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Table of Contents Page No.

1.0 Background

1.1 FIM-92 Stinger Missile 1

1.2 FIM-92 Stinger Missile Specifications 2

1.3 Maximum Speed 3

1.4 Maximum Range 3

1.5 Service Ceiling 3

2.0 Missile Guidance Navigation

2.1 Assumptions of the Model 3

2.2 Aiming the Missile 4-5

2.3 MATLAB Code 5-7

2.4 Danger Zones 8

3.0 Enemy Attack 9

3.1 Fighter Aircraft 9-11

3.2 Helicopter Gunships 11-12

3.3 Fighter Bombers 12-13

4.0 An Analysis of Proportional Navigation 13-15

5.0 Information Reliability 16

6.0 Conclusion 16-17

6.1 Critical Appraisal and Further Investigation 17-18

7.0 Appendix 19

8.0 References 20

9.0 Bibliography 21

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1.0 Background

1.1 FIM-92 Stinger Missile

The FIM-92 Stinger Missile is a type of MANPADS (Man-portable Air-defence system) used to

protect military ground forces from low-altitude enemy attack. It is currently manufactured by

Raytheon Missile Systems in the USA. The Stinger missile was first introduced in March 1972 when

the Redeye II missile was renamed as the FIM-92A Stinger. However, development of the then

named Redeye II missile began 5 years prior to this as an improvement on the FIM-43 Redeye

Missile. The Redeye was deemed by the Materiel Requirements Review Committee in 1960 to be

“not fast enough, could not maneuver (sic) soon enough, and could not discriminate well enough to

successfully engage its targets.”

The Low Altitude Air Defense (LAAD) Gunner's Handbook (2000) states that the Stinger uses

heat seeking technology to engage on the hottest part of the target (the engine) and “proportional

navigation algorithms to guide the missile to a predicted intercept point.” It also has an Identification

Friend or Foe (IFF) system ,an encoded radio system to avoid friendly fire. The missile can be fired

from the gunner’s shoulder which will be looked at in the model. It can also be fired from vehicles

such as the AN/TWQ-1 Avenger or M6 Linebacker. A small ejection motor launches the missile to a

safe distance approximately 9 metres away from the operator before the two-stage solid-fuel

sustainer accelerates the Stinger to its maximum speed.

There are 4 variants of the Stinger which have been developed in subsequent years after the

FIM-92A was introduced. Production of a fifth, the Stinger-RMP Block II ,began but was later

cancelled due to development being majorly behind schedule. The Stinger is made up of a seeker

head, guidance section, warhead, flight motor and launch motor shown in figure 1.

F

i

Figure 1- G Stinger Design (How Stuff Works)

The different variants carry all of

the same components in their designs

but physically appear slightly altered. As

with the design of the Stinger, the

specifications i.e. maximum speed,

service ceiling, maximum range etc.;

slightly alter with the different versions.

Therefore, the general specifications for

the FIM-92 Stinger missile will be used in

the model.

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1.2 FIM-92 Stinger Missile Specifications

The specifications alter across different sources as shown in chart 1. The information

available about the Stinger missile is limited due to classified data and therefore the data which

appears to be most accurate and agrees with other sources will be used within the model.

1 Directory of U.S. Military Rockets and Missiles, (2005),

2 HowStuffWorks, (1998),

3About.com US Military, (2012),

4 Richardcyoung.com, (2012)

The first and fourth sources are the most consistent with each other therefore these

specifications will be used in the model.

Length 1.52 m (5 ft)

Finspan 9.1 cm (3.6 in)

Diameter 7 cm (2.75 in)

Weight 10.1 kg (22.3 lb); complete system: 15.7 kg (34.7 lb)

Speed Mach 2.2+

Ceiling 3800 m (26200 ft)

Range 4800m (15700ft) RMP Block II: 8000 m (26000 ft)

Propulsion Atlantic Research MK 27 dual-thrust (boost/sustain) solid-fuelled rocket motor

Warhead 3 kg (6.6 lb) blast-fragmentation

Flight time 17 ± 2 seconds

Source Maximum Speed Service Ceiling Maximum Range

1 Mach 2.2+ 3800m (26200 ft) 4800 m (15700 ft) RMP Block II: 8000 m (26000 ft)

2 1,500 mph (2,400 kph, Mach 2)

Approximately 11,000 feet (3 km)

Approximately 5 miles (8 km)

3 Supersonic in flight 10,000 feet (3.046 kilometers)

1 to 8 kilometres

4 Mach 2.2 (FIM-92A) 3,500 m (FIM-92B/C) 3,800 m

(FIM-92A) greater than 4,000 m (FIM-92B/C) 4,800 m

Chart 2 - Full Stinger Specification from Directory of U.S. Military Rockets and Missiles, (2005)]

Chart 1 – Comparison of information from different sources.

