# Thrust-to-weight ratio

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Thrust-to-weight ratio is a dimensionless ratio of thrust to weight of a rocket, jet engine, propeller engine, or a vehicle propelled by such an engine that is an indicator of the performance of the engine or vehicle.

## Contents

The instantaneous thrust-to-weight ratio of a vehicle varies continually during operation due to progressive consumption of fuel or propellant and in some cases a gravity gradient. The thrust-to-weight ratio based on initial thrust and weight is often published and used as a figure of merit for quantitative comparison of a vehicle's initial performance.

## Calculation

The thrust-to-weight ratio is calculated by dividing the thrust (in SI units in newtons) by the weight (in newtons) of the engine or vehicle. Note that the thrust can also be measured in pound-force (lbf), provided the weight is measured in pounds (lb). Division using these two values still gives the numerically correct (dimensionless) thrust-to-weight ratio. For valid comparison of the initial thrust-to-weight ratio of two or more engines or vehicles, thrust must be measured under controlled conditions.

## Aircraft

The thrust-to-weight ratio and wing loading are the two most important parameters in determining the performance of an aircraft. [1] For example, the thrust-to-weight ratio of a combat aircraft is a good indicator of the maneuverability of the aircraft. [2]

The thrust-to-weight ratio varies continually during a flight. Thrust varies with throttle setting, airspeed, altitude and air temperature. Weight varies with fuel burn and payload changes. For aircraft, the quoted thrust-to-weight ratio is often the maximum static thrust at sea level divided by the maximum takeoff weight. [3] Aircraft with thrust-to-weight ratio greater than 1:1 can pitch straight up and maintain airspeed until performance decreases at higher altitude. [4]

In cruising flight, the thrust-to-weight ratio of an aircraft is the inverse of the lift-to-drag ratio because thrust is the opposite of drag, and weight is the opposite of lift. [5] A plane can take off even if the thrust is less than its weight: if the lift to drag ratio is greater than 1, the thrust to weight ratio can be less than 1, i.e. less thrust is needed to lift the plane off the ground than the weight of the plane.

${\displaystyle \left({\frac {T}{W}}\right)_{\text{cruise}}=\left({\frac {D}{L}}\right)_{\text{cruise}}={\frac {1}{\left({\frac {L}{D}}\right)_{\text{cruise}}}}}$

### Propeller-driven aircraft

For propeller-driven aircraft, the thrust-to-weight ratio can be calculated as follows: [6]

${\displaystyle {\frac {T}{W}}={\frac {550\eta _{p}}{V}}{\frac {\text{hp}}{\text{W}}}}$

where ${\displaystyle \eta _{p}\;}$ is propulsive efficiency (typically 0.8), ${\displaystyle hp\;}$ is the engine's shaft horsepower, and ${\displaystyle V\;}$is true airspeed in feet per second.

## Rockets

The thrust-to-weight ratio of a rocket, or rocket-propelled vehicle, is an indicator of its acceleration expressed in multiples of gravitational acceleration g. [7]

Rockets and rocket-propelled vehicles operate in a wide range of gravitational environments, including the weightless environment. The thrust-to-weight ratio is usually calculated from initial gross weight at sea level on earth [8] and is sometimes called Thrust-to-Earth-weight ratio. [9] The thrust-to-Earth-weight ratio of a rocket or rocket-propelled vehicle is an indicator of its acceleration expressed in multiples of earth's gravitational acceleration, g0. [7]

The thrust-to-weight ratio of a rocket improves as the propellant is burned. With constant thrust, the maximum ratio (maximum acceleration of the vehicle) is achieved just before the propellant is fully consumed. Each rocket has a characteristic thrust-to-weight curve, or acceleration curve, not just a scalar quantity.

The thrust-to-weight ratio of an engine is greater than that of the complete launch vehicle, but is nonetheless useful because it determines the maximum acceleration that any vehicle using that engine could theoretically achieve with minimum propellant and structure attached.

For a takeoff from the surface of the earth using thrust and no aerodynamic lift, the thrust-to-weight ratio for the whole vehicle must be greater than one. In general, the thrust-to-weight ratio is numerically equal to the g-force that the vehicle can generate. [7] Take-off can occur when the vehicle's g-force exceeds local gravity (expressed as a multiple of g0).

The thrust-to-weight ratio of rockets typically greatly exceeds that of airbreathing jet engines because the comparatively far greater density of rocket fuel eliminates the need for much engineering materials to pressurize it.

