Anyway, ramjet engines are self-sustaining. They only have to be catapulted at a threashold speed. After that they should go on accelerating till they reach the speed of light....theoretically.
That is why they need to be throttled and they are..
But Brahmos is restricted to Mach 2.5 +. I dont think that is done by a microcontroller, but rather its fuel gets over by the time it reaches Mach 2.9.
Sustaining Mach 3 is very tough..Aluminum is not a good enough material for this kind of speed, starts to lose strength becuase of aerothermal heating. For that, you need to move to Titanium (SR-71, Mig 25 examples here) and the cost shoots up exponentially... So my guess is it would be restricted to mach 2.5 becuase of materials reasons.
Once Brahmos reaches the targeted mach number, the thrust will be throttled back to be just in a sustaining mode..The full thrust of the engine and max fuel consumption is during the initial acceleration phase after the rocket booster jettisons and maybe during the final phase when it drops to seal level to sustain the top speed.
It must be noted that the range of the Brahmos in low-low profile is only 120 kms, which is less than half of its usual range of 290 kms (when launched in hi-lo profile).
This means that its speed is reduced when it cruises at just above sea-level, and implies drastic reduction in speed.
Ok. Go to the basic physics of this .. The total energy available to the missile after the rocket booster falls off, is the kinetic energy at this point, plus the energy value of the fuel it carries(with its associated conversion
efficiency into thrust).. Now since the resistance is exponentially higher at sea level, vs high altitude, for the given energy content in the fuel, the distance traveled at sea level will be far less than at altitude if the speed of the missle will be same. This is intuitive and is borne out by your observation on range.
However, you assume that the flight time at low altitude for 120km and at altitude for 290km is the same , maybe thinking that the fuel burn rate has to be constant irrespective of the altitude. That is not true. At low altitude, the engine can be throttled approriately to get max possible range (which mind you could be still less than that possible at altitude).
Anyway , check out
Ramjet in Wikipedia .. (Gosh, this Wikipedia is so awesome, so convenient, next best thing to sliced bread internetwise)