Correlation

0

10000

20000

30000

0 10000 20000 30000

Table E.1 fuel flow (pph)

(lb

m/h

r-lb

f)

(lbm/hr-lbf)

18-36



Model correlation - HBPR

High Bypass Ratio Turbofan Airflow Correlation

0

500

1000

1500

2000

2500

0 500 1000 1500 2000 2500

Table E.2 airflow (pps)

High Bypass Ratio Turbofan Thrust Correlation

0

10000

20000

30000

40000

50000

0 10000 20000 30000 40000 50000


High Bypass Ratio Turbofan SFC Correlation

0.3

0.5

0.7

0.9

0.3 0.5 0.7 0.9

Table E.1 SFC (sec)

High Bypass Ratio Turbofan fuel Flow Correlation

0

10000

20000

30000

0 10000 20000 30000

Table E.1 WdotF (pph)

(lb

m/h

r-lb

f)

(lbm/hr-lbf)

18-37



Model correlation - TBP

Turboprop Thrust Correlation

0

10000

20000

30000

0 10000 20000 30000


Turboprop SFC Correlation

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.2 0.4 0.6 0.8 1.0

Table E.3 SFC (sec)

Turboprop Fuel Flow Correlation

1000

3000

5000

7000

1000 3000 5000 7000

Table E.3 WdotF (Lbf)

(lb

m/h

r-lb

f)

(lbm/hr-lbf)

18-38



Database comparison - TBF

• Even though model Fan Fsp values generally match Raymer’s models at BPR = 0.8 and 8.0 by definition - We have no idea what Fan Fsp might look like at intermediate BPR values

- And we have no idea how they correlate with real ones• We can get answers by assuming values of Fsp-gg and

use Eq 18.18 to calculate Fan Fsp for typical enginesFsp-fn parametric

(Assumed Fsp-gg = 80)

0

20

40

60

80

100

0 2 4 6 8 10

BPR

Calculated values

Model values

Fsp-fn parametric(Assumed Fsp-gg = 90)

0

20

40

60

80

0 2 4 6 8 10

BPR

Calculated values

Model values

Est. upper bound

• The Fsp-gg = 80 data looks like it provides a better fit

18-39



Other data comparisons

• Actual engine performance data can also be used to check and/or calibrate parametric model estimates- For example, parametric model performance estimates for typical TBProp and TBFan engines can be compared to actual engines under the same flight conditions- But because of design differences, even real engines

will show performance variations- Nonetheless, the comparisons can be used to

generate multipliers to ensure the model estimates match actual engine performance ranges

• Comparisons with database TBProp and TBFan engine performance are shown in the following chart - TBProp model thrust available and SFC are seen to fit within the data spread, albeit somewhat optimistically

- TBFan thrust fits the data but TSFC is about 15% high- A 0.87 TBFan TSFC multiplier will compensate for it

18-40



Performance correlations

- Propulsion model estimate

TBProp power ratio at 250 kts

0.3

0.5

0.7

0.9

1.1

10 20 30 40 50

Altitude (Kft)

TPE331-14PT6A-41 (Flat rated)Other

TBProp SFC at 250 kts)

0.40

0.45

0.50

0.55

0.60

10 20 30 40 50

Altitude (Kft)

TPE331-14PT6A-41 (Flat rated)Other

TBFan Cruise thrust ratio(35-40Kft)

0.15

0.2

0.25

0.3

0 2 4 6 8 10

BPR

M = 0.7-0.85

0.63/36Kft

TBFan Cruise TSFC (35-40Kft)

0.5

0.6

0.7

0.8

0.9

1

0 2 4 6 8 10

BPR

M = 0.7-0.85

0.63/36Kft


18-41



A note about Turboprops

• Raymer’s Appendix E.3 TPB model is somewhat unique in that performance is expressed in terms of thrust and TSFC, not Shp or Eshp and SFC = WdotF/Hp

- This makes us work the problem backwards

- In a traditional propeller aircraft analysis, we first calculate Bhp available and then multiply by p to determine thrust horsepower (Thp) available

- The Breguet range equation includes p in the numerator and SFC is based on uninstalled Bhp

- In our model we calculate thrust and fuel flow directly

- We, therefore, have to calculate Thp from the definition Thp = T*V(fps)/550 = T*V(kts)/325.6 and then divide by p to get Shp

- Then we calculate SFC from fuel flow and Shp

18-42



Installation losses

We will capture these effects using simple installed performance knock down factors

- We will use 0.8 - 0.95 for TBJ and TBF installations- p will capture all losses for ICs and TBPs

During conceptual design, actual performance losses should be calculated for the specific designs studied

• An important issue for any engine model or data is installation losses- All installations degrade power or thrust available

compared to engine company test stand-type data - The differences are large enough to effect even pre-

concept design estimates• Jet engine losses derive from multiple factors

- Inlet and nozzle losses- Power extraction

• Turboprops also have to deal with prop efficiency• IC engine installations have similar losses (air

induction system, mufflers, generators and props)

- Bleed air- Etc.

