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• Missile Guidance– Zero Effort Miss – Proportional Navigation – Trajectories and Miss Distance – Augmented Proportional Navigation– Predictive Navigation– Optimal Navigation– Beam Rider and Pursuit Guidance
• Seekers– Seeker Measurements – Radar Seekers– Passive Seekers– Seeker Noise and Noise Reduction– Signal Processing
• Power and Power Conditioning• Missile Simulation
– Types and Uses of Simulation– 2-6-DOF Simulations and Their Uses– Adjoint Simulation– Current Capabilities and Future Trends
• Introduction– Types of Missiles– Missile Basing– Missile Systems Overview
• Warheads and Lethality• Missile Propulsion
– The Rocket Equation– Liquid and Solid Propellants– Multistage Rockets– Effects of Gravity and Drag
• Missile Autopilots and Control– Pitch/Yaw Autopilots– Inertial Instruments– Body Modes and Rate Saturation– Radomes and Their Effects– Adaptive Autopilots– Roll Autopilots and Roll-Yaw Coupling– Exoatmospheric Missiles
The Rocket Equation• As a rocket burns fuel, hot exhaust gas exits through a nozzle at the
back, and by conservation of momentum, the missile moves forward. The rocket equation describes a missile’s speed during boost, ignoring gravity and drag. To derive it, consider a small particle of exhaust gas of mass dm leaving a rocket’s nozzle at speed U. Its momentum is Udm. The missile has mass m and changes speed by an amount dv. Its momentum change is (m−dm)dv ≅ mdv. Conservation of momentum requires that mdv +Udm=0, since there are no external impulse applied.Hence U
dm
dv
.mdmUdv −=
.ln 00 ⎟
⎠⎞
⎜⎝⎛=−=∆
mm
Uvvv• The solution to this differential equation is
• This is one form of the rocket equation. m0 is the missile’s initial mass and v0 is its initial velocity. m is the missile’s mass after all its fuel is expend (called the burnout mass) and v is the burnout velocity. (More generally, m and v can be any mass and corresponding velocity.)
• The rocket equation shows that missile’s velocity results from expelling mass in a given direction in the form of exhaust gas. No air is needed for the rocket’s thrust to push against.
– On Jan 13, 1920, the New York Times ridiculed Robert Goddard for this assertion, saying he lacked "the knowledge ladled out daily in high schools.”
– Thirty five years later, the correctness of Goddard’s principle was proven correct by the successful operation of rockets in space. The Times published an apology in 1969, shortly after Apollo 11 landed Astronauts Armstrong and Aldrin on the moon.)
course. t the throughoufor notation shorthand thisuse will We. *dtd
dtdmm =&
• Equating ∆v from the two forms of the rocket equation, we get ./ UmF =− &It .kg/sec at fuelrocket burningby generated thrust theis /quantity The mmF &&−•
varies from one fuel to another, and equals the speed, U, of the hot gas exiting the rocket’s nozzle. It has the dimension of m/sec.
a
F
• The solution to this differential equation is .ln0
0 ⎟⎠⎞
⎜⎝⎛
+−=∆
tmmm
mFv
&&
.or )( Hence,0
0 tmmFdtdvdt
dvtmmF&
&+
=+=•
• Another way to derive the rocket equation is through Newton’s second law (F=ma). Consider a missile of mass m propelled by a rocket with constant thrust F. To produce the constant thrust, the rocket expels fuel at a constant rate, and the missile’s mass decreases at the this rate. The thrust F produces an acceleration, a, according to F=ma, with m
*,m&
mtmmm .0 where, as varying 0 <+= &&
• Instead of gmwwFmF &&&& =−− where,efficiency thrust measure to/ use scientistsrocket ,/the weight of fuel burned per second. The resulting quantity, called specific impulse, Isp, is defined by .
gU
wFI sp =−=&
• The dimension of Isp is seconds (in every system of units). Conventional rocket fuels have an Isp between 150 and 450 sec.
