Pitching moment

In

pitch

axis of a moving body.

The

chord

of the airfoil, the result is known as the pitching moment coefficient. This coefficient changes only a little over the operating range of angle of attack of the airfoil.

The moment coefficient for a whole airplane is not the same as that of its wing. The figure on the right shows the variation of moment with AoA for a stable airplane. The negative slope for positive α indicates stability in pitch. The combination of the two concepts of aerodynamic center and pitching moment coefficient make it relatively simple to analyse some of the flight characteristics of an aircraft.^[1]^{: Section 5.10}

Measurement

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 the quarter-chord point, $M_{c/4}$ is given by

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

where the indicated values of D and L are the drag and lift on the model, as measured by the force sensor.

Coefficient

The pitching moment coefficient is important in the study of the

longitudinal static stability

of aircraft and missiles.

The pitching moment coefficient $C_{m}$ is defined as follows^[1]^{: Section 5.4}

C_{m}={\frac {M}{qSc}}

where M is the pitching moment, q is the

chord

of the airfoil.

C_{m}

is a dimensionless coefficient so consistent units must be used for M, q, S and c.

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 angle of attack 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 about this point for a symmetric airfoil is zero.

The pitching moment is, by convention, considered to be positive when it acts to pitch the airfoil in the nose-up direction. Conventional cambered airfoils supported at the aerodynamic center pitch nose-down so the pitching moment coefficient of these airfoils is negative.^[2]