Quote:
Originally Posted by Fuzzy
I might have been familiar with it, but forgotten about it in non-use. But looking at it now I would suggest the following changes:
Drag = (S/S_m)*(rho/rho_m)*((V/Vm)^2)*Drag_m
Where S = area (cross-sectional or planform depending on body), rho = density, V = velocity, Drag = resistive force. However this is only true if Cdo == Cdo_m, which is not entirely true. A better example would be:
Drag = (S/S_m)*(rho/rho_m)*((V/Vm)^2)*(Cdo/Cdo_m)*Drag_m
Cdo and Cdo_m would need to be collected either from wind tunnel testing or CFD, and they definitely are a function of Re.
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The equation of similitude I derived does only work under the assumption that ratios in the dimensioning cannot change. If you halve the length, you halve everything including radial dimensions. The reason for this assumption is if length and width, for example, change disproportionately then the coefficient of drag also changes, as you stated, and it introduces complexities. I'm not even sure Cdo/Cdo_m is valid without sitting down with some paper to check it. The world of secondary flow and eddies makes their modeling relationship nonlinear rendering that a looser approximation at best, or wrong at worst. The goal of the drag modeling equation was eliminating the need for full scale testing, and you are correct, if we modify it by changing geometry disproportionately then we do need to make an actual scale model for testing.