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Not all of the given information is necessary for this model and is given for informational

purposes only. The maximum speed, service ceiling and range are the main three measurements

used.

1.3 Maximum Speed

The maximum speed of the Stinger is Mach 2.2 or equivalently 748.64 ms-1 (2 d.p.). However,

the Directory of U.S. Military Rockets and Missiles (2002) states that the Stinger has shown a “top-

speed at motor burnout can be as high as Mach 2.6 for certain trajactories. (sic)” This may only be

possible when the Stinger is travelling vertically towards the ground and the force of gravity is

increasing its speed. This is unlikely to happen unless the Stinger was fired from an aircraft or was

chasing a target which was travelling towards the ground. Consequently, a high speed of Mach 2.6

will be ignored as such trajectories will not be modelled.

1.4 Maximum Range

The maximum range is given as 15700 ft. (4800 m) or (or 26000 ft. for the cancelled Stinger-

RMP Block II). The value of the maximum range is questionable since calculating it using the flight

time average and the Stinger’s maximum speed gives a different result.

Mean flight time = 17 seconds Maximum Speed = 748.64 ms-1

12.7 km is almost triple the stated value of 4.8 km leading to a conclusion that the stated range is

an estimate based on a dynamic pursuit, or is limited not by the rocket but by another factor.

1.5 Service Ceiling

The service ceiling for the Stinger is given as 3800m or 26200 ft which is highly debatable since

applying the same argument as given in section 1.3 would show that the Stinger is capable of

reaching three times this altitude if fired vertically. An explanation for a this discrepancy could be

due to the Infrared seeker on the missile. “Certain gases in the atmosphere, primarily carbon dioxide

and water vapour (sic), absorb energy in the IR frequency spectrum.” Since the amount of water

vapour in the atmosphere alters as the altitude increases, this suggests that the IR seeker aboard the

Stinger would have problems detecting a target and so, the target must be within this service ceiling

to be able to lock onto it. This leads to the idea that if the Stinger can lock onto the target, it would

be able to chase it outside of the maximum range.

2.0 Missile Guidance Navigation

2.1 Assumptions of the Model

Missile preparation time is 5 seconds.

Time until Stinger explodes is taken as 19 seconds.

Minimum firing angle is taken as 100.

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No hangfires or misfires.

Toleration taken as 20 m i.e. once Stinger is 20 m from target, this is classed as a hit.

2.2 Aiming the Missile

The missile is initially aimed and fired at the

target, with a speed, bearing and elevation, worked out

using spherical polar coordinates.

Taking R as the position vector of the target relative to

the missile, this generates

(

| |)

(

)

Note: military literature uses the “elevation” angle, the angle between the missile and the

horizontal ground, whereas conventional polar coordinates measure from the vertical. Equally

military specifications are given in degrees when computations are carried out in radians. The code

is written to follow mathematical convention. The assumption made is that it is easier to program by

convention then change the specification for a user who is likely to be more familiar with degrees

The navigation of the missile is based on the

missile attempting to align with the targets path. This

is achieved by generating acceleration proportional to

the closing speed of the missile SR normal to the

missile’s velocity but parallel to the change in

rotational line of sight .

as a vector equation:

where

So is a vector with the magnitude of normal to and also the closing velocity .

The missile navigation equation may be modified so that the missile leads the target, aiming

at a predicted collision point, rather than at the current position of a moving target, this is achieved

by simply multiplying the calculated acceleration by a constant N.

Figure 2

Figure 3

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When running the code, no attempt is made to find analytical solutions. For simplicity the

system linearizes position and velocity functions according to a time interval width, h:

( ) ( ) ( )

( ) ( ) ( )

These iterations are continued until the distance between the missile and the target is below

a specified tolerance. This is perhaps a more realistic interpretation of the on-board calculations.

2.3 MATLAB Code

A sample code is shown below. This code models the target attempting to evade the Stinger,

but indicates the point in the code at which alternative flight paths can be examined. (see appendix)

function FlightTime = Yossarian(CONST)

%%% Yossarian.m

%%%Last Modified 22/03/2012

i = 1;

%%%%%%%%%%%%%%%% This area contains variables to change %%%%%%%%%

N = CONST ; %%%%% Constant of Proportional Navigation

PrepT = 5 ; %%% Time from spotting to launch

BOOMt = 19; % tMax flight time until detonation

maxRange = 4800;

Ceiling = 3800;

xT(i) = 10000 ; yT(i) = 12000 ;zT(i) = 2000; %Target Position

SpotDist = 8000;

