Thrust

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Thrust is a force described quantitatively by Newton's second and third laws. When a system ejects or accelerates mass in one direction, the accelerated mass exerts a force of equal magnitude but opposite direction on the system. In the case of flying bodies, thrust overcomes air resistance and the force of gravity, generates propulsion and causes acceleration. In particular, thrust serves as a parameter for the performance of jet engines and rocket engines.

The unit of thrust, like that of force in general, is the newton (N). Sometimes the obsolete unit kilopond (kp) is still used. Especially in English-speaking countries, the unit lbs or lbf is often used as an abbreviation for pounds or pounds force.

Basics

For jet engines, thrust is the preferred parameter, since direct power measurement at a drive shaft is not possible for pure jet engines. In the case of piston engines and propeller turbines, on the other hand, power is usually expressed in kilowatts. However, the relevant propulsive force emanating from a propeller driven by a piston engine or turbine is the thrust generated.

A PW4062 engine on a Boeing 747-400 produces a maximum thrust of approximately 62,100 lbf or 276 kN during takeoff. To achieve this thrust, three liters of kerosene are burned per second. Proof that an engine actually generates this thrust is demonstrated and certified on a test stand after production or repair.

A vertical take-off aircraft can only take off vertically if the thrust force is greater than the weight force of the aircraft, see also thrust-to-weight ratio. For a 17-ton Hawker Siddeley Harrier, for example, the 200 kN from its engine is sufficient to accelerate it vertically. In fixed-wing aircraft, the thrust need only be a fraction of the dead weight, since the wing "carries" the other part of the dead weight. This fraction is characterized by the glide ratio.

Currently (2006), the highest-thrust civil aircraft engine is the General Electric GE90-115B with 519 kN. In test runs it achieved a max. thrust of 569 kN. It is used for the Boeing 777-300ER.

Values for rockets are around 40,000 kN for the former Soviet N1 and Energija and the American Saturn V, 30,000 kN for the Space Shuttle, or 8,800 kN for the Delta IV Heavy.

Physical basics

jet engine thrust

Thrust is created by accelerating the air mass that has passed through it. For this purpose, kinetic energy must be supplied to the air. If the pressure loss caused by the thrust nozzle can be neglected, the nozzle is called adapted.

According to the law of conservation of momentum, the following applies to the net thrust of an engine:

$F_{{\mathrm {N}}}={\dot m}_{{\mathrm {raus}}}\cdot v_{{\mathrm {raus}}}-{\dot m}_{{\mathrm {rein}}}\cdot v_{{\mathrm {rein}}}$

with

$F_{{\mathrm {N}}}$ : Thrust (Force)

${\dot m}_{{\mathrm {raus}}}$ : mass flow rate of ejected air

${\dot m}_{{\mathrm {rein}}}$ : mass flow rate of the aspirated air

$v_{{\mathrm {raus}}}$ : velocity of the ejected air (velocity)

$v_{{\mathrm {rein}}}$ : velocity of the aspirated air

Since the gas expands due to the combustion of the fuel and the associated increase in temperature, and the increased volume must escape through the narrowed cross-section of the nozzle, the velocity c of the airflow increases (for more details see: jet engine). In propeller machines, the airflow acceleration is achieved by a driven propeller.

Since the engine nacelle generates a drag D (the drag of the aircraft can be neglected), this must be subtracted from the net thrust. This means that two aircraft can have different thrust even though they are equipped with the same engines (e.g. A350 and Boeing 787). The following therefore applies

$F=F_{{\mathrm {N}}}-D$

However, since air gets thinner the higher you fly, the mass flow also decreases with increasing altitude. So one defines an engine thrust at ISA-conditions and then says

$F=F_{{\mathrm {ISA}}}\cdot \left({\frac {\rho }{\rho _{{\mathrm {ISA}}}}}\right)^{{0{,}85}}$

where the air density (ρ - rho) can be estimated, for example, by the barometric altitude formula.

rocket thrust

When propelling a rocket, the speed is especially important when the fuel is exhausted.

For the shear momentum, (according to the momentum theorem ${\vec {F}}\cdot \Delta t=\Delta {\vec {p}}$ ):

$F\cdot \Delta t=\Delta m\cdot v_{s}$

F: Propulsive force

Δt: Burning time of the engine

Δm: Mass loss of the rocket due to the loss of the burnt fuel.

_vs: outflow velocity

Note: This is one of the rare cases in elementary mechanics where mass is not a constant. In this case, it is also easy to express the power of the rocket engine as $P=F\cdot v_{s}$ ! The effective exhaust velocity is also called the (mass) specific impulse of the rocket engine.

If the propulsion $F={\text{const.}}$ (not always given, see e.g. thrust curve for solid rockets), it follows for the terminal velocity $v_{t}$ with $v_{0}=0$ and consideration of the rocket empty mass $m_{{\mathrm {R}}}$ and the propellant mass $m_{{\mathrm {T}}}$ :

$v_{t}=v_{{\mathrm {s}}}\cdot \ln {\frac {m_{{\mathrm {R}}}+m_{{\mathrm {T}}}}{m_{{\mathrm {R}}}}}$ { "basic rocket equation".)

The terminal velocity increases with the ejection velocity (typical value is 4500 m/s) and the ratio of initial to terminal mass (typically 30:1 to 100:1). Corrections for drag must be considered analogous to the jet engine case.

An important use case for rocket engines is to overcome the acceleration due to gravity. To do this, the rocket must reach escape velocity $v_{{\mathrm {e}}}\approx 11200\,{\mathrm {m/s}}$ (e for escape) reach.

In a launch vehicle, for example, the final mass is approximately identical to the payload, only the latter reaches the target altitude (with the payload fairing):

Ariane 5G: launch mass ≈750 t, payload ≈20 t LEO, 7 t GTO, launch thrust ≈12,000 kN, maximum thrust ≈14,400 kN.

Launch of a Soyuz rocket

Questions and Answers

Q: What is thrust?

A: Thrust is a force or a push that occurs when a system pushes or accelerates mass in one direction, resulting in a force just as large in the opposite direction.

Q: How is thrust described in math and physics?

A: Isaac Newton's second and third laws describe the concept of thrust in math and physics.

Q: What kinds of vehicles and engines does thrust apply to?

A: Thrust applies to many kinds of vehicles and engines such as rockets, motorboats, propellers, and jet engines.

Q: How is thrust typically measured in the U.S.?

A: Thrust is measured in "pounds of thrust" in the U.S.

Q: How is thrust typically measured in the metric system?

A: In the metric system, thrust is measured in newtons.

Q: How many newtons of thrust equal one pound of thrust?

A: 4.45 newtons of thrust equals 1 pound of thrust.

Q: What does one pound of thrust represent?

A: One pound of thrust represents the amount of thrust it would take to keep a one-pound object unmoving against the force of gravity on Earth.