# 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

### Aircraft

Vehiclethrust-weight ratioNotes
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 154B 0.360Max take-off weight, full power (w/Kuznecov NK-82)
Tupolev Tu-160 0.363 [ citation needed ]Max 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 0.87With full fuel (1.07 with 50% fuel, 1.19 with 25% fuel)
HAL Tejas Mk 1 0.94With full fuel
CAC/PAC JF-17 Thunder 0.95With 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 1.5[ citation needed ]Take-off
Space Shuttle 3Peak

### Jet and rocket engines

EngineMassThrust, vacuumThrust-to-
weight ratio
(kN)(lbf)
RD-0410 nuclear rocket engine [18] [19] 2,000 kg (4,400 lb)35.27,9001.8
Pratt & Whitney J58 jet engine
(Lockheed SR-71 Blackbird) [20] [21]
2,722 kg (6,001 lb)15034,0005.6
Rolls-Royce/Snecma Olympus 593
turbojet with reheat
(Concorde) [22]
3,175 kg (7,000 lb)169.238,0005.4
Pratt & Whitney F119 [23] 1,800 kg (4,000 lb)9120,5007.95
RD-0750 rocket engine
three-propellant mode [24]
4,621 kg (10,188 lb)1,413318,00031.2
RD-0146 rocket engine [25] 260 kg (570 lb)9822,00038.4
Rocketdyne RS-25 rocket engine
(Space Shuttle Main Engine) [26]
3,177 kg (7,004 lb)2,278512,00073.1
RD-180 rocket engine [27] 5,393 kg (11,890 lb)4,15278.7
RD-170 rocket engine 9,750 kg (21,500 lb)7,8871,773,00082.5
F-1
(Saturn V first stage) [28]
8,391 kg (18,499 lb)7,740.51,740,10094.1
NK-33 rocket engine [29] 1,222 kg (2,694 lb)1,638368,000136.7
SpaceX Raptor 2 rocket engine [30] 1,600 kg (3,500 lb)2,256507,000143.8
Merlin 1D rocket engine,
full-thrust version [31] [32]
467 kg (1,030 lb)914205,500199.5

### Fighter aircraft

Thrust-to-weight ratios, fuel weights, and weights of different fighter planes
Specifications F-15K [lower-alpha 1] 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 fuel1.141.031.001.150.951.050.840.870.741.140.94
• Table for Jet and rocket engines: jet thrust is at sea level
• Fuel density used in calculations: 0.803 kg/l
• 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.
• J-10's engine rating is of AL-31FN.

## Notes

1. Pratt & Whitney engines
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. Archived from the original on 2019-10-31. 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. РД0410. Ядерный ракетный двигатель. Перспективные космические аппараты [RD0410. Nuclear Rocket Engine. Advanced launch vehicles] (in Russian). KBKhA - Chemical Automatics Design Bureau. Archived from the original on 30 November 2010.
17. "Aircraft: Lockheed SR-71A Blackbird". Archived from the original on 2012-07-29. Retrieved 2010-04-16.
18. "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.
19. "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
20. Military Jet Engine Acquisition, RAND, 2002.
21. "Конструкторское бюро химавтоматики" - Научно-исследовательский комплекс / РД0750. [«Konstruktorskoe Buro Khimavtomatiky» - Scientific-Research Complex / RD0750.]. KBKhA - Chemical Automatics Design Bureau. Archived from the original on 26 July 2011.
22. Wade, Mark. "RD-0146". Encyclopedia Astronautica . Retrieved 2009-09-25.
23. "RD-180" . Retrieved 2009-09-25.
24. Wade, Mark. "NK-33". Encyclopedia Astronautica. Retrieved 2022-08-24.
25. Sesnic, Trevor (2022-07-14). "Raptor 1 vs Raptor 2: What did SpaceX change?". Everyday Astronaut. Retrieved 2022-11-07.
26. Mueller, Thomas (June 8, 2015). "Is SpaceX's Merlin 1D's thrust-to-weight ratio of 150+ believable?". Quora. 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.
27. "SpaceX". SpaceX. Retrieved 2022-11-07.

## 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 vehicle that uses jet propulsion to accelerate without using the surrounding air. A rocket engine produces thrust by reaction to exhaust expelled at high speed. Rocket engines work entirely from propellant carried within the vehicle; therefore a rocket can fly in the vacuum of space. Rockets work more efficiently in a vacuum and incur a loss of thrust due to the opposing pressure of the atmosphere.

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 the effective exhaust gas velocity.

Flight or flying is the process by which an object moves through a space without contacting any planetary surface, either within an atmosphere or through the vacuum of outer space. This can be achieved by generating aerodynamic lift associated with gliding or propulsive thrust, aerostatically using buoyancy, or by ballistic movement.

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 oxidiser, unlike most combustion engines, so rocket engines can be used in a vacuum to propel spacecraft and ballistic missiles.

In aerodynamics, the lift-to-drag ratio is the lift generated by an aerodynamic body such as an aerofoil or aircraft, divided by the aerodynamic drag caused by moving through air. It describes the aerodynamic efficiency under given flight conditions. The L/D ratio for any given body will vary according to these flight conditions.

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 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. It is credited to the Russian scientist Konstantin Tsiolkovsky who independently derived it and published it in 1903, although it had been independently derived and published by the British mathematician William Moore in 1810, and later published in a separate book in 1813. American Robert Goddard also developed it independently in 1912, and German Hermann Oberth derived it independently about 1920.

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 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.

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."

Characteristic velocity or , or C-star is a measure of the combustion performance of a rocket engine independent of nozzle performance, and is used to compare different propellants and propulsion systems. c* should not be confused with c, which is the effective exhaust velocity related to the specific impulse by: . Specific Impulse and effective exhaust velocity are dependent on the nozzle design unlike the characteristic velocity, explaining why C-star is an important value when comparing different propulsion system efficiencies. c* can be useful when comparing actual combustion performance to theoretical performance in order to determine how completely chemical energy release occurred. This is known as c*-efficiency.

A thermal rocket is a rocket engine that uses a propellant that is externally heated before being passed through a nozzle to produce thrust, as opposed to being internally heated by a redox (combustion) reaction as in a chemical rocket.

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