who discovered it in 1852. It explains why you slice (or hook) your golf ball or why a good pitcher can throw a curve. The principles of the Magnus effect are even utilized in space as a spinning satellite can maintain its orbit longer due to the Magnus force, minimizing orbital decay.
AERODYNAMIC PITCHING MOMENTS
Consider the pressure distribution about a symmetrical airfoil at zero angle of attack (AOA) (Figure 3.23a). The large arrows show the sum of the low pressures on the top and bottom of the airfoil. They are at the center of pressure (CP) of their respective surfaces. The CP on the top of the airfoil and the CP on the bottom are located at the same point on the chord line. The large arrows indicate that the entire pressure on the top and bottom surfaces is acting at the CP. Because these two forces are equal and opposite in direction, no net lift is generated. Note also that the lines of action of these forces coincide, so there is no unbalance of moments about any point on the airfoil. Figure 3.23b shows the pressure distribution about a symmetrical airfoil at a positive angle of attack (AOA). There is now an imbalance in the upper surface and lower surface lift vectors, and positive lift is being developed. However, the two lift vectors still have the same line of action, passing through the CP. There can be no moment developed about the CP. We can conclude that symmetrical airfoils do not generate pitching moments at any AOA. It is also true that the CP does not move with a change in AOA for a symmetric airfoil.
Now consider a cambered airfoil operating at an AOA where it is developing no net lift (Figure 3.24a). Upper surface lift and lower surface lift are numerically equal, but their lines of action do not coincide. A nose‐down pitching moment develops from this situation. When the cambered airfoil develops positive lift (Figure 3.24b), the nose‐down pitching moment still exists. By reversing the camber, it is possible to create an airfoil that has a nose‐up pitching moment. Delta‐wing aircraft have a reversed camber trailing edge to control the pitching moments.
Figure 3.23 Pitching moments on a symmetrical airfoil (a) at zero AOA and (b) at positive AOA.
Figure 3.24 Pitching moments on a cambered airfoil: (a) zero lift, (b) developing lift.
Figure 3.25 Flaps extended pitching moments.
Source: U.S. Department of Transportation Federal Aviation Administration (2016a).
Aerodynamic pitching moments also occur when the pilot changes the camber of an airfoil during flight, as retracting or deploying flaps. When the trailing edge flaps are moved, the chord line changes resulting in a new AOA. When the AOA moves a pitching moment may develop, with initial flap settings the airplane may initially “balloon” due to the immediate increase in lift, then a general nose‐down pitching moment will develop. As shown in Figure 3.25, care must be taken during large power changes and significant trim settings (go‐around/missed approach) as increased pitching moments may be experienced. In some aircraft, a significant nose‐up pitching moment may occur with full deployment of trailing edge flaps as downwash over the horizontal stabilizer increases tail‐down force (airplane nose goes up).
AERODYNAMIC CENTER
For cambered airfoils, the CP moves along the chord line when the AOA changes. As the AOA increases, the CP moves forward and vice versa. This movement makes calculations involving stability and stress analysis very difficult from an engineering perspective. There is a point on an airfoil where the pitching moment is a constant with changing AOA, if the velocity is constant. This point is called the aerodynamic center (AC).
The AC, unlike the CP, does not move with changes in AOA. If we consider the lift and drag forces as acting at the AC, the calculations will be greatly simplified. The location of the AC varies slightly, depending on airfoil shape. Subsonically, it is between 23 and 27% of the chord back from the leading edge. Supersonically, the AC shifts to the 50% chord.
In summary, the pitching moment at the AC does not change when the angle of attack changes (at constant velocity) and all changes in lift effectively occur at the AC. As an airfoil experiences greater velocity, its AC commonly moves toward the trailing edge, with the AC near 25% chord subsonically and at 50% supersonically. A more detailed discussion on the aerodynamic center of a wing, and its relation to longitudinal stability, is found in Chapter 12.
ACCIDENT BRIEF: AIR MIDWEST FLIGHT 5481
On 8 January 2003, Air Midwest Flight 5481 experienced a loss of pitch control on takeoff in Charlotte, NC and crashed, killing 2 crew members and 19 passengers. Several factors that led to this accident were topics addressed within this chapter and deserve application to the principles of aerodynamics and safety of flight. Due to the length of the NTSB accident report (NTSB/AAR‐04/01), only the factors that directly relate to this chapter will be discussed, and it is recommended that the reader review the entire accident report.
The Beech 1900D has a typical horizontal stabilizer with an elevator hinged to the back. Normal travel of the elevator allows for up to 20° airplane nose up (ANU) and up to 14° airplane nose down (AND). As we discussed in Section 3.1.1.2, the elevator allows the pilot to pitch the aircraft around the lateral axis. Figure 3.26 shows the Beech 1900D pitch control system, note the turnbuckles, aft bellcrank, and their connection to the elevator.
Due to improper maintenance on the turnbuckles within the pitch control system, the elevator was rigged improperly – (simplified for this discussion) not allowing for full elevator authority – and thus restricted downward elevator travel. The actual elevator position was restricted to 7° AND. In addition to the maintenance errors, a complicating factor was the weight and balance of the aircraft itself. Actual weight and balance calculations of the true weights (versus average weights) and position of all passengers and cargo proved the aircraft was also loaded overweight and with an aft center of gravity. As will be discussed later in the textbook the position of the center of gravity in accordance with the manufacturer’s guidelines is imperative to aircraft safety. The aft center of gravity in the accident aircraft exacerbated the maintenance error.
Figure 3.26 Beech 1900D pitch control system.
Source: Courtesy: National Transportation Safety Board.
