Regarding Stall Speed at high altitude: The formula for stall speed is given by Vs (ktas) = Sqrt (295 L/qSClmax) where q is the density ratio. However since the speed is given in Vs (ktas), this part of the formula can be rewritten as Vs(ktas) = (SMOE)*(EAS) where SMOE = 1/sqrt(density ratio). When both equations are simplified the density ratios at altitude cancel out leaving only EAS. Position error also cancel each other. Refer to Classnotes for Basic Aerodynamics by Norbert R. Kluga 1991 page 124 from Embry-Riddle Aeronautical University and Flight Technique Analysis for Professional Pilots by Les Kumpula page 30 also from Embry-Riddle Aeronautical University.
Stall.....a viscous phenomenon.
Just to be pedantic, the above is
essentially wrong because you've made an incompressible flow assumption to ascertain the second flow equation (and forgotten about the compressibility correction), which will obviously not show a Mach number depedence!
Its fine for M<=0.3.
A better idea of the aerofoil C_p valid up to M~=0.7 would be to apply a Prandtl Glauert correction, whereupon
C_p = C_p(INC)/sqrt(1-M^2)
where
C_p(INC) is the incompressible flow pressure coefficient.
Above that, there are other pressure coefficient corrections, such as those given by von Karman & Tsien.
Bear in mind that the aerofoil lift is merely the integral of the pressure over the geometry.
The Mach number dependence in C_L(max) is obviously related to the, initially, advantageous presence of shock waves in the flow, which increase C_L(max) until the point of drag divergence, whereupon shock induced flow seperation means you suffer a collapse of lift.
So true stall speed is obviously a function of altitude i.e., density, (or alternatively remember that CAS is EAS plus a compressibility correction), but perhaps less/more intuitively (depending on how your mind works), a function of the similarity parameters, Mach Number and Reynolds Number.
Reynolds number is essentially a ratio expressing the relative importance of the inertial and viscous forces of a flow.
As Reynolds number tends to infinity, the viscous effects, become less and less important to consider.
Whereupon, one may conclude that stall being a viscous phenomenon, will display some dependence on Reynolds number. A good illustration of this dependence can be found in
Fundamentals of Flight by Richard Shevell, Pg 248. As it suggests, in flight tests, Reynolds numbers are often far higher than those found in tunnel testing, whereupon the demonstrated C_L(max)'s are somewhat higher.
The simple expanation for this is that the inertial effects in the flow are better able to combat the adverse pressure gradient and further delay separation at a given constant angle of attack.
For those interested,
Fundamentals of Flight by Richard Shevell also gives some graphs of the compressibility correction factor, F, on Pg 106/107 used in determining EAS's.
My $0.02
