Rocket Engine Nozzle - Optimum Shape

Optimum Shape

The ratio of the area of the narrowest part of the nozzle to the exit plane area is mainly what determines how efficiently the expansion of the exhaust gases is converted into linear velocity; the exhaust velocity and therefore the thrust of the rocket engine, although the gas properties have an effect as well.

The shape of the nozzle also modestly affects how efficiently the expansion of the exhaust gases is converted into linear motion. The simplest nozzle shape is a ~12 degree internal angle cone, which is about 97% efficient. Smaller angles give very slightly higher efficiency, larger angles give lower efficiency.

More complex shapes of revolution are frequently used, such as Bell nozzles or parabolic shapes. These give perhaps 1% higher efficiency than the cone nozzle, and can be shorter and lighter. They are widely used on launch vehicles and other rockets where weight is at a premium. They are, of course, harder to fabricate, so are typically more costly.

There is also a theoretical optimum nozzle shape for maximum exhaust speed, however, a shorter bell shape is typically used which gives better overall performance due to its much lower weight, shorter length, lower drag losses, and only very marginally lower exhaust speed.

Other design aspects affect the efficiency of a rocket nozzle; the nozzle's throat should be a smooth radius. The angle of the narrowing down to the throat also has an effect on the overall efficiency, but this is small. The exit of the nozzle needs to be as sharp as possible to minimize the chances of separation problems at low exit pressures.