Originally Posted by Mad (Flt) Scientist
Quote:
Originally Posted by Pugilistic Animus
(p-pinfinity)/(1/2rhoV^2)/Cpi=1/[1-M^2]^.5+ [M^2/1+{1-M^2}^.5]*(cpi/2)
or maybe just 1/[1-M^2]^.5 (end of PA quote)
Actually, no, mot just the "standard" Mach effect. Stall AOA ends up being a powerful function of freestream Mach, due to transonic effects in the (very accelerated) boundary layer. As a result the freestream Mach is not the Mach directly having the effect.
What you're alluding to is fine at more 'normal' AOAs.
To illustrate this further, I would redraw the diagram as shown here:
cL_AoA_M003.jpg
The (sub-critical) Mach effect cited by PA changes the lift-curve slope below cL-max. For swept wings, one could perhaps use the component of Mach normal to the wing 1/4-chord line in these equations?
With regard to stall AoA, for Mach between M1 (M1 in my diagram is low, say M=0,15) and M2 the flow is sub-critical (or low super-critical without causing shockwaves), and cL-max changes little, if at all. Above M2 the flow at high AoA is sufficiently super-critical to cause (local) shock-induced separation, and then cL-max reduces rapidly with increasing Mach.
Vs1g speeds published for one modern wide-body would seem to indicate M2=0,275 for that airplane in clean configuration.
regards,
HN39
EDIT:: For an experimental illustration of these aspects, see:
NACA Technical Note No. 1390