Thrust-to-weight ratio

Calculation

The thrust-to-weight ratio of an engine or vehicle is calculated by dividing its thrust by its weight (not to be confused with mass). The formula is:

\mathrm{TWR} = \frac{T}{W} = \frac{T}{m \cdot g}

where:

• T is the thrust, in newtons (N), kilograms-force (kgf), or pounds-force (lbf),
• W is the weight, in newtons (N), which can also be expressed as the product of:
  • mass m, in kilograms (kg) or pounds (lb), and
  • gravitational acceleration g, e.g., the standard gravitational acceleration on Earth of 9.80665 m/s2.

For valid comparison of the initial thrust-to-weight ratio of two or more engines or vehicles, thrust must be measured under controlled conditions. Because an aircraft's weight can vary considerably, depending on factors such as munition load, fuel load, cargo weight, or even the weight of the pilot, the thrust-to-weight ratio is also variable and even changes during flight operations. There are several standards for determining the weight of an aircraft used to calculate the thrust-to-weight ratio range.

• Empty weight – The weight of the aircraft minus fuel, munitions, cargo, and crew.
• Combat weight – Primarily for determining the performance capabilities of fighter aircraft, it is the weight of the aircraft with full munitions and missiles, half fuel, and no drop tanks or bombs.
• Max takeoff weight – The weight of the aircraft when fully loaded with the maximum fuel and cargo that it can safely takeoff with.

Aircraft

The thrust-to-weight ratio and lift-to-drag ratio are the two most important parameters in determining the performance of an aircraft.

The thrust-to-weight ratio varies continually during a flight. Thrust varies with throttle setting, airspeed, altitude, air temperature, etc. 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. Aircraft with thrust-to-weight ratio greater than 1:1 can pitch straight up and maintain airspeed until performance decreases at higher altitude.

A plane can take off even if the thrust is less than its weight as, unlike a rocket, the lifting force is produced by lift from the wings, not directly by thrust from the engine. As long as the aircraft can produce enough thrust to travel at a horizontal speed above its stall speed, the wings will produce enough lift to counter the weight of the aircraft.

:\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 in imperial units: :\frac{T}{W} = \frac{550\eta_\mathrm{p}}{V} \frac{\text{hp}}{W}, where \eta_\mathrm{p}; is propulsive efficiency (typically 0.65 for wooden propellers, 0.75 metal fixed pitch and up to 0.85 for constant-speed propellers), hp is the engine's shaft horsepower, and V;is true airspeed in feet per second, weight is in lbs.

The metric formula is: :\frac{T}{W}=\left(\frac{\eta_\mathrm{p}}{V}\right)\left(\frac{P}{W}\right).

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.

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 and is sometimes called thrust-to-Earth-weight ratio.{{cite web |access-date = 2009-02-22 |url-status = dead |archive-url = https://web.archive.org/web/20080320040846/http://www.daviddarling.info/encyclopedia/T/thrust-to-Earth-weight_ratio.html |archive-date = 2008-03-20

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. Take-off can occur when the vehicle's g-force exceeds local gravity (expressed as a multiple of g).

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 of flight with the variations in thrust due to speed and altitude, together with changes 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

Jet and rocket engines

Fighter aircraft

• 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

References

• John P. Fielding. Introduction to Aircraft Design, Cambridge University Press,
• Daniel P. Raymer (1989). Aircraft Design: A Conceptual Approach, American Institute of Aeronautics and Astronautics, Inc., Washington, DC.
• George P. Sutton & Oscar Biblarz. Rocket Propulsion Elements, Wiley,

References

1. [https://ntrs.nasa.gov/api/citations/19850010645/downloads/19850010645.pdf?attachment=true NASA Technical Memorandum 86352 - Some Fighter Aircraft Trends]
2. John P. Fielding, ''Introduction to Aircraft Design'', Section 3.1 (p.21)
3. (2016-05-09). "What it's Like to Fly the F-16N Viper, Topgun's Legendary Hotrod".
4. Daniel P. Raymer, ''Aircraft Design: A Conceptual Approach'', Equations 3.9 and 5.1
5. George P. Sutton & Oscar Biblarz, ''Rocket Propulsion Elements'' (p. 442, 7th edition) "thrust-to-weight ratio ''F''/''W_g'' is a dimensionless parameter that is identical to the acceleration of the rocket propulsion system (expressed in multiples of ''g''{{sub. 0) if it could fly by itself in a gravity-free vacuum"
6. George P. Sutton & Oscar Biblarz, ''Rocket Propulsion Elements'' (p. 442, 7th edition) "The loaded weight ''W_g'' is the sea-level initial gross weight of propellant and rocket propulsion system hardware."
7. [[Northrop Grumman B-2 Spirit]]
8. [[BAE Systems Hawk]]
9. [[Sukhoi Su-30MKM#Specifications .28Su-30MKM.29]]
10. Pike, John. "MiG-29 FULCRUM".
11. "AviationsMilitaires.net — Lockheed-Martin F-22 Raptor".
12. "Eurofighter Typhoon".
13. Lee, Kwan-Jie. "lwtech 2021 velocity and acceleration profiles of space shuttles".
14. "EASA.E.099 - MD-TJ series engines {{!}} EASA".
15. Wade, Mark. "RD-0410". [[Encyclopedia Astronautica]].
16. "". link. KBKhA - [[Chemical Automatics Design Bureau]]
17. "Aircraft: Lockheed SR-71A Blackbird".
18. "Factsheets : Pratt & Whitney J58 Turbojet". National Museum of the United States Air Force.
19. "Rolls-Royce SNECMA Olympus - Jane's Transport News".
20. [http://www.rand.org/pubs/monograph_reports/2005/MR1596.pdf Military Jet Engine Acquisition], RAND, 2002.
21. "PBS TJ40-G1NS". PBS Velká Bíteš.
22. KBKhA - [[Chemical Automatics Design Bureau]]. link
23. Wade, Mark. "RD-0146". [[Encyclopedia Astronautica]].
24. [http://www.astronautix.com/engines/ssme.htm SSME]
25. "RD-180".
26. [http://www.astronautix.com/engines/f1.htm Encyclopedia Astronautica: F-1]
27. Wade, Mark. "NK-33".
28. Sesnic, Trevor. (2022-07-14). "Raptor 1 vs Raptor 2: What did SpaceX change?".
29. Mueller, Thomas. (June 8, 2015). "Is SpaceX's Merlin 1D's thrust-to-weight ratio of 150+ believable?". Quora.
30. "SpaceX".