Editing Thrust

{{Short description|Reaction force}}
{{Other uses}}
{{More citations needed|date=December 2017}}
{{Use dmy dates|date=April 2020}}
[[File:F-35 Heritage Flight Team performs in Bell Fort Worth Alliance AirShow.jpg|upright=1.5|thumb|A [[Lockheed Martin F-35 Lightning II]] aircraft performing a vertical climb using its [[Pratt & Whitney F135]] jet engine, which produces {{cvt|43,000|lbf|N}} of thrust.<ref>{{Cite web |title=Lockheed Martin F-35 Joint Strike Fighter Succeeds in First Vertical Landing |url=https://news.lockheedmartin.com/2010-03-18-Lockheed-Martin-F-35-Joint-Strike-Fighter-Succeeds-in-First-Vertical-Landing |access-date=2024-04-04 |website=Media - Lockheed Martin}}</ref>]]

'''Thrust''' is a [[reaction (physics)|reaction]] [[force (physics)|force]] described quantitatively by [[Newton's third law]]. When a system expels or [[acceleration|accelerates]] [[mass]] in one direction, the accelerated mass will cause a force of equal [[magnitude (vector)|magnitude]] but opposite direction to be applied to that system.<ref>{{cite web|url=https://www.grc.nasa.gov/WWW/k-12/airplane/thrust1.html|title=What is Thrust?|website=www.grc.nasa.gov|access-date=2 April 2020|archive-url=https://web.archive.org/web/20200214214218/https://www.grc.nasa.gov/WWW/K-12/airplane/thrust1.html|archive-date=14 February 2020|url-status=live}}</ref>
The force applied on a surface in a direction perpendicular or [[normal vector|normal]] to the surface is also called thrust. Force, and thus thrust, is measured using the [[International System of Units]] (SI) in [[newton (unit)|newton]]s (symbol: N), and represents the amount needed to accelerate 1 kilogram of mass at the rate of 1 [[Metre per second squared|meter per second per second]].<ref>{{Cite web |title=Force and Motion: Definition, Laws & Formula {{!}} StudySmarter |url=https://www.studysmarter.co.uk/explanations/physics/force/force-and-motion/ |access-date=2022-10-12 |website=StudySmarter UK |language=en-GB}}</ref> In [[mechanical engineering]], force [[orthogonal]] to the main load (such as in parallel [[helical gear]]s) is referred to as [[statics|static thrust]].

== Examples ==
A [[fixed-wing aircraft]] propulsion system generates forward thrust when air is pushed in the direction opposite to flight. This can be done by different means such as the spinning blades of a [[Propeller (aircraft)|propeller]], the propelling jet of a [[jet engine]], or by ejecting hot gases from a [[rocket engine]].<ref>{{cite web|url=https://www.grc.nasa.gov/WWW/k-12/airplane/newton3.html|title=Newton's Third Law of Motion|website=www.grc.nasa.gov|access-date=2 April 2020|archive-url=https://web.archive.org/web/20200203022807/https://www.grc.nasa.gov/WWW/K-12/airplane/newton3.html|archive-date=3 February 2020|url-status=live}}</ref> Reverse thrust can be generated to aid braking after landing by reversing the pitch of variable-pitch propeller blades, or using a [[Thrust reversal|thrust reverser]] on a jet engine. [[Rotary wing aircraft]] use rotors and [[thrust vectoring]] [[V/STOL]] aircraft use propellers or engine thrust to support the weight of the aircraft and to provide forward propulsion.

A [[motorboat]] propeller generates thrust when it rotates and forces water backwards.

A [[rocket]] is propelled forward by a thrust equal in magnitude, but opposite in direction, to the time-rate of momentum change of the [[exhaust gas]] accelerated from the combustion chamber through the rocket engine nozzle. This is the [[exhaust velocity]] with respect to the rocket, times the time-rate at which the mass is expelled, or in mathematical terms:
:<math>\mathbf{T}=\mathbf{v}\frac{\mathrm{d}m}{\mathrm{d}t}</math>
Where '''T''' is the thrust generated (force), <math>\frac {\mathrm{d}m} {\mathrm{d}t}</math> is the rate of change of mass with respect to time (mass flow rate of exhaust), and '''v''' is the velocity of the exhaust gases measured relative to the rocket.

For vertical launch of a rocket the initial thrust at [[wikt:liftoff|liftoff]] must be more than the weight.

