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Thrust-to-weight ratio

## Summary

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.

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

Rocket vehicle Thrust-to-weight ratio vs specific impulse for different propellant technologies

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

Vehicle thrust-weight ratio Notes
Northrop Grumman B-2 Spirit 0.205[10] Max take-off weight, full power
Airbus A340 0.2229 Max take-off weight, full power (A340-300 Enhanced)
Airbus A380 0.227 Max take-off weight, full power
Boeing 747-8 0.269 Max take-off weight, full power
Boeing 777 0.285 Max take-off weight, full power (777-200ER)
Boeing 737 MAX 8 0.310 Max take-off weight, full power
Airbus A320neo 0.311 Max take-off weight, full power
Boeing 757-200 0.341 Max take-off weight, full power (w/Rolls-Royce RB211)
Tupolev 154B 0.360 Max take-off weight, full power (w/Kuznecov NK-82)
Tupolev Tu-160 0.363[citation needed] Max take-off weight, full afterburners
Concorde 0.372 Max take-off weight, full afterburners
Rockwell International B-1 Lancer 0.38 Max 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 0.94 With full fuel
CAC/PAC JF-17 Thunder 0.95 With 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 3 Peak

### Jet and rocket engines

Engine Mass Thrust, vacuum Thrust-to-
weight ratio
(kN) (lbf)
RD-0410 nuclear rocket engine[18][19] 2,000 kg (4,400 lb) 35.2 7,900 1.8
Pratt & Whitney J58 jet engine
(Lockheed SR-71 Blackbird)[20][21]
2,722 kg (6,001 lb) 150 34,000 5.6
Rolls-Royce/Snecma Olympus 593
turbojet with reheat
(Concorde)[22]
3,175 kg (7,000 lb) 169.2 38,000 5.4
Pratt & Whitney F119[23] 1,800 kg (4,000 lb) 91 20,500 7.95
RD-0750 rocket engine
three-propellant mode[24]
4,621 kg (10,188 lb) 1,413 318,000 31.2
RD-0146 rocket engine[25] 260 kg (570 lb) 98 22,000 38.4
Rocketdyne RS-25 rocket engine
(Space Shuttle Main Engine)[26]
3,177 kg (7,004 lb) 2,278 512,000 73.1
RD-180 rocket engine[27] 5,393 kg (11,890 lb) 4,152 78.7
RD-170 rocket engine 9,750 kg (21,500 lb) 7,887 1,773,000 82.5
F-1
(Saturn V first stage)[28]
8,391 kg (18,499 lb) 7,740.5 1,740,100 94.1
NK-33 rocket engine[29] 1,222 kg (2,694 lb) 1,638 368,000 136.7
SpaceX Raptor 2 rocket engine[30] 1,600 kg (3,500 lb) 2,256 507,000 143.8
Merlin 1D rocket engine,
full-thrust version[31][32]
467 kg (1,030 lb) 914 205,500 199.5

### Fighter aircraft

Thrust-to-weight ratios, fuel weights, and weights of different fighter planes
Specifications F-15K[a] F-15C MiG-29K MiG-29B JF-17 J-10 F-35A F-35B F-35C F-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) 17,010 14,379 12,723 10,900 06,586 09,250 13,290 14,515 15,785 19,673 6,560
Aircraft mass, full fuel (kg) 23,143 20,671 17,963 14,405 08,886 13,044 21,672 20,867 24,403 27,836 9,500
Aircraft mass, max. take-off load (kg) 36,741 30,845 22,400 18,500 12,700 19,277 31,752 27,216 31,752 37,869 13,300
Total fuel mass (kg) 06,133 06,292 05,240 03,505 02,300 03,794 08,382 06,352 08,618 08,163 02,458
T/W ratio, full fuel 1.14 1.03 1.00 1.15 0.95 1.05 0.84 0.87 0.74 1.14 0.94
T/W ratio, max. take-off load 0.72 0.69 0.80 0.89 0.70 0.80 0.57 0.67 0.57 0.84 0.70
• 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. ^ a b c 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. ^ Northrop Grumman B-2 Spirit
11. ^ BAE Systems Hawk
12. ^ "AviationsMilitaires.net — Dassault Rafale C". www.aviationsmilitaires.net. Archived from the original on 25 February 2014. Retrieved 30 April 2018.
13. ^ Sukhoi Su-30MKM#Specifications .28Su-30MKM.29
14. ^ "F-15 Eagle Aircraft". About.com:Inventors. Retrieved 2009-03-03.
15. ^ Pike, John. "MiG-29 FULCRUM". www.globalsecurity.org. Archived from the original on 19 August 2017. Retrieved 30 April 2018.
16. ^ "AviationsMilitaires.net — Lockheed-Martin F-22 Raptor". www.aviationsmilitaires.net. Archived from the original on 25 February 2014. Retrieved 30 April 2018.
17. ^ "Eurofighter Typhoon". eurofighter.airpower.at. Archived from the original on 9 November 2016. Retrieved 30 April 2018.
18. ^ Wade, Mark. "RD-0410". Encyclopedia Astronautica. Retrieved 2009-09-25.
19. ^ 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.
20. ^ "Aircraft: Lockheed SR-71A Blackbird". Archived from the original on 2012-07-29. Retrieved 2010-04-16.
21. ^ "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.
22. ^ "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
23. ^ Military Jet Engine Acquisition, RAND, 2002.
24. ^ "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.
25. ^ Wade, Mark. "RD-0146". Encyclopedia Astronautica. Retrieved 2009-09-25.
26. ^ SSME
27. ^ "RD-180". Retrieved 2009-09-25.
28. ^ Encyclopedia Astronautica: F-1
29. ^ Wade, Mark. "NK-33". Encyclopedia Astronautica. Retrieved 2022-08-24.
30. ^ Sesnic, Trevor (2022-07-14). "Raptor 1 vs Raptor 2: What did SpaceX change?". Everyday Astronaut. Retrieved 2022-11-07.
31. ^ 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.
32. ^ "SpaceX". SpaceX. Retrieved 2022-11-07.

## 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