Principles of Flight I

Theories in the Production of Lift
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. 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.

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.

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]

*Figure 3-3. 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.

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 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.

Viscosity
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. (An excellent website to demonstrate types of viscosity is found at the Cornell University website on viscosity, located at http:// atlas.geo.cornell.edu/education/student/viscosity.html.)

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 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,

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.
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.

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 the rotating cylinder. [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. Additionally, and as shown in Figure 3-4, 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 3-4, 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.

*Figure 3-4. 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.

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 3-4]

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 (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 3-5]

*Figure 3-5. Air pressure decreases in a venturi tube.

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.

Airfoil Design

An airfoil is a structure designed to obtain reaction upon its surface from the air through which it moves or that moves past such a structure. Air acts in various ways when submitted to different pressures and velocities; but this discussion is conﬁned to the parts of an aircraft that a pilot is most concerned with in ﬂight—namely, the airfoils designed to produce lift. By looking at a typical airfoil proﬁle, such as the cross section of a wing, one can see several obvious characteristics of design. [Figure 3-6] Notice that there is a difference in the curvatures (called cambers) of the upper and lower surfaces of the airfoil. The camber of the upper surface is more pronounced than that of the lower surface, which is usually somewhat ﬂat.

NOTE: The two extremities of the airfoil proﬁle also differ in appearance. The end, which faces forward in ﬂight, is called

Figure 3-6. Typical airfoil section.

the leading edge, and is rounded; the other end, the trailing edge, is quite narrow and tapered.

A reference line often used in discussing the airfoil is the chord line, a straight line drawn through the proﬁle connecting the extremities of the leading and trailing edges. The distance from this chord line to the upper and lower surfaces of the wing denotes the magnitude of the upper and lower camber at any point. Another reference line, drawn from the leading edge to the trailing edge, is the mean camber line. This mean line is equidistant at all points from the upper and lower surfaces.

An airfoil is constructed in such a way that its shape takes advantage of the air’s response to certain physical laws. This develops two actions from the air mass: a positive pressure lifting action from the air mass below the wing, and a negative pressure lifting action from lowered pressure above the wing.

As the air stream strikes the relatively ﬂat lower surface of a wing or rotor blade when inclined at a small angle to its direction of motion, the air is forced to rebound downward, causing an upward reaction in positive lift. At the same time, the air stream striking the upper curved section of the leading edge is deﬂected upward. An airfoil is shaped to cause an action on the air, and forces air downward, which provides an equal reaction from the air, forcing the airfoil upward. If a wing is constructed in such form that it causes a lift force greater than the weight of the aircraft, the aircraft will ﬂy.

If all the lift required were obtained merely from the deﬂection of air by the lower surface of the wing, an aircraft would only need a ﬂat wing like a kite. However, the balance of the lift needed to support the aircraft comes from the ﬂow of air above the wing. Herein lies the key to ﬂight.

It is neither accurate nor useful to assign speciﬁc values to the percentage of lift generated by the upper surface of an airfoil versus that generated by the lower surface. These are not constant values and vary, not only with ﬂight conditions, but also with different wing designs.

Different airfoils have different ﬂight characteristics. Many thousands of airfoils have been tested in wind tunnels and in actual ﬂight, but no one airfoil has been found that satisﬁes every ﬂight requirement. The weight, speed, and purpose of each aircraft dictate the shape of its airfoil. The most efﬁcient airfoil for producing the greatest lift is one that has a concave, or “scooped out” lower surface. As a ﬁxed design, this type of airfoil sacriﬁces too much speed while producing lift and is not suitable for high-speed ﬂight. Advancements in engineering have made it possible for today’s high-speed jets to take advantage of the concave airfoil’s high lift characteristics. Leading edge (Kreuger) ﬂaps and trailing edge (Fowler) ﬂaps, when extended from the basic wing structure, literally change the airfoil shape into the classic concave form, thereby generating much greater lift during slow ﬂight conditions.

On the other hand, an airfoil that is perfectly streamlined and offers little wind resistance sometimes does not have enough lifting power to take the airplane off the ground. Thus, modern airplanes have airfoils that strike a medium between extremes in design. The shape varies according to the needs of the airplane for which it is designed. Figure 3-7 shows some of the more common airfoil sections.

Figure 3-7. Airfoil designs.

Low Pressure Above In a wind tunnel or in ﬂight, an airfoil is simply a streamlined object inserted into a moving stream of air. If the airfoil proﬁle were in the shape of a teardrop, the speed and the pressure changes of the air passing over the top and bottom would be the same on both sides. But if the teardrop shaped airfoil were cut in half lengthwise, a form resembling the basic airfoil

(wing) section would result. If the airfoil were then inclined so the airﬂow strikes it at an angle (angle of attack (AOA)), the air moving over the upper surface would be forced to move faster than the air moving along the bottom of the airfoil. This increased velocity reduces the pressure above the airfoil.

