BASIC MISSILE DYNAMICS: PART 1

Gp Capt Noel Moitra VM

Presentation on Air Combat Tactics

Gwalior, India

1. This is a simple presentation on Missile Dynamics and how any given Missile Envelope is deduced, first published in 2005. The topic in itself is quite complex, so I will limit it to basic airman language. Depending on the feedback to this post on the Close Combat Missile (CCM), I might add posts on the Medium & Long Distance Beyond Visual Range Missiles. starting with the former.

Close Combat Missiles (CCM)

MATRA R550 Magic 1 AAM

2. Prelude

The CCM began its operational journey in the Vietnam War. The initial CCMs came in 1956 when US aircraft began equipping with AIM-4 Falcon, AIM-7 Sparrow, and AIM-9 Sidewinder. The Soviets introduced the K-5 missile in 1957. Ever since, CCMs have improved in both agility and range.

They also saw significant use in the Arab-Israeli wars and the Iran-Iraq war. A Pakistan Air Force Atlantique was shot down by an IAF MiG-21 in 1999 and, in Feb 2019, a PAF F-16 was shot down by an Indian MiG-21 Bison during air combat in response to the Balakot strike.

CCMs are typically powered by rocket motors, usually using solid fuel. Ramjet engines (used in Meteor missiles), are now becoming popular, as they allow for maintaining higher average speed across their engagement envelope. CCM “dog-fight” within visual range weapons have shorter ranges of below 16 kilometers and are designed for agility rather than range. Most use infrared guidance. More modern infrared-guided missiles can detect the heat of an aircraft’s skin, warmed by airflow friction, in addition to the fainter heat signature of the engine when the aircraft is seen from the side/head-on. Combined with excellent maneuverability, this gives them an all-aspect capability. The pilot can also use a helmet-mounted sight (HMS) to slew the missile seeker’s head towards the target for an off-boresight launch. Medium and long-range missiles are beyond visual range (BVR) AAMs. These use active or semi-active radar guidance, sometimes combined with inertial guidance. Passive anti-radiation homing missiles could be used against AEW&C aircraft. Most missiles have a conventional explosive blast, fragmentation, or continuous rod warheads that detonate on impact or through a proximity fuse.

I will first look at CCMs. Certain factors will be retained as constant, ie, Altitude, Velocity, Density, etc. For a given set of parameters, a specific missile has certain aspects that we need to understand:

a) 1 'G' Flight Range. (G=Force due to Gravity, 9.81m/sec²)

b) Off Bore-sight Ranges and energy-losing manoeuvres.

c) Guidance systems.

3. 1'G' Flight Range. The 1'G' Flight Range of a missile is a function of its thrust and acceleration, aerodynamic profile, the lowest speed at which its control surfaces are effective and its self-destruct time. A missile when launched will travel a fixed range. Let us call it 'X ' Km. The missile becomes ineffective some time before reaching 'X' Km as its velocity drops to a value too low for its controls to remain effective. This could be called 'Y' Km. We have not considered the mother aircraft (ac) speed yet. X is thus > Y, as drawn below.

4. Introduction of other Factors. Range 'Y' is its effective max launch range. It will self-destruct some time later (X). The launch aircraft may or may not chase the missile which is chasing the Target. Assuming that the launch aircraft is chasing the missile, then, in the time taken to travel 'Y' Km, the mother aircraft also travels forward by a distance equal to its flight speed in m/sec x time taken by the missile to reach 'Y'. Add the launch aircraft speed to its own and missile range increases to 'Y'+ ac speed in mtr/sec x time of the effective flight of the missile, in metres. Range increases to a figure 'Z'.

5. The target is moving away at its own speed. The missile has to chase and hit it before becoming ineffective. The max away travel is = target speed @ mtr/sec x the effective time of flight of the missile from its position at time of launch. This is where overtake speed comes into the picture. The target travel away can be termed 'A' mtr or Km as the case may be, as shown:

The true launch range becomes B= Z-A , valid only if the missile is launched from the line astern zone.