SpeedM = 10 %%% Ejection motor Speed

InThetaT = 4 * pi/3; %%% Initial bearing and inclination of target

InPhiT = pi/2; %%% and elevation of target

SpeedT = 400 %%% Targets cruising speed

MINangle = 10; %%% Minimum firing angle specified in degrees

%%%%%%%%%%%%%%%%%%%%% No more things to change %%%%%%%%%%%%%

hold on

MinRad = pi/2 - MINangle*pi/180; % Conv MINangle to Rad & elevation to Phi

VT = SpeedT*

[sin(InPhiT)*cos(InThetaT);sin(InPhiT)*sin(InThetaT);cos(InPhiT)] ;

%%%% Velocity vector of target

Zaxis = [0 ; 0; 1];

Xaxis = [ 1; 0 ;0];

h = 0.05; %%% Stepsize

t(1) = 0; %%%% time

xM(1) = 0 ;yM(1)= 0 ;zM(1) = 0; %%% Origin WRT Stinger

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R = [xT(i) - xM(i); yT(i) - yM(i); zT(i) - zM(i)];

PhiM = abs(acos(dot(R,Zaxis)/norm(R)));

dist = norm(R)

while t(i) - PrepT < 0 || dist > maxRange || zT(i) > Ceiling

%%% don’t fire till target in range

i = i + 1;

%%%%%%%%% Other Flightpaths are plugged into this section %%%%%%%%

xT(i) = xT(i-1) + h*VT(1); %%% VT is a vector , 1, 2 , 3 corres

yT(i) = yT(i-1) + h*VT(2); to i,j,k, notations

zT(i) = zT(i-1) + h*VT(3); %%% not to VT on loop 1 2 3

t(i) = t(i-1) + h ;

%%%%%%%%%%FlightPath Plugin Ends%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

xM(i) = 0 ;yM(i)= 0 ;zM(i) = 0;

VM = 0;

R = [xT(i) - xM(i); yT(i) - yM(i); zT(i) - zM(i)];

PhiM = abs(acos(dot(R,Zaxis)/norm(R)));

dist = norm(R)

end

plot3(xT,yT,zT ,'r')

LaunchT = t(i); %%%% Time of Firing

R = [xT(i) - xM(i); yT(i) - yM(i); zT(i) - zM(i)];

ThetaM = abs(acos(dot(R,Xaxis)/norm(R))); %%% Bearing and Elevation

PhiM = abs(acos(dot(R,Zaxis)/norm(R))); Missile is launched at;

Bearing = [sin(PhiM)* cos(ThetaM); sin(PhiM) * sin(ThetaM); cos(PhiM)];

VM = SpeedM * Bearing;

tol = 20; %%% given the speed of the missile, this is the short distance

it cannot fly through in one iteration.

dist(i) = norm(R)% as soon as gets within a radius, target is hit

plot3(xT,yT,zT ,'r')

plot3(xM,yM,zM, 'b')

while dist(i) > tol && t(i) < BOOMt + LaunchT

i = i+1;

vR = VT - VM;

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%%%%%%%%%%%%%%% Differernt Flight Paths Plugged in HERE %%%%%%%%%%%

if dist(i-1) > SpotDist

%%% ie when target does not feel in danger from missile

else

NormalT = cross(VM,R); %%%% Target calculates a vector normal to

the closing displacement and the velocity of the target

AccnT = NormalT/norm(NormalT);

AccnT(3)= abs(AccnT(3)); %% So plane will climb out of danger

SpeedT = SpeedT + 10*h; %%% Accelerate to run away

VT = SpeedT*(VT + AccnT*h*150)/norm((VT + AccnT*h*150)); %%%

xT(i) = xT(i-1) + h*VT(1);

yT(i) = yT(i-1) + h*VT(2);

zT(i) = zT(i-1) + h*VT(3);

xM(i) = xM(i-1) + h*VM(1);

yM(i) = yM(i-1) + h*VM(2);

zM(i) = zM(i-1) + h*VM(3);

%%%%%%%%%% End of Different Flightpath Plug in Code %%%%%%%%%%%%%%

R = [ xT(i) - xM(i); yT(i) - yM(i); zT(i) - zM(i)];

%%%% Formulas

OMEG = cross(vR,R)/dot(R,R); % Rotation Vector

AccnM = N * cross(vR , OMEG); %% Accn to change target.

if t - LaunchT < 2;

Booster = 330; %%% This is the initial accelerator rocket

%%%% accelerates in the direction of rocket travel.

else

Booster = 0;

end

SpeedM = SpeedM + h*Booster

VM = SpeedM*(VM - h* AccnM)/norm(VM - h* AccnM);

%%%% Velocity must be normalised then multiplied by speed

dist(i) = norm (R) ;

DISTANCE = dist(i)

t(i) = t(i-1)+h;

Time = t(i)

end

FlightTime = Time - LaunchT; %%% Time Missile is in the air.