Specific Impulse (Continued)• The most common form of the rocket equation is obtained by substituting U= Ispg into
• Combustion efficiency, burning temperature, rocket nozzle shape, and altitude all affect Isp. To account for the altitude effects, Isp is sometimes quoted both at sea level and in a vacuum. For example, the solid fuel HTPB (hydroxy-terminated polybutadiene) used in combination with aluminum in many solid rockets, has a sea level Isp of 254 sec and a vacuum Isp of 302 sec.
⎟⎠⎞
⎜⎝⎛=∆
mmgIv sp
0ln:)/ln( 0mmUv =∆
• Hence, Isp measures a fuel’s efficiency in converting weight into impulse, which can be written
],0[ interval timeaover burned is fuel theif constant, are and since and ,
thrusta delivers * rateat certain a with fuel burning , of definition theFrom ,twFwIF
wIIsp
spsp&&
&−=
−•
.gU
wtF
wFI sp =
∆∆=−=
&
∫∫ ∫ −=−=)(
0 0 0
tw
wsp
t t
sp dwIdtwIFdt &
)].([ or 0 twwIFt sp −=
. rateconstant at the decreases fuel theof weight thei.e, * w&
• Thus, burning an amount of fuel weighing ∆w over a period of time ∆t produces a total impulse of wItF sp∆=∆
Example--Isp• Isp is sometimes used incorrectly to compare the thrust-producing capability of rocket
fuels. This can lead to wrong conclusions because Isp is really measure of a fuel’s efficiency in producing impulse.
• For example, the conventional fuels that propel missiles to supersonic speeds and send satellites into space have Isp between 150 and 450 seconds, and some produce over a million lb of thrust.
• On the other hand, NASA’s ion engine, which produces thrust by accelerating ionized xenon atoms to 30 km/sec, has an Isp of 3(104)/g=3,100 sec. However, the ion engine produces only 92 mN of thrust (about 1/3 oz)*.
Ion Engine on NASA’s Deep Space 1 Satellite* Ion engines currently under development have demonstrated 1 N (0.225 lb) of thrust.
• The ion engine cannot produce enough thrust to lift itself off the ground, but it can very efficiently accelerate spacecraft to speeds of 5-10 km/sec in up to a year of continuous operation, after the spacecraft is first sent into space by a conventional rocket.
• The point to remember is that Isp= F∆t/∆w, so for a fixed amount of fuel, ∆w, high Isp implies a large product of thrust, F, and burning time, ∆t, not just high thrust.
Phases of Missile Flight• At launch, a missile begins its boost phase where it is accelerated to high speed in
the general direction of the target by an axial rocket booster using thrust vector control to follow a pre-computed trajectory. After its booster burns out, the missile enters the midcourse phase of flight, gliding at high speed on a pre-calculated, radar updated, approximate intercept course with its intended target.
• A missile does not track its target during midcourse. The midcourse phase serves to fly the missile into an acquisition basket from where it can acquire the target with its onboard seeker to begin homing.
• After booster burnout, the missile enters the terminal phase (also called the homing phase or end game), where is guided by changing the direction, not the magnitude,of its velocity vector*. Endoatmospheric missiles do this by rotating aerodynamic control surfaces (usually tails, wings or canards). Exoatmospheric missiles use divert thrusters for homing.
• In the next section, we discuss how missiles accurately control lateral acceleration in the homing phase so as to hit their targets or pass as close to them as possible.
CGCP V
aV, a
* In endo missiles, there is some slowdown due to atmospheric drag, but every effort is made to minimize it.
Introduction To Missile Autopilots• The purpose of an autopilot is to produce lateral missile
acceleration a in response to commanded acceleration ac.• Exoatmospheric missiles produce acceleration
perpendicular to their center lines using divert thrusters, which act through the missile’s CG.
• Endoatmospheric missiles create acceleration perpendicular to their centerlines using the aerodynamic force from the angle of attack α between the missile’s centerline and velocity vector.
