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:<math> \mathbf{A} </math> annak a körnek a területe, melyet a légcsavar súrol forgás közben.
=== Teljesítmény ===
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Egy sugárhajtómű teljesítménye az egységnyi idő alatt végzett munkával egyenlő, ezért a következő összefüggésből lehet számítani:
:<math> P = \mathbf{ PA} = \mathbf{ T}{vv_1} </math> ▼
Ez az érdekes eredmény azt mondja, hogy a sugárhajtómű teljesítménye nemcsak a (közel állandó értékű) tolóerőtől, hanem a repülőgép vagy hajó, rakéta sebességétől is függ. Ezért nehéz összehasonlítani egy egy dugattyús és egy sugárhajtású repülőmotor hatékonyságát.
A [[rocket]] is propelled forward by a thrust force equal in magnitude, but opposite in direction, to the time-rate of momentum change of the exhaust gas accelerated from the combustion chamber through the rocket engine nozzle. This is the exhaust velocity with respect to the rocket, times the time-rate at which the mass is expelled, or in mathematical terms:
:<math>\mathbf{T}=\frac{dm}{dt}\mathbf{v}</math>
where:
* '''T''' is the thrust generated (force)
* <math> \frac {dm} {dt} </math> is the rate of change of mass with respect to time (mass flow rate of exhaust);
* '''v''' is the speed of the exhaust gases measured relative to the rocket.
For vertical launch of a rocket the initial thrust must be more than the weight.
Each of the three [[Space Shuttle]] [[Space Shuttle Main Engine|Main Engines]] can produce a thrust of 1.8 [[meganewton|MN]], and each of the Space Shuttle's two [[Space Shuttle Solid Rocket Booster|Solid Rocket Boosters]] 14.7 MN, together 29.4 MN. Compare with the mass at lift-off of 2,040,000 kg, hence a weight of 20 MN.
By contrast, the [[simplified Aid for EVA Rescue]] (SAFER) has 24 thrusters of 3.56 N each.
In the air-breathing category, the AMT-USA AT-180 jet engine developed for [[radio-controlled aircraft]] produce 90 N (20 [[Pound-force|lbf]]) of thrust.<ref>{{cite web
| url = http://usamt.com/Mel/comm/comm_products.html
| title = AMT-USA jet engine product information
| accessdate = 2006-12-13
|archiveurl = http://web.archive.org/web/20061110025303/http://usamt.com/Mel/comm/comm_products.html |archivedate = 2006-11-10}}</ref> The GE90-115B engine fitted on the [[Boeing 777]]-300ER, recognized by the [[Guinness Book of World Records]] as the "World's Most Powerful Commercial Jet Engine," has a thrust of 569 kN (127,900 lbf).
==Thrust to power==
Thrust at zero speed is zero power. Power requires [[Work (physics)|work]] to be done, so zero velocity indicates zero work and zero power. Therefore the power of a rocket or aircraft engine is thrust times forward speed.
power ([[watt]]s) = thrust ([[newtons]]) x speed (metres/second)
power ([[horsepower]]) = thrust (lbf) x speed (feet/second) / 550
power (horsepower) = thrust (lbf) x speed (feet/minute) / 33000.
For example: the [[Messerschmitt Me 262]] with 3,960 pounds of thrust at 559 mph equates to 5,903 horsepower.
==Thrust to power==
A very common question is how to compare the thrust rating of a jet engine with the power rating of a piston engine. Such comparison is difficult, as these quantities are not equivalent. A piston engine does not move the aircraft by itself (the propeller does that), so piston engines are usually rated by how much power they deliver to the propeller. Except for changes in temperature and air pressure, this quantity depends basically on the throttle setting.
Now, a jet engine has no propeller – it pushes the aircraft by moving hot air behind it. One could imagine that a jet engine could be rated by how much power it transmits to the hot air on the exhaust (this depends basically on the throttle setting), but that quantity is not useful for anything (other than finding out how hot and fast the air is). The useful measurement is how much power the jet engine transmits to the aircraft through its thrust force. This is the propulsive power of the jet engine (do not confuse that with all the other power transfers the engine has – to create sound, to vibrate, to push hot air, etc.).
So let's find out the propulsive power of a jet engine from its thrust. Power is the force (F) it takes to move something over some distance (d) divided by the time (t) it takes to move that distance <ref>{{cite web
| url = http://www.aerospaceweb.org/question/propulsion/q0195.shtml
| title = Convert Thrust to Horsepower By Joe Yoon
| accessdate = 2009-05-01
}}</ref>:
:<math>\mathbf{P}=\mathbf{F}\frac{d}{t}</math>
In case of a rocket or a jet aircraft, the force is exactly the thrust produced by the engine. If the rocket or aircraft is moving at about a constant speed, then distance divided by time is just speed, so power is thrust times speed:<ref>"Introduction to Aircraft Flight Mechanics", Yechout & Morris</ref>
▲:<math>\mathbf{P}=\mathbf{T}{v}</math>
This formula looks very surprising, but it is correct: the ''propulsive power'' (or ''power available'' <ref>"Understanding Flight", Anderson & Eberbaht</ref>) of a jet engine increases with its speed. If the speed is zero, then the propulsive power is zero. If a jet aircraft is at full throttle but is tied to a very strong chain to a tree, then the jet engine produces no propulsive power. It certainly transfers a lot of power around, but all that is wasted. Compare that to a piston engine. The combination piston engine–propeller also has a propulsive power with exactly the same formula, and it will also be zero at zero speed –- but that is for the engine–propeller set. The engine alone will continue to produce its rated power at a constant rate, whether the aircraft is moving or not.
[[Image:two aircrafts tied to tree.png|thumb|Two aircraft tied to a tree]]
Now, imagine the strong chain is broken, and the jet and the piston aircraft start to move. At low speeds:
<blockquote>
The piston engine will have constant 100% power, and the propeller's thrust will vary with speed<br />
The jet engine will have constant 100% thrust, and the engine's power will vary with speed
</blockquote>
This shows why one cannot compare the rated power of a piston engine with the propulsive power of a jet engine – these are different quantities (even if the name "power" is the same). There isn't any useful power measurement in a jet engine that compares directly to a piston engine rated power.
==References==
{{Reflist}}
==See also==
*[[Aerodynamic force]]
*[[Gimballed thrust]], the most common thrust system in modern rockets
*[[Thrust-to-weight ratio]]
*[[Thrust vectoring]]
*[[Tractive effort]]
[[Category:Aerodynamics]]
[[Category:Force]]
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