# Thrust

Last updated A Lockheed Martin F-35 Lightning II aircraft performing a vertical climb using its Pratt & Whitney F135 jet engine, which produces 43,000 lbf (190,000 N) of thrust.

Thrust is a reaction force described quantitatively by Newton's third law. When a system expels or accelerates mass in one direction, the accelerated mass will cause a force of equal magnitude but opposite direction to be applied to that system.  The force applied on a surface in a direction perpendicular or normal to the surface is also called thrust. Force, and thus thrust, is measured using the International System of Units (SI) in newtons (symbol: N), and represents the amount needed to accelerate 1 kilogram of mass at the rate of 1 meter per second per second.  In mechanical engineering, force orthogonal to the main load (such as in parallel helical gears) is referred to as 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, the propelling jet of a jet engine, or by ejecting hot gases from a rocket engine.  Reverse thrust can be generated to aid braking after landing by reversing the pitch of variable-pitch propeller blades, or using a 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:

$\mathbf {T} =\mathbf {v} {\frac {\mathrm {d} m}{\mathrm {d} t}}$ Where T 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), and v is the velocity of the exhaust gases measured relative to the rocket.

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

Each of the three Space Shuttle Main Engines could produce a thrust of 1.8  meganewton, and each of the Space Shuttle's two Solid Rocket Boosters 14.7  MN (3,300,000  lbf ), together 29.4 MN. 

By contrast, the simplified Aid For EVA Rescue (SAFER) has 24 thrusters of 3.56 N (0.80 lbf) each. 

In the air-breathing category, the AMT-USA AT-180 jet engine developed for radio-controlled aircraft produce 90 N (20 lbf) of thrust.  The GE90-115B engine fitted on the Boeing 777-300ER, recognized by the Guinness Book of World Records as the "World's Most Powerful Commercial Jet Engine," has a thrust of 569 kN (127,900 lbf) until it was surpassed by the GE9X, fitted on the upcoming Boeing 777X, at 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, $\mathbf {P} ^{2}\propto \mathbf {T} ^{3}$ . 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:

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

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: 

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

$\mathbf {P} =\mathbf {T} {v}$ This formula looks very surprising, but it is correct: the propulsive power (or power available  ) 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:

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

If a powered aircraft is generating thrust T and experiencing drag 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 a 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 that must be resisted by a change in the aerodynamic force on the horizontal stabiliser.  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, MCAS. Early versions of MCAS malfunctioned in flight with catastrophic consequences, leading to the deaths of over 300 people in 2018 and 2019.  

## Related Research Articles A centripetal force is a force that makes a body follow a curved path. The direction of the centripetal force is always orthogonal to the motion of the body and towards the fixed point of the instantaneous center of curvature of the path. Isaac Newton described it as "a force by which bodies are drawn or impelled, or in any way tend, towards a point as to a centre". In the theory of Newtonian mechanics, gravity provides the centripetal force causing astronomical orbits. A jet engine is a type of reaction engine, discharging a fast-moving jet of heated gas that generates thrust by jet propulsion. While this broad definition may include rocket, water jet, and hybrid propulsion, the term jet engine typically refers to an internal combustion air-breathing jet engine such as a turbojet, turbofan, ramjet, or pulse jet. In general, jet engines are internal combustion engines. Mach number is a dimensionless quantity in fluid dynamics representing the ratio of flow velocity past a boundary to the local speed of sound. It is named after the Austrian physicist and philosopher Ernst Mach. A steam turbine is a machine that extracts thermal energy from pressurized steam and uses it to do mechanical work on a rotating output shaft. Its modern manifestation was invented by Charles Parsons in 1884. Fabrication of a modern steam turbine involves advanced metalwork to form high-grade steel alloys into precision parts using technologies that first became available in the 20th century; continued advances in durability and efficiency of steam turbines remains central to the energy economics of the 21st century. In physics and mechanics, torque is the rotational analogue of linear force. It is also referred to as the moment of force. It describes the rate of change of angular momentum that would be imparted to an isolated body.

Specific impulse is a measure of how efficiently a reaction mass engine creates thrust. For engines whose reaction mass is only the fuel they carry, specific impulse is exactly proportional to the effective exhaust gas velocity. A jet aircraft is an aircraft propelled by jet engines.

