Module 8.4–8.5 — High-speed airflow and flight stability

Scope

8.4 High-speed airflow: speed of sound, subsonic/transonic/supersonic flight, Mach number, critical Mach number, compressibility buffet, shock waves, aerodynamic heating, area rule, engine-intake airflow, and sweepback. 8.5 Flight stability and dynamics (added as a separate sub-module by Regulation (EU) 2023/989): longitudinal, lateral and directional stability, active and passive.

8.4 High-speed airflow

Speed of sound and Mach number

• The speed of sound depends only on air temperature: a = √(γ R T) ≈ 20.05 √T m/s (T in kelvin) ≈ 38.95 √T kt.
• ISA sea level (15 °C): about 340 m/s / 661 kt. At the tropopause (−56.5 °C): about 295 m/s / 573 kt.
• Mach number M = TAS ÷ local speed of sound. At constant TAS, climbing into colder air increases Mach number.

Worked example — Mach number

At FL350 OAT is −54 °C (219 K). a ≈ 38.95 × √219 ≈ 38.95 × 14.8 ≈ 576 kt. With TAS 470 kt: M = 470 ÷ 576 ≈ 0.82.

Flight regimes

Regime	Approximate Mach range	Characteristics
Subsonic	below about 0.75	Air treated as nearly incompressible at low speed; no shock waves
Transonic	about 0.75 to 1.2	Mixed subsonic and supersonic local flow; shock waves form on the wing
Supersonic	1.2 to 5	Entire flow supersonic; bow and oblique shocks
Hypersonic	above 5	Strong heating, dissociation effects

Critical Mach number (M_crit)

Air accelerates over the upper surface, so local flow reaches M = 1 before the aircraft does. M_crit is the free-stream Mach number at which local flow first reaches Mach 1 somewhere on the aircraft. Above M_crit a normal shock wave forms on the upper surface.

Effects of exceeding M_crit:

• Shock-induced separation behind the shock → compressibility (Mach) buffet, rapid increase in drag (wave drag, drag divergence), loss of lift.
• Mach tuck: on swept wings the shock moves aft and the CP moves aft, plus loss of downwash at the tail → nose-down pitch. Countered by Mach trim.
• Reduced control-surface effectiveness and possible control buzz.
• At high altitude the low-speed (stall) buffet and the high-speed (Mach) buffet speeds converge — the "coffin corner".

Shock waves

Shock	Flow change across it
Normal shock (perpendicular to flow)	Supersonic → subsonic; static pressure, temperature and density increase; velocity decreases; total pressure lost
Oblique shock	Flow turned into itself (concave corner); remains supersonic but slower; pressure, temperature, density increase
Expansion wave (Prandtl–Meyer)	Flow turned away (convex corner); velocity increases, pressure, temperature and density decrease

Raising M_crit — design features

• Sweepback: only the velocity component normal to the leading edge governs compressibility. Effective Mach ≈ M × cos Λ (Λ = sweep angle), so a 30° sweep raises M_crit by roughly 15 %. Drawbacks: tip stall tendency (pitch-up), reduced C_L max, Dutch roll.
• Thin aerofoils (low thickness/chord) and supercritical aerofoils (flatter upper surface, aft camber) delay and weaken the shock.
• Vortex generators re-energise the boundary layer behind the shock and reduce separation.
• Area rule (Whitcomb): the total cross-sectional area distribution along the aircraft should change smoothly; fuselage is "waisted" where the wing joins to reduce transonic wave drag.

Aerodynamic heating

Air brought to rest at the surface (stagnation) is heated: temperature rise ≈ (TAS in kt ÷ 100)² °C at subsonic speeds — about 25 °C at 500 kt. The total air temperature (TAT) probe reads this ram rise; static air temperature (SAT) must be computed. At high supersonic speeds heating limits structural materials (aluminium alloys lose strength above about 120–150 °C).

Engine intakes for high-speed aircraft

• A gas turbine compressor needs subsonic air at its face (about M 0.4–0.5).
• Subsonic intakes are divergent (pitot type): air slows down and static pressure rises (ram recovery).
• Supersonic intakes use a convergent–divergent shape and/or centre-body (spike) or ramps to create a series of oblique shocks then a weak normal shock, slowing air efficiently. Variable geometry keeps the shock system positioned as Mach number changes.
• Intake airflow is affected by angle of attack, sideslip, ice and foreign objects; a disturbed intake flow can cause compressor stall/surge.

8.5 Flight stability and dynamics

Definitions

• Static stability: initial tendency after a disturbance — positive (returns), neutral (stays), negative (diverges).
• Dynamic stability: what happens over time — oscillations that damp out (positive), continue (neutral) or grow (negative). An aircraft needs positive static stability to have positive dynamic stability, but static stability alone does not guarantee it.
• Passive stability: provided by the airframe design itself (tailplane, dihedral, fin). Active stability: provided by systems — yaw dampers, Mach trim, fly-by-wire stability augmentation, autostabilisers.

Longitudinal stability (pitch, about the lateral axis)

• Provided mainly by the tailplane: a nose-up disturbance increases tailplane angle of attack, generating a restoring nose-down moment.
• CG position is the key factor: the CG must be ahead of the neutral point. The distance between them is the static margin.
  • Forward CG → more stable, heavier controls, higher stall speed, more trim drag.
  • Aft CG → less stable, lighter controls, risk of over-control; beyond the aft limit the aircraft becomes unstable.
• Long-period oscillation in pitch with speed and height exchange = phugoid; short-period pitch oscillation is normally heavily damped.

Lateral stability (roll, about the longitudinal axis)

Lateral stability is the tendency to return wings level after a sideslip produced by a wing drop. Contributors:

Feature	Effect
Dihedral	Lower wing meets the sideslip at higher angle of attack → more lift → rolls back
Sweepback	Lower (into-wind) wing has more effective span normal to flow → more lift — sweep gives a "dihedral effect"
High wing / pendulum effect	Keel surface and fuselage position give stabilising rolling moment
Anhedral	Destabilising; used on high-wing/swept aircraft to reduce excess lateral stability

Directional stability (yaw, about the normal axis)

• Provided by the fin and fuselage side area aft of the CG (weathercock effect); dorsal and ventral fins add to it.
• Sweepback also gives a directional stabilising effect (advancing wing has more drag).

Interaction of lateral and directional stability

Condition	Result
Strong lateral, weak directional stability	Dutch roll — combined yaw/roll oscillation; common on swept-wing aircraft; damped by a yaw damper
Strong directional, weak lateral stability	Spiral instability — gradually tightening descending spiral

Key fact: Swept-wing jets are prone to Dutch roll because sweepback adds strong lateral stability; the yaw damper (an active system) is the usual cure. Spiral instability is the opposite combination.