6. Summary:

X = Max missile travel range before self destruct

Y = Max self travel range of missile before loss of effective control

Z = Max effective travel range after launch from the mother ac

A = Tgt travel away, reducing missile effective range.

B = Actual missile range as fed into basic computations for final result.

MATRA R550 Magic 2

7. The Beam Attack.

When approaching the target from abeam, the launch range will be 'Z' Km. Since we are dealing in secs, the lateral travel of the tgt ac may be considered as minimal, both in metres and geometric degrees. While it is not as simple as it may seem , it will suffice for the nonce. If coming in from dead head-on, the range will be maximum, a function of the closure rate of the two ac, not the overtake. It is assumed that the missile under consideration has the thermal ability to detect hot spots. Essentially , it should sense target skin friction thermal signature and the efflux heat, which disperses conically with its locus the exhaust pipe or jet nozzle. Smart missiles have the ability to focalise the efflux but need super-sensors to add the two as they are at differing thermal-band ranges The simplest graphic design for an abeam launch is as shown below. With Z as the basic launch range, the beam attack will give you approx 1.8-2.0 B, with 3.5- 4.0 B as the head on launch range. Now we can progress to define the envelope of the CCM. It will be as shown below, in its simplest form :

8. The missile has a finite range, as we saw. It depends entirely on its energy, which is a sum of its dynamic + static energy, ie, ac launch speed, its own speed as imparted by its thrusters, and altitude. If, for any reason the missile has to move sideways, it turns with an attendant energy loss. Energy is quantified as: MH + 1/2 MV², with M being its mass, H being height and 'V' its velocity. Any turn is an acceleration, and eats into its reserve of energy. Its Centripetal Force is = mass x accn written as (W)² / r and Drag =1/2PV²S. These have to be added and taken out of its reserve, affecting it adversely by reducing range. Under the best conditions, frictional drag at release from the launcher is kept at its lowest, by using Teflon interfaces and Titanium rails.

9. As an aside, there are 2 types of release , viz., twin-vice clamps and one-way rails. The former was used in the earlier days as it was very simple and effective. At launch, the clamps just opened up and the missile fell off as its fuel lit up. In about 01 sec, the missile would have reached around 0.8 M. But it would have dropped 05 m and lose another 15 m in the next sec. Remember S=1/2 gt², S being Gravity drop. This was unsuitable for low flying ac. In the rails system, the missile starts to tip nose down as its C of G moves out, ahead of the rails. The outcome is an undesirable Twisting Moment, a Math.term. The solution lay with ultra-high boost at T=0, easy as the exhaust piping was part of its body. Once boosted to its max capable velocity, thrust reduces smoothly in the initial coast phase to zero. The missile is designed to climb at some optimum angle for a specific time to counter the loss in ht and controlled by a/c Wpn Cmptrs. Latest generation ac use solid fuel rear-section tubing that burn from out to in and rear to front, but only at extremely high temps.This is created by the very last 5% of the fuel. The K-13 Missile had a fixed degree of climb at 3.5º till supersonic (1.0-1.02'), explaining how its exhaust gases entered the ac intake or interfered with the incoming airflow, resulting in a flame-out. Most ex- MiG 21 jockeys will support this statement.

10. Role of Aspect Angle. Now for the complicated part. What if you are not dead astern of the tgt ac and at zero aspect as shown in the first few diagrams? You can have an ac dead ahead but travelling across you as in Fig 3. Angle of sight = ZERO, angle of flight =90º. To reduce the complexity of calculations, let us break up the 90* segment into 90 segments of 01º each. Effectively, we are increasing aspect angle by 01º at a time. In Trigonometry, sin 0º [zero drgrees]=zero, and its value increases significantly only > sin 60º. Hence sin 0 tends to 1 as 0 tends to 90º. This can be stated mathematically as:

R~ [sin 0(0->90º).

