Thrust-to-weight ratio

From Wikipedia, the free encyclopedia

Thrust-to-weight ratio is the 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.

[edit] 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.

[edit] 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]

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

[edit] Propeller-driven aircraft

For propeller-driven aircraft, the thrust-to-weight ratio can be calculated as follows:^[5]

$\frac{T}{W}=\left(\frac{\eta_p}{V}\right)\left(\frac{P}{W}\right)$

where $\eta_p\;$ is propulsive efficiency at true airspeed $V\;$

$P\;$ is engine power

[edit] 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.^[6]

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.^[7] This 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 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.^[6] 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.

[edit] 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)

$\frac{T}{W}=\frac{3,820\ \mathrm{kN}}{(5,307\ \mathrm{kg})(9.807\ \mathrm{m/s^2})}=0.07340\ \frac{\mathrm{kN}}{\mathrm{N}}=73.40\ \frac{\mathrm{N}}{\mathrm{N}}=73.40$

[edit] Aircraft

Vehicle	T/W	Scenario
Concorde	.373^{[citation needed]}
English Electric Lightning	0.63^{[citation needed]}	maximum takeoff weight, no reheat
F-15 Eagle	1.04^[9]	nominally loaded
F-16 Fighting Falcon	1.096^{[citation needed]}
Hawker Siddeley Harrier	1.1^{[citation needed]}
Dassault Rafale	1.13^{[citation needed]}
Mikoyan MiG-29	1.13^{[citation needed]}
Eurofighter Typhoon	1.18^{[citation needed]}
English Electric Lightning	~1.2^[10]	light weight, full reheat
Space Shuttle	1.5	Take-off ^[11]
F-15 Eagle	~1.6^[10]	light weight, full afterburner
Space Shuttle	3	Peak (throttled back for astronaut comfort)^[12]

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.

[edit] Engines

Engine	Thrust-to-weight ratio
Concorde's Rolls-Royce/Snecma Olympus 593 turbojet	4.0 with reheat^[13]
J-58 (SR-71 Blackbird jet engine)	5.2^[14]
Space shuttle's SSME rocket engine	73.12^[15]
RD-180 rocket engine	73.4
NK-33 rocket engine	136.66^[16]

[edit] Fighter Aircraft

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	43,864	43,408	48,200	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	?	?	83,500
Total fuel weight (lb)	13,523	13,874	11,552	7,729	5,130	8,366	14,828	11,247	16,130	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	0.91	0.92	0.83	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)	83,00 (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	19,901	19,698	21,862	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	?	?	37,869
Total fuel weight (kg)	6,133	6,292	5,240	3,505	2,300	3,794	6,731	5,101	7,315	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	0.91	0.92	0.83	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
Fuel weight of F-35 is taken as litres and converted.
CFT - Conformal fuel tanks.
na - Information Not Available / Not Applicable.
Table composed by http://www.fighterplanes.tk team.

[edit] 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

[edit] Notes

^ Daniel P. Raymer, Aircraft Design: A Conceptual Approach, Section 5.1
^ John P. Fielding, Introduction to Aircraft Design, Section 4.1.1 (p.37)
^ John P. Fielding, Introduction to Aircraft Design, Section 3.1 (p.21)
^ Daniel P. Raymer, Aircraft Design: A Conceptual Approach, Equation 5.2
^ Daniel P. Raymer, Aircraft Design: A Conceptual Approach, Equation 5.1
^ ^a ^b ^c 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”
^ 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.”
^ "Thrust-to-Earth-weight ratio". The Internet Encyclopedia of Science. http://www.daviddarling.info/encyclopedia/T/thrust-to-Earth-weight_ratio.html. Retrieved on 2009-02-22.
^ >"F-15 Eagle Aircraft". About.com:Inventors. http://inventors.about.com/library/inventors/blF_15_Eagle.htm. Retrieved on 2009-03-03.
^ ^a ^b Section 9 "The English Electric (BAC) Lightning". Vectorsite. http://www.vectorsite.net/aveeltg.html. Retrieved on 2009-03-03.
^ Thrust: 6.781 million lbf, Weight: 4.5 million lb"Space Shuttle". Absoluteastronomy. http://www.absoluteastronomy.com/topics/Space_Shuttle. Retrieved on 2009-03-03.
^ "Space Shuttle". Absoluteastronomy. http://www.absoluteastronomy.com/topics/Space_Shuttle. Retrieved on 2009-03-03.
^ http://www.faa.gov/about/office_org/headquarters_offices/AEP/supersonic_noise/media/1-Panel3-Brines_Smith-AADC.pdf
^ Aircraft: Lockheed SR-71A Blackbird
^ SSME
^ Astronautix NK-33 entry

[0] Daniel P. Raymer, Aircraft Design: A Conceptual Approach, Section 5.1

[1] John P. Fielding, Introduction to Aircraft Design, Section 4.1.1 (p.37)

[2] John P. Fielding, Introduction to Aircraft Design, Section 3.1 (p.21)

[3] Daniel P. Raymer, Aircraft Design: A Conceptual Approach, Equation 5.2

[4] Daniel P. Raymer, Aircraft Design: A Conceptual Approach, Equation 5.1

[sutton-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 g₀) 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] "Thrust-to-Earth-weight ratio". The Internet Encyclopedia of Science. http://www.daviddarling.info/encyclopedia/T/thrust-to-Earth-weight_ratio.html. Retrieved on 2009-02-22.

[8] >"F-15 Eagle Aircraft". About.com:Inventors. http://inventors.about.com/library/inventors/blF_15_Eagle.htm. Retrieved on 2009-03-03.

[vector-9] Section 9 "The English Electric (BAC) Lightning". Vectorsite. http://www.vectorsite.net/aveeltg.html. Retrieved on 2009-03-03.

[10] Thrust: 6.781 million lbf, Weight: 4.5 million lb"Space Shuttle". Absoluteastronomy. http://www.absoluteastronomy.com/topics/Space_Shuttle. Retrieved on 2009-03-03.

[11] "Space Shuttle". Absoluteastronomy. http://www.absoluteastronomy.com/topics/Space_Shuttle. Retrieved on 2009-03-03.

[12] ttp://www.faa.gov/about/office_org/headquarters_offices/AEP/supersonic_noise/media/1-Panel3-Brines_Smith-AADC.pdf

[13] Aircraft: Lockheed SR-71A Blackbird

[14] SSME

[15] Astronautix NK-33 entry

[1]

[2]

[3]

[4]

[5]

[6]

[7]

[8]

[9]

[10]

[11]

[12]

[13]

[14]

[15]

[16]

Thrust-to-weight ratio

From Wikipedia, the free encyclopedia

Contents

[edit] Calculation

[edit] Aircraft

[edit] Propeller-driven aircraft

[edit] Rockets

[edit] Examples

[edit] Aircraft

[edit] Engines

[edit] Fighter Aircraft

[edit] References

[edit] Notes

Views

Personal tools

Navigation

Search

Interaction

Toolbox

Languages