|There has been a lot of arguments over the performance of A2A missiles here -- some of which are well backed by facts, some are so far out there it is like claiming that they fly on hyperdrive.
I want to take this opportunity to introduce everyone to a very simple formula that can be used for estimating the performance of a missile. It goes like this:-
Change in Velocity (Delta V) = 10 x Specific Impulse x LN (initial weight / final weight) m/s
This assumes that all the fuel is used to get the missile as fast as possible and none is used to provide just enough thrust to sustain a given velocity. In otherwords, it assumes an all-boost motor not a boost sustain motor.
For example, let'a take a look at the AIM-120A AMRAAM which we have some decent info on...
Launch weight = 335 lbs (Published stats)
Motor weight = 156 lbs (WPU-6/B HTPB rocket motor weight as per Raytheon)
Approximate specific impulse = 245 seconds (typical of HTPB solid motors)
Approximate fuel fraction of motor = 85% (typical of robust aluminum cased aerospace rocket motors)
OK... if 85% of the motor's mass is the fuel, we have about 132 lbs of fuel in the AMRAAM-A -- roughly a 39.4% fuel fraction (sounds about right). So let's run the numbers...
Delta V = 10 x 245 x LN(335/(335-132)) = 1227 m/s
The formula predicts that the AMRAAM will go about 1227 m/s (~Mach 3.7) faster than it started. If it is launched at say Mach 1.5 it'll be going Mach 5.2. In reality the AMRAAM doesn't go that fast. The reason is that not all the fuel is used to get it as fast as possible. The AMRAAM's motor is a boost-sustain design. It is probably grained to take the weapon to abut Mach 2.5~2.8 faster than it started at (Mach 4+ in a typical Mach 1.5 release). The rest of the fuel is shaped to burn much more slowly to keep it's velocity at or near the achieved maximum out to a longer range before the motor burns out.