Thrust-to-weight ratio is a ratio of thrust to weight of a rocket, jet engine, propeller engine, or a vehicle propelled by such an engine. It is a dimensionless quantity and 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. 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 the initial performance of vehicles.
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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. It is a true 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 manoeuvrability 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 changes of payload. 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 equal to drag, and weight is equal to lift.[4]
Propeller-driven aircraft
For propeller-driven aircraft, the thrust-to-weight ratio can be calculated as follows:[5]
where 
is propulsive efficiency at true airspeed 
is engine power
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.[6]
Rockets and rocket-propelled vehicles operate in a wide range of gravitational environments, including the weightless environment. It is customary to calculate the thrust-to-weight ratio using initial gross weight at sea-level on earth.[7] This 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 of an engine is larger for the bare engine than for the whole launch vehicle. The thrust-to-weight ratio of a bare engine is of use since 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 has to be more than one. In general, the thrust-to-weight ratio is numerically equal to the g-force that the vehicle can generate.[6] Provided the vehicle's g-force exceeds local gravity (expressed as a multiple of g0) then takeoff can occur.
Many factors affect a thrust-to-weight ratio, and it typically varies over the flight with the variations of thrust due to speed and altitude, and the weight due to the remaining propellant and payload mass. The main factors that affect thrust 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)
Aircraft
| Vehicle | T/W | Scenario |
|---|---|---|
| Concorde | .373[citation needed] | |
| English Electric Lightning | 0.63[citation needed] | maximum takeoff weight, no reheat |
| F-15 Eagle | 1.04[9] | nominally loaded |
| F-16 Fighting Falcon | 1.096[citation needed] | |
| Hawker Siddeley Harrier | 1.1[citation needed] | |
| Dassault Rafale | 1.13[citation needed] | |
| Mikoyan MiG-29 | 1.13[citation needed] | |
| Eurofighter Typhoon | 1.25[10] | |
| English Electric Lightning | ~1.2[11] | light weight, full reheat |
| Space Shuttle | 1.5 | Take-off [12] |
| F-15 Eagle | ~1.6[11] | light weight, full afterburner |
| Space Shuttle | 3 | Peak (throttled back for astronaut comfort)[13] |
Note that the above duct engined aircraft do not have a thrust-to-weight ratio greater than one at maximum take-off weight, whereas rockets do.
Jet and Rocket Engines
| Jet or Rocket engine | Mass, kg | Jet or rocket thrust, kN | Thrust-to-weight ratio |
|---|---|---|---|
| RD-0410 nuclear rocket engine[14][15] | 2000 | 35.2 | 1.8 |
| J-58 (SR-71 Blackbird jet engine)[16] | 5.2 | ||
| Concorde's Rolls-Royce/Snecma Olympus 593 turbojet with reheat[17][18] |
3175 | 169.2 | 5.4 |
| RD-0750 rocket engine, three-propellant mode[19] | 4621 | 1413 | 31.2 |
| RD-0146 rocket engine[14] | 260 | 98 | 38.5 |
| Space shuttle's SSME rocket engine[20] | 3177 | 2278 | 73.2 |
| RD-180 rocket engine[21] | 5393 | 4152 | 78.6 |
| F-1 (Saturn V first stage)[22] | 8391 | 7740.5 | 94.1 |
| NK-33 rocket engine sea-level[23] | 1222 | 1510 | 126.1 |
| NK-33 rocket engine vaccum[23] | 1222 | 1638 | 136.8 |
Rocket thrusts are vaccuum thrusts unless otherwise noted
Fighter Aircraft
Table a: Thrust To Weight Ratios, Fuels Weights, and Weights of Different Fighter Planes
| Specifications / Fighters | F-15K | F-15C | Mig-29K | Mig-29A | JF-17 | J-10 | F-35A | F-35B | F-35C | F-22 |
|---|---|---|---|---|---|---|---|---|---|---|
| Engine(s) Thrust Maximum (lbf) | 58,320 (2) | 46,900 (2) | 39,162 (2) | 36,600 (2) | 18,300 (1) | 27,557 (1) | 39,900 (1) | 39,900 (1) | 39,900 (1) | 70,000 (2) |
| Aircraft Weight Empty (lb) | 31,700 | 28,600 | 25,909 | 24,030 | 14,134 | 19,544 | 29,036[2] | 32,161[3] | 32,070[4] | 43,340 |
| Aircraft Weight Full fuel (lb) | 45,223 | 42,474 | 37,461 | 31,759 | 19,264 | 27,910 | 47,510 | 46,164 | 52,155 | 61,340 |
| Aircraft Weight Full fuel + CFT (lb) | 54,916 | 52,167 | na | na | na | na | na | na | na | na |