This isn't yet an equation, only a starting point. We have not yet included the fact that the rate of change of 0 becomes insignificant after the 60º point. This may be written as:

1 0.86

R~ [sin 0(60-90º) + [sin 0(0-60º) .

.87 0

Again, this is not complete as the acceleration factor is yet to be fed in. Any change in either direction or speed, the components of velocity, is actually an acceleration, which is scientifically defined as the rate of change of velocity, or a~v/ t . We will leave it as such for the moment.

11. Simplification. We know that sin 30=1/2, sin 45=1/ √2 = 0.7, sin 60= .87 and that sin 90=1. Thus, progression can be seen as 1/2 from zero to 30º. Simpler still, accn based on angular change is 1/2 / 30 or 0.167 units per degree between zero and 30º. It is 0.225 units per degree between 30-45º, 0.45 units from 45 to 60º tapering sharply thereafter to a low 0.04 units per degree. This is reflected in launch ranges increasing by 'B' x 0.167 / degree up to 30º, then at 'B' x 0.225 upto 45º and finally 'B' x 0.02 by 90º. This will show up as a jerky jig, as the 30º range will jump to the 31º pt.

12. Integration. Now that we have more data, we can start to develop an equation, removing any jerky parameters. Thus we can introduce a simple equation, albeit slightly incorrect.

0 .17 0 .225

Thus, R= [ sin 0-30º [sin 30-45º and so on upto 90º. Such calculations

0 0 .17

will be transferred into drawing an envelope of launch range of a CCM. Herein lies the difficulty, as the missile will be required to turn to hit the target. Each turn costs energy and results in a drop in range. Let us introduce some other factors that constitute the algorithm that provides a launch envelope:

a) Radar accuracy.

b) Radar lock.

c) Missile lock and head capability.

d) Relative turn rates of the mother ac, target and missile as computed by the launch control computer and provided to the Display Systems, both audio and visual.

e) Missile control systems in flight.

f) Missile explosion command system.

g) Latax.

h) Boresight angles.

i) Angle of Attack and high G.

j) SEP Curves.

k) Human Factors.

13. Each factor has its own CEP. Assuming that each is 99%, the end result will be 99 x 99 ten or nine times. Practically, we work at 95% CEP. At 95% CEP, the SSKP will work out to 0.60. At 99% , SSKP is as low as 72%. Salvo firing improves SSKP to 84%.

The Matra MICA multi-role AAM

14. Drawing Firing Envelopes. Let us look at the earlier equation again. We had said that :

0.17 0.225

R= [ sin 0-30º [sin 30-45º and so on upto 90º. Taking an SSKP of 0.8 with

0.0 0.17

8 n 0.02

99% CEP, we can state that R~ [ [ [ sin 0-90 < @ 01º> <g=k> < F =N ~t >, ie, at 1'G',

0 1 0.0

with ‘n’= no of multiplicands of the variables involved, power loss 'F' at a fixed rate N, normal with respect to the time factor 't ' & 1G. This will give us a 1G envelope at its simplest. The one most important factor is lateral accn or Latax, as it controls both pitch angle and moment of force at launch. Angles beyond abeam are not yet under study in this article. But an actual beam launch has to consider the fact that the final impact will be close to the astern for heat seeking heads. The weapons computer calculates the lead angle required for a laterally moving target and modifies the algorithm controlling the firing envelope in question. Standard Deviation has been utilised but in a simplistic form. This is simple to understand. Alls well so far and I hope that somebody actually understands and then takes time off to teach the ignorant.

15. In order to look beyond 1G, CAD Programmes and Std Deviation become mandatory. This is Greek and Latin to all of us, self included. Yet, it is necessary and will form the bulk of my next and concluding article on CCMs. We will see that time-tested formulae are no longer valid. As an example, the pro-turn component of thrust at high AOA is to be added and change the standard rules totally. Add to that thrust vector 3D swivel and the entire gamut of turn performance is overhauled. Add off-boresight launch and where do we reach ? We shall see.