Many factors affect thrust-to-weight ratio. The instantaneous value typically varies over the duration flight with the variations in thrust due to speed and altitude, together with changed in weight due to the amount of remaining propellant, and payload mass. Factors with the greatest effect include freestream air temperature, pressure, density, and composition. Depending on the engine or vehicle under consideration, the actual performance will often be affected by buoyancy and local gravitational field strength.

## Examples

The Russian-made RD-180 rocket engine (which powers Lockheed Martin’s Atlas V) produces 3,820 kN of sea-level thrust and has a dry mass of 5,307 kg.[ citation needed ] Using the Earth surface gravitational field strength of 9.807 m/s², the sea-level thrust-to-weight ratio is computed as follows: (1 kN = 1000 N = 1000 kg⋅m/s²)

${\displaystyle {\frac {T}{W}}={\frac {3,820\ \mathrm {kN} }{(5,307\ \mathrm {kg} )(9.807\ \mathrm {m/s^{2}} )}}=0.07340\ {\frac {\mathrm {kN} }{\mathrm {N} }}=73.40\ {\frac {\mathrm {N} }{\mathrm {N} }}=73.40}$

### Aircraft

VehicleT/WScenario
Northrop Grumman B-2 Spirit 0.205 [10] Max take-off weight, full power
Airbus A340 0.2229Max take-off weight, full power (A340-300 Enhanced)
Airbus A380 0.227Max take-off weight, full power
Boeing 747-8 0.269Max take-off weight, full power
Boeing 777 0.285Max take-off weight, full power (777-200ER)
Boeing 737 MAX 8 0.310Max take-off weight, full power
Airbus A320neo 0.311Max take-off weight, full power
Boeing 757-200 0.341Max take-off weight, full power (w/Rolls-Royce RB211)
Tupolev Tu-160 0.363Max take-off weight, full afterburners
Concorde 0.372Max take-off weight, full afterburners
Rockwell International B-1 Lancer 0.38Max take-off weight, full afterburners
BAE Hawk 0.65 [11]
Lockheed Martin F-35 A 0.87 with full fuel (1.07 with 50% fuel, 1.19 with 25% fuel)
HAL Tejas Mk 1 1.o7With full fuel
Dassault Rafale 0.988 [12] Version M, 100% fuel, 2 EM A2A missile, 2 IR A2A missiles
Sukhoi Su-30MKM 1.00 [13] Loaded weight with 56% internal fuel
McDonnell Douglas F-15 1.04 [14] Nominally loaded
Mikoyan MiG-29 1.09 [15] Full internal fuel, 4 AAMs
Lockheed Martin F-22 >1.09 (1.26 with loaded weight and 50% fuel) [16] Combat load?
General Dynamics F-16 1.096[ citation needed ]
Hawker Siddeley Harrier 1.1[ citation needed ] VTOL
Eurofighter Typhoon 1.15 [17] Interceptor configuration
Space Shuttle 1.5Take-off
Space Shuttle 3Peak

### Jet and rocket engines

Jet or rocket engine MassThrust, vacuum Thrust-to-
weight ratio
(kg)(lb)(kN)(lbf)
RD-0410 nuclear rocket engine [18] [19] 2,0004,40035.27,9001.8
J58 jet engine (SR-71 Blackbird) [20] [21] 2,7226,00115034,0005.2
Rolls-Royce/Snecma Olympus 593
turbojet with reheat (Concorde) [22]
3,1757,000169.238,0005.4
Pratt & Whitney F119 [23] 1,8003,9009120,5007.95
RD-0750 rocket engine, three-propellant mode [24] 4,62110,1881,413318,00031.2
RD-0146 rocket engine [25] 2605709822,00038.4
Rocketdyne RS-25 rocket engine [26] 3,1777,0042,278512,00073.1
RD-180 rocket engine [27] 5,39311,8904,152933,00078.5
RD-170 rocket engine9,75021,5007,8871,773,00082.5
F-1 (Saturn V first stage) [28] 8,39118,4997,740.51,740,10094.1
NK-33 rocket engine [29] 1,2222,6941,638368,000136.7
Merlin 1D rocket engine, full-thrust version [30] 4671,030825185,000180.1