| Aircraft Weight Max Take-off load (lb) | 81,000 | 68,000 | 49,383 | 39,690 | 28,000 | 42,500 | 60,000 | na | na | 83,500 |
| Total fuel weight (lb) | 13,523 | 13,874 | 11,552 | 7,729 | 5,130 | 8,366 | 18,480 | 14,003 | 20,085[5] | 18,000 |
| Total fuel weight +CFT (lb) | 23,216 | 23,567 | na | na | na | na | na | na | na | na |
| T/W ratio (Thrust / AC weight full fuel) | 1.29 | 1.1 | 1.05 | 1.15 | 0.95 | 0.99 | 0.84 | 0.86 | 0.77 | 1.14 |
Table b: Thrust To Weight Ratios, Fuels Weights, and Weights of Different Fighter Planes (In International System)
| In International System | F-15K | F-15C | Mig-29K | Mig-29A | JF-17 | J-10 | F-35A | F-35B | F-35C | F-22 |
|---|---|---|---|---|---|---|---|---|---|---|
| Engine(s) Thrust Maximum (kgf) | 26,456 (2) | 21,274 (2) | 17,762 (2) | 16,600 (2) | 8,300 (1) | 12,509 (1) | 18,098 (1) | 18,098 (1) | 18 098 (1) | 31,764 (2) |
| Aircraft Weight Empty (kg) | 14,379 | 12,973 | 11,750 | 10,898 | 6,411 | 8,865 | 13,170 | 14,588 | 14,547 | 19,673 |
| Aircraft Weight Full fuel (kg) | 20,512 | 19,265 | 16,990 | 14,403 | 8,711 | 12,659 | 21,552 | 20,940 | 23,647 | 27,836 |
| Aircraft Weight Full fuel + CFT (kg) | 24,908 | 23,661 | na | na | na | na | na | na | na | na |
| Aircraft Weight Max Take-off load (kg) | 36,741 | 30,845 | 22,400 | 18,000 | 12,700 | 19,277 | 27,200 | na | na | 37,869 |
| Total fuel weight (kg) | 6,133 | 6,292 | 5,240 | 3,505 | 2,300 | 3,794 | 8,382 | 6,352 | 9,100 | 8,163 |
| Total fuel weight +CFT (kg) | 10,529 | 10,688 | na | na | na | na | na | na | na | na |
| T/W ratio (Thrust / AC weight full fuel) | 1.29 | 1.1 | 1.05 | 1.15 | 0.95 | 0.99 | 0.84 | 0.86 | 0.77 | 1.14 |
- Fuel density used in calculations = 0.803 Kilograms/Liter
- The Number inside ( ) brackets is the Number of Engine(s).
- Engines powering F-15K are the Pratt & Whitney Engines, not General Electric's.
- 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 0.99
- J-10's empty weight & fuel weight is an estimate.
- 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 1.06
- CFT - Conformal fuel tanks.
- na - Information Not Available / Not Applicable.
- Table composed by http://www.fighterplanes.tk team.
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
- ^ Daniel P. Raymer, Aircraft Design: A Conceptual Approach, Section 5.1
- ^ John P. Fielding, Introduction to Aircraft Design, Section 4.1.1 (p.37)
- ^ John P. Fielding, Introduction to Aircraft Design, Section 3.1 (p.21)
- ^ Daniel P. Raymer, Aircraft Design: A Conceptual Approach, Equation 5.2
- ^ Daniel P. Raymer, Aircraft Design: A Conceptual Approach, Equation 5.1
- ^ 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”
- ^ 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.”
- ^ "Thrust-to-Earth-weight ratio". The Internet Encyclopedia of Science. http://www.daviddarling.info/encyclopedia/T/thrust-to-Earth-weight_ratio.html. Retrieved 2009-02-22.
- ^ >"F-15 Eagle Aircraft". About.com:Inventors. http://inventors.about.com/library/inventors/blF_15_Eagle.htm. Retrieved 2009-03-03.
- ^ Kampflugzeugvergleichstabelle Mader/Janes
- ^ a b Section 9 "The English Electric (BAC) Lightning". Vectorsite. http://www.vectorsite.net/aveeltg.html. Retrieved 2009-03-03.
- ^ Thrust: 6.781 million lbf, Weight: 4.5 million lb"Space Shuttle". Wikipedia. http://en.wikipedia.org/wiki/Space_shuttle. Retrieved 2009-09-10.
- ^ "Space Shuttle". Wikipedia. http://en.wikipedia.org/wiki/Space_shuttle. Retrieved 2009-09-10.
- ^ a b Wade, Mark. "RD-0410". Encyclopedia Astronautica. http://www.astronautix.com/engines/rd0410.htm. Retrieved 2009-09-25.
- ^ "«Konstruktorskoe Buro Khimavtomatiky» - Scientific-Research Complex / RD0410. Nuclear Rocket Engine. Advanced launch vehicles". KBKhA - Chemical Automatics Design Bureau. http://www.kbkha.ru/?p=8&cat=11&prod=66. Retrieved 2009-09-25.
- ^ Aircraft: Lockheed SR-71A Blackbird
- ^ "ROLLS-ROYCE SNECMA OLYMPUS - Jane's Transport News". http://www.janes.com/transport/news/jae/jae000725_1_n.shtml. Retrieved 2009-09-25. "With afterburner, reverser and nozzle ... 3,175 kg ... Afterburner ... 169.2 kN"
- ^ [1]
- ^ "«Konstruktorskoe Buro Khimavtomatiky» - Scientific-Research Complex / RD0750.". KBKhA - Chemical Automatics Design Bureau. http://www.kbkha.ru/?p=8&cat=11&prod=57. Retrieved 2009-09-25.
- ^ SSME
- ^ "RD-180". http://www.astronautix.com/engines/rd180.htm. Retrieved 2009-09-25.
- ^ http://www.astronautix.com/engines/f1.htm
- ^ a b Astronautix NK-33 entry
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