Thrust-to-weight ratio

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.

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. Note that the thrust can also be measured in pound-force (lbf) provided the weight is measured in pounds (lb); the division of these two values still gives the numerically correct thrust-to-weight 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. For example, the thrust-to-weight ratio of a combat aircraft is a good indicator of the maneuverability of the aircraft.

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.

In cruising flight, the thrust-to-weight ratio of an aircraft is the inverse of the lift-to-drag ratio because thrust is the inverse of drag, and weight is the inverse of lift.

$\left({\frac {T}{W}}\right)_{cruise}={\frac {1}{({\frac {L}{D}})_{cruise}}}$

Propeller-driven aircraft

For propeller-driven aircraft, the thrust-to-weight ratio can be calculated as follows:

${\frac {T}{W}}=\left({\frac {\eta _{p}}{V}}\right)\left({\frac {P}{W}}\right)$

where $\eta _{p}\;$ is propulsive efficiency at true airspeed $V\;$

$P\;$ is engine power

Rockets

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.

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. 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 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. 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 pressurize 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. 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
B-2 Spirit	0.205	Max take-off weight
Concorde	0.373	Max take-off weight, full reheat
BAE Hawk	0.65
Rafale	0.988	Version M, 100% fuel, 2 EM A2A missile, 2 IR A2A missiles
Su-30MKM	1.00	Loaded weight with 56% internal fuel
F-15	1.04	Nominally loaded
Typhoon	1.07	100% fuel, 2 IRIS-T, 4 MBDA Meteor
MiG-29	1.09	Full internal fuel, 4 AAMs
F-22	> 1.09 (1.26 with loaded weight and 50% fuel)	Maximum takeoff weight, dry thrust
F-16	1.096
Harrier	1.1
Space Shuttle	1.5	Take-off
Space Shuttle	3	Peak (throttled back for astronaut comfort)

Jet and rocket engines

Jet or rocket engine	Mass		Thrust		Thrust-to- weight ratio
	(kg)	(lb)	(kN)	(lbf)
RD-0410 nuclear rocket engine	2,000	4,400	35.2	7,900	1.8
J58 jet engine (SR-71 Blackbird)	2,722	6,001	150	34,000	5.2
Rolls-Royce/Snecma Olympus 593 turbojet with reheat (Concorde)	3,175	7,000	169.2	38,000	5.4
Pratt & Whitney F119	1,800	3,900	91	20,500	7.95
RD-0750 rocket engine, three-propellant mode	4,621	10,188	1,413	318,000	31.2
RD-0146 rocket engine	260	570	98	22,000	38.4
Rocketdyne RS-25 rocket engine	3,177	7,004	2,278	512,000	73.1
RD-180 rocket engine	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)	8,391	18,499	7,740.5	1,740,100	94.1
NK-33 rocket engine	1,222	2,694	1,638	368,000	136.7
Merlin 1D rocket engine, full-thrust version	467	1,030	825	185,000	180.1

Fighter aircraft

Table b: Thrust-to-weight ratios, fuel weights, and weights of different fighter planes (in metric units)

In International System	F-15K	F-15C	MiG-29K	MiG-29B	JF-17	J-10	F-35A	F-35B	F-35C	F-22	LCA Mk-1
Engine(s) thrust maximum (N)	259,420 (2)	208,622 (2)	176,514 (2)	162,805 (2)	81,402 (1)	122,580 (1)	177,484 (1)	177,484 (1)	177,484 (1)	311,376 (2)	84,000 (1)
Aircraft weight, empty (kg)	17,010	14,379	12,723	10,900	06,586	09,250	13,290	14,515	15,785	19,673	6,560
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	9,080
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	13,300
Total fuel weight (kg)	06,133	06,292	05,240	03,505	02,300	03,794	08,382	06,352	08,618	08,163	02,458
T/W ratio (full fuel)	1.14	1.03	1.00	1.15	1.09	0.96	0.84	0.87	0.74	1.14	0.98

Table a: Thrust-to-weight ratios, fuel 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	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	18,000
T/W ratio (full fuel)	1.14	1.03	1.00	1.15	1.09	0.96	0.84	0.87	0.74	1.14

• Fuel density used in calculations: 0.803 kg/l
• The number inside brackets is the number of engines.
• 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.
• Engines powering F-15K are the Pratt & Whitney engines.
• 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 1.10
• J-10's empty weight and fuelled weight are estimates.
• 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 1.08

See also

• Power-to-weight ratio
• Factor of safety

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

External links

• NASA webpage with overview and explanatory diagram of aircraft thrust to weight ratio