Lesson 1: Aerodynamics as a Science
Section 3 - Newton's Laws of Motion
Newton’s three Laws of Motion are very important in the study of movement of aircraft. The third law in particular can directly be applied to aerodynamics.
The motion of an aircraft through the air can be explained and described by physical principals discovered over 300 years ago by Sir Isaac Newton. Newton worked in many areas of mathematics and physics. He developed the theories of gravitation in 1666, when he was only 23 years old. Twenty years later, in 1686, he presented his three laws of motion in the "Principia Mathematica Philosophiae Naturalis."
NEWTON'S FIRST LAW
Newton's first law states that every object will remain at rest or in uniform motion in a straight line unless compelled to change its state by the action of an external force. This is normally taken as the definition of inertia.
The key point here is that if there is no net force acting on an object (if all the external forces cancel each other out) then the object will maintain a constant velocity. If that velocity is zero, then the object remains at rest. If an external force is applied, the velocity will change because of the force.
Some facts to bear in mind regarding Newton's First law are as follows:
When flying at a constant altitude: If Thrust and Drag are equal, aircraft holds constant airspeed.
If Thrust is increased: Aircraft accelerates - airspeed increases. Drag depends on airspeed - Drag increases.
When Drag is again equal to Thrust: Aircraft no longer accelerates but holds a new, higher constant airspeed.
NEWTON'S SECOND LAW
Newton’s second law explains how the velocity will change. The law defines a force to be equal to change in momentum (mass times velocity) per change in time. For an object with a constant mass, the second law can be more easily expressed as the product of an object's mass and its acceleration (F = ma). For an external applied force, the change in velocity depends on the mass of the object. A force will cause a change in velocity; and likewise, a change in velocity will generate a force. The equation works both ways.
NEWTON'S THIRD LAW
Newton’s third law 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 force on object A. Here, bear in mind that the forces are exerted on different objects. The third law can be used to explain the generation of lift by a wing and the production of thrust by a jet engine.
For Newton’s First Law, every object will remain at rest or in uniform motion in a straight line unless compelled to change its state by the action of an external force. This is usually referred to as the definition of inertia. Here, there is no net force resulting from unbalanced forces acting on an object, if all the external forces cancel each other out, then the object will maintain a constant velocity. If that velocity is zero, then the object remains at rest. And if an additional external force is applied, the velocity will change because of that force.
An aircraft in flight is a very good example of the first law of motion. There are four major forces acting on an aircraft: lift, weight, thrust, and drag. If we consider the motion of an aircraft at a constant altitude, we can neglect the lift and weight. An aircraft that is cruising will fly at a constant airspeed and the thrust will exactly balance the drag of the aircraft.
However, if the pilot changes the thrust of the engine, the thrust and drag are no longer in balance. If the thrust is increased, the aircraft will accelerate and the velocity will increase. This is also cited in Newton’s first law: an external force will change the velocity of the object.
The drag of the aircraft, like the lift, depends on the square of the velocity. So the drag will increase with increased velocity. In time, the new drag will be equal to the new thrust level and at that point, the forces will again balance out, and the acceleration will stop. The airplane continues to fly at a new constant velocity that would be higher than the initial velocity.
Newton’s Second Law 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. The momentum is defined to be the mass of an object times its velocity. If the mass is a constant, the second law reduces to the more familiar product of a mass and an acceleration (F = ma).
Since acceleration is a change in velocity with a change in time, we can also write this equation in the third form shown on the slide. The important fact is that a force will cause a change in velocity; and likewise, a change in velocity will generate a force. The velocity, force, acceleration, and momentum have both a magnitude and a direction associated with them. Scientists and mathematicians call this a vector quantity (magnitude plus direction).
FORCE = MASS x ACCELERATION or F = ma
For Newton’s Third Law, 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. Again, keep in mind that different forces are exerted on different objects.
For aircraft, the principal of action and reaction is very important. It helps to explain the generation of lift from an airfoil. In this case, the air is deflected downward by the action of the airfoil, and in reaction the wing is pushed upward. Similarly, for a spinning ball, the air is deflected to one side, and the ball reacts by moving in the opposite direction.
A jet engine also produces thrust through action and reaction. The engine produces hot exhaust gases which flow out the back of the engine. In reaction, a thrusting force is produced in the opposite direction.
Bibliography
Allen, John E. Aerodynamics: A Space Age Survey. New York: Harper & Row, 1963.
Encyclopedia Britannica. Technology Education – Aerodynamics. www.geocities.com/tech_ed_2000.
Glenn Research Center. Beginner’s Guide to Aerodynamics. www.grc.nasa.gov/www/K-12/airplane/bga.html.
Von Braun, Wernher, Ordway, III, F. I., and Dooling, D. Space Travel: A History. New York: Harper & Row, 1985.
Wegener, Peter P. What Makes Airplanes Fly? New York: Springer-Verlag, 1991.
