Question

The British Spitfire was a fighter aircraft used in WWII was probably the first production aircraft to use an elliptical wing. The elliptical wing theoretically minimizes the induced drag (e=1). The Mk IIA Spitfire has the following properties.

Wingspan (b)	32 ft, 6 in
Wing area (S)	231 ft2
Max speed	390 mph at 18,000 ft altitude
Loaded weight	7,400 lb
Airfoil	NACA 2412

Assume the wing planform area is simply the span*chord. What is the wing chord Reynolds number of the Spirfire at max altitude and 284.0 mph. You'll need to adjust for viscosity using Sutherland's law. Give your answer to zero decimal places.

Answer 1

Given:

wingspan (b) = 32ft, 6in = 32.5 ft

wingarea (S) = 231ft2

Therefore, the chord length (l) = S/b = 7.11 ft

Assume air temperature at 18000ft = -20oC = 253 K

From Sutherlands law,

viscosity = (C1 x T3/2)/(T+C2), where C1 and C2 are coeffecients.

For air, C1 and C2 are 1.458 x 10-6 kg/m-s-K1/2, and 110.4 K

Therefore, Viscosity at that altitude is 1.61 x 10-5 kg/m-s = 0.039 lb/ft-h

Assume density of air = 0.06 lb/ft3

And, Reynolds number = Re = (0.06*284*7.11)/0.039 = 3106