• An autopilot’s time constant is the approximate time it takes for the missile to achieve a commanded acceleration.
ac
tAcceleration Commanda
tIdeal Zero Order Autopilot (No Delay, No Accl Limit)
Missile Control• Missiles use tail, wing, canard, or thrusters to maneuver and control their attitude.
Some missiles use a combination of these control systems.– Thrusters are used exclusively to control exo missiles, and sometimes in combination
with other types of controls in endo missiles.– In tail- and canard-controlled missiles, the control surfaces are placed as far as possible
from the CG to produce the maximum pitch/yaw moment. In wing control, surfaces are located at or near the CG.
– In endoatmospheric missiles, fixed surfaces are often added to improve stability and, in tail- and canard-controlled missiles, to increase forces at the CP for high lateral acceleration.
• Tail control– Allows uniform component mass distribution (seeker and
warhead (if any) front, avionics and power mid, control surfaces and actuators aft).
– Most stable in supersonic flight (minimal roll problems from downwash from fixed surfaces)
– Lowest drag on control surfaces (with positive static margin).
– Highest angle of attack without control surfaces stalling (with positive static margin).
– Initial motion in wrong direction (corrected with forward thrusters) and slightly reduced lift from tails.
– Produces largest moment for given control surface area.– Slightly more efficient than tail control because initial
motion is in right direction (if static margin is positive).– Canards can stall at relatively low angle of attack.– Downwash from canards complicates roll control.– Nonuniform component mass distribution (seeker and control
system must be at front).• Wing control
– Minimizes angle of attack, reducing body drag and relaxing seeker FOV requirement.
– Allows angle of attack to be controlled directly, eliminating the need for accelerometers in simple missiles.
– Wings must be large compared to tails or canards, increasing drag, servo motor size, power consumption, missile mass, and volume requirements.
– Requirement to pivot wing at or near CG makes the missile sensitive to CG and CP shifts.
• Exoatmospheric missiles use divert and attitude control thrusters to accelerate missile normal its center line and maintain attitude directly. No aerodynamic problems in space.
Exoatmospheric Missiles• Exoatmospheric missiles obey the same six Euler
equations as endoatmospheric missiles. Making the same assumptions as before, the motion decouples into two orthogonal planes described by the same linear differential equations,
• Outside the atmosphere these equations can be mechanized directly using divert and attitude controlthrusters to provide Fy and Mz. There is no need for aerodynamic coefficients.
• Exo missiles can fly at any angle of attack, α, without concern for aerodynamic forces, and an exo seeker can point at a target continuously (σ ≈ψ). Just as in the endo case, missile acceleration, so it is necessary to divide acceleration commands by cosγ.
• Radomes are unnecessary, eliminating the problems of radome error slope.• The exoatmospheric missile’s airframe response does not change with flight conditions, so
open loop autopilots could be considered. However, an IMU is necessary for midcourse fly out and position and rate feedback enhance thruster firing precision, improving both miss distance and fuel economy. Hence gyro and accelerometer feedback are used in most designs.
• Although there is no atmospherically-induced roll, roll control is still desirable (though not mandatory), because it prevents precession, reduces image smearing the on seeker’s focal plane array, and decouples lateral missile motion from attitude.
• As divert and attitude control system (DACS) fuel burns, the missile’s CG shifts, causing the divert thrusters to produce moment as well as the desired lateral ∆V. This is the largest source of unwanted coupling in exo missiles, and the ACS must be sized to counter it.
Homing Guidance Introduction• Missiles make measurements for homing guidance with on-board seekers that track
the line-of-sight (LOS) to the target, and sometimes measure the range and range rate also. In command guided missiles, a radar makes the LOS measurement by tracking the missile and the target from the ground, then uplinks commands to the missile.
• The homing guidance laws we will derive apply to both endoatmospheric and exoatmospheric missiles. Exo intercepts can be easier because their targets usually cannot maneuver and there are no aerodynamic or aero-optical effects in space.