18-43



Example - TBProp

1. Our TBProp UAV weighs 1918 lbm, has a balanced field length requirement of 3000 ft (ground roll = 1500 ft) and Clto = 1.49 and wing loading of W0/Sref = 30 psf (qto = 20.2 psf , takeoff speed = 77.2 kts). We assumed a nominal cruise of 180 kts at 27.4Kft, an initial cruise weight (w4) = 1726 and a cruise lift-to-drag ratio (LoDcr) of 23. What size engine is required for takeoff and will it meet cruise requirements?

2. From RayAD Figure 5.4, the required prop aircraft ground roll takeoff parameter for is 220 where

TOP =[W0/Sref]/[CLt/o*(Bhp0/W0)] = = qt/o/(Bhp0/W0)

Bhp0/W0 = qto/220 = 0.092- Engine size, therefore, is

BHP0 = 1918Klb*0.092 = 176.5 Bhp

or

18-44



TBProp takeoff estimate

3. Because propeller models have singularities at V=0, the TBProp is sized at V = V0 = 50 kts (M = 0.076) - At an assumed p = 0.8*, takeoff thrust (T0) can be

calculated directly by definition of BHP orT0 Bhp0*550*p/KTAS*1.689 = 919.6 lbf

- Equation 18.8 is solved for total airflow using chart 18.33 TBP model values or Wdota = 919.6/[90/134 +5*(50/50)*(133/134)] = 163.2 pps

- Knowing WdotA0, the TBP model can now predict thrust, airflow and fuel flow at cruise conditions

- For simplicity, this will be done only once at Vcr = 180 kts and an altitude of 27.4 Kft (M=0.3)- Then it will be programmed in a spreadsheet

* p is assumed to account for all installation losses

18-45



TBProp cruise estimate

4.Equations 18.9-11 provide estimates of total airflow (WdotA) at cruise (M=0.302), where

= ([email protected])*(1+.2M^2)^3.5 = 0.3556 = ([email protected])*(1+.2M^2) = 0.8264

WdotA = WdotA0*/sqrt() = 64 pps- Core airflow by definition of BPR is Wdota/(BPR+1) or

for BPR = 133, Wdota-gg = 0.48 pps

- Fuel flow is calculated using the model fuel-to-air ratio value f/a = 0.0292 corrected for , or ….

WdotF = WdotA-gg*(f/a)* ^.75 = 0.012 pps or 43.4 pph- Equation 5.8 is used to calculate Ta where

Ta = WdotA*(Fsp-gg/(1+BPR)+Fsp-fn*(V0/V) *(BPR/(1+BPR))

= 64*(90/134+5*(50/180)*(133/134) = 130.9 lbf

18-46



TBProp cruise - cont’d

- Thp is calculated using Eq 18.2 or

Thp =130.9*180/325.6 = 72.4 Hp while

Shp = 72.4/0.8 = 90.4 Bhp- Finally SFCcr WdotF/Shp is calculated and found

to be SFCcr = 43.4pph/90.4Bhp = 0.48 pph/Bhp

- Next we need to compare thrust “available” against thrust “required” drag

- We get this by dividing weight by LoDcr or

D ≈ 1726lbm/23 = 75 lbf which is 57% of Ta and shows that the TBProp meets cruise thrust requirements at 180 kts

18-47



TBProp summary

1. Select takeoff speed (Vto), calculate qto [W/S]/Clto2. Estimate takeoff Bhp0 required (RadAD Fig 5.4)3. Select takeoff “sizing” speed = V0 (i.e. 50 kts)4. Calculate Tavail at sizing speed (Ta0 = 325.6pBhp0/V0)5. Calculate WdotA0 from Fsp and Ta0 at V0 (Eq 18-8, BPR = 133)

TBP sizing

1. Select speed (KTAS) & and altitude (h) 2. Calculate , and M at h (atmosphere spreadsheet)3. “Correct” and for M (Eqs 18-10 and 18-11)4. Calculate total (prop+engine) WdotA (Eq 18-9)5. Calculate engine airflow (WdotA-gg = WdotA/[BPR+1])6. Calculate corrected fuel-to-air ratio (Eq 18.7)7. Calculate fuel flow (WdotF= WdotA-ggcorrected fuel-to-air ratio)8. Calculate thrust available (Eq 18-8)9. Calculate uninstalled Bhp (= TaKTAS/[325.6 p)10. Calculate uninstalled SFC [SFC = WdotF/Bhp(uninst)]11. Check that Ta > D = W/LoD

TBP performance

18-48



Typical example - TBFan

1. Our TBFan alternative weighs 2914 lbm, has a balanced field length requirement of 3000 ft (ground roll = 1500 ft) and Clto = 1.49 and wing loading of W0/Sref = 40 psf (qto = 26.9 psf , takeoff speed = 89.1 kts). We assumed nominal cruise at 300 kts at 27.4Kft, an initial cruise weight (w4) = 2645lbm and a cruise lift-to-drag ratio (LoDcr) of 22.5.

