Calculating equivalent horsepower for a jet engine

[FreeBob]

Trying to remember some basics. I know the thrust of a jet engine. I'm thinking about equivalent HP. I can establish HP at a given speed, but what about while accelerating? I will display my ignorance here :(

Power for static, non accelerating flight:
Power = [Thrust x Airspeed]
Thrust equals drag so not accelerating

Power for accelerating flight?
Power = [Thrust x Airspeed] + [Mass * Accel * Airspeed]

At brake release, velocity is essentially zero, so all power goes to accelerate the mass until drag starts to build. Before any motion takes place, power is zero, but as airspeed builds, drag increases but thrust is greater, so all the power of the jet engine accelerating the mass. Does HP jump to max thrust horsepower at the moment of brake release and is zero when brakes are locked?
At cruise speed, thrust equals drag, so all power goes to oppose drag and the acceleration term goes to zero.

Sound right?

 

[haruspex]

Power = [Thrust x Airspeed] + [Mass * Accel * Airspeed]

Doesn't the thrust include the net force producing the acceleration? Ma = net force = thrust - drag.

 

[FreeBob]

Power = F * V So the jet engine's power is it's cruise thrust times the cruise velocity

When the jet engine is at full throttle, while accelerating to cruise speed, the thrust is approximately the same but the velocity is increasing from zero to cruise velocity. So at V/2 (while accelerating) the power would be only 1/2 as much as at cruise, which doesn't make sense to me. My thought is that the power is the same as at cruise (V) but the components are now two elements:
1) the power at that instantaneous velocity, V/2 * Thrust
2) the power consumed in accelerating the mass. The Force that is accelerating the mass is Thrust minus the drag (which is increasing with speed).

So I think I"m agreeing with you :)

 

[mfb]

Power = F * V

This equation is true independent of the acceleration.
While cruising F is equal to the drag force, while accelerating on the runway drag is lower so the aircraft accelerates.

So at V/2 (while accelerating) the power would be only 1/2 as much as at cruise, which doesn't make sense to me.

The thrust can be higher. Thrust and throttle setting are not the same thing.

 

[FreeBob]

This equation is true independent of the acceleration.
While cruising F is equal to the drag force, while accelerating on the runway drag is lower so the aircraft accelerates.The thrust can be higher. Thrust and throttle setting are not the same thing.

This equation is true independent of the acceleration.
While cruising F is equal to the drag force, while accelerating on the runway drag is lower so the aircraft accelerates.The thrust can be higher. Thrust and throttle setting are not the same thing.

I understand that Thrust can be greater than Drag which accelerates the aircraft. I am just trying to renconcile the "power" that the engine is producing. When the a/c is barely moving, based on P = F*V, the power would be very low, which doesn't make sense unless you can calculate the power going to create the acceleration. I am assuming the answer is F = m * a, so for accelerating power, the equation is P = m * a * v. I'm looking for whether or not this is correct for calculating the jet engines power before reaching cruise.

 

[CWatters]

The equation should be...

Power = thrust * velocity = {drag + (mass*acceleration)} * velocity

 

[mfb]

When the a/c is barely moving, based on P = F*V, the power would be very low, which doesn't make sense unless you can calculate the power going to create the acceleration.

The power is very low. If you can neglect drag, then F=ma and power is P=Fv=mav - you get the same result, at low speed the power is very low.
At least the fraction of the power that is used. Turbines in a standing airplane are mainly heating the surrounding air.

 

[OldYat47]

Power is dependent on velocity. Remember that power is the rate of doing work. Work = force X distance, power = force X distance / time or force X velocity. No velocity, no power. Once the jet powered vehicle gets moving then thrust X velocity = power and acceleration = (thrust - drag) / mass. Don't think of power and force as similar, they are quite different.