High-speed flight

081 Principles of FlightChapter 6

Speed of sound & Mach

Formula — Local speed of sound (LSS)

a = √(γ × R × T)
LSS ≈ 38.95 × √T(K)
LSS estimate ≈ 644 ÷ (1.2 × TAT°C)
Mach = TAS / LSS

Key fact

Below tropopause: ECTM relationship. Above tropopause: temperature constant → LSS/TAS/Mach constant. At constant FL, temperature change affects TAS only — Mach unchanged. Climbing at constant TAS: may exceed MMO. Descending at constant Mach: may exceed VMO.

Flight regimes

Regime	Characteristics
Subsonic	Up to MCRIT — no shock waves
Transonic	MCRIT to ~M1.3; supersonic + subsonic regions; CD increases then decreases; CLMAX ↓, 1g stall speed ↑
Supersonic	M1.3–M5; CP further aft; rectangular pressure distribution

Key fact

MCRIT: first local Mach 1 on upper wing surface (usually root, max thickness). No shock waves below MCRIT. Above MCRIT: buffeting, pitch-down tendency, stick force stability decreases. MCRIT ↑ with mass decrease (lower AoA), sweepback, thinner wing. MCRIT ↓ with mass increase, flap/control deflection down, larger camber.

Shock waves

Key fact

Normal shock: supersonic→subsonic, higher compression, greatest total pressure loss. Oblique shock: velocity decreases, flow remains supersonic. Expansion wave: velocity increases to supersonic. First shock evidence: upper surface, wing root, near max thickness. Shock perpendicular to local airflow. CP moves aft to 20–50% chord in transonic flight.

Key fact

MCDR (drag divergence): greater than MCRIT; CD rises rapidly (wave drag). Shock stall: boundary layer separation at shock — can occur at lowest AoA of high-speed stalls.

Tuck-under & Mach trim

Key fact

Tuck-under: nose-down pitching entering transonic range (only above MCRIT) — reduction in downwash at stabilizer. Mach trim: compensates for decreased stick force stability (static longitudinal stability actually increases). Adjusted via stabilizer incidence (not elevator trim tab) or trim tank. Mach trim failure → reduce Mach number.

Buffet & coffin corner

Key fact

High-speed buffet: shock wave + separation interaction. Buffet-free range decreases with: altitude ↑, mass ↑, load factor ↑ (pull-up). Increases in push manoeuvre (lower AoA). 1.3g margin: manoeuvre at 1.3g causes buffet onset — limits max cruise altitude. Coffin corner: stall speed = critical Mach — too slow and too fast simultaneously.

Exam trap

VA less significant at high cruise altitudes — buffet onset becomes limiting before VA. Low-speed buffet and Mach buffet define the corner of the flight envelope.

Design for high speed

Key fact

Sweepback: MCRIT ↑ (~1.154× theoretically, ~half practically vs straight wing); slower transonic drag rise; higher CD in cruise; HLDs less effective. Thin wings: delay shock, ↑ MCRIT. Area ruling: smooth cross-section (“coke bottle”) reduces wave drag. Supercritical aerofoil: larger nose radius, flatter upper surface — minimal shock just above MCRIT. Vortex generators: reduce wave drag and shock-induced separation.

Control effectiveness

Key fact

Aileron deflection less effective transonic — only partly affects pressure distribution. High-frequency buzz from hinge moment fluctuations. Vertical fin can stall at excessive fin AoA. Stabilizer may stall before wing — icing on tailplane can induce unrecoverable pitch-down dive.

Turns, climbs & glides (forces summary)

Formula — Load factor in turn

n = 1 / cos bank
L = W / cos bank
Turn radius r = TAS² / (g × tan bank)
Rate of turn ≈ (g × tan bank) / V

Key fact

Level turn: thrust = drag; horizontal component of lift = centripetal force; AoA must increase. 45° bank: centripetal force = weight. Glide: max range at VMD (L/D max); headwind ↓ range, tailwind ↑; max endurance (glide time) at VMP, reduced mass ↑ duration. Climb: load factor below 1 (L = W cos γ).