Advanced Aerodynamics: High-Speed Effects, Sweep and Load Factor
Advanced aerodynamics in the NZ ATPL tests high-speed compressibility, swept-wing behaviour, stability and control, and high-lift or drag-reduction devices. Questions usually ask you to predict the direction and magnitude of a change, not merely name a component.
High-speed and swept-wing effects
- As Mach number rises, local airflow over the upper surface accelerates. When it first reaches M 1.0 locally, the free-stream Mach is M_crit. A further rise causes shock-induced separation, buffet and possibly Mach tuck: the shock moves aft, producing a nose-down pitching moment.
- Sweep delays M_crit because mainly the velocity component normal to the leading edge drives the chordwise pressure distribution: M_eff ≈ M cos Λ. Sweep also reduces lift-curve slope, increases dihedral effect and can worsen Dutch roll, hence yaw dampers.
- Vortex generators re-energise the boundary layer and delay separation. Spoilers reduce lift and increase drag. Winglets cut induced drag by reducing tip vortices. Leading-edge devices raise CLmax and improve stall behaviour.
Load factor and drag
In a coordinated level turn, n = 1/cos φ. At 45° bank, n = 1.414 and stall speed rises by √1.414 = 1.189, about 19%. At 60°, n = 2 and stall speed rises by 41%. Induced drag is D_i = W²/(qπb²e); at constant weight and altitude, doubling TAS quadruples q and cuts induced drag to one quarter. Parasite drag, D_p = ½ρV²SC_D0, rises fourfold.
Worked example: W = 50,000 N, span 20 m, e = 0.80, sea-level ρ = 1.225 kg/m³, V = 100 m/s. q = ½ × 1.225 × 100² = 6,125 Pa. D_i = 50,000² / (6,125 × π × 20² × 0.80) = 406 N. At 200 m/s, q is four times larger, so D_i ≈ 102 N.
Traps
Do not confuse M_crit with M_MO. Do not assume sweep improves low-speed climb or field performance. Use TAS in drag equations but groundspeed in turn-radius or climb-gradient calculations. Check whether a question asks for total load factor or incremental load; they differ.