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Pitching moment coefficient is fundamental to the definition of aerodynamic center of an airfoil. The aerodynamic center is defined to be the point on the chord line of the airfoil at which the pitching moment coefficient does not vary with angle of attack, [ 1 ] : Section 5.10 or at least does not vary significantly over the operating range of ...
The aerodynamic center is the point at which the pitching moment coefficient for the airfoil does not vary with lift coefficient (i.e. angle of attack), making analysis simpler. [ 1 ] d C m d C L = 0 {\displaystyle {dC_{m} \over dC_{L}}=0} where C L {\displaystyle C_{L}} is the aircraft lift coefficient .
This is an example of a common shorthand notation for stability derivatives. The "M" indicates it is a measure of pitching moment changes. The indicates the changes are in response to changes in angle of attack. This stability derivative is pronounced "see-em-alpha".
The moment equation is the time derivative of the angular momentum: = where M is the pitching moment, and B is the moment of inertia about the pitch axis. Let: =, the pitch rate. The equations of motion, with all forces and moments referred to wind axes are, therefore:
This leverage is a product of moment arm from the center of gravity and surface area. Correctly balanced in this way, the partial derivative of pitching moment with respect to changes in angle of attack will be negative: a momentary pitch up to a larger angle of attack makes the resultant pitching moment tend to pitch the aircraft back down.
In February 1976, work commenced to automate the methods contained in the USAF Stability and Control DATCOM, specifically those contained in sections 4, 5, 6 and 7.The work was performed by the McDonnell Douglas Corporation under contract with the United States Air Force in conjunction with engineers at the Air Force Flight Dynamics Laboratory in Wright-Patterson Air Force Base.
The coefficients used for moment are similar to coefficients of lift, drag, and thrust, and are likewise dimensionless; however, these must include a characteristic length, in addition to the area; the span is used for rolling or yawing moment, and the chord is used for pitching moment
Roll moment is a moment, which is a product of a force and a distance, that tends to cause a vehicle to roll, that is to rotate about its longitudinal axis. [1]