Wing Forces
Saturday, October 2nd, 2010The lift force of a wing vaies directly with the square of the velocity and inversely with the absolute temp.?
For a given test the lift force was 23 pounds. If the velocity is increased by 15% and the absolute temperature id decreased by 5%, what is the new lift force?
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Let F denote the lift force, v the velocity, and T the absolute temperature. Then the given statement is expressed by
F = kv² / T
where k is some constant.
Now, suppose F=23 for some velocity v0 and some temperature T0. Then
23 = k(v0)² / T0
If v1 = 1.15v0 (i.e., increase v0 by 15%) and T1 = 0.95T0 (i.e., decrease T0 by 5%), then
F = k(1.15v0)² / (0.95T0)
F = k(1.3255 v0²) / (0.95T0)
F = (1.3255/0.95) k (v0)² / T0
But k (v0)² / T0 = 23, so
F = (1.3255/0.95) 23 ≈ 32.02 lb