Each of the three [[Space Shuttle Main Engine]]s could produce a thrust of 1.8&nbsp;[[meganewton]], and each of the Space Shuttle's two [[Space Shuttle Solid Rocket Booster|Solid Rocket Boosters]] {{convert|14.7|MN|lbf|abbr=on|lk=on}}, together 29.4&nbsp;MN.<ref>{{cite web|url=http://www.braeunig.us/space/specs/shuttle.htm|title=Space Launchers - Space Shuttle|website=www.braeunig.us|access-date=16 February 2018|archive-url=https://web.archive.org/web/20180406061909/http://www.braeunig.us/space/specs/shuttle.htm|archive-date=6 April 2018|url-status=live}}</ref>

By contrast, the [[Simplified Aid for EVA Rescue]] (SAFER) has 24 thrusters of {{convert|3.56|N|lbf|abbr=on}} each.<ref>{{Cite journal |last1=Handley |first1=Patrick M. |last2=Hess |first2=Ronald A. |last3=Robinson |first3=Stephen K. |date=2018-02-01 |title=Descriptive Pilot Model for the NASA Simplified Aid for Extravehicular Activity Rescue |url=https://arc.aiaa.org/doi/10.2514/1.G003131 |journal=Journal of Guidance, Control, and Dynamics |volume=41 |issue=2 |pages=515–518 |doi=10.2514/1.G003131 |bibcode=2018JGCD...41..515H |issn=0731-5090|url-access=subscription }}</ref>

In the air-breathing category, the AMT-USA AT-180 jet engine developed for [[radio-controlled aircraft]] produce 90&nbsp;N (20 [[Pound-force|lbf]]) of thrust.<ref>{{cite web
| url = http://usamt.com/Mel/comm/comm_products.html
| title = AMT-USA jet engine product information
| access-date = 13 December 2006
| archive-url = https://web.archive.org/web/20061110025303/http://usamt.com/Mel/comm/comm_products.html
| archive-date = 10 November 2006
| url-status = dead
}}</ref> The [[General Electric GE90|GE90]]-115B engine fitted on the [[Boeing 777]]-300ER has a thrust of 569&nbsp;kN (127,900&nbsp;lbf). It was recognized by ''[[Guinness World Records]]'' as the "World's Most Powerful Commercial Jet Engine"  until it was surpassed by the [[General Electric GE9X|GE9X]] (fitted on the upcoming [[Boeing 777X]]), with 609 kN (134,300 lbf).

==Concepts==
===Thrust to power===
The power needed to generate thrust and the force of the thrust can be related in a [[non-linear]] way. In general, <math>\mathbf{P}^2 \propto \mathbf{T}^3</math>. The proportionality constant varies, and can be solved for a uniform flow, where <math>v_\infty</math> is the incoming air velocity, <math>v_d</math> is the velocity at the actuator disc, and <math>v_f</math> is the final exit velocity:

:<math>\frac{\mathrm{d}m}{\mathrm{d}t} = \rho A {v}</math>

:<math>\mathbf{T} = \frac{\mathrm{d}m}{\mathrm{d}t} \left (v_f - v_\infty \right ), \frac{\mathrm{d}m}{\mathrm{d}t} = \rho A v_d</math>

:<math>\mathbf{P} = \frac{1}{2} \frac{\mathrm{d}m}{\mathrm{d}t} (v_f^2 - v_\infty^2), \mathbf{P} = \mathbf{T}v_d</math>

Solving for the velocity at the disc, <math>v_d</math>, we then have:
:<math>v_d = \frac{1}{2}(v_f + v_\infty)</math>

When incoming air is accelerated from a standstill – for example when hovering – then <math>v_\infty = 0</math>, and we can find:

:<math>\mathbf{T} = \frac{1}{2} \rho A {v_f}^2, \mathbf{P} = \frac{1}{4} \rho A {v_f}^3</math>

From here we can see the <math>\mathbf{P}^2 \propto \mathbf{T}^3</math> relationship, finding:

:<math>\mathbf{P}^2 = \frac{\mathbf{T}^3}{2 \rho A}</math>

The inverse of the proportionality constant, the "efficiency" of an otherwise-perfect thruster, is proportional to the area of the cross section of the propelled volume of fluid (<math>A</math>) and the density of the fluid (<math>\rho</math>). This helps to explain why moving through water is easier and why aircraft have much larger propellers than watercraft.

===Thrust to propulsive power===
A very common question is how to compare the thrust rating of a jet engine with the power rating of a piston engine. Such comparison is difficult, as these quantities are not equivalent. A piston engine does not move the aircraft by itself (the propeller does that), so piston engines are usually rated by how much power they deliver to the propeller. Except for changes in temperature and air pressure, this quantity depends basically on the throttle setting.

