Pitching moment

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A graph showing coefficient of pitching moment with respect to angle of attack. The negative slope for positive α indicates stability in pitching.
A graph showing coefficient of pitching moment with respect to angle of attack. The negative slope for positive α indicates stability in pitching.

In aerodynamics, the pitching moment on an airfoil is a moment produced by a vertical force applied at a distance forward or aft from the aerodynamic center of the airfoil, causing the aircraft to pitch up or down[1].


The lift on an airfoil acts at a point called the center of pressure. However, as angle of attack changes on a cambered airfoil, there is movement of the center of pressure forward and aft. This makes analysis difficult when attempting to use the concept of the center of pressure. One of the remarkable properties of a cambered airfoil is that, even though the center of pressure moves forward and aft, if the lift is imagined to act at a point called the aerodynamic center the moment of the lift force changes in proportion to the square of the airspeed. If the moment is divided by the dynamic pressure, the area and chord of the airfoil, to compute a pitching moment coefficient, this coefficient changes only a little over the operating range of angle of attack of the airfoil. The combination of the concepts of the aerodynamic center and the pitching moment coefficient make it relatively simple to analyse some of the flight characteristics of an aircraft.


[edit] Coefficient

The pitching moment coefficient is important in the study of the longitudinal static stability of aircraft and missiles.

The pitching moment coefficient is defined as follows[1]

C_m=\frac{M}{qSc}

where M is the pitching moment in foot-pounds or newton-meters, q is the dynamic pressure, S is the planform area, and c is the length of the chord of the airfoil.

In the case of a symmetric airfoil, the lift force acts through one point for all angles of attack, and the center of pressure does not move as it does in a cambered airfoil. Consequently the pitching moment coefficient for a symmetric airfoil is zero.

The aerodynamic center of an airfoil is usually close to 25% of the chord behind the leading edge of the airfoil. When making tests on a model airfoil, such as in a wind-tunnel, if the force sensor is not aligned with the quarter-chord of the airfoil, but offset by a distance x, the pitching moment about that point, Mc / 4 is given by

M_{c/4} = M_\text{indicated} + \mathbf{x}\times (D_\text{indicated}, L_\text{indicated}).


[edit] References

  1. ^ Preston, Ray (2006). Main Wing Stability. Aerodynamics Text. Selkirk College. Retrieved on 2006-04-01.
  • Piercy N A V - Aerodynamics. English Universities Press. London. 1943. pp384-386.

[edit] See also