plot3(xM,yM,zM, 'b') %%% 3D Plots

plot3(xT,yT,zT ,'r')

end

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2.4 Danger Zones

Figure 4 is a visual representation of the ‘danger zones’ dependent on the speed of the

aircraft and the initial position of the aircraft (flying directly away), as it tries to escape. The red area

is where the Stinger missile always hits its target (according to the MATLAB simulation). The amber

area is where the Stinger missile does hit the target but within 15-19 seconds. Given the Stinger

could explode during this time; the area is classed as a maybe area. It is not an area that an enemy

would feel comfortable in but the operator may be reluctant to fire the Stinger missile due to fear of

missing and wasting it. The green area is where the Stinger does not hit the target. This would be

classed as the ‘safe’ zone so it is unlikely the missile would be launched.

Although these graphs are simplistic, they are designed to demonstrate the possible areas

maths can be used to assist in the decision making of a pilot and Stinger operator. They show that

the speed of the aircraft is a very important aspect of defence and attack. Although the Stinger

missile is faster than all the various speeds investigated, the important point to note is that due to

the fact the Stinger destructs between 15 and 19 seconds, all the aircraft has to do is survive for that

length of time. It therefore stands to reason that the further away the aircraft begins this survival

mission the greater chance of success it has and these graphs demonstrate this. The focal point of

the report is from the point of view of the Stinger, so these graphs could be very beneficial if the

operators had the speed of the aircraft they are trying to hit. They could prevent hopeless causes

being pursued.

450 ms-1 500 ms-1

550 ms-1 600 ms-1

400 ms-1

Range (metres)

Alt

itu

de

(met

res)

Figure 4 – Danger Zones

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3.0 Enemy attack

The aim of the model is to assess the Stinger’s capabilities against various incoming enemy

attacks. This will be done by looking at which scenario the Stinger is successful in taking out the

target, how fast the missile can accomplish this and how well the Stinger is able to reach and chase a

target. In all of the MATLAB output; the target’s flight path will be shown as a red line and the

Stinger’s flight path as a blue line. There are a range of types of enemy attacks to model which will

test the Stinger’s effectiveness in succeeding.

3.1 Fighter Aircraft

Fighter aircrafts are designed for air-to-air

combat with other aircraft. They are known for their

speed and manoeuvrability. An example of such

fighter aircraft is the Lockheed Martin F-22 Raptor.

Lockheed Martin (n.d.) states that the Raptor can fly

at around Mach 2 with afterburners and The Official

Website of the U.S. Air Force (n.d.) states a service

ceiling of 15 kilometres making an escape from a

Stinger missile possible. It also explains that “The combination of stealth, integrated avionics and

supercruise drastically shrinks surface-to-air missile engagement envelopes and minimizes enemy

capabilities to track and engage the F-22.” This also decreases the chance of a Stinger attacking the

aircraft.

Figure 6 is a MATLAB plot that shows the path of the F-22 RAPTOR whilst a Stinger missile is

launched at it using a varying constant of proportional navigation (from 1-10). The figure

demonstrates that when the fighter, which is capable of Mach 2, only uses its speed to try and avoid

the Stinger, it will fail to escape.

Figure 5 - Lockheed Martin F-22 Raptor (FAS)

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2000

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me

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Figure 6

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Figure 9 is the MATLAB output that was produced when the F-22 Raptor, was modelled

carrying out a ‘fly away’ path. The Raptor realises that there is a Stinger missile in the area and it

attempts to turn and get away using its speed. As the fighter has a possible speed of Mach 2 the pilot

decides this is a sensible choice of action. Figure 9 shows that under this simulation the Stinger fails

to hit its target on all 10 simulations. Figures 8 and 9 demonstrate the difference the speed of the

fighter jet makes on its survival prospects. In figure 9 the Raptor is capable of Mach 2 and can escape

as long as it spots the Stinger in time. In figure 8 however, the Stinger will hit the fighter aircraft

every time as it is only travelling at a speed of Mach 1.

Figure 10 demonstrates this further as it shows the various times of success compared to the

constant of proportional navigation. This result means that fighter pilots and Stinger operators must

be able to calculate how far away the opposition is (i.e. the plane from the Stinger and vice versa),

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2000

4000

6000

8000

10000

12000

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1000

2000

3000

4000

5000

6000

x

y

Figure 9 – U turn at Mach 2

x

y

Figure 8 – U turn at Mach 1

Figure 7 shows the time each of

the simulations take to hit the target in

relation to the constant of

proportional navigation that is used.

This graph shows that for this

particular scenario in which the fighter

jet is flying at Mach 2 the optimal

proportional navigation constant is 2.

This; alongside the results from the

other simulations suggest that there is

not one optimal choice of constant for

all scenarios.

