Thrust-to-weight ratio

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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 the initial performance of vehicles.

Contents

• 1 Calculation
• 2 Aircraft
  • 2.1 Propeller-driven aircraft
• 3 Rockets
• 4 Examples
  • 4.1 Aircraft
  • 4.2 Jet and Rocket Engines
  • 4.3 Fighter Aircraft
• 5 See also
• 6 References
  • 6.1 Notes
• 7 External links

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]

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

Rocket vehicle Thrust-to-weight ratio vs Isp 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 pressurise 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)

Aircraft

Vehicle	T/W	Scenario
Concorde	0.373[citation needed]	Max Takeoff Weight, Full Reheat
Lightning	0.63[citation needed]	maximum takeoff weight, No Reheat
Lightning	~1.2[9]	on an empty weight basis, full reheat
F-22	>1.09 (1.26 with loaded weight & 50% fuel)[10]	Maximum takeoff weight, Dry Thrust
MiG-29	1.09[10]	Full internal fuel, 4 AAMs
F-15	1.04[11]	nominally loaded
F-16	1.096[citation needed]
Harrier	1.1[citation needed]
Typhoon	1.07 (100% fuel, 2 IRIS-T, 4 MBDA Meteor)[12]
Space Shuttle	1.5	Take-off [13]
Rafale	0.988 (100% fuel, 2 EM A2A missile, 2 IR A2A missile) version M [14]
Space Shuttle	3	Peak (throttled back for astronaut comfort)[15]

Jet and Rocket Engines

Jet or Rocket engine	Mass (kg)	Mass (lb)	Thrust (kN)	Thrust (lbf)	Thrust-to-weight ratio
RD-0410 nuclear rocket engine[16][17]	2,000	4,400	35.2	7,900	1.8
J58 jet engine (SR-71 Blackbird)[18][19]	2,722	6,000	150	34,000	5.2
Rolls-Royce/Snecma Olympus 593 turbojet with reheat (Concorde)[20]	3,175	7,000	169.2	38,000	5.4
Pratt & Whitney F119[21]	1,800	3,900	91	20,500	7.95
RD-0750 rocket engine, three-propellant mode[22]	4,621	10,190	1,413	318,000	31.2
RD-0146 rocket engine[16]	260	570	98	22,000	38.4
SSME rocket engine (Space Shuttle)[23]	3,177	7,000	2,278	512,000	73.1
RD-180 rocket engine[24]	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)[25]	8,391	18,500	7,740.5	1,740,100	94.1
NK-33 rocket engine[26]	1,222	2,690	1,638	368,000	136.7
Merlin 1D rocket engine[27]	440	970	690	160,000	159.9

Rocket thrusts are vacuum thrusts unless otherwise noted