 Pitching moment

A pitching moment is a torque about an aircraft pitch axis, associated with rotation of the nose upward or downward. It requires a reference point, an axis and a sign convention; the numerical value is not an intrinsic property of a force alone.^[ref]

For a planar chord-line example, take $x$ positive aft along the airfoil chord, $z$ positive toward the upper surface, and a nose-up moment as positive. An upward chord-normal aerodynamic force $N$ applied at $x_f$ has moment about a chord-line reference $x_0$,Thus a stipulated upward $N=100\mathrm{N}$ acting $0.050\mathrm{m}$ behind the leading edge gives $M(0)=-5.0\mathrm{N}\mathrm{m}$, a nose-down moment. Moving the reference aft to $x_0=0.020\mathrm{m}$ gives $-3.0\mathrm{N}\mathrm{m}$ without changing the force.

For a distributed aerodynamic load, the same translation law givesDividing by the same $qSc$ yields the reference-point transformation of a pitching moment coefficient. Replacing $N$ by lift is an approximation unless the body and flow axes coincide; with a stated angle of attack, the full vector transformation accounts for drag as well.

Net force can vanish while a pitching moment remains. Two stipulated chord-normal forces, $+100\mathrm{N}$ at $x=0.20\mathrm{m}$ and $-100\mathrm{N}$ at $x=0$, have $N=0$ and $M=-20\mathrm{N}\mathrm{m}$. They form a couple; no finite location of a single zero resultant represents that load.

When $N\ne 0$ and a chord-line resultant is meaningful, its center of pressure satisfies $x_{\mathrm{cp}}=x_0-M(x_0)/N$. This zero-moment location differs from an aerodynamic center, where moment is approximately insensitive to angle of attack in a specified regime. The latter can have a nonzero moment, especially for a cambered airfoil.^[ref]