• A target’s speed and capability to maneuver, deliberately or inadvertently, determine the missile homing guidance law best suited to intercept it.
– Stationary, or slowly moving targets are the easiest to intercept, and guidance laws for them can use simple seeker measurements of the look angle between the missile’s center line and the LOS. Such missiles have minimal requirements for inertial instruments, but perform poorly against moving or maneuvering targets.
– For faster moving targets and maneuvering targets, commanding missile acceleration proportional to the LOS turning rate is very effective, and most of today’s homing missiles rely on this measurement. However, LOS turning rate measurements require accurate rate gyros aboard the missile to measure and remove body rates and/or a gimbaled seeker head.
– Combining estimates of target acceleration with LOS turning rate can reduce miss distance, but if the target acceleration estimates are inaccurate, they can increase miss distance relative to what it would have been if the estimate were not used.
– By taking missile and target time constants and acceleration limits into account, optimum homing guidance laws maximize a missile’s effectiveness against maneuvering targets.
Homing Guidance Law Development• Early guided missiles were command guided by ground based radar, which tracked
the missile and its target and uplinked guidance commands. • Some early missiles engaged their targets by flying directly at them. The guidance
law simply aligned velocity vector (in command guided missiles) or the missile center line (in missiles with seekers) with the target. This technique, called pure pursuit, always ended up in a tail-chase, and had limited effectiveness against moving targets.
• In another early homing technique, called beam rider guidance, the missile was commanded to fly along a radar beam from the launcher to the target. Beam rider missiles had poor performance against fast-moving targets. They tended to oscillate about the beam and waste energy by reacting to noise and beam jitter. They also required large acceleration as they approached their targets.
• Proportional navigation (PN) was developed in the late 1940’s and tested in the early 1950’s. PN commands a missile to accelerate in proportion to the LOS turning rate, allowing it to arrive at a predicted future point simultaneously with the target. PN has been found to be very effective against most targets of interest. Because of its great success, some form of PN is still used today in most missiles.
• Highly maneuverable targets require homing guidance laws that account for missile autopilot time constants and acceleration limits. While, these optimum homing lawsoutperform PN, they still use LOS turning rate as a primary variable.
Missile Guidance Using Line-Of-Sight Change• The figures below show a missile intercepting a target by accelerating laterally to
keep the line of sight (LOS) angle constant. The technique is the basis for a very effective homing guidance law. It has similarities to a method used for centuries by sailors to prevent ship collisions by avoiding “constant bearing, decreasing range.”
Intercept: LOS Angle Remains Constant(Constant Bearing Decreasing Range)
Zero-Effort Miss• In deriving homing guidance laws, it is useful to know what the miss distance would
be if the missile and target did nothing but continue on their current courses (VM and VT in the diagram below). This is called the zero-effort miss (ZEM). It is the miss distance, calculated at any time, t, during the homing phase, assuming neither the missile nor the target accelerates (in any direction) from time t until their closest point of approach (CPA) at time tf.
• The logic behind ZEM is that if we know how far a missile will miss its target without effort, an acceleration can be applied that will reduce that miss. A homing guidance law can then be derived using ZEM by repeating the process: “Find ZEM, compute missile acceleration to reduce ZEM”, …, throughout the homing phase.
.gotyyZ &+=
• Define the relative missile-target y-displacement as y=yT−yM, then the miss distance, y(tf), assuming no accelerations take place during time interval tgo is the ZEM, Z.
. written becan this),( Defining .)()( and 0,)( then(CPA),approach ofpoint closest of time the If .)()()(
is range the, and timesany twofor Then consant. is , rate, range theAssume
gofgoff
f
trrtttrtttrtrtrttrr
tr
&&&
&
−≅−=−−≅≈==−+=
•
ττττ
• Previous charts showed that planar analyses can be used for LOS motion of without loss of generality. The planar diagram at the right shows a missile, M, and its target, T, moving with velocities VM and VT respectively, withthe x-axis along the initial LOS, as in the previous charts.