1 2 3 4 5 6 7 8 9 10

4.88

4.9

4.92

4.94

4.96

4.98

5

5.02

5.04

5.06

Proportional Navigation Constant

Tim

e u

nti

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tru

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n o

f ta

rget

(sec

on

ds)

Figure 7

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and also know the various speeds of opposition

aircraft. These findings further support the

need for mathematical modelling data within a

combat situation, given the unit cost of the

missile ($38,000) and the risk of alerting the

aircraft to the Stinger team.

It is unlikely the operator of the Stinger

could calculate all of this in a split second so

this information must be supplied prior to the

operator using the missile,

3.2 Helicopter Gunships

Used to provide support for troops on the ground, an

example of an attack helicopter is the Bell AH-1G Huey Cobra.

The Military Factory (2003) states the service ceiling to be

approximately 3.7 kilometres with a maximum speed of 141 mph

(63ms-1). These are well within the missile specifications, so it is

unnecessary to investigate the same scenarios as the fighter.

The LAAD Gunners Handbook (2000) states that the

Stinger missile launched from a MANPADS cannot fire at

targets below a 10 degree elevation from the ground, to

account for the flight after launch but before the rocket fires.

Clearly, once the Stinger has locked on to the target, the missile is capable of chasing a target

into this region.

Figure 11 - Bell AH-1G Huey Cobra

(Helicopter Histories)

This 10 degree limit creates a

region where the helicopter is “safe”.

So this scenario investigates the

capabilities of a helicopter in this

region.

This simulation (Figure 12)

shows a Cobra accidentally coming

into the firing field of a Stinger missile

crew, and then attempting to flee

back to a safe region (marked in

green), after being targeted. -1500

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0500

10001500 -500

0

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1500

0

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200

300

400

y

Low Flying Helicopter

x

Alltitu

de

Altitu

de

(metr

es)

Range (metres)

Figure 12, The Low Flying Gunship.

1 2 3 4 5 6 7 8 9 1010.4

10.5

10.6

10.7

10.8

10.9

11

11.1

11.2

11.3

Proportional Navigation Constant

Tim

e u

ntil de

str

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n o

f ta

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t (s

eco

nds)

Figure 10

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Having established the existence of a safe region, it is necessary to investigate the helicopter’s ability

to operate in such a region. Chart 3 shows the effective range of some of the weapons available to a

Bell Cobra, and the maximum safe height if using these weapons against a Stinger missile crew.

This demonstrates that there is a significant danger to a Stinger missile team from a

helicopter that is hugging the ground, but if the Stinger is able to lock on to the cobra then it can be

easily brought down.

It is important to recognise that by flying below the missile’s field of view, the helicopter will

come into range of other anti-air measures, potentially making RPGs and small-arms fire a threat.

The effectiveness of a Stinger could be measured as an area-denial weapon, preventing incoming

helicopters from flying at a preferred altitude.

3.3 Fighter Bombers

Given that strategic bombers operate well above the Stinger ceiling, it was decided to instead investigate the Lockheed AC-130H. The Official Website of the U.S. Air Force (n.d.) states that it has a cruising speed of 300 mph or around Mach 0.4 and the service ceiling is around 7.58 kilometres. However, the gunship is only likely to fly near this altitude when it is not in the attack zone since the armament aboard is only effective from a lower altitude. The armament comprises of two M61 20mm Vulcan cannons, one L60 40mm Bofors cannon and one M102 105mm howitzer as stated by the Federation of American Scientists (2011). The Compendium of Armaments and Military Hardware (1987) indicates that an M61 Vulcan Cannon has a maximum effective slant range of 2000 metres, therefore the target can reasonably be expected to operate below the missile’s ceiling on attack.

Weapon Effective Range(m) Safe Height ( ) (m)

M197 Gatling gun Firing M53 Ammunition

1000 176

Hydra 70 Rocket Pod 8000 (Greater than Stinger)

1410

TOW Missile 3750 661

Figure 13 - Lockheed AC-130H

(Lockheed Martin)

Time

until

target is

destroye

d

(seconds

)

Figure 14 shows that the

lowest time until destruction of the

target is around 6.31 seconds with a

proportional navigation constant of

any number between 3 and 26.

0 5 10 15 20 25 30 35 40 45 50

6.3

6.31

6.32

6.33

6.34

6.35

6.36

6.37

6.38

6.39

Figure 14

Proportional Navigation Constant

Tim

e u

nti

l des

tru

ctio

n o

f ta

rget

(se

con

ds)

Chart 3 – Bell Cobra Weapons Range

- 13 -

The stinger is clearly a significant threat to the Ac 130.