Applying Bernoulli’s Principle of Pressure, the increase in the speed of the air across the top of an airfoil produces a drop in pressure. This lowered pressure is a component of total lift. The pressure difference between the upper and lower surface of a wing alone does not account for the total lift force produced.

The downward backward ﬂow from the top surface of an airfoil creates a downwash. This downwash meets the ﬂow from the bottom of the airfoil at the trailing edge. Applying Newton’s third law, the reaction of this downward backward ﬂow results in an upward forward force on the airfoil.

High Pressure Below

A certain amount of lift is generated by pressure conditions underneath the airfoil. Because of the manner in which air ﬂows underneath the airfoil, a positive pressure results, particularly at higher angles of attack. But there is another aspect to this airﬂow that must be considered. At a point close to the leading edge, the airﬂow is virtually stopped (stagnation point) and then gradually increases speed. At some point near the trailing edge, it again reaches a velocity equal to that on the upper surface. In conformance with Bernoulli’s principle, where the airﬂow was slowed beneath the airfoil, a positive upward pressure was created i.e., as the ﬂuid speed decreases, the pressure must increase. Since the pressure differential between the upper and lower surface of the airfoil increases, total lift increases. Both Bernoulli’s Principle and Newton’s Laws are in operation whenever lift is being generated by an airfoil.

Pressure Distribution

From experiments conducted on wind tunnel models and on full size airplanes, it has been determined that as air ﬂows along the surface of a wing at different angles of attack, there are regions along the surface where the pressure is negative, or less than atmospheric, and regions where the pressure is positive, or greater than atmospheric. This negative pressure on the upper surface creates a relatively larger force on the wing than is caused by the positive pressure resulting from the air striking the lower wing surface. Figure 3-8 shows the pressure distribution along an airfoil at three different angles of attack. The average of the pressure variation for any given angle of attack is referred to as the center of pressure (CP). Aerodynamic force acts through this CP. At high angles of attack, the CP moves forward, while at low angles of attack the CP moves aft. In the design of wing structures, this CP

Figure 3-8. Pressure distribution on an airfoil and CP changes with AOA.

travel is very important, since it affects the position of the air loads imposed on the wing structure in both low and high AOA conditions. An airplane’s aerodynamic balance and controllability are governed by changes in the CP.

Airfoil Behavior

Although speciﬁc examples can be cited in which each of the principles predict and contribute to the formation of lift, lift is a complex subject. The production of lift is much more complex than a simple differential pressure between upper and lower airfoil surfaces. In fact, many lifting airfoils do not have an upper surface longer than the bottom, as in the case of symmetrical airfoils. These are seen in high-speed aircraft having symmetrical wings, or on symmetrical rotor blades for many helicopters whose upper and lower surfaces are identical. In both examples, the relationship of the airfoil with the oncoming airstream (angle) is all that is different. A paper airplane, which is simply a ﬂat plate, has a bottom and top exactly the same shape and length. Yet these airfoils do produce lift, and “ﬂow turning” is partly (or fully) responsible for creating lift.

As an airfoil moves through air, the airfoil is inclined against the airﬂow, producing a different ﬂow caused by the airfoil’s relationship to the oncoming air. Think of a hand being placed outside the car window at a high speed. If the hand is inclined in one direction or another, the hand will move upward or downward. This is caused by deﬂection, which in turn causes the air to turn about the object within the air stream. As a result of this change, the velocity about the object changes in both magnitude and direction, in turn resulting in a measurable velocity force and direction.

A Third Dimension

To this point the discussion has centered on the ﬂow across the upper and lower surfaces of an airfoil. While most of the lift is produced by these two dimensions, a third dimension, the tip of the airfoil also has an aerodynamic effect. The highpressure area on the bottom of an airfoil pushes around the tip to the low-pressure area on the top. [Figure 3-9] This action creates a rotating ﬂow called a tip vortex. The vortex ﬂows behind the airfoil creating a downwash that extends back to the trailing edge of the airfoil. This downwash results in an overall reduction in lift for the affected portion of the airfoil.

Figure 3-9. Tip vortex.

Manufacturers have developed different methods to counteract this action. Winglets can be added to the tip of an airfoil to reduce this ﬂow. The winglets act as a dam preventing the vortex from forming. Winglets can be on the top or bottom of the airfoil. Another method of countering the ﬂow is to taper the airfoil tip, reducing the pressure differential and smoothing the airﬂow around the tip.

Summary

Modern general aviation aircraft have what may be considered high performance characteristics. Therefore, it is increasingly necessary that pilots appreciate and understand the principles upon which the art of flying is based. For additional information on the principles discussed in this chapter, visit the National Aeronautics and Space Administration (NASA) Beginner’s Guide to Aerodynamics at http://www.grc.nasa. gov/WWW/K-12/airplane/index.html.

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