Question

A model of an air ship is to be studied. The prototype is envisaged to be 8 m long with a diameter of 750 mm and the model is to be 300 mm long. What should the diameter of the model be? What should the diameter velocity in a wind tunnel be to simulate actual conditions? If the drag on the full model is found to be x N, what would the drag on the prototype be?

Answer 1

For geometric similarity, all the dimensions between prototype and model must be scaled in the same ratio.

Geometric scaling = 8 / 0.3 = 0.75 / D_model

D_model = 0.028125 m = 28.125 mm

For simulating actual conditions, Reynolds number should be the same.

Re = V*D / neu

Since both model and prototype are tested in air, kinematic viscosity neu is same for both.

V_prototype * 0.75 = V_model * 0.028125

V_model  / V_prototype = 26.67

Drag force D = C_d * 1/2 * rho * V² * A

Since Area A ~ D², we get

D_model  / D_prototype = (V_model  / V_prototype )² * (D_model  / D_prototype )²

x/ D_prototype = 26.67² * (0.028125 / 0.75)²

D_prototype = x N