2. From RayAD Figure 5.4, the required jet aircraft ground roll takeoff parameter for is 100 where

TOP =[W0/Sref]/[CLt/o*(T0/W0)] = = qt/o/(Bhp0/W0)

T0/W0 = qto/100 = 0.269- Engine size, therefore, is

T0 = 2914*0.269 = 784 lbf

18-49



TBFan performancewhere

3. The TBF model also has a singularity at V=0 and is sized at V = V0 by solving for WdotA0

Fsp0 = Fsp-gg/(1+BPR)+ Fsp-fn*(BPR/(1+BPR)

T0 = WdotA0*Fsp04. Therefore for BPR = 5.0, Fsp-gg = 90, Fsp-fn = 30

(vs. 25 at BPR = 8) and T0 = 784 lbf WdotA0 = 784/(90/6+30*5/6) = 19.6 pps

5. Performance at other conditions is determined using Equations 18.9-11 and V0 = 100 kts. For example, at h = 27.4 Kft, V = 300 Kts (M = 0.503) :

= (@27.4Kft)*(1+.2M^2)^3.5 = 0.37969= (@27.4ft)*(1+.2M^2) = 0.8527

WdotA = WdotA0*delta/sqrt() = 8.4pps

where

and

and

18-50



- By definition core airflow (Wdota-gg) = Wdota/(BPR+1) or for BPR = 5, Wdota-gg = 1.4 pps

- Fuel flow is calculated using the model fuel-to-air ratio value f/a = 0.0292 corrected for , or WdotF = WdotAgg*(f/a0)* ^.75 = 0.037 pps or 131 pph

- Equation 18.8 once again is used to calculate thrust T = WdotA*[Fsp-gg/(1+BPR)+Fsp-fn*(V0/V)

*(BPR/(1+BPR)] = 8.4*(90/6+30*(100/300)*(5/6)) = 197 lbf

and TSFC = 131pph/197lbf = 0.67pph/lbf

- At a LODcr of 22.5 and initial cruise weight =2623 lbm, D = 116.6 lbf compared to TBFan T (uninstalled) = 198 lbf. If we assume a 5% installation loss, Ta = 188 lbf, which is enough to meet the cruise thrust requirements

TBFan performance - cont’d

18-51



TBFan summary

1. Select speed (KTAS) & and altitude (h) 2. Calculate , and M at h (atmosphere spreadsheet)3. “Correct” and at M (Eqs 5-13 and 5-14)4. Calculate WdotA (Eq 5-12)5. Calculate core airflow (WdotA-gg = WdotA/[BPR+1])6. Calculate corrected fuel-to-air ratio (Eq 5.10)7. Calculate fuel flow (WdotF = WdotA-ggcorrected fuel-to-air ratio)8. Calculate uninstalled thrust (Eq 5-11)9. Calculate installed thrust (Tinst = Tuninstinstallation factor)10. Calculate installed TSFC (TSFC = WdotF /Tinst11. Check that Tinst > D = W/LoD

TBF performance

1. Select BPR 2. Select Fsp-fn = f(BPR) Chart 5b-13 3. Select takeoff speed (Vto), calculate qto [W/S]/Clto4. Estimate takeoff T0 required (RadAD Fig 5.4)5. Select takeoff “sizing” speed = V0 (i.e. 100 kts)6. Calculate WdotA0 from Fsp and T0 at V0 (Eq 18-8)

TBF sizing

18-52



Concluding remarks

• Our parametric models predict reasonable performance for a range of types, altitudes and subsonic speeds

• Although approximate, they capture effects not included in traditional parametrics, e.g. RayAD equations 10.4-15.- They can be used for pre-concept design studies until

better data is available• The models are approximate and are valid only at

subsonic speeds• The models do not capture temperature or RPM limits

obvious in RayAD Appendix E plots• The models do the best job of predicting airflow • The model do the worst job of predicting HBPR and TBP

performance at low-altitude and high-speeds. - Typically, these engines are not operated under such

conditions and the errors have little practical effect• During conceptual design engine company models

should be used

18-53



Expectations

You should now understand

• Propulsion parametrics and parametric models

• Where they come from

• How they are used

• The limits of their applicability

18-54



Homework

1. Write spreadsheet programs to calculate uninstalled IC, TBProp and TBFan engine performance with airspeed (or M) and altitude (or delta & theta) as inputs - (team grade)

2. Run your TBProp and TBFan models for the example problems (charts 18-43 through 18-50) and compare results (team grade)- Identify any errors in my example problems

3. Using a balanced field length criteria for takeoff, size engines for your proposed air vehicle (individual grades)

4. Use the team spreadsheets to calculate uninstalled engine performance at takeoff and dash (target ID) speeds for your proposed air vehicle (individual)

5. Compare TBProp and/or TBFan results to ASE261.Engine.Models.xls and identify differences (individual grades)

Week 2

18-55



Intermission

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18-1 Design of UAV Systems Propulsionc 2002 LM Corporation Lesson objective - to discuss Propulsion...

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