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Looking at lift

A practical approach to teaching lift

Teaching flight students about lift, a force created that is equal to or greater than weight and acting in the opposite direction, usually involves the principles espoused by Daniel Bernoulli and Sir Isaac Newton. Bernoullian and Newtonian lift explain the "miracle of flight." Also fundamental to understanding lift is the somewhat complicated-looking Lift Equation, which explains the interrelationships of the factors affecting lift. However, because of its mathematical, esoteric appearance, it may be difficult to practically apply the equation to day-to-day teaching. The purpose of this article is to review the Lift Equation and discuss its practical use when teaching flight students about lift--for example, during slow flight operations.

For an airfoil, there is a relationship between lift and four interrelated factors: coefficient of lift, air density, wing surface area, and airspeed. The coefficient of lift, affected by angle of attack and airfoil shape, can be thought of as a measure of how efficiently the wing is transforming dynamic pressure (one-half times the air density times the square of airspeed) into lift. At a higher angle of attack, with the same wing surface area and dynamic pressure, a higher coefficient of lift is generated, up to a maximum value. For example, by increasing angle of attack from 3 degrees (typical of a cruising condition) to 12 degrees, the coefficient of lift increases by more than 100 percent. Beyond a critical angle of attack, however, the wing stalls.

When actual flight altitude and/or calculated density altitude increases, as associated with increasing ambient temperatures, air density (mass or weight of air per cubic foot) usually decreases. When flight altitude, temperature, barometric pressure, and humidity are relatively constant, air density also is fairly constant. When air density decreases--on a hot summer day, for example, and especially at a high-elevation airport--pilots usually are concerned about decreased lift. Likewise, because air density decreases with altitude, an airplane must fly with either a higher angle of attack or a higher airspeed to generate the same lift at higher altitudes, thus obeying the Lift Equation.

Wing surface area may be varied to some extent on airplanes equipped with area-increasing Fowler flaps. If large, area-increasing leading- and trailing-edge flaps are not employed, wing surface area remains constant.

Lift is also directly proportional to airspeed; in fact, lift is equal to the square of airspeed. For example, by doubling airspeed from 50 to 100 knots indicated airspeed (KIAS), lift quadruples. Both pitch attitude and power settings affect airspeed and, therefore, the amount of lift generated by an airfoil.

The above four factors operate simultaneously and in the presence of each other to affect lift. For lift to increase, one or more of the four factors on the right side of the equal sign must increase, and vice versa (Figure 1). The coefficient of lift, vis-à-vis angle of attack, and airspeed are under pilot control while air density and wing surface area, for all practical purposes may be considered as constants.

Slow flight implies maneuvering at the slowest airspeed at which the airplane is capable of maintaining controlled flight without indications of a stall; this is usually three to five knots greater than stalling speed. Flight at minimum controllable airspeed is emphasized; i.e., a speed at which any further increase in angle of attack, load factor, or reduction in power will cause an immediate stall. Students are expected to slow the airplane from cruising airspeed to minimum controllable airspeed and maintain the altitude, heading, airspeed, and bank angle specified by the appropriate Practical Test Standards. During slow-flight maneuvering, students learn the characteristics of flight at very slow airspeeds--namely, sloppy controls and ragged response to control inputs. This develops a "feel" for the airplane at very slow airspeeds that helps students avoid inadvertent stalls and to operate the airplane with precision.

While in slow flight, actual thrust no longer acts parallel and opposite to the flight path and drag. Actual thrust is inclined upwards. In this situation thrust has two components: one acting perpendicular or 90 degrees to the flight path in the direction of lift; while the other acts along the flight path. Wing loading (wing lift) is actually less at slow speeds than at cruise speeds because the vertical component of thrust helps support the airplane.

The transition from cruise flight to slow flight is characterized by gradual decreases in engine power with simultaneous increases in pitch attitude, necessary to maintain altitude. As airspeed continues to decrease to the slow minimum controllable airspeed, an angle of attack higher than that required at cruise speed is needed, followed by gradual increases in the engine power setting (compare Figures 1 and 2). Induced drag, resulting directly from the production of lift (lift vector is tilted rearward, a force opposite to the path of flight), dominates as angle of attack increases and airspeed decreases. Induced drag varies inversely as the square of airspeed. For example, reducing airspeed by half, from 100 KIAS to 50 KIAS, increases induced drag by four times. Additionally, the airplane may be operating in the region of reversed power requirement, the infamous "back side of the power/airspeed curve." This is so named because the curve changes direction and curls up on the low-speed side of the airspeed range.

It is the combination of slow airspeed and high angle of attack that makes the Lift Equation relevant when teaching slow flight maneuvering. For example, consider an airplane in level cruise flight at an indicated airspeed of 100 KIAS. Assume minimal controllable airspeed for this airplane is 50 KIAS. The student decreases the airspeed from 100 KIAS to 50 KIAS. To maintain lift, and thus altitude, the student is instructed to simultaneously pitch the nose up in order to attain a higher angle of attack (Figure 2). In teaching this maneuver it is important to point out that pitch attitude and angle of attack are related but not necessarily equal to each other. When decreasing one factor on the right side of the equal sign of the Lift Equation (airspeed), another factor on the same side of the equal sign must be increased proportionately (coefficient of lift via angle of attack) to maintain lift.

Applying the Lift Equation as explained above allows students a practical opportunity to manipulate some of the variables in the equation (airspeed and coefficient of lift). Having students manipulate and see the relationships between airspeed, angle of attack, and altitude as during slow flight is one of those "teachable moments" promoting two laws of learning: primacy and intensity. When taught the first time, this approach may result in an almost unshakable understanding of the Lift Equation and slow flight.

Michael J. Banner is a professor at the University of Florida in Gainesville. A CFII, he has more than 2,200 hours of flight time.

By Michael J. Banner

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