# Thrust-to-weight ratio

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 indicates 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 vehicles initial performance.

## Calculation

The thrust-to-weight ratio can be calculated by dividing the thrust (in SI units – in newtons) by the weight (in newtons) of the engine or vehicle and is a dimensionless quantity. Note that the thrust can also be measured in pound-force (lbf) provided the weight is measured in pounds (lb); the division of these two values still gives the numerically correct 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]

In cruising flight, the thrust-to-weight ratio of an aircraft is the inverse of the lift-to-drag ratio because thrust is the inverse of drag, and weight is the inverse of lift.[4]

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

### Propeller-driven aircraft

For propeller-driven aircraft, the thrust-to-weight ratio can be calculated as follows:[5]

${\displaystyle {\frac {T}{W}}=\left({\frac {550\eta _{p}}{V}}\right)\left({\frac {hp}{W}}\right)}$

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.[6]

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[7] and is sometimes called Thrust-to-Earth-weight ratio.[8] 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.[6]

The thrust-to-weight ratio for a rocket varies as the propellant is burned. If the thrust is constant, then 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 exceeds that of the whole 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 more than one. In general, the thrust-to-weight ratio is numerically equal to the g-force that the vehicle can generate.[6] 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 a thrust-to-weight ratio. The instantaneous value typically varies over the flight with the variations of thrust due to speed and altitude along with the weight due to the remaining propellant and payload mass. The main factors 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

Vehicle T/W Scenario
B-2 Spirit 0.205[9] Max take-off weight, full power
Airbus A380 0.227 Max take-off weight, full power
Boeing 737 MAX 8 0.310 Max take-off weight, full power
Airbus A320neo 0.311 Max take-off weight, full power
Tu-160 0.363 Max take-off weight, full afterburners
Concorde 0.372 Max take-off weight, full reheat
B-1 Lancer 0.38 Max take-off weight, full afterburners
BAE Hawk 0.65[10]
F-35 0.87 with full fuel (1.07 with 50% fuel)
Rafale 0.988[11] Version M, 100% fuel, 2 EM A2A missile, 2 IR A2A missiles
Su-30MKM 1.00[12] Loaded weight with 56% internal fuel
MiG-29 1.09[14] Full internal fuel, 4 AAMs
F-22 > 1.09 (1.26 with loaded weight and 50% fuel)[15] Combat load?
F-16 1.096[citation needed]
Harrier 1.1[citation needed] VTOL
Typhoon 1.15[16] Interceptor configuration
Space Shuttle 1.5 Take-off
Space Shuttle 3 Peak (throttled back for astronaut comfort)

### Jet and rocket engines

Jet or rocket engine Mass Thrust (vacuum) Thrust-to-weight ratio
(kg) (lb) (kN) (lbf)
RD-0410 nuclear rocket engine[17][18] 2,000 4,400 35.2 7,900 1.8
J58 jet engine (SR-71 Blackbird)[19][20] 2,722 6,001 150 34,000 5.2
Rolls-Royce/Snecma Olympus 593
turbojet with reheat (Concorde)[21]
3,175 7,000 169.2 38,000 5.4
Pratt & Whitney F119[22] 1,800 3,900 91 20,500 7.95
RD-0750 rocket engine, three-propellant mode[23] 4,621 10,188 1,413 318,000 31.2
RD-0146 rocket engine[24] 260 570 98 22,000 38.4
Rocketdyne RS-25 Space Shuttle Main Engine[25] 3,177 7,004 2,278 512,000 73.1
RD-180 rocket engine[26] 5,393 11,890 4,152 933,000 78.5
RD-170 rocket engine 9,750 21,500 7,887 1,773,000 82.5
F-1 (Saturn V first stage)[27] 8,391 18,499 7,740.5 1,740,100 94.1
NK-33 rocket engine[28] 1,222 2,694 1,638 368,000 136.7
Merlin 1D rocket engine, full-thrust version [29] 467 1,030 825 185,000 180.1

