Slipping the Surly Bonds

In his poem "High Flight," John Gillespie Magee, Jr. writes: "Oh, I have slipped the surly bonds of earth and danced the skies on laughter-silvered wings." In this well-known work, the author describes what makes flight such a majestic means of transportation. But what sets flight apart from the gravity-bound methods of travel? Lift. Without lift, flight would not be possible. It is unfortunate that although understanding the aerodynamic force of lift is important for pilots at every experience level, many pilots really don't have a clear idea of how lift is created or of the effect that lift has on an aircraft's flight path.

Student pilots are taught that an aircraft in straight and level unaccelerated flight produces lift equal to the aircraft's weight. A correct assumption can be made that the aircraft must be able to create an amount of lift equal to its weight to be in unaccelerated equilibrium. One could further assume that for an aircraft to climb, the amount of lift must be greater than its weight, but that assumption is correct only while the flight path is being deflected. Excess lift, meaning more lift than weight, deflects or accelerates the flight path. The deflection will be in the direction of the net force. The net upward force is the lift minus the weight. Assuming the aircraft is right-side-up, the net force is upward, as is the deflection of the flight path. If the excess lift is maintained, the flight path will continue to deflect until the flight path curves back on itself, as in an aerobatic loop. The greater the amount of excess lift, the tighter the radius of curvature of the flight path.

So, if excess lift doesn't make an aircraft climb, what does? The answer is excess thrust. Imagine the extreme example of a jet fighter climbing straight up. The wings are almost unnecessary because the force that permits the climb is the thrust in excess of the aircraft's weight. The excess lift deflects the flight path and the excess thrust sustains the flight path. If a light trainer attains a high airspeed it could theoretically convert the speed into excess lift by increasing the angle of attack. The excess lift can be used to deflect the flight path to a rather impressive climb angle, but unfortunately the engine cannot produce the necessary thrust to sustain the climb angle. The airspeed will decrease until the aircraft stalls and the flight path is deflected downward. The downward deflection of the flight path is caused by deficit lift, which occurs when lift is less than weight.

Lift is produced by airfoils. An airfoil is defined as anything, such as an airplane's wings, that efficiently creates lift. Of course, with sufficient airflow just about any object can produce lift -- a person sticking a hand out of a moving car feels upward and downward pressure as the angle of the hand is changed, and a cow can "fly" in a tornado, as seen in a recent fictional movie -- but an airfoil is designed specifically to produce lift.

A flat plate, similar to a hand, will deflect the airflow of the relative wind downward due to the high pressure created on the underside of the plate. The relative wind is the airflow over an airfoil created by motion through an air mass. The relative wind is composed of individual streamlines, which are the various pathways taken by the flowing molecules that make up the air.

Sir Isaac Newton's first law of motion states that objects in motion will continue to move in a straight line at a constant velocity unless acted on by an outside force. The outside force acting on the streamline is created by the airfoil. Newton's third law of motion states that when two objects are in contact the force of one object on another is equal in magnitude and opposite in direction to the force of the second on the first. This means that because the airfoil is pushing downward on the streamlines, the streamlines are pushing upward on the airfoil. The upward force that is perpendicular to the wingspan and to the relative wind is defined as lift.

The lift that is created by a flat surface is known as "kite effect" because, as the name implies, it is what allows kites to fly. A pilot can use the kite effect to good advantage when performing soft-field takeoffs. Because the intent of this takeoff procedure is to transfer weight from the wheels to the wings as soon as possible, an initial high-pitch attitude is established. The high angle on the wings deflects the airflow downward at speeds much less than stall speed.

But anyone who has seen an airplane wing knows that it is curved, not flat. The upper-surface curve is called camber and its purpose is to increase the low-speed effectiveness of the airfoil. By curving the upper surface of the airfoil, the atmospheric pressure exerted on the upper-wing surface can be reduced. The reduced upper pressure supplements the increased lower pressure in deflecting the airflow downward. It may help to think of a streamline as a meandering river. The river is deflected away from high topography such as hills and mountains and is deflected toward areas of low elevation such as valleys. Likewise, the airflow above the airfoil is deflected downward toward the lower pressure on the upper-wing surface, and the airflow below the wing is deflected downward away from the higher pressure developed on the lower-wing surface.

The curved surface creates lower pressure due to a combination of two laws of physics: conservation of matter and conservation of energy. Conservation of matter, also known as the principle of continuity, states that matter cannot be created or destroyed. Similarly, energy can neither be created or destroyed, but can only be converted from one form to another.

The reason why the curved upper-wing surface increases the velocity of the relative wind and reduces the atmospheric pressure can be demonstrated in a venturi, a short tube with a constriction in the middle that is used to measure air pressure and velocity. In a venturi, as the cross-sectional area decreases, the velocity of the fluid must increase. Assuming incompressible flow, as happens in low-speed flight below 200 knots, the density of the fluid remains constant. If the mass flow is to remain constant, which it must because of continuity, the velocity of the fluid must increase as the cross-sectional area decreases. Mass flow remains constant because mass is not being created, destroyed, or stored in the venturi. Simply stated, what goes in, goes out. Not only is the mass flow into the venturi equal to the mass flow out, but the mass flow is also constant at all points along the venturi. Thus, as the cross-sectional area decreases, the velocity of the fluid must increase for mass flow to stay constant. Therefore, the speed of the streamlines over the top of the wing is faster than those below the wing.