4.0 An analysis of proportional navigation

So far in the analysis of various

scenarios, the proportional navigation

formulae have not shown a significantly

improved time over simple heat seeking

solutions. This section will investigate

whether benefits to this method exist.

Consider figure 16.

In this (somewhat contrived) example; of a

plane executing a barrel roll, the heat

seeking missile marked in green follows a

significantly different path to that of the missiles using proportional navigation guidance.

Proportional navigation can be considered as the missile aiming at a point which the target is

predicted to reach. Recall the formula:

All of the inputs to this formula are

the linear instantaneous values from each

iteration. Therefore the “predicted”

collision point would be a linear 0 5 10 15 20 25 30 35 40 45 507.4

7.6

7.8

8

8.2

8.4

8.6

8.8

9

Flig

ht

Tim

e

Constant

Comparison of Different Navigation Constants

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y

The Barrel Roll

x

Altitude

Figure 15 shows the

destruction of the fighter bomber as it

flies around its intended path. The

target had an initial altitude of 3

kilometres, a range in the x-direction

of 0.6 kilometres and a range in the y-

direction of 4 kilometres. The

MATLAB output demonstrates a

Stinger flight time as 6.06 seconds

and as can be seen in figure 15, the

gunship only managed to travel

approximately one sixth of its

intended flight path. This shows that

the AC-130H barely had a chance to

engage the ground.

A

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Figure 15.

y x

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Figure 16

Figure 17

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0 5 10 15 20 25 30 35 40 45 506

6.5

7

7.5

8

8.5

9

Constant N

Collis

ion T

ime

Comparison of Navigaiton Constants Against Straight Line Flight Paths

continuation of the current target flight path, and a higher constant would cause the missile to be

less able to cope with an aircraft following a tight curve. However, the opposite is true with

proportional navigation striking the target approximately half a second earlier.

From figure 17 it can be seen that as the constant (N) increases, the flight times and paths

tend to a limit, equally notice the minimum value at

Zarchan (1994) states that the constant of

proportional navigation is typically between 2 and 7

(with 1 being heat seeker navigation only). To

investigate this further, numerous experiments on

the previous scenarios were carried out using

random values for speed, position, bearing and

altitude. This will test whether there is an optimum

setting for all scenarios or whether a Stinger team

must first predict the target’s behaviour.

When considering a flight path that follows a

straight line, all modelled flight times have reached

a minimum for constants greater than 3, with in one

case a difference being around 1.5 seconds.

Although, perhaps unclear from the graph there

was a slight increase of around 0.01 seconds for

navigational constants greater than 20.

Further models confirm that the minimum

times to collision are within the region 2 and 10

seconds, with higher constants giving a higher time

shown in figures 19, 20, 21 and 22. Alarmingly for

some fast planes the standard heat seeker model

took more than 19 seconds to reach the target, implying that the target successfully escaped.

0 5 10 15 20 25 30 35 40 45 50

3.5

4

4.5

5

5.5

6

6.5

7Wide Circle Flightpath

Tim

e

Navigation Constant

0 5 10 15 20 25 30 35 40 45 508

10

12

14

16

18

20

Constant

Tim

e

Comparisons of Flight Times for a U Turn Evasion

Figure 20

Figure 19

Figure 18

0 5 10 15 20 25 30 35 40 45 502

4

6

8

10

12

14

16

18

20

Constant

Tim

e

Barrel Roll ComparisonsFigure 21

- 15 -

0 5 10 15 20 25 30 35 40 45 502

2.5

3

3.5

4

4.5

5

Constant N

Flight T

ime

Proportional Navigation and the Helicopter

0 2000 4000 6000 8000 10000-2

0

2

x 104

0

1000

2000

3000

4000

5000

x

Proportional Evasion with Proportional Persuit

y

Alti

tude

As an aside when considering the

helicopter (figure 22) there was no difference in

flight times larger than a hundredth of a second

(which was the same size as the stepsize used

in the code).

Given that proportional navigation

strikes sooner and strikes targets otherwise

missed, or at the worst is negligible,

proportional navigation seems to be a

beneficial system of equations.

Proportional navigation was originally developed as a method to avoid shipping collisions,

and indeed is still used to allow Unmanned Drones to operate safely around military airstrips. With

this in mind, a slightly adapted form was used to calculate an evasion manoeuvre. Essentially the

target is turning normal to the velocity of the Stinger, while trying to climb.

A pilot could well be optimistic. This target has successfully survived for 19 seconds whilst

being pursued by a significantly faster missile. However this is only possible if the Stinger is working

without proportional navigation, the pilot can judge an evasion course as fast as the Stinger can

recalculate its trajectory (an inhuman 100 iterations per second), and can outturn the missile.

Figure 22

Fig 23

Fig 24

- 16 -

However, even taking this unrealistic worst case scenario, implementing the proportional navigation

method ensures a collision after 8.65 seconds (fig 24). This is not a viable escape tactic.

