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How to Calculate Pitch Moment

The pilot is guiding the plane steadily when he positions the wing of the plane back. The moment when a plane suddenly changes its pitch, up or down, is the pitch moment. As long as the plane is flying in a steady ascent or descent, there is no pitch moment; when the ascent or descent of the plane becomes constant, ascending or descending at a steady pace, the pitch moment ends. The book "Aerodynamics of the Airplane" describes pitch moment as the sum of a force-couple independent of lift (zero moment) and a term (or calculation) proportional to the lift.

Things You'll Need

Calculator

Instructions

- 1
  Calculate the torque that acts on the aerodynamic center of the aircraft created by the wing at the pitch moment. Multiply the lift of the wing at the pitch moment by the distance from the aerodynamic center of the aircraft and the point on the wing where the pitch moment is created. Add these two calculations together.
- 2
  Calculate the distance from the location in the wing where the pitch moment is created to the tail of the plane. Multiply that distance by the wing reference area (the area of the trapezoidal portion of the wing that protrudes from the plane into the center line of the plane). Divide that number by the reference chord multiplied by the wing reference area. Multiply that product by the tail lift coefficient. Add to this number the calculation of the torque of the tail at the pitch moment. Subtract the sum of this calculation from the figure obtained in Step 1.
- 3
  Reduce the calculation of the torque of the tail (derived in Step 2) to account for the neutralizing effect of the T-tail, if the airplane has one. The T-tail reduces the velocity and torque of the pitch moment and increases the number of the final calculation in Step 2, resulting in an overall less sharp pitch moment. (A T-tail is a horizontal stabilizing tail that is mounted to the vertical stabilizer. The piece, when mounted, resembles a "T.") The precise formulas for interpolating the effect of the T-tail as well as related detailed components of the tail and fuselage can be derived from Standford University's Aeronautics Longitudinal Static Stability page.
- 4
  Determine the effect the fuselage contribution will have on the pitching moment, which is affected by the angle of attack. Stanford University professor of aeronautics Ilan Kroo states that the destabilizing effect of the fuselage depends on the fuselage length, the fuselage width, the wing sweep, the aspect ratio and location on the fuselage. Add or subtract the effects of the fuselage on the pitch moment using empirical or computer formulas designed for each specific aspect of the fuselage and plane stability.

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