Aeronautical Engineering/Excess power eqn.
QUESTION: Dear Sir,
Could you please explain how I should go about drawing an FBD, of a rocket traveling vertically upwards, which will let me develop excess power eqn. for it? Assuming it is not flying at steady state conditions and gravity acting on it is opposite to direction of flight.
ANSWER: Jeff - you simply draw a box around the body or assume the outer surface is that box and sum all forces and accelerations acting on the body.
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I appreciate the reply. Actually no force is shown acting on the rocket. The only forces I can think of are thrust acting upwards and gravity downwards. Is that right? And if so, how should I deduce the excess power equation from that information? I guess I'm finding it tricky because I don't really know what an excess power eqn. is comprised of. Could you tell me about the excess power eqn.?
Jeff - The forces on a rocket are the thrust, drag and weight assuming the side forces from wind are zero. A thrust greater than drag plus weight will cause the rocket to accelerate. Your force-body-diagram will show three forces and one acceleration. All forces are changing with time and airspeed.
The thrust force exerted by the rocket is:
F = mdot Ve + (pe - po)Ae where mdot is the mass flow rate of the exhaust, Ve is the exhaust velocity, pe is the exhaust pressure, po is the atmospheric pressure, and Ae is the exhaust area. If we know the jet velocity downstream, Vo, where the exhaust and atmospheric pressures are equal then:
F = mdot Vo
The rocket thrust power is Pt = FVo = mdot Vo^2.
The rocket drag power is Pd = DV, where D = rocket drag and V = rocket flight speed
The power consumed by drag plus weight is:
Pdw = (D+W) V
I am not sure of the definition of excess power, but I assume it is:
Pt - Pdw ; i.e., the difference between rocket power and power absorbed by drag and weight. Excess power will cause the rocket to accelerate.