Is the efficiency of a rocket jet engine during the phase of acceleration in earth's atmophere 10, 20, 30, or 45%

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A rocket has four basic forces acting on it when in flight. These forces are lift, weight, thrust and drag. The lift force acting on a rocket in flight is usually pretty small. The other three forces, however, all directly impact the maximum height the rocket can reach. Weight is a function of how each component of the rocket is designed. The lighter the rocket is, the higher it will be able to go all else being equal. Thrust is generated by the rocket's motor. The more thrust the motor produces, the higher it will go. However, neither of these forces is heavily dependent on the nose shape. The force that has the most effect and does vary significantly with the shape of the nose is drag.

a rocket flying at Mach 0.85  with an exhaust velocity of Mach 10, would have a predicted overall energy efficiency of 5.9%.

Thus efficiency depends on speed of the rocket higher speed more efficient.

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