> Using your equation and assuming a 2mph wind, then:
> Vr=2/0.1763 = 11.34mph
> Why is this so much less than the previous estimates?
Because planning on only 2 mph wind is not generally a good ideas for
other reasons. The best example would be avoiding large tip-off angles
and subsequent low trajectory, which while stable, isn't necessarily a
good idea. But the question was stability, and the way that stability is
significantly affected by subsonic airspeed is when the assumptions made
for stability are violated. One of the primary assumptions in most
stability analysis (all except cardboard cutout, which is in error for
other reasons) is that the fins continue flying and do not stall. A
conservative stall angle for most airfoils is about 10 degrees.
To me the real issue is on the other end of the scale. For instance,
a 20 fps wind gets you 113 fps for a launch rod speed. This is
super-conservative, because although the fins may be stalled, the lift
doesn't actually go to 0, and the model is still driven in the right
direction to reduce the angle of attack. This violates the stability
analysis assumptions, so how conservative it is depends on factors
outside a simple stability analysis. For instance, how fast it recovers
depends greatly on the restoring forcem, the inertia, the shape of the
lift curve post-stall, and on and on. It probably defies closed-form
analysis. Egg lofters, superrocs, and other models with typically small
fins (despite huge stability margins), and high inertia are the models
of most concern.
It's my contention that short periods of instability right at the
end of the launch rod are more common than we think, because the effects
are masked by other things, and the model accelerates through it before
significant deviations occur.
The fact of the matter is that even the 2 mph is conservative when
talking about stability. An old issue of Model Rocketeer (late 60's)
described an R&D report wherein an analysis and experiments were done
with no launch rod at all. I repeated some of those myself, and was
surprised at how many times I got away with no ill stability effects. Of
course, it was those times it *did* go ape-doody from either stability
or extreme tip-of that make it a bad idea.