### Fighter aircraft

Table a: Thrust-to-weight ratios, fuel weights, and weights of different fighter planes
SpecificationsFighters
F-15K F-15CMiG-29KMiG-29B JF-17 J-10 F-35AF-35BF-35CF-22 LCA Mk-1
Engines thrust, maximum (N)259,420 (2)208,622 (2)176,514 (2)162,805 (2)81,402 (1)122,580 (1)177,484 (1)177,484 (1)177,484 (1)311,376 (2)89,800 (1)
Aircraft mass, empty (kg)17,01014,37912,72310,90006,58609,25013,29014,51515,78519,6736,560
Aircraft mass, full fuel (kg)23,14320,67117,96314,40508,88613,04421,67220,86724,40327,8369,500
Aircraft mass, max. take-off load (kg)36,74130,84522,40018,50012,70019,27731,75227,21631,75237,86913,300
Total fuel mass (kg)06,13306,29205,24003,50502,30003,79408,38206,35208,61808,16302,458
T/W ratio, full fuel1.141.031.001.150.930.960.840.870.741.141.07
Table b: Thrust-to-weight ratios, fuel weights, and weights of different fighter planes (in United States customary units)
SpecificationsFighters
F-15KF-15CMiG-29KMiG-29BJF-17J-10F-35AF-35BF-35CF-22LCA Mk-1
Engines thrust, maximum (lbf)58,320 (2)46,900 (2)39,682 (2)36,600 (2)18,300 (1)27,557 (1)40,000 (1)40,000 (1)40,000 (1)70,000 (2)20,200 (1)
Aircraft weight empty (lb)37,50031,70028,05024,03014,52020,39429,30032,00034,800 [31] 43,34014,300
Aircraft weight, full fuel (lb)51,02345,57439,60231,75719,65028,76047,78046,00353,80061,34020,944
Aircraft weight, max. take-off load (lb)81,00068,00049,38340,78528,00042,50070,00060,00070,00083,50029,100
Total fuel weight (lb)13,52313,87411,55207,72705,13008,36618,48014,00319,000 [31] 18,00005,419
T/W ratio, full fuel1.141.031.001.150.930.960.840.870.741.140.96
• Table for Jet and rocket engines: jet thrust is at sea level
• Fuel density used in calculations: 0.803 kg/l
• The number inside brackets is the number of engines.
• For the metric table, the T/W ratio is calculated by dividing the thrust by the product of the full fuel aircraft weight and the acceleration of gravity.
• Engines powering F-15K are the Pratt & Whitney engines.
• MiG-29K's empty weight is an estimate.
• JF-17's engine rating is of RD-93.
• JF-17 if mated with its engine WS-13, and if that engine gets its promised 18,969 lb then the T/W ratio becomes 1.10
• J-10's empty weight and fuelled weight are estimates.
• J-10's engine rating is of AL-31FN.
• J-10 if mated with its engine WS-10A, and if that engine gets its promised 132 kN (29,674 lbf) then the T/W ratio becomes 1.08

## Related Research Articles

A jet engine is a type of reaction engine discharging a fast-moving jet that generates thrust by jet propulsion. While this broad definition can include rocket, water jet, and hybrid propulsion, the term jet engine typically refers to an internal combustion airbreathing jet engine such as a turbojet, turbofan, ramjet, or pulse jet. In general, jet engines are internal combustion engines.

A rocket is a spacecraft, aircraft, vehicle or projectile that obtains thrust from a rocket engine. Rocket engine exhaust is formed entirely from propellant carried within the rocket. Rocket engines work by action and reaction and push rockets forward simply by expelling their exhaust in the opposite direction at high speed, and can therefore work in the vacuum of space.

Spacecraft propulsion is any method used to accelerate spacecraft and artificial satellites. In-space propulsion exclusively deals with propulsion systems used in the vacuum of space and should not be confused with space launch or atmospheric entry.

A single-stage-to-orbit vehicle reaches orbit from the surface of a body using only propellants and fluids and without expending tanks, engines, or other major hardware. The term usually, but not exclusively, refers to reusable vehicles. To date, no Earth-launched SSTO launch vehicles have ever been flown; orbital launches from Earth have been performed by either fully or partially expendable multi-stage rockets.

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 exhaust gas velocity.

Delta-v, symbolized as v and pronounced delta-vee, as used in spacecraft flight dynamics, is a measure of the impulse per unit of spacecraft mass that is needed to perform a maneuver such as launching from or landing on a planet or moon, or an in-space orbital maneuver. It is a scalar that has the units of speed. As used in this context, it is not the same as the physical change in velocity of the vehicle.

A scramjet is a variant of a ramjet airbreathing jet engine in which combustion takes place in supersonic airflow. As in ramjets, a scramjet relies on high vehicle speed to compress the incoming air forcefully before combustion, but whereas a ramjet decelerates the air to subsonic velocities before combustion using shock cones, a scramjet has no shock cone and slows the airflow using shockwaves produced by its ignition source in place of a shock cone. This allows the scramjet to operate efficiently at extremely high speeds.