5.0 Information Reliability

The Guardian Newspaper (2005), quoting “Magoudi,A (2005) Rendez-vous - the

Psychoanalysis of François Mitterrand”, claimed that after the attack on HMS Sheffield in 1982

Falklands war, the French president provided Britain with disarm codes for the French-made Exocet

missile. Given that the Exocet is roughly contemporaneous with the Stinger missile, and that like the

Exocet, the Stinger is a widely exported weapon, it is not unreasonable to consider that the Stinger

may also have such a disarm system.

This investigation did not model such a system and truthfully no evidence is available to

support the existence of such. Instead, treat this as a succinct example of the difficulty in obtaining

up to date reliable information in the murky field of missile technology.

6.0 Conclusion

While a standard heat seeking missile proved effective, utilising proportional navigation

calculations lead to the missile hitting targets that would otherwise be missed. This also led to a

reduction in times until a successful hit. It is a military, not a mathematical judgement as to the

benefits of a half second earlier kill, but the mathematics and application of this method are not

much more complicated than that of heat seeking, so it can perhaps be assumed that the costs are

not significantly greater.

The ceiling limit severely reduces the ability of the Stinger to engage all targets apart from

helicopters, with most of the aircraft considered having a service ceiling greater than that of the

missile, and only coming into the Stinger’s kill region when on an attack run. When defending against

high level strategic bombing the Stinger is useless.

When considering evasion, this research suggests that speed is more of a vital factor than

manoeuvrability, given that the simulated Stinger was able to successfully neutralise a target that

could turn much sharper than any realistic aircraft, but the F-22 Raptor (travelling at Mach 2) was

able to flee along a straight line.

This implies that the Stinger Missile may be showing its age. Recall that the Stinger was

developed in the 1970’s and first fired in anger during the 1982 Falklands War. These simulations

have shown that it is extremely capable against slower moving aircraft, such as fighter-bombers and

helicopters; however the Stinger’s Mach 2.2 is no longer an unrealistic speed for a modern fighter jet

to counter.

This investigation identified two types of “safe zones”, those below 10o of the ground, and

those distant enough for a fast aircraft to escape, however these “safe zones” only proved safe if the

target remained in them, with two scenarios in which the target attempts an escape leading to a

successful hit.

- 17 -

The “safe zones” should be considered from the point of view of the enemy pilots, although

there are regions where the missile did not hit all of the time, these regions still represented a

significant risk for a pilot to enter. As a deterrent weapon the stinger need not necessarily fire to

defend against attack.

This demonstrates the utility of the Stinger as an area denial weapon, effectively protecting a

region from attack by forcing targets to fly outside of preferred regions. Equally these safe zones can

be countered by coordinated fields of fire from other Stinger Missiles, or alternatively coordinating

with alternative anti air weaponry.

Ultimately the effectiveness of a Stinger depends on the definition of success. What

constitutes a success or a failure for a Stinger missile or conversely for the opponent? In a war of

attrition, the loss of an aircraft is significantly more costly than expenditure of a stinger. Equally a

high priority target defended with Stingers may be worth risking an attack on, especially given the

recent development of unmanned aerial vehicles that do not put friendly lives at risk. These kind of

‘worst case’ and’ best case’ evaluations must be carried out and ‘weighted’ before military decisions

can be made.

6.1 Critical Appraisal and Areas for Further Investigation

Terrain

Within this report, the terrain was effectively disregarded, the model was created on the

basis that the ground was flat and there was no possible obstacles. In the real world however, war

does not discriminate by location or terrain. This report hasn’t considered defending an island for

example, it hasn’t considered fighting on the beaches, or fighting on the landing grounds or fields

and it hasn’t considered fighting in streets or hills. If there was further time available, this report

would never surrender in the pursuit of modelling all these scenarios to discover how successful a

Stinger missile is.

The question that this report hasn’t answered but must be considered in the wider context of

war, is what constitutes as a success or a failure for a Stinger missile or conversely for the opposition

attacking? What is seen as a success by one side could be seen as failure by the other side depending

on a variety of factors such as resources and how much weight is put on a particular target. For

example, if one side only had a limited supply of aircrafts they would be very reluctant to risk these if

they felt the Stinger missile could succeed, if however the loss of aircraft wasn’t seen as a significant

negative, when compared to the possible positive repercussions of the mission, i.e. killing the

opposition leader then they might be more willing to attack. These kind of ‘worst case’ and’ best

case’ evaluations must be carried out and ‘weighted’ before military decisions can be made. This is of

particular interest in relation to the Stinger missile because the Stinger missile is often seen as a very

successful because in effect it is a deterrent.