In classical mechanics, impulse is the integral of a force, F, over the time interval, t, for which it acts. Since force is a vector quantity, impulse is also a vector quantity. Impulse applied to an object produces an equivalent vector change in its linear momentum, also in the resultant direction. The SI unit of impulse is the newton second (N⋅s), and the dimensionally equivalent unit of momentum is the kilogram meter per second (kg⋅m/s). The corresponding English engineering unit is the pound-second (lbf⋅s), and in the British Gravitational System, the unit is the slug-foot per second (slug⋅ft/s).

In continuum mechanics, the Froude number is a dimensionless number defined as the ratio of the flow inertia to the external field. The Froude number is based on the speed–length ratio which he defined as:

Blade element theory (BET) is a mathematical process originally designed by William Froude (1878), David W. Taylor (1893) and Stefan Drzewiecki (1885) to determine the behavior of propellers. It involves breaking a blade down into several small parts then determining the forces on each of these small blade elements. These forces are then integrated along the entire blade and over one rotor revolution in order to obtain the forces and moments produced by the entire propeller or rotor. One of the key difficulties lies in modelling the induced velocity on the rotor disk. Because of this the blade element theory is often combined with momentum theory to provide additional relationships necessary to describe the induced velocity on the rotor disk, producing blade element momentum theory. At the most basic level of approximation a uniform induced velocity on the disk is assumed: Stokes flow, also named creeping flow or creeping motion, is a type of fluid flow where advective inertial forces are small compared with viscous forces. The Reynolds number is low, i.e. . This is a typical situation in flows where the fluid velocities are very slow, the viscosities are very large, or the length-scales of the flow are very small. Creeping flow was first studied to understand lubrication. In nature, this type of flow occurs in the swimming of microorganisms and sperm. In technology, it occurs in paint, MEMS devices, and in the flow of viscous polymers generally.

In fluid dynamics, drag is a force acting opposite to the relative motion of any object moving with respect to a surrounding fluid. This can exist between two fluid layers or between a fluid and a solid surface.

In physics, the Einstein relation is a previously unexpected connection revealed independently by William Sutherland in 1904, Albert Einstein in 1905, and by Marian Smoluchowski in 1906 in their works on Brownian motion. The more general form of the equation is The maximal total range is the maximum distance an aircraft can fly between takeoff and landing. Powered aircraft range is limited by the aviation fuel energy storage capacity considering both weight and volume limits. Unpowered aircraft range depends on factors such as cross-country speed and environmental conditions. The range can be seen as the cross-country ground speed multiplied by the maximum time in the air. The fuel time limit for powered aircraft is fixed by the available fuel and rate of consumption.

In aerospace engineering, concerning aircraft, rocket and spacecraft design, overall propulsion system efficiency is the efficiency with which the energy contained in a vehicle's fuel is converted into kinetic energy of the vehicle, to accelerate it, or to replace losses due to aerodynamic drag or gravity. Mathematically, it is represented as , where is the cycle efficiency and is the propulsive efficiency.  In mathematics, potential flow around a circular cylinder is a classical solution for the flow of an inviscid, incompressible fluid around a cylinder that is transverse to the flow. Far from the cylinder, the flow is unidirectional and uniform. The flow has no vorticity and thus the velocity field is irrotational and can be modeled as a potential flow. Unlike a real fluid, this solution indicates a net zero drag on the body, a result known as d'Alembert's paradox.

Blade element momentum theory is a theory that combines both blade element theory and momentum theory. It is used to calculate the local forces on a propeller or wind-turbine blade. Blade element theory is combined with momentum theory to alleviate some of the difficulties in calculating the induced velocities at the rotor.

An axial fan is a type of fan that causes gas to flow through it in an axial direction, parallel to the shaft about which the blades rotate. The flow is axial at entry and exit. The fan is designed to produce a pressure difference, and hence force, to cause a flow through the fan. Factors which determine the performance of the fan include the number and shape of the blades. Fans have many applications including in wind tunnels and cooling towers. Design parameters include power, flow rate, pressure rise and efficiency.

Propeller theory is the science governing the design of efficient propellers. A propeller is the most common propulsor on ships, and on small aircraft.

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