Editing Rocket engine (section)

==Overall performance==
Rocket technology can combine very high thrust ([[meganewton]]s), very high exhaust speeds (around 10 times the speed of sound in air at sea level) and very high thrust/weight ratios (>100) ''simultaneously'' as well as being able to operate outside the atmosphere, and while permitting the use of low pressure and hence lightweight tanks and structure.

Rockets can be further optimised to even more extreme performance along one or more of these axes at the expense of the others.

===Specific impulse===
{{Specific impulse|align=right}}
{{Main|Specific impulse}}

The most important metric for the efficiency of a rocket engine is [[impulse (physics)|impulse]] per unit of [[propellant]], this is called [[specific impulse]] (usually written <math>I_{sp}</math>). This is either measured as a speed (the ''effective exhaust velocity'' <math>v_{e}</math> in metres/second or ft/s) or as a time (seconds). For example, if an engine producing 100 pounds of thrust runs for 320 seconds and burns 100 pounds of propellant, then the specific impulse is 320 seconds. The higher the specific impulse, the less propellant is required to provide the desired impulse.

The specific impulse that can be achieved is primarily a function of the propellant mix (and ultimately would limit the specific impulse), but practical limits on chamber pressures and the nozzle expansion ratios reduce the performance that can be achieved.

===Net thrust===
{{Main|Thrust}}
Below is an approximate equation for calculating the net thrust of a rocket engine:<ref>{{cite book|author=George P. Sutton|author2=Oscar Biblarz|name-list-style=amp|title=Rocket Propulsion Elements|edition=8th|publisher=Wiley Interscience|date=2010|isbn=9780470080245|url=https://archive.org/details/Rocket_Propulsion_Elements_8th_Edition_by_Oscar_Biblarz_George_P._Sutton/page/34/mode/2up}} See Equation 2-14.</ref>

{{block indent|<math>F_n = \dot{m}\;v_{e} = \dot{m}\;v_{e-opt} + A_{e}(p_{e} - p_{amb})</math>}}

{| border="0" cellpadding="2" style="margin-left:1em"
|-
|align=right|where:
|&nbsp;
|-
!align=right|<math>\dot{m}</math>
|align=left|=&nbsp; exhaust gas mass flow
|- 
!align=right|<math>v_{e}</math>
|align=left|=&nbsp; effective exhaust velocity (sometimes otherwise denoted as ''c'' in publications)
|-
!align=right|<math>v_{e-opt}</math>
|align=left|=&nbsp; effective jet velocity when Pamb = Pe
|-
!align=right|<math>A_{e}</math>
|align=left|=&nbsp; flow area at nozzle exit plane (or the plane where the jet leaves the nozzle if separated flow)
|-
!align=right|<math>p_{e}</math>
|align=left|=&nbsp; static pressure at nozzle exit plane
|-
!align=right|<math>p_{amb}</math>
|align=left|=&nbsp; ambient (or atmospheric) pressure
|}

Since, unlike a jet engine, a conventional rocket motor lacks an air intake, there is no 'ram drag' to deduct from the gross thrust. Consequently, the net thrust of a rocket motor is equal to the gross thrust (apart from static back pressure).

The <math>\dot{m}\;v_{e-opt}\,</math> term represents the momentum thrust, which remains constant at a given throttle setting, whereas the <math>A_{e}(p_{e} - p_{amb})\,</math> term represents the pressure thrust term. At full throttle, the net thrust of a rocket motor improves slightly with increasing altitude, because as atmospheric pressure decreases with altitude, the pressure thrust term increases. At the surface of the Earth the pressure thrust may be reduced by up to 30%, depending on the engine design. This reduction drops roughly exponentially to zero with increasing altitude.

Maximum efficiency for a rocket engine is achieved by maximising the momentum contribution of the equation without incurring penalties from over expanding the exhaust. This occurs when <math>p_{e} = p_{amb}</math>. Since ambient pressure changes with altitude, most rocket engines spend very little time operating at peak efficiency.

Since specific impulse is force divided by the rate of mass flow, this equation means that the specific impulse varies with altitude.

===Vacuum specific impulse, I<sub>sp</sub>===

Due to the specific impulse varying with pressure, a quantity that is easy to compare and calculate with is useful. Because rockets [[choked flow|choke]] at the throat, and because the supersonic exhaust prevents external pressure influences travelling upstream, it turns out that the pressure at the exit is ideally exactly proportional to the propellant flow <math> \dot{m}</math>, provided the mixture ratios and combustion efficiencies are maintained. It is thus quite usual to rearrange the above equation slightly:<ref>{{cite book|author=George P. Sutton|author2=Oscar Biblarz|name-list-style=amp|title=Rocket Propulsion Elements|edition=8th|publisher=Wiley Interscience|date=2010|isbn=9780470080245|url=https://archive.org/details/Rocket_Propulsion_Elements_8th_Edition_by_Oscar_Biblarz_George_P._Sutton/page/34/mode/2up}} See Equation 3-33.</ref>

{{block indent|<math> F_{vac} = C_f\, \dot{m}\, c^*</math>}}

and so define the ''vacuum Isp'' to be:

