# Measurement of a missile's trajectory and maneuver

1. Oct 20, 2015

### Armed Update

Hey I am trying to tweak a Fighter jet game to make it more realistic. I am trying to the US Air Force AIM-120D AMRAAM missile like what it can do in real life.

The question is what is the effective range of the missile against a maneuvering target or evading target, for a fighter let say 6Gs at a typical subsonic speed of Mach 0.8.

The AIM-120 weighs around 330 lbs and can go a range of 180 km at a max trajectory and pull around 30 Gs max probably at its burnout phase around 10km. Its average speed is around Mach 5 at that burnout phase. Also if the launcher jet is moving at Mach 2, how will that effect the missile?

2. Oct 20, 2015

### A.T.

The point of simulation games is to simulate such aspects, because there is no general answer for the "effective range". It depends on too many factors, including the guidance logic of the missile, which is probably secret anyway.

3. Oct 20, 2015

### Armed Update

Yeah I just want to the the physics of the missile, not the top secret stuff.

I looked at this calculator.
http://www.mrmont.com/teachers/physicsteachershelper-proj.html

Is there a calculator to measure the change of speed of an object while in its trajectory. For example if you throw a certain weight at a certain speed at a certain angle, how will the speed change at its acscent, ymax and land?

A missile's max G is probably not at its max speed(end of boost phase) but when its in a middle ground between speeds since you can't have too much speed for maneuver.

4. Oct 20, 2015

### tfr000

How realistic do you want to get? Solid rocket motors can have different thrust profiles by varying the shape of the burning surface of the fuel. What about air drag? Acceleration ("Gs") depends on those and also on whatever maneuvering is done. Guidance is complicated, especially if you're trying to hit a moving target that doesn't want to be hit. If you Google "velocity to be gained" and "curve of pursuit" you might come up with something.

5. Oct 20, 2015

### Armed Update

I am ignoring the motor. Air Air missiles loose their fuel once they are burned out and they are moving at their max speeds and descanting. Burnout usually happens at 9 secs and at Mach 4 at high altiutdes(15-20 km) So I want to focus on the trajectory there.

Air resistance matters a lot. However, it is in coronation of the mach 4 speed after burnout. If at a lower altitude the speed degreases due to drag.

I want to focus on loss of speed first. The speed of the projectile is the hypotenuse of vertical and horizontal velocity correct?

So if the projectile is launched Mach 4 at a certain degree I find the horizontal and vertical velocity by using SOHCAHTOA, then minus the 9.6 m/s to the horizonal velocity until I get to zero(highest point of the trajectoy) while finding the speed that each point. Then do the same thing to find the speed of projectile on descent.

Aircraft usually pull around 6 Gs for a sustained turn. Since my AMRAAM is 30 G it should be the maneuverable at the point where it is around Mach 3. If it goes to Mach 2 it will probably be around 20 Gs total. And after that the missile will be very capable of being outmanuvered from a "yo-yo manuver" or S move..

But what about planes moving in a straight line away from you? Lets say the airplane moves at Mach 1.2 average in the evasion run. Is there a way to calculate the range before the missile could be outrun?

How do you calculate the speed a various points of trajectories in the chart above?

Last edited: Oct 20, 2015