A jet engine has no propeller, so the propulsive power of a jet engine is determined from its thrust as follows. Power is the force (F) it takes to move something over some distance (d) divided by the time (t) it takes to move that distance:<ref>{{cite web
| url = http://www.aerospaceweb.org/question/propulsion/q0195.shtml
| title = Convert Thrust to Horsepower
| first = Joe
| last = Yoon
| access-date = 1 May 2009
| archive-url = https://web.archive.org/web/20100613154846/http://www.aerospaceweb.org/question/propulsion/q0195.shtml
| archive-date = 13 June 2010
| url-status = live
}}</ref>

:<math>\mathbf{P}=\mathbf{F}\frac{d}{t}</math>

In case of a rocket or a jet aircraft, the force is exactly the thrust (T) produced by the engine. If the rocket or aircraft is moving at about a constant speed, then distance divided by time is just speed, so power is thrust times speed:<ref>{{cite book |title=Introduction to Aircraft Flight Mechanics |first1=Thomas |last1=Yechout |first2=Steven|last2=Morris |isbn=1-56347-577-4}}</ref>

:<math>\mathbf{P}=\mathbf{T}{v}</math>

This formula looks very surprising, but it is correct: the ''propulsive power'' (or ''power available'' <ref>{{cite book |title=Understanding Flight |first1=David |last1=Anderson |first2=Scott |last2=Eberhardt |publisher=McGraw-Hill |isbn=0-07-138666-1 |date=2001}}</ref>) of a jet engine increases with its speed. If the speed is zero, then the propulsive power is zero. If a jet aircraft is at full throttle but attached to a static test stand, then the jet engine produces no propulsive power, however thrust is still produced. The combination [[piston engine]]–propeller also has a propulsive power with exactly the same formula, and it will also be zero at zero speed – but that is for the engine–propeller set. The engine alone will continue to produce its rated power at a constant rate, whether the aircraft is moving or not.

Now, imagine the strong chain is broken, and the jet and the piston aircraft start to move. At low speeds:

<blockquote>
The piston engine will have constant 100% power, and the propeller's thrust will vary with speed<br />
The jet engine will have constant 100% thrust, and the engine's power will vary with speed
</blockquote>

===Excess thrust===
If a powered aircraft is generating thrust T and experiencing [[Aerodynamic drag|drag]] D, the difference between the two, T&nbsp;−&nbsp;D, is termed the excess thrust. The instantaneous performance of the aircraft is mostly dependent on the excess thrust.

Excess thrust is a [[Euclidean vector|vector]] and is determined as the vector difference between the thrust vector and the drag vector.

===Thrust axis===

The thrust axis for an airplane is the [[line of action]] of the total thrust at any instant. It depends on the location, number, and characteristics of the jet engines or propellers. It usually differs from the drag axis. If so, the distance between the thrust axis and the drag axis will cause a [[moment (physics)|moment]] that must be resisted by a change in the aerodynamic force on the horizontal stabiliser.<ref>Kermode, A.C. (1972) ''Mechanics of Flight'', Chapter 5, 8th edition. Pitman Publishing. {{ISBN|0273316230}}</ref> Notably, the [[Boeing 737 MAX]], with larger, lower-slung engines than previous 737 models, had a greater distance between the thrust axis and the drag axis, causing the nose to rise up in some flight regimes, necessitating a pitch-control system, [[Maneuvering Characteristics Augmentation System|MCAS]]. Early versions of MCAS malfunctioned in flight with catastrophic consequences, leading to the [[Boeing 737 MAX groundings|deaths of over 300 people]] in 2018 and 2019.<ref>{{Cite web|url=https://www.aljazeera.com/news/2019/03/control-system-scrutiny-ethiopian-airlines-crash-190311094532350.html|title=Control system under scrutiny after Ethiopian Airlines crash|website=Al Jazeera|access-date=7 April 2019|archive-url=https://web.archive.org/web/20190428062403/https://www.aljazeera.com/news/2019/03/control-system-scrutiny-ethiopian-airlines-crash-190311094532350.html|archive-date=28 April 2019|url-status=live}}</ref><ref>{{Cite web|url=https://theaircurrent.com/aviation-safety/what-is-the-boeing-737-max-maneuvering-characteristics-augmentation-system-mcas-jt610/|title=What is the Boeing 737 Max Maneuvering Characteristics Augmentation System?|date=14 November 2018|website=The Air Current|language=en-US|access-date=7 April 2019|archive-url=https://web.archive.org/web/20190407184426/https://theaircurrent.com/aviation-safety/what-is-the-boeing-737-max-maneuvering-characteristics-augmentation-system-mcas-jt610/|archive-date=7 April 2019|url-status=live}}</ref>

==See also==

* {{Annotated link |Aerodynamic force}}
* {{Annotated link |Astern propulsion}}
* {{Annotated link |Gas turbine engine thrust}}
* {{Annotated link |Gimballed thrust}} (most common in modern rockets) 
*{{Annotated link |Pound (force)}}
** "Pound of thrust": thrust (force) required to accelerate one pound at one [[standard gravity|g]] 
* {{Annotated link |Stream thrust averaging}}
* {{Annotated link |Thrust-to-weight ratio}}
* {{Annotated link |Thrust vectoring}}
* {{Annotated link |Thrust reversal}}
* {{Annotated link |Tractive effort}}

==References==
{{Reflist}}

{{Authority control}}

[[Category:Aircraft aerodynamics]]
[[Category:Force]]
[[Category:Temporal rates]]