on Earth); approximately 9.807 m/s |} For a perfectly expanded nozzle case, where , the formula becomes In cases where this may not be so, since for a rocket nozzle is proportional to , it is possible to define a constant quantity that is the vacuum for any given engine thus: and hence: which is simply the vacuum thrust minus the force of the ambient atmospheric pressure acting over the exit plane. Essentially then, for rocket nozzles, the ambient pressure acting on the engine cancels except over the exit plane of the rocket engine in a rearward direction, while the exhaust jet generates forward thrust. Aerostatic back-pressure and optimal expansion As the gas travels down the expansion part of the nozzle, the pressure and temperature decrease, while the speed of the gas increases. The supersonic nature of the exhaust jet means that the pressure of the exhaust can be significantly different from ambient pressure – the outside air is unable to equalize the pressure upstream due to the very high jet velocity. Therefore, for supersonic nozzles, it is actually possible for the pressure of the gas exiting the nozzle to be significantly below or very greatly above ambient pressure. If the exit pressure is too low, then the jet can separate from the nozzle. This is often unstable, and the jet will generally cause large off-axis thrusts and may mechanically damage the nozzle. This separation generally occurs if the exit pressure drops below roughly 30–45% of ambient, but separation may be delayed to far lower pressures if the nozzle is designed to increase the pressure at the rim, as is achieved with the SSME (1–2 psi at 15 psi ambient). In addition, as the rocket engine starts up or throttles, the chamber pressure varies, and this generates different levels of efficiency. At low chamber pressures the engine is almost inevitably going to be grossly over-expanded. Optimal 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. 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 has a ~15° cone half-angle,