Editing Jet aircraft (section)

==Propulsive efficiency==
{{main|Propulsive efficiency}}
In aircraft ''overall propulsive efficiency'' <math>\eta</math> is the efficiency, in percent, with which the energy contained in a vehicle's propellant is converted into useful energy, to replace losses due to [[air drag]], gravity, and acceleration. It can also be stated as the proportion of the mechanical energy actually used to propel the aircraft. It is always less than 100% because of kinetic energy loss to the exhaust, and less-than-ideal efficiency of the propulsive mechanism, whether a [[Propeller (aircraft)|propeller]], a jet exhaust, or a fan. In addition, propulsive efficiency is greatly dependent on [[air density]] and airspeed.

Mathematically, it is represented as <math>\eta = \eta_c \eta_p</math><ref>[http://www.hq.nasa.gov/pao/History/SP-468/ch10-3.htm ch10-3<!-- Bot generated title -->] {{webarchive|url=https://web.archive.org/web/20100914184628/http://www.hq.nasa.gov/pao/History/SP-468/ch10-3.htm |date=2010-09-14 }}</ref> where <math>\eta_c</math> is the [[cycle efficiency]] and <math>\eta_p</math> is the propulsive efficiency. The cycle efficiency, in percent, is the proportion of energy that can be derived from the energy source that is converted to mechanical energy by the [[engine]].

[[File:Propulsive efficiency.png|thumb|right|Dependence of the propulsive efficiency (<math>\eta_p</math>) upon the vehicle speed/exhaust speed ratio (v/c) for rocket and jet engines]]

For jet aircraft the ''propulsive efficiency'' (essentially [[Energy conservation|energy efficiency]]) is highest when the engine emits an exhaust jet at a speed that is the same as, or nearly the same as, the vehicle velocity. The exact formula for air-breathing engines as given in the literature,<ref>K.Honicke, R.Lindner, P.Anders, M.Krahl, H.Hadrich, K.Rohricht. Beschreibung der Konstruktion der Triebwerksanlagen. Interflug, Berlin, 1968</ref><ref name=spt>Spittle, Peter. [http://users.encs.concordia.ca/~kadem/Rolls%20Royce.pdf "Gas turbine technology"] {{webarchive|url=https://web.archive.org/web/20141031143409/http://users.encs.concordia.ca/~kadem/Rolls%20Royce.pdf |date=2014-10-31 }} p507, ''[[Rolls-Royce plc]]'', 2003. Retrieved: 21 July 2012.</ref> is

:<math>\eta_p = \frac{2}{1 + \frac{c}{v}}</math>

where ''c'' is the exhaust speed, and ''v'' is the speed of the aircraft.