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Thrust

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Reaction force

For other uses, seeThrust (disambiguation).

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ALockheed Martin F-35 Lightning II aircraft performing a vertical climb using itsPratt & Whitney F135 jet engine, which produces 43,000 lbf (190,000 N) of thrust.^[1]

Thrust is areaction force described quantitatively byNewton's third law. When a system expels oraccelerates mass in one direction, the accelerated mass will cause a force of equalmagnitude but opposite direction to be applied to that system.^[2]The force applied on a surface in a direction perpendicular ornormal to the surface is also called thrust. Force, and thus thrust, is measured using theInternational System of Units (SI) innewtons (symbol: N), and represents the amount needed to accelerate 1 kilogram of mass at the rate of 1meter per second per second.^[3] Inmechanical engineering, forceorthogonal to the main load (such as in parallelhelical gears) is referred to asstatic thrust.

Examples

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Afixed-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 apropeller, the propelling jet of ajet engine, or by ejecting hot gases from arocket engine.^[4] Reverse thrust can be generated to aid braking after landing by reversing the pitch of variable-pitch propeller blades, or using athrust reverser on a jet engine.Rotary wing aircraft use rotors andthrust vectoring V/STOL aircraft use propellers or engine thrust to support the weight of the aircraft and to provide forward propulsion.

Amotorboat propeller generates thrust when it rotates and forces water backwards.

Arocket is propelled forward by a thrust equal in magnitude, but opposite in direction, to the time-rate of momentum change of theexhaust gas accelerated from the combustion chamber through the rocket engine nozzle. This is theexhaust velocity with respect to the rocket, times the time-rate at which the mass is expelled, or in mathematical terms:

\mathbf {T} =\mathbf {v} {\frac {\mathrm {d} m}{\mathrm {d} t}}

WhereT is the thrust generated (force), ${\frac {\mathrm {d} m}{\mathrm {d} t}}$ is the rate of change of mass with respect to time (mass flow rate of exhaust), andv is the velocity of the exhaust gases measured relative to the rocket.

For vertical launch of a rocket the initial thrust atliftoff must be more than the weight.

Each of the threeSpace Shuttle Main Engines could produce a thrust of 1.8 meganewton, and each of the Space Shuttle's twoSolid Rocket Boosters 14.7 MN (3,300,000 lbf), together 29.4 MN.^[5]

By contrast, theSimplified Aid for EVA Rescue (SAFER) has 24 thrusters of 3.56 N (0.80 lbf) each.^[6]

In the air-breathing category, the AMT-USA AT-180 jet engine developed forradio-controlled aircraft produce 90 N (20lbf) of thrust.^[7] TheGE90-115B engine fitted on theBoeing 777-300ER has a thrust of 569 kN (127,900 lbf). It was recognized byGuinness World Records as the "World's Most Powerful Commercial Jet Engine" until it was surpassed by theGE9X (fitted on the upcomingBoeing 777X), with 609 kN (134,300 lbf).

Concepts

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Thrust to power

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The power needed to generate thrust and the force of the thrust can be related in anon-linear way. In general, $\mathbf {P} ^{2}\propto \mathbf {T} ^{3}$ . The proportionality constant varies, and can be solved for a uniform flow, where $v_{\infty }$ is the incoming air velocity, $v_{d}$ is the velocity at the actuator disc, and $v_{f}$ is the final exit velocity:

{\frac {\mathrm {d} m}{\mathrm {d} t}}=\rho A{v}

\mathbf {T} ={\frac {\mathrm {d} m}{\mathrm {d} t}}\left(v_{f}-v_{\infty }\right),{\frac {\mathrm {d} m}{\mathrm {d} t}}=\rho Av_{d}

\mathbf {P} ={\frac {1}{2}}{\frac {\mathrm {d} m}{\mathrm {d} t}}(v_{f}^{2}-v_{\infty }^{2}),\mathbf {P} =\mathbf {T} v_{d}

Solving for the velocity at the disc, $v_{d}$ , we then have:

v_{d}={\frac {1}{2}}(v_{f}-v_{\infty })

When incoming air is accelerated from a standstill – for example when hovering – then $v_{\infty }=0$ , and we can find:

\mathbf {T} ={\frac {1}{2}}\rho A{v_{f}}^{2},\mathbf {P} ={\frac {1}{4}}\rho A{v_{f}}^{3}

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

\mathbf {P} ^{2}={\frac {\mathbf {T} ^{3}}{2\rho A}}

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 ( $A {\displaystyle A}$ ) and the density of the fluid ( $\rho$ ). This helps to explain why moving through water is easier and why aircraft have much larger propellers than watercraft.

Thrust to propulsive power

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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:^[8]

\mathbf {P} =\mathbf {F} {\frac {d}{t}}

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:^[9]

\mathbf {P} =\mathbf {T} {v}

This formula looks very surprising, but it is correct: thepropulsive power (orpower available^[10]) 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 combinationpiston 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:

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

Excess thrust

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If a powered aircraft is generating thrust T and experiencingdrag D, the difference between the two, T − D, is termed the excess thrust. The instantaneous performance of the aircraft is mostly dependent on the excess thrust.

Excess thrust is avector and is determined as the vector difference between the thrust vector and the drag vector.

Thrust axis

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The thrust axis for an airplane is theline 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 amoment that must be resisted by a change in the aerodynamic force on the horizontal stabiliser.^[11] Notably, theBoeing 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,MCAS. Early versions of MCAS malfunctioned in flight with catastrophic consequences, leading to thedeaths of over 300 people in 2018 and 2019.^[12]^[13]