ZEM. toconverted with laws existingsimply be out to edlater turn which ZEM,using laws guidance new discoveredy assert the tosome led
has iprelationsh thisof Ignorance . rate, turningLOS the torelatedclosely is ZEM
σ
σ
&
&•
• The xy and rσ systems are rectangular and polar coordinate representations of the same problem. We retain both because rectangular coordinates are usually easier to work with, while missile seekers make measurements in polar coordinates.
rVM
VT
y
y
x),( MM yx
),( TT yxσ
written becan ZEMand .)( gotrrrZ σσσ && ++=
, ating,Differenti σσ &&& rry +≅
.sin σσ rry ≅=
, chart last thefromBut rtr go −=&
.σ&gortZ =so
small, is since right, at the diagram thefrom so ,by given is ZEMchart thatlast thefrom
recall , and Mbetween ZE iprelationsh thederive To
effort. zero with occursIntercept solve. tonothing is there,0 If .0 provided 0* 2 =≠>= ZZZV
• Russian mathematician Aleksandr Lyapunov (1857-1918) developed a stability theory which follows from the fact that a quantity that is always positive and decreasing approaches zero asymptotically. Lyapunov’s theorem states that for a system with state vector x, if a scalar function V(x) can be found with the following two properties for all nonzero x, ,0)( and 0)( <> xx VV &
then the system is asymptotically stable (||x(t)||→ 0 asymptotically as t→∞).• Lyapunov’s theorem enables the derivation of a very effective homing guidance law.
is and *,0Then .)(),( choose and , and be variablesstate Let the 22
as by controlled is PN using ZEMof econvergenc then the,constant essdimensionl positive, a be Let
Λ
−Λ•rK& Λ
⎟⎟⎠
⎞⎜⎜⎝
⎛−=
ftt
ZtZ 1)0()(
* Note that K need not be constant here, just positive.
.0 as long as , ing with vary very well worksPN fact,In shows. Eappendix of derivation theas necessary,not isn restrictio thisHowever, math. hesimplify t oconstant t was that assumed it was PN derivingIn **
. offunction a as belowgiven ison Accelerati .considered be alsomust on accelerati missilebut e,convergenc rapidfor large of usesuggest right
at theshown vs1)0()()(
0Z
tt
tt
ZtZt
ff
Λ
=⎟⎟⎠
⎞⎜⎜⎝
⎛−==
Λ
τρ
• This is the usual form of the PN law. The plots of
2
20
2
0
20
22
1)(
)()/1(
−Λ
Λ
−Λ
Λ
⎟⎟⎠
⎞⎜⎜⎝
⎛−
Λ=
−Λ=
−
−Λ=Λ=
−Λ−=Λ−=
fff
f
f
f
gogoM
tt
tZ
ttt
Z
ttttZ
tZ
trZrra&
&&&σ
• A plot of the normalized PN acceleration,
• Both large and small Λ demand high missile acceleration. To avoid exceeding acceleration limits, intermediate values are needed. Therefore, most missiles use
Missile Seeker Systems• Missile seekers make the measurements for target detection and homing by sensing the
radio frequency (RF), infrared (IR), and/or visible energy that targets emit or reflect. • Passive IR seekers (e.g, THAAD, EKV) detect IR energy emitted from targets using a focal
plane array (FPA), scanning detector, or a single detector with a spinning reticle. – Some IR seekers also include a visible sensor, which measures reflected visible light. – Anti-radiation missiles (e.g, HARM) use passive RF seekers that home directly on the radar
transmissions from ground- or sea-based anti-aircraft radar. • Active seekers (e.g, PAC-3, Standard Missile) track targets with on-board radar.• Semi-active seekers (e.g, Patriot) detect radar energy reflected from targets tracked and
illuminated by ground- or ship-based radar.• With command guidance, no seeker is used. Both the missile and target are tracked by
ground radar, where guidance commands are computed and uplinked to the missile.
