3.3.1 Newton’s Basic Laws of Motion #
The formulation of lift has historically been the adaptation over the past few centuries of basic physical laws. These laws, although seemingly applicable to all aspects of lift, do not answer how lift is formulated.
The fundamental physical laws governing the forces acting upon an aircraft in flight were adopted from theories developed before any human successfully flew an aircraft, growing out of the Scientific Revolution that began in Europe in the 1600s. One of the best known contributors was Sir Isaac Newton, who not only formulated the law of universal gravitation, but also described the three basic laws of motion.
Newton’s First Law: “Every object persists in its state of rest or uniform motion in a straight line unless it is compelled to change that state by forces impressed on it.” Nothing starts or stops moving until some outside force causes it to do so. An aircraft at rest on the ramp remains at rest unless a force strong enough to overcome its inertia is applied; once moving, its inertia keeps it moving, subject to the other forces acting on it.
Newton’s Second Law: “Force is equal to the change in momentum per change in time. For a constant mass, force equals mass times acceleration.”
When a body is acted upon by a constant force, its resulting acceleration is inversely proportional to the mass of the body and directly proportional to the applied force. It covers both changes in direction and speed, including positive acceleration and deceleration.
Newton’s Third Law: “For every action, there is an equal and opposite reaction.” In an airplane, the propeller pushes back the air; consequently, the air pushes the propeller (and the airplane) forward. In a jet, the engine pushes a blast of hot gases backward, and the equal and opposite reaction forces the airplane forward.
3.3.2 Magnus Effect #
In 1852, the German physicist and chemist Heinrich Gustav Magnus (1802–1870) made experimental studies of the aerodynamic forces on spinning spheres and cylinders. (The effect had already been mentioned by Newton in 1672, apparently in regard to spheres or tennis balls.) These experiments led to the discovery of the Magnus Effect, which helps explain the theory of lift.
3.3.3 Flow of Air Against a Nonrotating Cylinder #
If air flows against a cylinder that is not rotating, the flow of air above and below the cylinder is identical and the forces are the same. [Figure 3-3A]
3.3.4 A Rotating Cylinder in a Motionless Fluid #
In Figure 3-3B, the cylinder is rotated clockwise and observed from the side while immersed in a fluid. The flow around the rotating cylinder differs from the flow around a stationary cylinder due to resistance caused by two factors: viscosity and friction.
Viscosity #
Viscosity is the property of a fluid or semifluid that causes it to resist flowing. This resistance is measurable due to the molecular tendency of fluids to adhere to each other to some extent. High-viscosity fluids resist flow; low-viscosity fluids flow easily. Pouring similar amounts of oil and water down two identical ramps shows the difference: the water flows freely while the oil flows much more slowly. Grease is very viscous because its molecules resist flow; hot lava is another viscous fluid. All fluids are viscous and resist flow whether this resistance is observed or not. Air’s viscosity cannot easily be observed, but air does resist flow to some extent. In the case of the rotating cylinder immersed in a fluid (oil, water, or air), the fluid resists flowing over the cylinder’s surface.
Friction #
Friction is the second factor at work when a fluid flows around a rotating cylinder. It is the resistance one surface encounters when moving over another, and it exists between a fluid and the surface over which it flows.
If identical fluids are poured down two ramps, they flow the same way at the same speed; but if one ramp is coated with small pebbles, that rough surface impedes the flow. All surfaces, no matter how smooth they appear, are not truly smooth and impede the flow of a fluid. Both a wing’s surface and the rotating cylinder have a certain roughness, at a microscopic level, causing resistance to flow. This reduction in airflow velocity about a surface is caused by skin friction or drag.
When passing over a surface, molecules actually adhere to it. Thus:
- Air particles near the surface, which resist motion, have a relative velocity near zero; the roughness of the surface impedes their motion.
- Due to the viscosity of the fluid, the molecules on the surface entrain (pull) the surrounding flow above them in the direction of rotation due to the adhesion of the fluid to itself.
There is also a difference between flow around a rotating cylinder and around a nonrotating one. The molecules at the surface of the rotating cylinder move clockwise with it; due to viscosity, they entrain others above them, resulting in increased fluid flow in the clockwise direction. Substituting air for other fluids gives a higher velocity of air movement above the cylinder, simply because more molecules are moving clockwise.
3.3.5 A Rotating Cylinder in a Moving Fluid #
When the cylinder rotates in a fluid that is also moving, the result is a higher circulatory flow in the direction of rotation. [Figure 3-3C] By adding fluid motion, the magnitude of the flow increases.
The highest differences of velocity are 90° from the relative motion between the cylinder and the airflow. As shown in Figure 3-4, at point “A” a stagnation point exists where the airstream impinges on the front of the airfoil’s surface and splits—some air goes over, some under. Another stagnation point exists at “B,” where the two airstreams rejoin at identical velocities. Viewed from the side, an upwash is created ahead of the airfoil and a downwash at the rear. The highest velocity is at the top of the airfoil, the lowest at the bottom. Because these velocities are associated with the airfoil, they are called local velocities. The difference in velocity above and below the wing results in higher pressure at the bottom and lower pressure on top.
This low-pressure area produces an upward force known as the Magnus Effect—the physical phenomenon whereby an object’s rotation affects its path through a fluid, including air. Two early aerodynamicists, Martin Kutta and Nicolai Joukowski, eventually measured and calculated the forces for the lift equation on a rotating cylinder (the Kutta-Joukowski theorem). To summarize: an airfoil with a positive angle of attack develops air circulation about the upper surface of the wing. Its sharp trailing edge forces the rear stagnation point to be aft of the trailing edge, while the front stagnation point falls below the leading edge. [Figure 3-4]
3.3.6 Bernoulli’s Principle of Differential Pressure #
A half-century after Newton formulated his laws, Daniel Bernoulli, a Swiss mathematician, explained how the pressure of a moving fluid (liquid or gas) varies with its speed of motion. Bernoulli’s Principle states that as the velocity of a moving fluid increases, the pressure within the fluid decreases. This principle explains what happens to air passing over the curved top of an airplane wing.
A practical application of Bernoulli’s Principle is the venturi tube. It has an air inlet that narrows to a throat (constricted point) and an outlet section that increases in diameter toward the rear; the outlet diameter is the same as the inlet. At the throat, the airflow speeds up and the pressure decreases; at the outlet, the airflow slows and the pressure increases. [Figure 3-5] As a wing moves through the air, the flow across its curved top surface increases in velocity, creating a low-pressure area.
Although Newton, Magnus, Bernoulli, and hundreds of other early scientists did not have today’s sophisticated laboratories, they provided great insight into the contemporary understanding of how lift is created.