{{block indent|<math>v_{evac} = C_f\, c^* \,</math>}}

where:

{{block indent|1=<math>c^*</math> &thinsp;= &thinsp;the [[characteristic velocity]] of the combustion chamber (dependent on propellants and combustion efficiency)}}
{{block indent|1=<math>C_f</math> &thinsp;= &thinsp;the thrust coefficient constant of the nozzle (dependent on nozzle geometry, typically about 2)}}

And hence:
{{block indent|<math> F_n = \dot{m}\, v_{evac} - A_{e}\, p_{amb}</math>}}

===Throttling===

Rockets can be throttled by controlling the propellant combustion rate <math> \dot{m}</math> (usually measured in kg/s or lb/s). In liquid and hybrid rockets, the propellant flow entering the chamber is controlled using valves, in [[solid rocket]]s it is controlled by changing the area of propellant that is burning and this can be designed into the propellant grain (and hence cannot be controlled in real-time).

Rockets can usually be throttled down to an exit pressure of about one-third of ambient pressure<ref name=Sutton/> (often limited by flow separation in nozzles) and up to a maximum limit determined only by the mechanical strength of the engine.

In practice, the degree to which rockets can be throttled varies greatly, but most rockets can be throttled by a factor of 2 without great difficulty;<ref name=Sutton/> the typical limitation is combustion stability, as for example, injectors need a minimum pressure to avoid triggering damaging oscillations (chugging or combustion instabilities); but injectors can be optimised and tested for wider ranges.

For example, some more recent liquid-propellant engine designs that have been optimised for greater throttling capability ([[BE-3]], [[Raptor (rocket engine)|Raptor]]) can be throttled to as low as 18–20 per cent of rated thrust.<!-- eg, Blue Orgin BE-3 --><ref name="sn20150407">
{{cite news |last1=Foust|first=Jeff |title=Blue Origin Completes BE-3 Engine as BE-4 Work Continues |url=http://spacenews.com/blue-origin-completes-be-3-engine-as-be-4-work-continues/ |access-date=2016-10-20 |work=Space News |date=2015-04-07 }}</ref><!-- eg, SpaceX Raptor --><ref name="sfi20160927">{{cite news |url= http://www.spaceflightinsider.com/organizations/space-exploration-technologies/elon-musk-shows-off-interplanetary-transport-system/ |title= Elon Musk Shows Off Interplanetary Transport System |publisher= Spaceflight Insider |last= Richardson |first= Derek |date= 2016-09-27 |access-date= 2016-10-20 |archive-date= 2016-10-01 |archive-url= https://web.archive.org/web/20161001225649/http://www.spaceflightinsider.com/organizations/space-exploration-technologies/elon-musk-shows-off-interplanetary-transport-system/ |url-status= dead }}</ref>

Solid rockets can be throttled by using shaped grains that will vary their surface area over the course of the burn.<ref name="Sutton" />

===Energy efficiency===
{{Further|Rocket#Energy efficiency}}
[[File:Rocket propulsion efficiency.svg|thumb|Rocket vehicle mechanical efficiency as a function of vehicle instantaneous speed divided by effective exhaust speed. These percentages need to be multiplied by internal engine efficiency to get overall efficiency.]]
Rocket engine nozzles are surprisingly efficient [[heat engines]] for generating a high speed jet, as a consequence of the high combustion temperature and high [[compression ratio]]. Rocket nozzles give an excellent approximation to [[adiabatic expansion]] which is a reversible process, and hence they give efficiencies which are very close to that of the [[Carnot cycle]]. Given the temperatures reached, over 60% efficiency can be achieved with chemical rockets.

For a ''vehicle'' employing a rocket engine the energetic efficiency is very good if the vehicle speed approaches or somewhat exceeds the exhaust velocity (relative to launch); but at low speeds the [[Propulsive efficiency|energy efficiency]] goes to 0% at zero speed (as with all [[jet propulsion]]). <!--- it's very counterintuitive, a way to look at it is that energy= force x distance, but at zero speed you have no movement and you lose lots of energy in the jet --->See [[Rocket#Energy efficiency|Rocket energy efficiency]] for more details.
{{clear}}

===Thrust-to-weight ratio===
{{Main|thrust-to-weight ratio}}
Rockets, of all the jet engines, indeed of essentially all engines, have the highest thrust-to-weight ratio. This is especially true for liquid-fueled rocket engines.

This high performance is due to the small volume of [[pressure vessel]]s that make up the engine—the pumps, pipes and combustion chambers involved. The lack of inlet duct and the use of dense liquid propellant allows the pressurisation system to be small and lightweight, whereas duct engines have to deal with air which has around three orders of magnitude lower density.

{{Engine thrust to weight table}}

Of the liquid fuels used, density is lowest for [[liquid hydrogen]]. Although hydrogen/oxygen burning has the highest [[specific impulse]] of any in-use chemical rocket, hydrogen's very low density (about one-fourteenth that of water) requires larger and heavier turbopumps and pipework, which decreases the engine's thrust-to-weight ratio (for example the RS-25) compared to those that do not use hydrogen (NK-33).