Flight Mechanics: aircraft performance, static and dynamic stability, and trim
Flight Mechanics tests whether you can turn the equations of motion into numbers: performance (climb, range, endurance, take-off and landing), static stability and trim, and the dynamic modes of an aircraft.
Core relations
- Steady level flight: L = W, T = D, so minimum thrust = W/(L/D)max. With a parabolic drag polar CD = CD0 + KCL², minimum drag occurs at CL = √(CD0/K) and (L/D)max = 1/(2√(CD0K)).
- Rate of climb = excess power/W = (T − D)V/W; absolute ceiling is where excess power vanishes.
- Jet Breguet range R = (V/TSFC)(L/D) ln(W0/W1); propeller range R = (η/c)(L/D) ln(W0/W1). Endurance peaks at minimum power required, range at minimum drag.
- Longitudinal static stability needs a negative pitching-moment slope; static margin = (x_np − x_cg)/c̄, positive for stability. Neutral point moves aft with a larger tail volume ratio.
- Dynamic modes: the short-period oscillation and the long-period phugoid (nearly constant angle of attack), plus the spiral and Dutch-roll lateral modes.
Worked example
An aircraft weighing 80 kN has (L/D)max = 16. Minimum thrust required in level flight = 80/16 = 5 kN. The aircraft flies this condition at the CL for minimum drag, not at minimum speed and not at (L/D) for minimum power.
Traps
- Confusing minimum-thrust speed with minimum-power speed; they differ by a factor of √3 in CL.
- Using true airspeed where knots of calibrated airspeed are given, or forgetting density change with altitude.
- Sign conventions in stability derivatives - the tail contribution to Cmα is destabilising when the tail lift slope is positive and the tail arm is neglected.
- Misidentifying the phugoid as the short-period mode in a "which mode has nearly constant α" question.