### Fighter aircraft

Table b: Thrust-to-weight ratios, fuel weights, and weights of different fighter planes (in metric units)
In International System F-15K F-15C MiG-29K MiG-29B JF-17 J-10 F-35A F-35B F-35C F-22 LCA Mk-1
Engine(s) 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 0.93 0.96 0.84 0.87 0.74 1.14 0.96
T/W ratio (max take-off load) 0.72 0.69 0.80 0.89 0.65 0.65 0.57 0.67 0.57 0.84 0.69
Table a: Thrust-to-weight ratios, fuel weights, and weights of different fighter planes
Specifications / Fighters F-15K F-15C MiG-29K MiG-29B JF-17 J-10 F-35A F-35B F-35C F-22 LCA Mk-1
Engine(s) thrust maximum (lbf) 58,320 (2) 46,900 (2) 39,682 (2) 36,600 (2) 18,300 (1) 27,557 (1) 39,900 (1) 39,900 (1) 39,900 (1) 70,000 (2) 20,200 (1)
Aircraft weight empty (lb) 37,500 31,700 28,050 24,030 14,520 20,394 29,300 32,000 34,800[30] 43,340 14,300
Aircraft weight, full fuel (lb) 51,023 45,574 39,602 31,757 19,650 28,760 47,780 46,003 53,800 61,340 20,944
Aircraft weight, max take-off load (lb) 81,000 68,000 49,383 40,785 28,000 42,500 70,000 60,000 70,000 83,500 29,100
Total fuel weight (lb) 13,523 13,874 11,552 07,727 05,130 08,366 18,480 14,003 19,000[30] 18,000 05,419
T/W ratio (full fuel) 1.14 1.03 1.00 1.15 0.93 0.96 0.84 0.87 0.74 1.14 0.96
T/W ratio (max take-off load) 0.72 0.69 0.80 0.89 0.65 0.65 0.57 0.67 0.57 0.84 0.69
• 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

## 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. ^ Daniel P. Raymer, Aircraft Design: A Conceptual Approach, Equation 5.2
5. ^ Daniel P. Raymer, Aircraft Design: A Conceptual Approach, Equations 3.9 and 5.1
6. ^ 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"
7. ^ 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."
8. ^ "Thrust-to-Earth-weight ratio". The Internet Encyclopedia of Science. Archived from the original on 2008-03-20. Retrieved 2009-02-22.
9. ^ Northrop Grumman B-2 Spirit
10. ^ BAE Systems Hawk
11. ^ "AviationsMilitaires.net — Dassault Rafale C". www.aviationsmilitaires.net. Archived from the original on 25 February 2014. Retrieved 30 April 2018.
12. ^ Sukhoi Su-30MKM#Specifications .28Su-30MKM.29
13. ^ "F-15 Eagle Aircraft". About.com:Inventors. Retrieved 2009-03-03.
14. ^ Pike, John. "MiG-29 FULCRUM". www.globalsecurity.org. Archived from the original on 19 August 2017. Retrieved 30 April 2018.
15. ^ "AviationsMilitaires.net — Lockheed-Martin F-22 Raptor". www.aviationsmilitaires.net. Archived from the original on 25 February 2014. Retrieved 30 April 2018.
16. ^ "Eurofighter Typhoon". eurofighter.airpower.at. Archived from the original on 9 November 2016. Retrieved 30 April 2018.
17. ^ Wade, Mark. "RD-0410". Encyclopedia Astronautica. Retrieved 2009-09-25.
18. ^ "«Konstruktorskoe Buro Khimavtomatiky» - Scientific-Research Complex / RD0410. Nuclear Rocket Engine. Advanced launch vehicles". KBKhA - Chemical Automatics Design Bureau. Retrieved 2009-09-25.
19. ^ "Aircraft: Lockheed SR-71A Blackbird". Archived from the original on 2012-07-29. Retrieved 2010-04-16.
20. ^ "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.
21. ^ "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
22. ^ Military Jet Engine Acquisition, RAND, 2002.
23. ^ "«Konstruktorskoe Buro Khimavtomatiky» - Scientific-Research Complex / RD0750". KBKhA - Chemical Automatics Design Bureau. Retrieved 2009-09-25.
24. ^ Wade, Mark. "RD-0146". Encyclopedia Astronautica. Retrieved 2009-09-25.
25. ^ SSME
26. ^ "RD-180". Retrieved 2009-09-25.
27. ^ Encyclopedia Astronautica: F-1
28. ^ Astronautix NK-33 entry
29. ^ 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.
30. ^ a b "Lockheed Martin Website". Archived from the original on 2008-04-04.