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. 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.
==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.Daniel P. Raymer, Aircraft Design: A Conceptual Approach, Section 5.1 For example, the thrust-to-weight ratio of a combat aircraft is a good indicator of the manoeuvrability of the aircraft.John P. Fielding, Introduction to Aircraft Design, Section 4.1.1 (p.37)
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.John P. Fielding, Introduction to Aircraft Design, Section 3.1 (p.21)
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.Daniel P. Raymer, Aircraft Design: A Conceptual Approach, Equation 5.2
:\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:Daniel P. Raymer, Aircraft Design: A Conceptual Approach, Equation 5.1
:\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.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”
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.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.” This is sometimes called Thrust-to-Earth-weight ratio. 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.
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. 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. 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 	
English Electric Lightning	0.63 	maximum takeoff weight, no reheat
F-15 Eagle 	1.04> 	nominally loaded
F-16 Fighting Falcon 	1.096 	
Hawker Siddeley Harrier 	1.1 	
Dassault Rafale 	1.13 	
Mikoyan MiG-29 	1.01 	
Eurofighter Typhoon 	1.25Kampflugzeugvergleichstabelle Mader/Janes	
English Electric Lightning	~1.2Section 9 	light weight, full reheat
Space Shuttle 	1.5 	Take-off Thrust: 6.781 million lbf, Weight: 4.5 million lb
F-15 Eagle 	~1.6 	light weight, full afterburner
Space Shuttle 	3 	Peak (throttled back for astronaut comfort)
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===
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=== 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 	32,161 	32,070 	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 	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===
Category:Jet engines
Category:Rocket engines
Category:Engineering ratios
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