# Efficiency Loss of Rocket Engine in a Vacuum Due to Underexpansion

A rocket engine in the vacuum will experience efficiency loss due to under-expansion in which the pressure of the exhaust is greater than the ambient pressure, which in a vacuum is near zero.

How great is this efficiency loss in real-world terms? The thrust equation has a term in which the ambient pressure is subtracted from the exhaust pressure and multiplied by the cross-sectional nozzle exit plane area. This actually increases the thrust, yet we speak of under-expansion being an efficiency loss. Where is that loss and how great is it in real-world terms.

I tend to think of it, perhaps too simplistically, in terms of geometric vectors with a diagonal force broken down into X and Y vectors. In an ambient engine where exhaust pressure equals ambient, the exhaust gas is longitudinal behind nozzle mostly X vector. As plume expansion occurs with under-expansion, force that could have been imparted in X direction is wasted in Y direction. The question is how much force, as a percentage of thrust?

If we have a small engine less than 25,000lbf of thrust, suppose it fires, in the vacuum of space, say with like Chang'e5 landing, with 25,000 lbs of thrust, doesn't this mean it actually only produces a smaller amount of thrust due to plume expansion, the loss of force in Y vector, or is this already factored into the rating? So if I need to propel say 10,000 lbs, in a vacuum, launch or land in the vacuum scenario, don't I actually need an engine with more thrust than this because of the Y-vector thrust losses? I want to understand theoretically, not for any one specific scenario. How great is the efficiency loss in the real world? How do we explain or quantify the loss when the rocket thrust equation shows a theoretical gain in thrust? Does the efficiency loss due to Y-vector expansion exceed the theoretical thrust gain from rocket thrust equation? Thank you for anyone that can answer.

• Some rocket nozzles are optimized for atmospheric pressure, some for vacuum. Aerospikes are an odd design that gets OK performance in both. See Are Aerospikes Better Than Bell Nozzles? for more Commented Jan 20 at 23:03