Ah, but does anybody really KNOW anything, for sure? I mean, there are relative truths, for any given context, but are there really any absolute Truths, with a capital "T"?
"Look out Mav, he's going metaphysical!", says Goose.
Hm. Let's try again.
Everybody knows that the stall speed at a given weight w which is less than the maximum gross weight W is given by the following formula:
Vs(w) = sqrt(w/W) x Vs(W)
But who can derive it from first principles? Who, dare we ask?
Well, it's "Hurts To Pee" to the rescue!
We know from the lift equation that lift is proportional to the coefficient of lift times velocity squared. There's a constant in there (density of air, fudge factor to make the units work out) so we thus know that:
L = k Cl V^^2 and ell = k Cl v^^2
where, at stall at max gross, L is the lift and V is the velocity, and for stall at less than max gross, ell is the lift and v is the velocity.
But wait. A wing always stalls at the same angle of attack - Cl (coefficient of lift) is the same in both of the above. So if we make a big K:
K = kCl
we can substitute and get
L = K V^^2 and ell = K v^^2
But in level flight, we know lift equals weight. Therefore we know that L = W and ell = w, where W is the max gross weight and w is the current weight. Substitute:
W = K V^^2 and w = K v^^2
Rearrange the left-hand equation, solving for K:
K = W / V^^2
substitute K into right-hand equation:
w = W / V^^2 x v^^2
Isolate v^^2 on the right side:
V^^2 x w/W = v^^2
take the square root of both sides:
v = sqrt(w/W) V
and there you go.
But what would I know. I'm just an ignorant idiot that doesn't "know" anything, according to a sarcastic taxi-driving *sshole like you