• Endoatmospheric seeker design must account for atmospheric transmission by including operation at wavelengths* least attenuated by the atmosphere along with other design criteria. The diagram below shows atmospheric transmission vs wavelength.
• At RF wavelengths above 2.5 cm (x-band and lower frequencies) atmospheric attenuation can be ignored in seeker design.
• For higher σ measurement accuracy, Ku-band and W-band (35 GHz and 94 GHz), (8 mm and 2 mm respectively, can be used to take advantage of the relative low attenuation at these wavelengths.
• In the infrared, MWIR wavelengths of 3-5 µm and LWIR wavelengths of 8-12 µm have relatively low atmospheric attenuation as does the visible band.
• Exoatmospheric seekers can operate at any wavelength without attenuation. Sometimes they operate in wavebands most attenuated by the atmosphere to view objects without the complication of earthshine and avoid terrestrial interference (intentional or inadvertent).
Michael Faraday (1791-1867)Discovered electromagnetic induction--
the generation of electricity in a conductor by an electromagnetic field
produced by current in separate conductor.
Robert Watson-Watt (1892-1973)Led the British research that developed and
demonstrated the first radar in 1935. Watson-Watt designed and deployed a chain of radars along the British coast in 1939 that were instrumental in the British winning the
Battle of Britian.
James Clark Maxwell (1831-1779)In one of the most elegant theories of all time, developed four partial differential equations
that describe and unify electricity, magnetism, and the propagation of electromagnetic waves
Radar Seekers--Angle and Range Measurement• Most missile radars transmit many different waveforms. The
most common is a train of narrow pulses, each containing many cycles of the transmitted energy as shown at the right.
• The number of cycles a radar transmits each second is called its frequency, which is measured in Hertz (Hz).
– One Hz=one cycle per second, hence Hz has dimension sec-1. – The period of the radar frequency is T=1/f (sec).– A radar’s wavelength λ (meters) is the distance between
successive peaks of its transmitted energy in space.
1
1
}
– Radar waves travel at the speed of light, c=3(108) meters/sec, so frequency f and wavelength λ are related by λf=c.
– The formulas above apply to all portions of the electromagnetic spectrum (IR, viz, etc), not just radar.• Radars transmit electromagnetic waves and track the LOS angle σ via the energy reflected
back from targets using a parabolic dish antenna or a phased array. Their angular accuracy is approximately their beam width θ=λ/D, where D is the diameter of the dish or array. for homing is then found by filtering (usually Kalman filtering).
• Radar can also measure a target’s range r by the time ∆t it takes a transmitted pulse to reach the target and return. Since the round trip distance is 2r=c∆t, the range is r=c∆t/2.
– Recall that for proportional navigation, the missile commands an acceleration The range measurements can be used to estimate or it can be measured directly by doppler radar.
– Optimum homing laws use an estimate of time-to-go, tgo, which, as we saw, is closely approximated by Hence, both r measurement and estimates are needed for optimum homing.
The Radar Equation• Consider a radar transmitting power Ptr uniformly in all directions (isotropic radiation). A
sphere of radius r centered at the transmitter has area 4πr2, so the power density J0 through its surface is J0=Ptr/(4πr2). With an antenna of gain* G, the power density is Jr=GJ0, hence, with an antenna, the power density through the sphere (where the energy is focused) will be
• A target r meters away will act like a reflector of some area σ m2, called the radar cross section** (RCS), echoing a fraction of the transmitted power back to the radar receiver. The power density at the receiver will be
222 )4(4 rGP
rJJ tr
rrec πσ
πσ
==
• If the radar uses a receiving antenna of effective area A1, it will measure power Prec=A1Jrec=A1PtrGσ/(4πr2)2. Like most radars, missile radar seekers are monostatic (i.e., they use the same antenna to transmit and receive). It can be shown that the gain of an antenna with effective area A1 is G=4πA1/λ 2 , so A1=Gλ2/(4π), and the received power is
.4 2r
GPJ trr π
=
trrec Pr
GP 43
22
)4( πσλ
=
• This is the radar equation. Note that the power received by the missile’s seeker is inversely proportional to the fourth power of the missile-target range r.
