Thrust-to-weight ratio

Template:Short description 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 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 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 a vehicle's initial performance.

Calculation

The thrust-to-weight ratio is calculated by dividing the thrust (in SI units – in newtons) by the weight (in newtons) of the engine or vehicle. The weight (N) is calculated by multiplying the mass in kilograms (kg) by the acceleration due to gravity (m/s²). The thrust can also be measured in pound-force (lbf), provided the weight is measured in pounds (lb). Division using these two values still gives the numerically correct (dimensionless) 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.

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.<ref>NASA Technical Memorandum 86352 - Some Fighter Aircraft Trends</ref>

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.<ref>John P. Fielding, Introduction to Aircraft Design, Section 3.1 (p.21)</ref> Aircraft with thrust-to-weight ratio greater than 1:1 can pitch straight up and maintain airspeed until performance decreases at higher altitude.<ref name="thedrive20160509">{{#invoke:citation/CS1|citation |CitationClass=web }}</ref>

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.

<math>\left(\frac{T}{W}\right)_\text{cruise} = \left(\frac{D}{L}\right)_\text{cruise} = \frac{1}{\left(\frac{L}{D}\right)_\text{cruise}}.</math>

Propeller-driven aircraft

For propeller-driven aircraft, the thrust-to-weight ratio can be calculated as follows in imperial units:<ref>Daniel P. Raymer, Aircraft Design: A Conceptual Approach, Equations 3.9 and 5.1</ref>

<math>\frac{T}{W} = \frac{550\eta_\mathrm{p}}{V} \frac{\text{hp}}{W},</math>

where <math>\eta_\mathrm{p}\;</math> 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 <math>V\;</math>is true airspeed in feet per second, weight is in lbs.

The metric formula is:

<math>\frac{T}{W}=\left(\frac{\eta_\mathrm{p}}{V}\right)\left(\frac{P}{W}\right).</math>

Rockets

File:Thrust to weight ratio vs Isp.png

Rocket vehicle thrust-to-weight ratio vs specific impulse 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.<ref name="sutton">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 g₀) if it could fly by itself in a gravity-free vacuum"</ref>

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<ref>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."</ref> and is sometimes called thrust-to-Earth-weight ratio.<ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref> 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.<ref name="sutton"/>

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.<ref name="sutton"/> 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 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

Vehicle	thrust-weight ratio	Notes
Northrop Grumman B-2 Spirit	0.205<ref>Northrop Grumman B-2 Spirit</ref>	Max take-off weight, full power
Airbus A340-300 Enhanced	0.2229	Max take-off weight, full power
Airbus A380	0.227	Max take-off weight, full power
Boeing 747-8	0.269	Max take-off weight, full power
Boeing 777-200ER	0.285	Max take-off weight, full power
Boeing 737 MAX 8	0.311	Max take-off weight, full power
Airbus A320neo	0.310	Max take-off weight, full power
Boeing 757-200	0.341	Max take-off weight, full power (w/Rolls-Royce RB211)
Tupolev 154B	0.360	Max take-off weight, full power (w/Kuznetsov NK-8-2)
Tupolev Tu-160	0.363 Template:Citation needed	Max take-off weight, full afterburners
Concorde	0.372	Max take-off weight, full afterburners
Rockwell International B-1 Lancer	0.38	Max take-off weight, full afterburners
HESA Kowsar	0.61	With full fuel, afterburners.
BAE Hawk	0.65<ref>BAE Systems Hawk</ref>
Lightning F.6	0.702	Max take-off weight, full afterburners
Lockheed Martin F-35 A	0.87 Template:Citation needed	With full fuel (1.07 with 50% fuel, 1.19 with 25% fuel)
HAL Tejas Mk 1	1.07	With full fuel
CAC/PAC JF-17 Thunder	1.07	With full fuel
Dassault Rafale	citation	CitationClass=web }}</ref>	Version M, 100% fuel, 2 EM A2A missile, 2 IR A2A missiles
Sukhoi Su-30MKM	1.00<ref name="Wikipedia">Sukhoi Su-30MKM#Specifications .28Su-30MKM.29</ref>	Loaded weight with 56% internal fuel
McDonnell Douglas F-15	citation	CitationClass=web }}</ref>	Nominally loaded
Mikoyan MiG-29	citation	CitationClass=web }}</ref>	Full internal fuel, 4 AAMs
Lockheed Martin F-22	Template:Sort
General Dynamics F-16	1.096Template:Citation needed (1.24 with loaded weight & 50% fuel)
Hawker Siddeley Harrier	1.1Template:Citation needed	VTOL
Eurofighter Typhoon	citation	CitationClass=web }}</ref>	Interceptor configuration
Sukhoi Su-35	1.30
Space Shuttle	citation	CitationClass=web }}</ref>	Take-off
Simorgh (rocket)	1.83
Space Shuttle	3	Peak

