Tactical Missile Maneuverability

Tactical radar-guided missiles use a seeker with a radome. The radome causes a refraction or bending of the incom­ing radar wave, which in turn, gives a false indication of target location. This phenomenon can cause problems if the missile is highly maneuverable. One parameter that measures maneuverability is the so-called missile (pitch) turning rate frequency (or bandwidth) defined by (2)

y — a, y(tf) — 0

(tf — t)2

def У

N

a

a

PNG Miss Distance Performance: Impact of System Dynamics

For the two cases considered above, the associated relative displacement y & RX satisfies

where y denotes the time rate of change of flight path angle and a denotes angle-of-attack (AOA). o)a measures

* LD, Sref =

Splan ‘

(14)

ю

a

1 + 0.75 Splan

Sref

def Y t gQSref Cl

(9)

aVm

W

a

a

(12)

|L( jo>)^NVcR —

юа Vm

constant e > 0. This result however, requires that the guidance-control-seeker bandwidth ю satisfies

1

V

m

(13)

ю

a

RNVc

From this, it follows that юа decreases with increasing mis­sile altitude and with decreasing missile speed Vm.

Radome Effects: Homing-Robustness Trade-offs

Let ю denote the guidance-control-seeker bandwidth.

• Homing Requirement. If ю is too small, homing is poor and large miss distances result. Typically, we de­sire

юа<ю (10)

that is, the guidance-control-seeker bandwidth should be sufficiently large so that the closed-loop system “accommodates” the maneuverability capabilities of the missile, which implies that the guidance-control — seeker bandwidth ю must be large when юа is large (low altitude and high missile speed Vm).

• Robustness Requirement. If ю were too large, how­ever, it is expected that problems can occur. This result in part, is because of radome-aerodynamic feedback of the missile acceleration am into X. Assuming n-pole dynamics, it can be shown that the missile accelera-

(11)

where G = NVc represents the guidance system, F =

ю n

(——- ) represents the flight control system, R is the

і + ю

radome slope (can be positive or negative), and A = -—— denotes the missile transfer function from am

0^aVm

to pitch rate в For stability robustness, we require the associated open-loop transfer function

the rate at which the missile rotates (changes flight path) by an equivalent AOA. Assuming that the missile is mod­eled as a “flying cylinder” (8) with length L and diameter

D, it has a lift coefficient CL = 2a[1 + 0.75 plan a], where

Sref

Noting that am = VmY is the missile

= FG[X — R0] = FG[X — RAam] =

tion am takes the form

L=f FGRA = NVc

юа = — = a

1 + FGRA

pg Vm Sref

nD2

FG

4

ю

m

acceleration, Q = ^ pVm the dynamic pressure, W = mg the missile weight, and p the density of air, it follows that

to satisfy an attenuation specification such as — <s for some sufficiently small

s + ю

The lower inequality should be satisfied for good homing. The upper inequality should be satisfied for good robust­ness with respect to radome effects.

• When юа is small (e. g., at high altitudes or low speeds), designers make the guidance-control-seeker band­width ю small but sufficiently large to accommodate missile maneuverability (i. e., satisfy the lower in­equality). In such a case, radome effects are small and the guidance loop remains stable yielding zero miss distance after a sufficiently long flight. One can, typically, improve homing performance by increasing ю and N. If they are increased too much, radome ef­fects become significant, miss distance can be high, and guidance loop instability can set in.

• When юа is large (e. g., at low altitudes or high speeds), designers would still like to make the guidance — control-seeker bandwidth ю sufficiently large to ac­commodate missile maneuverability (i. e., satisfy the lower inequality). This, result generally, can be accom­plished provided that radome effects are not too sig­nificant. Radome effects will be significant ifVm is too small, (R^ N, Vc) are too large, or юа is too small (i. e., too high an altitude and/or too low a missile speed Vm ).

Given the above, it therefore follows that designers are generally forced to trade off homing performance (band­width) for stability robustness properties. Missiles using thrust vectoring (e. g., exoatmospheric missiles) experience similar performance-stability robustness trade-offs.

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