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Thrust on an airplane

Thrust is the force that moves an aircraft through the air. Thrust is generated by the engines of the airplane.


Equations for Newton's 2nd law of motion

Newton's second law of motion defines a force to be equal to the differential change in momentum per unit time as described by the calculus of mathematics, which Newton also developed.


Diagram of Newton's 3rd law of motion

Newton's third law of motion states that for every action (force) in nature there is an equal and opposite reaction. In other words, if object A exerts a force on object B, then object B also exerts an equal and opposite force on object A.


Thrust is one of the four aerodynamic forces acting on an aircraft in flight. It is the force that pushes an aircraft through the air. 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 Sir 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 x 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, measured in horsepower, that the engine produces and to the efficiency of the propeller. An engine with more horsepower 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 x 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. This force is thrust.

The equation for calculating the thrust of an engine with the same pressure both inside and outside of the engine is F = (me/te x Ve) – (mi/ti x Vi), where me is an amount (mass) of the gas exiting the engine and te is the amount of time it takes for all of this mass of gas to pass through a given area. Ve is the velocity of this exiting gas, mi is an amount (mass) of the air just before it enters the front of the engine, and ti is the time it takes for this mass to pass through a given area. Vi 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 (The word “newtons” is written as a lower-case word even though it comes from Sir Isaac Newton's name.). 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.

—Dan Johnston


Smith, Hubert. The Illustrated Guide to Aerodynamics, 2nd edition. Blue Ridge Summit, Pa.: TAB Books, 1992.

Wegener, Peter P. What Makes Airplanes Fly? New York: Springer-Verlag, 1991.

“Thrust Equation” http://www.lerc.nasa.gov/www/K-12/airplane/thrsteq.html

“Jet Engines” and “Reciprocating Engines” http://library.thinkquest.org/25486/english/

“What Is Thrust/” http://www.grc.nasa.gov/WWW/K-12/airplane/thrust1.html

Educational Organization

Standard Designation  (where applicable

Content of Standard

American Association for the Advancement of Science


Students will develop an understanding of the scientific principle of motion.

National Council of Teachers of Mathematics


Understand meaning of mathematical operations

International Technology Education Association

Standard 2

International Technology Education Association

Standard 9