* Gain is achieved by focusing the radar energy through only a portion of the sphere. The ratio of a radar’s power with an antenna to its isotropically radiated power is defined as the antenna’s gain.
Radar Bands• Radar wavelengths and frequencies are shown below. Most missile systems
operate in the C, X, or Ka band. Higher frequencies are preferred because they allow better angular resolution and the components are smaller, however, atmospheric attenuation restricts the use of some bands above X. Ka and W are attractive because of reduced attenuation in portions of these bands.
• Improvements in inexpensive, light weight components is still needed above Ka band.
• In the semi-active system shown, let the radar-target distance be r1 and the missile-target distance r2, and call the ground radar illuminator and seeker antenna gains G1 and G2 respectively.
• As in the active seeker case, the power density at the target is .4 2
1
11 r
GPJ tr
r π=
The power density reflected back the the missile seeker is
• If the seeker uses a receiving antenna of effective area A, it will measure power Prec=AJrec=APtrG2σ/(4πr1
2)(4πr22). From the formula for antenna gain, A=G2λ2/4π, the received power is
trrec Prr
GGP 2
22
13
221
)4( πσλ
=
r2
r1
G1
G2
• Semi-active missile systems are attractive due to their long acquisition range and because a missile’s mass and cost are lower without a radar transmitter; also a ground radar can be much larger and more powerful than a missile-borne radar. For example, if a ground radar antenna’s diameter is 10 times that of a missile seeker’s antenna, and transmitts100 times the power, the G1Ptr product is 10,000 times larger than the GPtr product obtainable with an active seeker aboard the missile. Before the advent of semiconductor electronics, most homing missiles were semi-active.
• But semi-active systems are often less effective than active systems. Three reasons for this are:– As the missile closes on the target, the power reflected back to its seeker increases faster with an
active missile seeker than with the semiactive (r2−4, vs r2
−2, assuming r1 is nearly constant). – Multiple targets are difficult to handle with semiactive missile systems. Separate frequencies or
codes are needed to control each target. Semi-active ground systems become less effective with each additional target they must track, until they finally become overwhelmed.
– The powerful illuminator is easy to detect and jam or target.
Radar vs IR Seeker Detectors• An x-band radar seeker with λ=3 cm, a 25 cm aperture, and fl=15 cm produces a
resolution limited spot 2.44(λ/D)fl=4.4 cm in diameter, while a 10 µm LWIR seeker with the same parameters produces a 15 µm spot.
• With such a small spot, the sensor for an IR seeker usually consists of an array (called a focal plane array(FPA)) of many (up to several million) small detectors, called pixels (picture elements), which can form a two-dimensional image of a target if it is close enough.
• Radar seekers usually have only one detecting element, and do not image targets in this way.
• A seeker’s field of view is the angular width it can see. The field of view of a radar or passive seeker is FOV=1.22 λ/D. Note that a radar seeker’s FOV is the same as its beam width.
• The FOV of a single pixel of a FPA is called the instantaneous field of view (IFOV). The FOV of a passive seeker is its instantaneous field of view multiplied by the number of pixels in a row or column of the FPA. Thus for a 265x256 FPA operating at λ=9 µm with a 20 cm aperture, IFOV=1.22(9)(10-6)/0.2=5.5µr, and the field of view is 256(5.5)(10-6)=14 mr=0.81°.