Jet and rocket engines

Engine	Mass	Thrust, vacuum		Thrust-to- weight ratio
		(kN)	(lbf)
MD-TJ42 powered sailplane jet engine<ref>{{#invoke:citation/CS1|citation	CitationClass=web }}</ref>	3.85kg (8.48 lb)	0.35	78.7	9.09
RD-0410 nuclear rocket engine<ref name="astronautix1">{{#invoke:citation/CS1|citation	CitationClass=web }}</ref><ref name="KBKhA-RD0410">{{#invoke:citation/CS1|citation	CitationClass=web }}</ref>	Template:Convert	35.2	Template:Convert	{{#expr:35.2/(2,000*0.00980665)round 1}}
Pratt & Whitney J58 jet engine (Lockheed SR-71 Blackbird)<ref>{{#invoke:citation/CS1|citation	CitationClass=web }}</ref><ref>{{#invoke:citation/CS1|citation	CitationClass=web }}</ref>	Template:Convert	150	Template:Convert	{{#expr:150/(2,722*0.00980665)round 1}}
Rolls-Royce/Snecma Olympus 593 turbojet with reheat (Concorde)<ref>{{#invoke:citation/CS1|citation	CitationClass=web }}</ref>	Template:Convert	169.2	Template:Convert	{{#expr:169.2/(3,175*0.00980665)round 1}}
Pratt & Whitney F119<ref>Military Jet Engine Acquisition, RAND, 2002.</ref>	Template:Cvt	Template:Convert	20,500	7.95
citation	CitationClass=web }}</ref>	Template:Cvt	0.425	Template:Convert	{{#expr:425/(3.6*9.80665)round 2}}
RD-0750 rocket engine three-propellant mode<ref name="KBKhA-RD0750">{{#invoke:citation/CS1|citation	CitationClass=web }}</ref>	Template:Convert	1,413	Template:Convert	{{#expr:1,413/(4,621*0.00980665)round 1}}
RD-0146 rocket engine<ref name="astronautix2">{{#invoke:citation/CS1|citation	CitationClass=web }}</ref>	Template:Convert	98	Template:Convert	{{#expr:98/(260*0.00980665)round 1}}
Rocketdyne RS-25 rocket engine (Space Shuttle Main Engine)<ref>SSME</ref>	Template:Convert	2,278	Template:Convert	{{#expr:2,278/(3,177*0.00980665)round 1}}
RD-180 rocket engine<ref>{{#invoke:citation/CS1|citation	CitationClass=web }}</ref>	Template:Convert	4,152	Template:Convert	{{#expr:4,152/(5,383*0.00980665)round 1}}
RD-170 rocket engine	Template:Convert	7,887	Template:Convert	{{#expr:7,887/(9,750*0.00980665)round 1}}
F-1 (Saturn V first stage)<ref>Encyclopedia Astronautica: F-1</ref>	Template:Convert	7,740.5	Template:Convert	{{#expr:7,740.5/(8,391*0.00980665)round 1}}
NK-33 rocket engine<ref name="NK33">Template:Cite encyclopedia</ref>	Template:Convert	1,638	Template:Convert	{{#expr:1,638/(1,222*0.00980665)round 1}}
SpaceX Raptor 3 rocket engine<ref>{{#invoke:citation/CS1|citation	CitationClass=web }}</ref>	Template:Convert	2,746	Template:Convert	183.6
Merlin 1D rocket engine, full-thrust version<ref name="Merlin 1D">{{#invoke:citation/CS1|citation	CitationClass=web }}</ref><ref>{{#invoke:citation/CS1|citation	CitationClass=web }}</ref>	Template:Cvt	914	205,500	199.5

Fighter aircraft

Thrust-to-weight ratios, fuel weights, and weights of different fighter planes

Specifications	F-15KTemplate:Efn	F-15C	MiG-29K	MiG-29B	JF-17	J-10	F-35A	F-35B	F-35C	F-22	LCA Mk-1
Engines thrust, maximum (N)	259,420 (2)	208,622 (2)	176,514 (2)	162,805 (2)	84,400 (1)	122,580 (1)	177,484 (1)	177,484 (1)	177,484 (1)	311,376 (2)	84,516 (1)
Aircraft mass, empty (kg)	17,010	14,379	12,723	10,900	7,965	09,250	13,290	14,515	15,785	19,673	6,560
Aircraft mass, full fuel (kg)	23,143	20,671	17,963	14,405	11,365	13,044	21,672	20,867	24,403	27,836	9,500
Aircraft mass, max. take-off load (kg)	36,741	30,845	22,400	18,500	13,500	19,277	31,752	27,216	31,752	37,869	13,500
Total fuel mass (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	1.07	1.05	0.84	0.87	0.74	1.14	1.07
T/W ratio, max. take-off load	0.72	0.69	0.80	0.89	0.70	0.80	0.57	0.67	0.57	0.84	0.80

• 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.

See also

• Power-to-weight ratio
• Factor of safety

References

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

External links

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