- 18 -

Psychology

Another factor that this report hasn’t considered is the human element involved. The

psychology of the pilot could have an impact on what measures they employ to avoid the Stinger.

The pilot could consider being captured as a worse scenario than dying due to the possibility of

torture. If they held the opposite view however, and the opposition had a reputation for dealing with

prisoners of war in a humane manner then they might choose to eject from their aircraft rather than

risk dying.

Equally having a stinger missile may be a significant morale boost to those on the ground.

The psychological factor is an issue for all aspects of war as it is impossible to truly know how

an individual would react to a certain scenario so assumptions must be made in respect to

mathematical modelling.

Change in final stage pursuit

A limitation of the model is the tolerance level. That is to say that if the Stinger (within the

model) got within a certain distance of the target then this would be classed as a ‘hit’. This also did

not take into account the shape and size of the aircraft.

The Stinger missile has the capacity to change targeting methods during the final stage of

pursuit, to aim at other areas of the aircraft than the exhaust heat, as the aircraft has been modelled

as a point with a tolerance, this has not been evaluated.

Heat Detector

The scope and timescale of this report has made it difficult to investigate every aspect of the

issues the Stinger might face. For example it has not looked into the effect the sun has on the ability

of the Stinger to lock onto a target, similarly it has not looked into infrared jamming of the Stinger or

the deployment of flares as a defensive mechanism of the aircraft being pursued by the Stinger. The

report did however account for certain characteristics of the heat detector component of the

Stinger. Figures from the LAAD Gunner’s Handbook (2000) were used in respect to this heat detector

but these were effectively ‘rough and ready’ estimates used and if further investigation was carried

out with greater time and resources then these characteristics would be honed to take account of

differing climates and conditions.

Cost

It is naïve to think that there is no monetary factor when assessing a weapon’s effectiveness.

Deployment of the stinger may not be preferable to deploying cheaper if somewhat less effective

armaments.

The Ground

One other aspect that has been difficult to model has been the Stinger’s relationship with the

ground. The models were designed on the basis that the Stinger must be fired above 10 degrees

from the ground. This fact was difficult to ascertain concrete evidence to support, though the LAAD

- 19 -

Gunner’s Handbook (2000) did provide us with one such fact so it was decided to model on this

basis. Possible issues that the Stinger might have with the ground is the difficulty in distinguishing

between the heat of the aircraft and the ground, also it was noted that the Stinger could crash into

the ground before it really got going if it was aimed at aircraft under 10 degrees. Obviously this is

dependent on where the Stinger was fired from as a Stinger fired from a helicopter would obviously

not have these issues.

- 20 -

7.0 Appendices

%%%% yossarianrepeat.m

for j = 1:1:50 %%% A simple loop to run many iterations of a code for different constants

CONST(j) = j; %%% Investigate effect of different constants of PPN on flight time

FlightTime(j) = Yossarian(CONST(j))

end

figure

plot(CONST,FlightTime,'g-')

%%%% Plugin code for a straight line

ThetaTC(i) = ThetaTC(i-1) ; %% Straight Line

xT(i) = xT(i-1) + h*AcVel * cos(ThetaTC(i));

yT(i) = yT(i-1) + h*AcVel * sin(ThetaTC(i));

zT(i) = zT(i-1) ;

%%%% Plugin for a wide curve

ThetaTC(i) = ThetaTC(i-1) + 0.0001*pi;

xT(i) = xT(i-1) - h*AcVel * cos(ThetaTC(i));

yT(i) = yT(i-1) - h*AcVel * sin(ThetaTC(i));

zT(i) = zT(i-1) ; %%% Circle of constant height.

%%%% Plugin for The Barrel Roll

if t(i-1) < loopstart PhiTC(i) = PhiTC(i-1); kk=0; else PhiTC(i) = PhiTC(i-1) - 2*pi*h/5; kk=1;

- 21 -

end xT(i) = xT(i-1) + h*Tvel * sin(PhiTC(i)) * cos(ThetaTC(i))-

kk*50*h*sin(ThetaTC(i)) ;

yT(i) = yT(i-1) + h*Tvel * sin(PhiTC(i)) * sin(ThetaTC(i))+

kk*50*h*cos(ThetaTC(i));

zT(i) = zT(i-1) + h*Tvel * cos(PhiTC(i));

8.0 References

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Military Factory (2003) Bell AH-1 Cobra / HueyCobra (Bell 209) Attack Helicopter. Available at: http://www.militaryfactory.com/aircraft/detail.asp?aircraft_id=13 (Accessed: 2 March 2012)

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SinoDefence.com (2002) YingJi-91 (Kh-31P) Anti-Radiation Missile. Available at: http://www.sinodefence.com/airforce/weapon/kh31.asp (Accessed: 11 March 2012)

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