# Calculating Rocket Engine Power from Force and Burntime

I am struggling to relate power to force. The example that I am working on in my head is a model rocket. This model rocket (sans engine) has a mass of 50g. Its engine has a mass of 10g (for the purposes of this question, let's ignore the change of mass as a result of propellant consumption). The engine is capable of exerting a 5 N force for 0.3 seconds. To summarize:

• Rocket mass: 50g
• Engine mass: 10g
• Engine thrust: 5N
• Engine burn time: 0.3s

How would one calculate the "power" of the engine? I have thought of the following procedure:

1. Calculate the weight of the rocket + engine

$$F_{g_{rocket}} = (60g)(-9.8ms^{-1}) = -0.59N$$

1. Calculate the acceleration of the rocket as a result of the rocket's thrust

$$a_{rocket} = {F_{net} \over m_{rocket}} = {4.41N\over0.06kg} = 73.5ms^{-2}$$

1. Calculate the displacement of the rocket during the burn time

$$D = {1 \over 2}a_{rocket}t^2 = (0.5)(73.5ms^{-2})(0.3s)^2 = 3.31 m$$

1. Calculate the work performed.

$$W = (5N)(3.31m) = 16.55J$$

1. Find power by dividing work by the time.

$$P = {16.55J \over 0.3s} = 55.17W$$

However, the concept that I am struggling with is that this procedure means that the engine's power / energy is dependent on the mass of the rocket? For example, reducing the mass of the rocket would means a greater net upwards acceleration and also displacement, therefore the work performed would be greater since displacement is greater and thrust is constant. Wouldn't a chemical rocket engine have a predetermined amount of potential (chemical) energy, therefore be able to convert that to an invariable amount of kinetic energy? So, therefore I am a bit confused and my procedure must be wrong?

• "reducing the mass of the rocket would means a greater net force" - Why is this true? Dec 9, 2019 at 17:39
• Sorry, that was incorrect, I mean only to say greater acceleration. Dec 9, 2019 at 17:44

However, the concept that I am struggling with is that this procedure means that the engine's power / energy is dependent on the mass of the rocket?

Much more troublesome is that the power is also dependent on the speed of the rocket. The faster the rocket is going, the more power you calculate is coming from the engine! This reason is why rocket engine power is rarely discussed and thrust is.

Wouldn't a chemical rocket engine have a predetermined amount of potential (chemical) energy, therefore be able to convert that to an invariable amount of kinetic energy?

The first part is true. But at low speeds, much of the energy content of the engine is going into the kinetic energy of the exhaust, which you are ignoring. At higher speeds the starting KE of fuel becomes quite significant.

In whatever frame you want to measure, you get something like this:

$$KE_{fuel, init} + KE_{rocket, init} + E_{fuel} = KE_{exhaust, final} + KE_{rocket, final}$$

You could probably determine the chemical power of the fuel combustion, but the ratio of how that power goes into the KE of the rocket vs the KE of the fuel is changing as the rocket changes speed.

Why is the work done by a rocket engine greater at higher speeds?

• Thank you, I am understanding this much more clearly now! Dec 9, 2019 at 18:19