A rocket engine uses stored rocket propellants as the reaction mass for forming a high-speed propulsive jet of fluid, usually high-temperature gas. Rocket engines are reaction engines, producing thrust by ejecting mass rearward, in accordance with Newton's third law. Most rocket engines use the combustion of reactive chemicals to supply the necessary energy, but non-combusting forms such as cold gas thrusters and nuclear thermal rockets also exist. Vehicles propelled by rocket engines are commonly called rockets. Rocket vehicles carry their own oxidizer, unlike most combustion engines, so rocket engines can be used in a vacuum to propel spacecraft and ballistic missiles.

A propellant is a mass that is expelled or expanded in such a way as to create a thrust or other motive force in accordance with Newton's third law of motion, and "propel" a vehicle, projectile, or fluid payload. In vehicles, the engine that expels the propellant is called a reaction engine. Although technically a propellant is the reaction mass used to create thrust, the term "propellant" is often used to describe a substance which is contains both the reaction mass and the fuel that holds the energy used to accelerate the reaction mass. For example, the term "propellant" is often used in chemical rocket design to describe a combined fuel/propellant, although the propellants should not be confused with the fuel that is used by an engine to produce the energy that expels the propellant. Even though the byproducts of substances used as fuel are also often used as a reaction mass to create the thrust, such as with a chemical rocket engine, propellant and fuel are two distinct concepts.

In aerospace engineering, the propellant mass fraction is the portion of a vehicle's mass which does not reach the destination, usually used as a measure of the vehicle's performance. In other words, the propellant mass fraction is the ratio between the propellant mass and the initial mass of the vehicle. In a spacecraft, the destination is usually an orbit, while for aircraft it is their landing location. A higher mass fraction represents less weight in a design. Another related measure is the payload fraction, which is the fraction of initial weight that is payload. It can be applied to a vehicle, a stage of a vehicle or to a rocket propulsion system.

A multistage rocket or step rocket is a launch vehicle that uses two or more rocket stages, each of which contains its own engines and propellant. A tandem or serial stage is mounted on top of another stage; a parallel stage is attached alongside another stage. The result is effectively two or more rockets stacked on top of or attached next to each other. Two-stage rockets are quite common, but rockets with as many as five separate stages have been successfully launched.

The Tsiolkovsky rocket equation, classical rocket equation, or ideal rocket equation is a mathematical equation that describes the motion of vehicles that follow the basic principle of a rocket: a device that can apply acceleration to itself using thrust by expelling part of its mass with high velocity can thereby move due to the conservation of momentum.

In spaceflight, an orbital maneuver is the use of propulsion systems to change the orbit of a spacecraft. For spacecraft far from Earth an orbital maneuver is called a deep-space maneuver (DSM).

Spacecraft flight dynamics is the application of mechanical dynamics to model how the external forces acting on a space vehicle or spacecraft determine its flight path. These forces are primarily of three types: propulsive force provided by the vehicle's engines; gravitational force exerted by the Earth and other celestial bodies; and aerodynamic lift and drag.

A rocket engine nozzle is a propelling nozzle used in a rocket engine to expand and accelerate combustion products to high supersonic velocities.

In aircraft and rocket 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.

A reaction engine is an engine or motor that produces thrust by expelling reaction mass, in accordance with Newton's third law of motion. This law of motion is commonly paraphrased as: "For every action force there is an equal, but opposite, reaction force."

In astronautics, a powered flyby, or Oberth maneuver, is a maneuver in which a spacecraft falls into a gravitational well and then uses its engines to further accelerate as it is falling, thereby achieving additional speed. The resulting maneuver is a more efficient way to gain kinetic energy than applying the same impulse outside of a gravitational well. The gain in efficiency is explained by the Oberth effect, wherein the use of a reaction engine at higher speeds generates a greater change in mechanical energy than its use at lower speeds. In practical terms, this means that the most energy-efficient method for a spacecraft to burn its fuel is at the lowest possible orbital periapsis, when its orbital velocity is greatest. In some cases, it is even worth spending fuel on slowing the spacecraft into a gravity well to take advantage of the efficiencies of the Oberth effect. The maneuver and effect are named after the person who first described them in 1927, Hermann Oberth, an Austro-Hungarian-born German physicist and a founder of modern rocketry.

A cold gas thruster is a type of rocket engine which uses the expansion of a pressurized gas to generate thrust. As opposed to traditional rocket engines, a cold gas thruster does not house any combustion and therefore has lower thrust and efficiency compared to conventional monopropellant and bipropellant rocket engines. Cold gas thrusters have been referred to as the "simplest manifestation of a rocket engine" because their design consists only of a fuel tank, a regulating valve, a propelling nozzle, and the little required plumbing. They are the cheapest, simplest, and most reliable propulsion systems available for orbital maintenance, maneuvering and attitude control.