To depart from the main theme, it should be stated that air is a fluid, given the definition of a fluid as anything that continually deforms or flows in response to an applied force. When a person stands on a solid, such as a ladder, the solid is compressed and pushes back with an equal force supporting the weight of the individual. But if a person tries to stand on air or water, both fluids, the weight is not supported and the person sinks as the fluid is continually deformed. From this example, it is clear why air is considered a fluid.

Now that the increase in velocity has been explained, it's time to look at the effect of velocity on pressure. Under the law of the conservation of energy, assuming frictionless flow, the total energy of the fluid remains constant as the velocity is increased. The total energy of the fluid is the sum of its kinetic and potential energies. The kinetic energy is attributed to the speed and mass of the fluid. The formula for kinetic energy is one-half of the mass multiplied by the squared velocity, or KE = m v². Because a fluid is made up of millions of molecules, its mass is expressed as a function of its density. The Greek letter rho is used to represent density. The kinetic energy of a fluid is measured by its dynamic pressure (q). The formula for dynamic pressure is similar to kinetic energy: q = Greek letter rho v². The dynamic pressure increases linearly with the density; that is, if the density of the fluid is doubled, so is the dynamic pressure. Also, the dynamic pressure increases with the square of the velocity.

In a fluid, the potential energy is a function of the static pressure (p). Air pressure may be compared to a compressed spring: the greater the compression, the higher the potential energy. Therefore, the greater the static pressure, the higher the potential energy.

As the incompressible fluid moves through the venturi, the increasing velocity increases the dynamic pressure (and also the kinetic energy). Due to the conservation of energy, any increase in kinetic energy must be accompanied by an equal decrease in potential energy, also known as static pressure. Thus, as the velocity of the fluid increases, the static pressure decreases.

An airfoil with a curved upper surface acts as a venturi. The speed of the airflow over the upper surface is increased, and the pressure is then decreased. The greater the curvature, or camber, the greater the acceleration and the lower the pressure. That is why low-speed airfoils require a greater amount of camber than do high-speed airfoils.

To approximate the quantity of lift that an airfoil can produce, the lift equation incorporates the factors that can affect lift production. The amount of lift produced (L) is equal to the dynamic pressure (q) multiplied by the coefficient of lift (Cl) and the wing area (S): L = q Cl S. The coefficient of lift is the ratio of the amount of dynamic pressure converted to lift pressure. For example, if an aircraft is flying at a speed and density resulting in a dynamic pressure of 100 pounds per square foot and is flying at an angle of attack resulting in a Cl of 0.5, then 50% of the dynamic pressure is being converted to lift pressure. That would be 50 pounds per square foot (100 lbs/ft² x 0.5). To determine how many pounds of lift a wing is producing, the lift pressure must be multiplied by the wing area (S). If the wing has 1,000 square feet of area, then 50,000 pounds of lift (50 lbs/ft² x 1,000 ft²) are being produced. Substituting the formula for dynamic pressure (q = Greek letter rho v²) into the lift equation, the final formula becomes L = Greek letter rho v² Cl S.

In a practical application of the lift equation, a pilot can adjust the lift being produced by changing either the speed of the airplane or the angle of attack. The angle of attack is the angle between the chord line and the relative wind. The chord line is the imaginary line connecting the farthest-forward point on the wing (the leading edge) and the farthest-aft point of the wing (the trailing edge). As the pilot increases the angle of attack, the coefficient of lift (Cl) increases until the wing stalls. This stalling angle of attack results in the highest coefficient of lift, or Clmax. When an airfoil stalls, the streamlines of the relative wind no longer follow the upper curvature, and the reduced upper pressure is lost.

Understanding lift production results in a quandary. It may be tempting to ask, "Is it the pressure difference between the upper and lower surfaces of the airfoil that produces the lift, or is it the deflection of the airflow that creates the lift?" The answer is "yes." Another way to ask this chicken-and-egg question is, " Does the pressure deflect the airflow, or does the deflected airflow create the pressure?" Again, the answer is "yes."

These enigmatic answers reflect the existence of two schools of thought on lift production. Aeronautical engineers conducting tests in wind tunnels may tend to measure the deflection of the streamlines to calculate the lift produced by an airfoil, and have been known to refer to pilots as "air benders" because of the observed streamline deflection while producing lift. Pilots, however, tend to think not of deflected airflow, but of pressure differences between the upper- and lower-wing surface. The important point is that the correct amount of lift can be determined from either method.

While it is true that a pilot can still be competent without a complete understanding of the concepts of aerodynamics, this understanding is one attribute that separates professional flight crew members from mere pilots.

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