A vertical stabilizing fin on a land-speed-record car is L=1.65 m long and H=0.7

Question

A vertical stabilizing fin on a land-speed-record car is L=1.65 m long and H=0.785 m tall. The vehicle is to be driven at the Bonneville Salt Flats in Utah where the elevation is 1340 m and the summer temperature reaches 50 degrees C. The car's speed is 560 km/hr (155.56 m/s).

(a) Evaluate the length Reynold's Number of the fin.

(b) Estimate the location of transition from laminar to turbulent flow in the boundary layer.

(c) Calculate the power required to overcome skin friction drag on the fin.

Explanation / Answer

a) Re is proportional to airspeed and wing chord Re = V x I / v Where: V = Relative speed (m/sec) I = typical "length" of a solid body (M) v = cinematic viscosity of the air (sec/m2) The cinematic viscosity is to a certain extent dependent on the density of the air, but for our aircraft flying below 12,000 ft., it can be assumed constant (equivalent to 15 x 106 sec/m2 in metric) Re = (155.56 x 1.65) / (15 x 10-6) = 17111600 vmph b) Reynolds found that the transition occurred between Re = 2000 and 13000, depending on the smoothness of the entry conditions. When extreme care is taken, the transition can even happen with Re as high as 40000. On the other hand, Re = 2000 appears to be about the lowest value obtained at a rough entrance

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