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. In fact, one must consider the many airfoils that are symmetrical, yet produce significant lift.
The fundamental physical laws governing the forces acting upon an aircraft in flight were adopted from postulated theories developed before any human successfully flew an aircraft. The use of these physical laws grew out of the Scientific Revolution, which began in Europe in the 1600s. Driven by the belief the universe operated in a predictable manner open to human understanding, many philosophers, mathematicians, natural scientists, and inventors spent their lives unlocking the secrets of the universe. One of the best known 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.” This means that 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 it is moving, its inertia keeps it moving, subject to the various other forces acting on it. These forces may add to its motion, slow it down, or change its direction.
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 is directly proportional to the applied force. This takes into account the factors involved in overcoming Newton’s First Law. It covers both changes in direction and speed, including starting up from rest (positive acceleration) and coming to a stop (negative acceleration or deceleration).
Newton’s Third Law: “For every action, there is an equal and opposite reaction.”
In an airplane, the propeller moves and pushes back the air; consequently, the air pushes the propeller (and thus the airplane) in the opposite direction—forward. In a jet airplane, the engine pushes a blast of hot gases backward; the force of equal and opposite reaction pushes against the engine and forces the airplane forward.
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.
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 3A]
In Figure 3B, the cylinder is rotated clockwise and observed from the side while immersed in a fluid. The rotation of the cylinder affects the fluid surrounding the cylinder. The flow around the rotating cylinder differs from the flow around a stationary cylinder due to resistance caused by two factors: viscosity and friction.
Figure 3. A illustrates uniform circulation. B illustrates the increased airflow over the top of a rotating cylinder. The airflow speed is further increased when the rotating cylinder is in a moving stream of air (C). The air molecules near the surface of an object are slowed and almost stationary. D is an example of typical aircraft grade aluminum used in aircraft construction to include wings and leading edges of wings as shown in E (left). When magnified at 1,500x (E, right), polished aluminum is visibly rough. This demonstrates why airflow is affected by molecular irregularities of the surface.
Viscosity is the property of a fluid or semifluid that causes it to resist flowing. This resistance to flow 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.
Similar amounts of oil and water poured down two identical ramps demonstrate the difference in viscosity. The water seems to flow freely while the oil flows much more slowly.
Since molecular resistance to motion underlies viscosity, grease is very viscous because its molecules resist flow. Hot lava is another example of a viscous fluid. All fluids are viscous and have a resistance to flow whether this resistance is observed or not. Air is an example of a fluid whose viscosity can not be observed.
Since air has viscosity properties, it will resist flow to some extent. In the case of the rotating cylinder within an immersed fluid (oil, water, or air), the fluid (no matter what it is) resists flowing over the cylinder’s surface.
Friction is the second factor at work when a fluid flows around a rotating cylinder. Friction is the resistance one surface or object encounters when moving over another and exists between a fluid and the surface over which it flows. If identical fluids are poured down the ramp, they flow in the same manner and at the same speed. If one ramp’s surface is coated with small pebbles, the flow down the two ramps differs significantly. The rough surface ramp impedes the flow of the fluid due to resistance from the surface (friction). It is important to remember that all surfaces, no matter how smooth they appear, are not smooth and impede the flow of a fluid. Both the surface of a wing and the rotating cylinder have a certain roughness, albeit at a microscopic level, causing resistance for a fluid to flow. This reduction in velocity of the airflow about a surface is caused by skin friction or drag. When passing over a surface, molecules actually adhere (stick, cling) to the surface, illustrated by the rotating cylinder in a fluid that is not moving. Thus, 1. In the case of the rotating cylinder, air particles near the surface that resist motion have a relative velocity near zero. The roughness of the surface impedes their motion. 2. Due to the viscosity of the fluid, the molecules on the surface entrain, or pull, the surrounding flow above it in the direction of rotation due to the adhesion of the fluid to itself. There is also a difference in flow around the rotating cylinder and in flow around a nonrotating cylinder. The molecules at the surface of the rotating cylinder are not in motion relative to the cylinder; they are moving clockwise with the cylinder. Due to viscosity, these molecules entrain others above them resulting in an increase in fluid flow in the clockwise direction. Substituting air for other fluids results in a higher velocity of air movement above the cylinder simply because more molecules are moving in a clockwise direction.
When the cylinder rotates in a fluid that is also moving, the result is a higher circulatory flow in the direction of the rotating cylinder. [Figure 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. Additionally, and as shown in Figure 4, at point “A,” a stagnation point exists where the air stream impacts (impinges) on the front of the airfoil’s surface and splits; some air goes over and some under. Another stagnation point exists at “B,” where the two airstreams rejoin and resume at identical velocities. When viewed from the side, an upwash is created ahead of the airfoil and downwash at the rear.
In the case of Figure 4, the highest velocity is at the top of the airfoil with the lowest velocity at the bottom. Because these velocities are associated with an object (in this case, an airfoil) they are called local velocities as they do not exist outside the lift-producing system, in this case an airfoil. This concept can be readily applied to a wing or other lifting surface. Because there is a difference of velocity above and below the wing, the result is a a higher pressure at the bottom of the wing and a lower pressure on the top of the wing.
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, to include 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 the Magnus effect, an airfoil with a positive AOA 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 4]
Figure 4. Air circulation around an airfoil occurs when the front stagnation point is below the leading edge and the aft stagnation point is beyond the trailing edge
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 (liquid or gas) increases, the pressure within the fluid decreases. This principle explains what happens to air passing over the curved top of the airplane wing. A practical application of Bernoulli’s Principle is the venturi tube. The venturi tube has an air inlet that narrows to a throat (constricted point) and an outlet section that increases in diameter toward the rear. The diameter of the outlet is the same as that of the inlet. At the throat, the airflow speeds up and the pressure decreases; at the outlet, the airflow slows and the pressure increases. [Figure 5] Since air is recognized as a body and it is accepted that it must follow the above laws, one can begin to see how and why an airplane wing develops lift. As the wing moves through the air, the flow of air across the curved top surface increases in velocity creating a low-pressure area. Although Newton, Magnus, Bernoulli, and hundreds of other early scientists who studied the physical laws of the universe did not have the sophisticated laboratories available today, they provided great insight to the contemporary viewpoint of how lift is created.
Figure 5. Air pressure decreases in a veturi tube.