This glossary of aerospace engineering terms pertains specifically to aerospace engineering, its sub-disciplines, and related fields including aviation and aeronautics. For a broad overview of engineering, see glossary of engineering.

## References

• John P. Fielding. Introduction to Aircraft Design, Cambridge University Press, ISBN   978-0-521-65722-8
• Daniel P. Raymer (1989). Aircraft Design: A Conceptual Approach, American Institute of Aeronautics and Astronautics, Inc., Washington, DC. ISBN   0-930403-51-7
• George P. Sutton & Oscar Biblarz. Rocket Propulsion Elements, Wiley, ISBN   978-0-471-32642-7

### Notes

1. Daniel P. Raymer, Aircraft Design: A Conceptual Approach, Section 5.1
2. John P. Fielding, Introduction to Aircraft Design, Section 4.1.1 (p.37)
3. John P. Fielding, Introduction to Aircraft Design, Section 3.1 (p.21)
4. Nickell, Paul; Rogoway, Tyler (2016-05-09). "What it's Like to Fly the F-16N Viper, Topgun's Legendary Hotrod". The Drive. Retrieved 2019-10-31.
5. Daniel P. Raymer, Aircraft Design: A Conceptual Approach, Equation 5.2
6. Daniel P. Raymer, Aircraft Design: A Conceptual Approach, Equations 3.9 and 5.1
7. George P. Sutton & Oscar Biblarz, Rocket Propulsion Elements (p. 442, 7th edition) "thrust-to-weight ratio F/Wg is a dimensionless parameter that is identical to the acceleration of the rocket propulsion system (expressed in multiples of g0) if it could fly by itself in a gravity-free vacuum"
8. George P. Sutton & Oscar Biblarz, Rocket Propulsion Elements (p. 442, 7th edition) "The loaded weight Wg is the sea-level initial gross weight of propellant and rocket propulsion system hardware."
9. "Thrust-to-Earth-weight ratio". The Internet Encyclopedia of Science. Archived from the original on 2008-03-20. Retrieved 2009-02-22.
10. "AviationsMilitaires.net — Dassault Rafale C". www.aviationsmilitaires.net. Archived from the original on 25 February 2014. Retrieved 30 April 2018.
11. "F-15 Eagle Aircraft". About.com:Inventors. Retrieved 2009-03-03.
12. Pike, John. "MiG-29 FULCRUM". www.globalsecurity.org. Archived from the original on 19 August 2017. Retrieved 30 April 2018.
13. "AviationsMilitaires.net — Lockheed-Martin F-22 Raptor". www.aviationsmilitaires.net. Archived from the original on 25 February 2014. Retrieved 30 April 2018.
14. "Eurofighter Typhoon". eurofighter.airpower.at. Archived from the original on 9 November 2016. Retrieved 30 April 2018.
15. Wade, Mark. "RD-0410". Encyclopedia Astronautica . Retrieved 2009-09-25.
16. "Aircraft: Lockheed SR-71A Blackbird". Archived from the original on 2012-07-29. Retrieved 2010-04-16.
17. "Factsheets : Pratt & Whitney J58 Turbojet". National Museum of the United States Air Force. Archived from the original on 2015-04-04. Retrieved 2010-04-15.
18. "Rolls-Royce SNECMA Olympus - Jane's Transport News". Archived from the original on 2010-08-06. Retrieved 2009-09-25. With afterburner, reverser and nozzle ... 3,175 kg ... Afterburner ... 169.2 kN
19. Military Jet Engine Acquisition, RAND, 2002.
20. "«Konstruktorskoe Buro Khimavtomatiky» - Scientific-Research Complex / RD0750". KBKhA - Chemical Automatics Design Bureau . Retrieved 2009-09-25.
21. Wade, Mark. "RD-0146". Encyclopedia Astronautica . Retrieved 2009-09-25.
22. "RD-180" . Retrieved 2009-09-25.
23. Mueller, Thomas (June 8, 2015). "Is SpaceX's Merlin 1D's thrust-to-weight ratio of 150+ believable?" . Retrieved July 9, 2015. The Merlin 1D weighs 1030 pounds, including the hydraulic steering (TVC) actuators. It makes 162,500 pounds of thrust in vacuum. that is nearly 158 thrust/weight. The new full thrust variant weighs the same and makes about 185,500 lbs force in vacuum.
24. "Lockheed Martin Website". Archived from the original on 2008-04-04.