Thrust-to-weight ratio

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, and in some cases due to 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 the initial performance of vehicles.

Contents

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 dimensionless quantity.

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]

\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]

\frac{T}{W}=\left(\frac{\eta_p}{V}\right)\left(\frac{P}{W}\right)

where \eta_p\; is propulsive efficiency at true airspeed V\;

P\; 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]

It is important to note that the thrust-to-weight ratio for a rocket varies as the propellant gets utilized. If the thrust is constant, then the maximum ratio (maximum acceleration of the vehicle) is achieved just before the propellant is fully consumed (propellant weight is practically zero at this point). So for each rocket there a characteristic thrust-to-weight curve or acceleration curve, not just a scalar quantity.

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.

The thrust to weight ratio of rockets is typically far higher than that of airbreathing jet engines. This is because of the much higher density of the material that is formed into the exhaust, compared to that of air; so far less engineering materials are needed for pressurising it.

Many factors affect a thrust-to-weight ratio, and the instantaneous value 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. 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)

\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
Concorde .373 Max Takeoff Weight, Full Reheat
English Electric Lightning 0.63 maximum takeoff weight, No Reheat
F-22 Raptor 0.84[9] maximum takeoff weight, Dry Thrust
Mikoyan MiG-29 1.1
F-15 Eagle 1.04[10] nominally loaded
F-16 Fighting Falcon 1.096
Hawker Siddeley Harrier 1.1
Eurofighter Typhoon 1.25[11]
English Electric Lightning ~1.2[12] light weight, full reheat
Space Shuttle 1.5 Take-off [13]
F-15 Eagle ~1.6[12] light weight, full afterburner
F-22 Raptor 1.61 [9] light weight, full afterburner
Dassault Rafale 1.69[14] light weight, full afterburner
Space Shuttle 3 Peak (throttled back for astronaut comfort)[15]

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[16][17] 2000 35.2 1.8
J-58 (SR-71 Blackbird jet engine)[18][19] 2722 150 5.2
Concorde's Rolls-Royce/Snecma Olympus 593
turbojet with reheat[20][21]		 3175 169.2 5.4
RD-0750 rocket engine, three-propellant mode[22] 4621 1413 31.2
RD-0146 rocket engine[16] 260 98 38.5
Space Shuttle's SSME rocket engine[23] 3177 2278 73.2
RD-180 rocket engine[24] 5393 4152 78.6
F-1 (Saturn V first stage)[25] 8391 7740.5 94.1
NK-33 rocket engine[26] 1222 1638 136.8

Rocket thrusts are vacuum 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-29B JF-17 J-10 F-35A F-35B F-35C F-22
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)
Aircraft Weight Empty (lb) 37,500 31,700 28,050 24,030 14,520 20,394 29,300 32,000 34,800[27] 43,340
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
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
Total fuel weight (lb) 13,523 13,874 11,552 07,727 05,130 08,366 18,480 14,003 19,000[27] 18,000
T/W ratio (Thrust / AC weight full fuel) 1.14 1.03 1.00 1.15 0.93 0.96 0.84 0.87 0.74 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-29B JF-17 J-10 F-35A F-35B F-35C F-22
Engine(s) Thrust Maximum (kgf) 26,456 (2) 21,274 (2) 18,000 (2) 16,600 (2) 08,300 (1) 12,500 (1) 18,098 (1) 18,098 (1) 18 098 (1) 31,764 (2)
Aircraft Weight Empty (kg) 17,010 14,379 12,723 10,900 06,586 09,250 13,290 14,515 15,785 19,673
Aircraft Weight Full fuel (kg) 23,143 20,671 17,963 14,405 08,886 13,044 21,672 20,867 24,403 27,836
Aircraft Weight 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
Total fuel weight (kg) 06,133 06,292 05,240 03,505 02,300 03,794 08,382 06,352 08,618 08,163
T/W ratio (Thrust / AC weight full fuel) 1.14 1.03 1.00 1.15 0.93 0.96 0.84 0.87 0.74 1.14

See also

References

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, Equation 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. http://www.daviddarling.info/encyclopedia/T/thrust-to-Earth-weight_ratio.html. Retrieved 2009-02-22. 
  9. ^ a b http://www.aviationsmilitaires.net/display/aircraft/87/f_a-22
  10. ^ "F-15 Eagle Aircraft". About.com:Inventors. http://inventors.about.com/library/inventors/blF_15_Eagle.htm. Retrieved 2009-03-03. 
  11. ^ Kampflugzeugvergleichstabelle Mader/Janes
  12. ^ a b Section 9 "The English Electric (BAC) Lightning". Vectorsite. http://www.vectorsite.net/aveeltg.html. Retrieved 2009-03-03. 
  13. ^ Thrust: 6.781 million lbf, Weight: 4.5 million lb"Space Shuttle". Wikipedia. http://en.wikipedia.org/wiki/Space_shuttle. Retrieved 2009-09-10. 
  14. ^ http://www.aviationsmilitaires.net/display/variant/1
  15. ^ "Space Shuttle". Wikipedia. http://en.wikipedia.org/wiki/Space_shuttle. Retrieved 2009-09-10. 
  16. ^ a b Wade, Mark. "RD-0410". Encyclopedia Astronautica. http://www.astronautix.com/engines/rd0410.htm. Retrieved 2009-09-25. 
  17. ^ "«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. 
  18. ^ Aircraft: Lockheed SR-71A Blackbird
  19. ^ "Factsheets : Pratt & Whitney J58 Turbojet". National Museum of the United States Air Force. http://www.nationalmuseum.af.mil/factsheets/factsheet.asp?id=880. Retrieved 2010-04-15. 
  20. ^ "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" 
  21. ^ [1]
  22. ^ "«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. 
  23. ^ SSME
  24. ^ "RD-180". http://www.astronautix.com/engines/rd180.htm. Retrieved 2009-09-25. 
  25. ^ http://www.astronautix.com/engines/f1.htm
  26. ^ Astronautix NK-33 entry
  27. ^ a b "Lockheed Martin Website". http://www.lockheedmartin.com/products/f35/f-35specifications/f-35c-cv-specifications.html. 

External links