Principles of Flight

The PPL lesson covered lift, drag, the stall and the controls at low speed. Jet airliners fly fast and high, where the air behaves differently: compressibility, shock waves and Mach limits, swept wings, high-altitude buffet margins and the handling of an engine failure on a multi-engine aircraft.

1. Mach number and the speed of sound

• The speed of sound depends only on temperature: about 38.94 × √(absolute temperature in K) knots – 661 kt at 15 °C, 573 kt at −56.5 °C.
• Mach number = TAS ÷ local speed of sound. At FL370, M0.78 is about 447 kt TAS.
• Flight regimes: subsonic (below about M0.75), transonic (about M0.75–1.2, with mixed subsonic and supersonic flow), supersonic.

2. Critical Mach number and shock waves

• Air speeds up over the wing, so the flow reaches the speed of sound somewhere on the wing before the aircraft does. That flight Mach number is the critical Mach number (M_CRIT).
• Above it, a shock wave forms on the upper surface. Behind the shock the pressure jumps and the boundary layer can separate: wave drag rises sharply, buffet starts (Mach buffet) and the centre of pressure moves aft.
• Mach tuck: the aft-moving centre of pressure and the loss of downwash on the tail pitch the nose down at high Mach. Mach trim systems correct it automatically.
• The aircraft has a maximum operating Mach number, M_MO, (and V_MO lower down); the overspeed warning protects them.

3. Designing for high speed

• Wing sweep raises M_CRIT: only the airflow component at right angles to the leading edge counts, roughly speed × cos(sweep). A 25° sweep (typical for the A320 and 737) raises M_CRIT by about 10%.
• Thin wings and supercritical aerofoils (flat upper surface) delay and weaken the shock.
• Vortex generators re-energise the boundary layer and delay separation behind the shock.
• The area rule shapes the fuselage and wing so that the total cross-section changes smoothly, reducing wave drag.

4. Swept-wing behaviour

• Tip stall: the tips of a swept wing tend to stall first. Because they are behind the CG, losing their lift makes the nose pitch up deeper into the stall. Washout, slats and stall fences fight this.
• Dutch roll: a combined yawing and rolling oscillation – swept wings give strong lateral stability compared with directional stability. A yaw damper stops it.
• Swept wings have a lower lift slope, so they fly at higher angles of attack on approach – hence the large flap and slat systems.

5. The stall in airliners

• Stall warning: stick shaker, aural warning, buffet; on Airbus in normal law, the alpha protection and alpha floor (automatic TOGA thrust).
• Deep stall: on T-tail aircraft with rear engines, the turbulent wake of the stalled wing can blanket the tailplane and make recovery impossible – the reason for stick pushers on such types.
• Recovery (any jet): reduce the angle of attack (nose down) first, then level the wings, then adjust thrust – at high altitude you may need to lose several thousand feet. Do not try to "power out" of a stall with the nose up.

6. The high-altitude envelope

As altitude increases, the stall speed in Mach terms rises and the buffet Mach number falls – the buffet margin shrinks. Where the two meet is the aerodynamic ceiling, informally the "coffin corner". Airlines keep at least a 1.3 g buffet margin (protection against a 40° bank or a gust) when choosing the cruise level.

7. Load factor and the flight envelope

• The V-n diagram shows the allowed combinations of speed and load factor: for transport aircraft +2.5 g / −1 g clean, +2 g / 0 g with flaps.
• V_A (design manoeuvring speed): full control deflection is safe below it. Above it, abrupt full inputs can overstress the structure – and repeated full rudder reversals are not safe at any speed.
• The turbulence penetration speed (V_RA / M_RA) balances protection from stalling in a gust against protection from overstress.

8. Asymmetric thrust

• An engine failure on a multi-engine aircraft gives a yawing moment towards the dead engine, opposed with rudder.
• V_MCA: the minimum speed at which control can be kept with the critical engine inoperative, with no more than 5° of bank towards the live engine. Below V_MCA the rudder is not enough – reduce thrust on the live engine or lower the nose to regain speed.
• On propeller aircraft the critical engine is the one whose failure is hardest to control (the left engine when both turn clockwise, because of the P-factor). Most jets have no critical engine.
• "Dead foot, dead engine": the foot that is not pushing the rudder is on the side of the failed engine.

9. Stability terms

• Static stability: the initial tendency to return after a disturbance. Dynamic stability: whether the oscillations die out.
• Longitudinal modes: the short-period pitch oscillation (quick, well damped) and the phugoid (slow exchange of height and speed over a minute or more).
• Spiral instability: a slow divergence into a tightening descending turn if left alone – the cause of the graveyard spiral.

Flying it at Levant

Watch the speed tape in cruise: the gap between the minimum and maximum speeds is small at high level, so a wrong step climb or strong turbulence can bring you to buffet. Use the turbulence penetration speed, keep the yaw damper on, and practise the engine-out take-off – rudder first, then trim, at V2.

Check yourself

1. What is the critical Mach number? The flight Mach number at which the airflow first reaches the speed of sound somewhere on the aircraft.
2. What does a swept wing do to the critical Mach number? It raises it.
3. Why does a swept wing pitch up at the stall? The tips stall first, and they are behind the CG.
4. What is the first action to recover from a stall in a jet? Reduce the angle of attack (nose down).
5. What maximum bank does the definition of V_MCA allow? 5° towards the live engine.

Simulation training material based on standard ATPL theory. Always follow the aircraft's FCOM and approved procedures.