Focal Plane Arrays And Read Out Electronics• A focal plane array (FPA) is an array of 4 to 1,000,000 detectors, called pixels, which are sensitive to a
portion of the IR spectrum. Each pixel is 20-30 µm in size in missile seekers. • FPAs consist of two parts: a pixel array (UV, Visible, or IR) and a read out electronics (ROE) chip,
bonded to the pixel array by indium bumps, which also provide electrical contact. • The ROE converts the large number of individual pixel outputs into a pulse train, reducing the number of
output wires from tens of thousands to under 100. • Frame rate is the number of times the entire array is read out each second. Frame rates of 10-100 Hz are
typical in missile seekers. The frame rate must be short enough to avoid smearing the target image and long enough to allow adequate energy collection before readout. Readout A/D speed also limits the frame rate (e.g, a 512 x 512 FPA operating at 50 Hz with 16 bit words must transfer over 200 Mb/sec)
• All the pixels of a seeker’s FPA observe the FOV for some fraction of each frame, called the integration time. During the integration time, the photoelectrons are collected in small capacitors behind each pixel in the ROE, called wells. The storage capacity of the wells limits the dynamic range of FPAs to about 10,000-100,000 and also limits the S/N.
• An array of microlenses can be bonded to the FPA to increase its sensitivity when the fill factor is small. It also improves nuclear hardness because the microlenses do not refract high energy radiation. However, microlenses increase cost.
Passive Seekers• Passive missile seekers usually operate in the infrared (IR) spectrum, which is
subdivided into short wave IR (SWIR) (1 µm to 3 µm), medium wave IR (MWIR), (3 µm to 5 µm), long wave IR (LWIR) (8 µm to 12 µm), and very long wave IR (beyond 12 µm)*.
• In addition to a FPA (usually in dewar for cooling), passive seekers include optical components (lenses, mirrors, stops, and baffles).
• Many different optical configurations are possible for IR seekers. Their purpose is to magnify incoming IR energy, and direct it onto the detector by mirrors and/or lenses. One common configuration, called a Cassigrain system, is shown below.
rPixel
FPA
PhotonsFPA
Dewar
Stop
PrimaryMirror
SecondaryMirror
LensesBaffle
SWIRMWIR
LWIRVLWIR
* 5-8 µm is missing from these definitions because the atmosphere is nearly opaque in this band. However, it can be used for exoatmospheric missiles.
Boost Your Skillswith On-Site CoursesTailored to Your NeedsThe Applied Technology Institute specializes in training programs for technical
professionals. Our courses keep you current in the state-of-the-art technology that isessential to keep your company on the cutting edge in today’s highly competitivemarketplace. For 20 years, we have earned the trust of training departments nationwide,and have presented on-site training at the major Navy, Air Force and NASA centers, and for alarge number of contractors. Our training increases effectiveness and productivity. Learnfrom the proven best.
ATI’s on-site courses offer these cost-effective advantages:
• You design, control, and schedule the course.
• Since the program involves only your personnel, confidentiality is maintained. You canfreely discuss company issues and programs. Classified programs can also be arranged.
• Your employees may attend all or only the most relevant part of the course.
• Our instructors are the best in the business, averaging 25 to 35 years of practical, real-world experience. Carefully selected for both technical expertise and teaching ability, theyprovide information that is practical and ready to use immediately.
• Our on-site programs can save your facility 30% to 50%, plus additional savings byeliminating employee travel time and expenses.
• The ATI Satisfaction Guarantee: You must be completely satisfied with our program.
We suggest you look at ATI course descriptions in this catalog and on the ATI website.Visit and bookmark ATI’s website at http://www.ATIcourses.com for descriptions of allof our courses in these areas:
• Communications & Computer Programming
• Radar/EW/Combat Systems
• Signal Processing & Information Technology
• Sonar & Acoustic Engineering
• Spacecraft & Satellite Engineering
I suggest that you read through these course descriptions and then call me personally, JimJenkins, at (410) 531-6034, and I’ll explain what we can do for you, what it will cost, and whatyou can expect in results and future capabilities.
Our training helps you and your organizationremain competitive in this changing world.
Register online at www.aticourses.com or call ATI at 888.501.2100 or 410.531.6034
