Editing Rocket engine (section)

===Nozzle===
{{Main|Rocket engine nozzle}}
[[File:Rocket thrust.svg|thumb|right|Rocket thrust is caused by pressures acting in the combustion chamber and nozzle. From Newton's third law, equal and opposite pressures act on the exhaust, and this accelerates it to high speeds.]]
The hot gas produced in the combustion chamber is permitted to escape through a narrow space, called as the throat, to increase the velocity until it reaches Mach 1, and then through a diverging expansion section. When sufficient pressure is provided to the nozzle (about 2.5–3 times ambient pressure), the nozzle ''[[choked flow|choke]]s'' and a supersonic jet is formed, dramatically accelerating the gas, converting most of the thermal energy into kinetic energy. Exhaust speeds vary, depending on the [[expansion ratio]] the nozzle is designed for, but exhaust speeds as high as ten times the [[speed of sound]] in air at sea level are not uncommon. About half of the rocket engine's thrust comes from the unbalanced pressures inside the combustion chamber, and the rest comes from the pressures acting against the inside of the nozzle (see diagram). As the gas expands ([[Adiabatic process|adiabatically]]) the pressure against the nozzle's walls forces the rocket engine in one direction while accelerating the gas in the other.

{{Anchor|opt_expansion}} <!-- add anchor for diagram references --->
[[File:Rocket nozzle expansion.svg|thumb|right|upright|The four expansion regimes of a de Laval nozzle:
• under-expanded
• perfectly expanded
• over-expanded
• grossly over-expanded]]
The most commonly used nozzle is the [[de Laval nozzle]], a fixed geometry nozzle with a high expansion-ratio. The large bell- or cone-shaped nozzle extension beyond the throat gives the rocket engine its characteristic shape.

The exit [[static pressure#Static pressure in fluid dynamics|static pressure]] of the exhaust jet depends on the chamber pressure and the ratio of exit to throat area of the nozzle. As exit pressure varies from the ambient (atmospheric) pressure, a choked nozzle is said to be
* '''under-expanded''' (exit pressure greater than ambient),
* '''perfectly expanded''' (exit pressure equals ambient),
* '''over-expanded''' (exit pressure less than ambient; [[shock diamond]]s form outside the nozzle), or
* '''grossly over-expanded''' (a [[shock wave]] forms inside the nozzle extension).

In practice, perfect expansion is only achievable with a variable–exit-area nozzle (since ambient pressure decreases as altitude increases), and is not possible above a certain altitude as ambient pressure approaches zero. If the nozzle is not perfectly expanded, then loss of efficiency occurs. Grossly over-expanded nozzles lose less efficiency, but can cause mechanical problems with the nozzle. Fixed-area nozzles become progressively more under-expanded as they gain altitude. Almost all de Laval nozzles will be momentarily grossly over-expanded during startup in an atmosphere.<ref name="HuzelAndHuang">{{cite book
 |last = Huzel
 |first = Dexter K.
 |last2 = Huang
 |first2 = David H.
 |date = 1 January 1971
 |title = NASA SP-125, Design of Liquid Propellant Rocket Engines, Second Edition
 |url = https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19710019929_1971019929.pdf
 |publisher = NASA
 |page = <!-- or pages= -->
 |archive-url = https://web.archive.org/web/20170324150551/https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19710019929_1971019929.pdf/
 |archive-date = 24 March 2017
 |url-status = dead
 |access-date = 7 July 2017
 }}</ref>

Nozzle efficiency is affected by operation in the atmosphere because atmospheric pressure changes with altitude; but due to the supersonic speeds of the gas exiting from a rocket engine, the pressure of the jet may be either below or above ambient, and equilibrium between the two is not reached at all altitudes (see diagram).

====Back pressure and optimal expansion====
For optimal performance, the pressure of the gas at the end of the nozzle should just equal the ambient pressure: if the exhaust's pressure is lower than the ambient pressure, then the vehicle will be slowed by the difference in pressure between the top of the engine and the exit; on the other hand, if the exhaust's pressure is higher, then exhaust pressure that could have been converted into thrust is not converted, and energy is wasted.

To maintain this ideal of equality between the exhaust's exit pressure and the ambient pressure, the diameter of the nozzle would need to increase with altitude, giving the pressure a longer nozzle to act on (and reducing the exit pressure and temperature). This increase is difficult to arrange in a lightweight fashion, although is routinely done with other forms of jet engines. In rocketry a lightweight compromise nozzle is generally used and some reduction in atmospheric performance occurs when used at other than the 'design altitude' or when throttled. To improve on this, various exotic nozzle designs such as the [[plug nozzle]], [[stepped nozzles]], the [[expanding nozzle]] and the [[aerospike engine|aerospike]] have been proposed, each providing some way to adapt to changing ambient air pressure and each allowing the gas to expand further against the nozzle, giving extra thrust at higher altitudes.

When exhausting into a sufficiently low ambient pressure (vacuum) several issues arise. One is the sheer weight of the nozzle—beyond a certain point, for a particular vehicle, the extra weight of the nozzle outweighs any performance gained. Secondly, as the exhaust gases adiabatically expand within the nozzle they cool, and eventually some of the chemicals can freeze, producing 'snow' within the jet. This causes instabilities in the jet and must be avoided.

On a [[De Laval nozzle]], exhaust gas flow detachment will occur in a grossly over-expanded nozzle.  As the detachment point will not be uniform around the axis of the engine, a side force may be imparted to the engine. This side force may change over time and result in control problems with the launch vehicle.

Advanced [[altitude compensating nozzle|altitude-compensating]] designs, such as the [[aerospike engine|aerospike]] or [[plug nozzle]], attempt to minimize performance losses by adjusting to varying expansion ratio caused by changing altitude.