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Pitching moment changes pitch angle A graph showing coefficient of pitching moment with respect to angle of attack for an airplane.. In aerodynamics, the pitching moment on an airfoil is the moment (or torque) produced by the aerodynamic force with respect to the aerodynamic center on the airfoil .
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.
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 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 .
They then calculate the righting moment at this angle, which is determined using the equation: = Where RM is the righting moment, GZ is the righting arm and Δ is the displacement. Because the vessel displacement is constant, common practice is to simply graph the righting arm vs the angle of heel.
To provide a characteristic figure that can be compared among various wing shapes, the mean aerodynamic chord (abbreviated MAC) is used, although it is complex to calculate. The mean aerodynamic chord is used for calculating pitching moments. [4]
a=chord, b=thickness, thickness-to-chord ratio = b/a The F-104 wing has a very low thickness-to-chord ratio of 3.36%. In aeronautics, the thickness-to-chord ratio, sometimes simply chord ratio or thickness ratio, compares the maximum vertical thickness of a wing to its chord.