# thrust

## In rocketry

Thrust is the forward force generated by a rocket. Thrust is produced by the expulsion of a reaction mass, such as the hot gas products of a chemical reaction.

In an optimum situation (see below), thrust equals the product of the mass expelled from the rocket in unit time (the propellant mass flow rate) and the exhaust velocity (the average actual velocity of the exhaust gases). If *F* is the thrust, *m _{p}* the propellant flow rate, and

*v*the effective velocity, then

_{e}

*F = m _{p}v_{e}* (1)

At first glance, it might seem that a constant thrust would lead to a constant acceleration, but this not the case. Even when the propellant flow rate and exhaust velocity are constant, so that the thrust is constant, a rocket will accelerate at an increasing rate because the rocket's overall mass decreases as propellant is used up. The total change in velocity of a rocket due to a specific thrust, acting in a straight line, is given by an important formula known as the rocket equation.

In some situations, as of a rocket rising from Earth's surface, a large thrust acting over a relatively short period is essential. But in other situations, as of a probe on a deep space mission, the key factor is not so much the amount of thrust, which only determines the acceleration, but the final velocity. A high final velocity can be achieved by a propulsion system that produces a low thrust but expels material over long periods at a high velocity – for example, an ion engine.

Equation (1) only holds true when the pressure of the outgoing exhaust exactly equals the ambient (outside) pressure. If this is not the case, then an extra term comes into play, and the thrust is given by:

*F = m _{p}v_{e} + (p_{e} - p_{a})A_{e}* (2)

where *p _{e}* is the exhaust pressure,

*p*the ambient pressure, and

_{a}*A*the area of the exit of the rocket nozzle. The first term in this equation is called the momentum thrust, and the second the pressure thrust.

_{e}

**Average thrust** is the average instantaneous force that the engine produces during its burn. It is equal to
the total impulse divided
by the burn time.

## In aerodynamics

In aerodynamics, thrust is one of the four forces of flight acting on an aircraft, the others being weight, drag, and lift. Thrust must be greater than drag to achieve the forward acceleration needed for takeoff and to increase an aircraft's speed in level flight. An aircraft flying at a constant speed will have thrust equal to drag.

Two of Isaac Newton's laws of motion relate to force, and thus to thrust. His second law defines force as the product of mass and acceleration of the mass (F = mass × acceleration). The more force exerted on an object of a given mass, the greater its acceleration. Newton's third law states that every action has an equal and opposite reaction.

An airplane's engine is responsible for producing thrust. With a reciprocating, or internal combustion engine – the earliest common type of aircraft engine – the engine provides power to the propeller, which produces the thrust. The amount of thrust is related to the amount of power that the engine produces and to the efficiency of the propeller. An engine with more power will produce more thrust if the efficiency of the propeller remains constant. Similarly, a more efficient propeller will generate more thrust if the engine power remains constant. (Propeller efficiency is a measure of how much of the power produced by the engine actually is converted to thrust. Some power delivered to the propeller gets lost before it becomes thrust because of drag and other factors.)

Internal combustion engines are used on propeller aircraft (other than turboprops, which combine a jet engine with a propeller). These engines rely on pistons moving inside of cylinders to compress air and, at the same time, mix this air with the fuel to form a fine mist. This mist is then ignited by sparks from sparkplugs that cause small explosions. These explosions force the movement of the pistons that drive the engine and spin the propellers. Sometimes superchargers are used to compress the air before it reaches the cylinders.

A spinning propeller produces thrust for the same reason the shape of the wing produces lift. Air rushes up the leading edge of a propeller blade (the edge that is moving into the airflow). The air slows as it runs down the trailing edge. This causes higher pressure at the backside of the propeller blade and results in force directed toward the lower pressure of the front. This forward-directed force is thrust. The Wright brothers were the first to recognize the similarity between airplane wings and propellers.

At the end of World War II, Germany built the first jet engine that would soon be used to propel aircraft. Jet engines work by igniting fuel combined with compressed oxygen inside the engine, resulting in large quantities of gas being quickly released out the rear of the aircraft. The extremely high acceleration of the mass of gas creates a large force that behaves according to Newton's second law of motion (F = m × a). Newton's third law explains what happens next: a resulting force is created in the opposite direction from the force of gas that is being expelled out the plane's exhaust, in the forward direction.

The equation for calculating the thrust of an engine with the same pressure
both inside and outside of the engine is F = (m_{e}/t_{e} × V_{e}) - (m_{i}/t_{i} × V_{i}),
where m_{e} is an amount (mass) of the gas exiting the engine and
t_{e} is the amount of time it takes for all of this mass of gas
to pass through a given area. V_{e} is the velocity of this exiting
gas, m_{i} is an amount (mass) of the air just before it enters
the front of the engine, and t_{i} is the time it takes for this
mass to pass through a given area. V_{i} is the velocity of the
entering air. To make the terms more understandable, the terms with the
subscript "e" refer to events and amounts relating to the exit of gas. The
terms with the subscript "i" refer to events and amounts relating to the
intake of gas.

In other words, the total thrust created is the force of the gas being ejected out of the back of the engine minus the force of the gas entering at the front.

Thrust, like any other force, is measured in either newtons or pounds. Jet engines are usually rated according to the amount of thrust they can produce. Although internal combustion engines also produce thrust by means of the propeller, those used on vehicles are usually described in terms of the amount of power they produce, expressed in horsepower.