Stalling — Page 179, Lesson 214

Let's pick up with the effect of Mach number on stall speed. This is where compressibility starts to intrude on the stalling picture. As an aircraft flies faster, the streamline pattern around the wing changes. Up to about four tenths the speed of sound — that's Mach 0.4 — these changes are negligible. Faster than about M 0.4, they start to become significant. This phenomenon is known as compressibility, and it's covered fully in Chapter 13. Here's the physical mechanism. Pressure waves, generated by the passage of a wing through the air, propagate ahead of the wing at the speed of sound. These pressure waves upwash air ahead of the wing towards the lower pressure on the top surface. At low speed, the streamline pattern is affected far ahead of the wing, and the air has a certain distance in which to upwash. As speed increases, the wing gets closer to its leading pressure wave, and the streamline pattern is affected a shorter distance ahead. So the air must approach the wing at a steeper angle. This change in the streamline pattern accentuates the adverse pressure gradient near the leading edge, and flow separation occurs at a reduced angle of attack. Above M 0.4, CLMAX decreases, as shown in Figure 7.29. Now let's tie this back to the 1g stall speed formula: VS1g = √(L / (½ ρ CLMAX S)) If CLMAX decreases, VS1g will increase. That's the direct consequence. Now, why does Mach number increase with altitude at constant EAS? To maintain a constant EAS as altitude increases, TAS is increased. Also, outside air temperature decreases with increasing altitude, causing the local speed of sound to decrease. Mach number is proportional to TAS and inversely proportional to the local speed of sound, a: M = TAS / a Therefore, at a constant EAS, Mach number will increase as altitude increases. Figure 7.30 shows the variation of stalling speed with altitude at constant load factor, n. Such a curve is called the stalling boundary for the given load factor, in which altitude is plotted against equivalent airspeed. At this load factor — 1g — the aircraft cannot fly at speeds to the left of this boundary. Over the lower range of altitude, stall speed does not vary with altitude. That's because at these low altitudes, the Mach number at VS is less than M 0.4 — too low for compressibility effects to be present. Eventually, at approximately 30,000 feet, the Mach number at VS has increased with altitude to such an extent that these effects are important, and the rise in stalling speed with altitude becomes apparent. Using the example aeroplane from earlier, the VS1g of 150 knots is equal to M 0.4 at approximately 29,000 feet using ISA values. So the summary is: as altitude increases, stall speed is initially constant, then increases, due to compressibility.