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Originally Posted by GenKreton
The equation of similitude I derived does only work under the assumption that ratios in the dimensioning cannot change.
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When I first sat down with it I copied (w^2/w_m^2)^2 by accident (was doing multiple things at the same time.) I think this is what lead me to consider S/S_m.
Quote:
Originally Posted by GenKreton
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.
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I worked it into a spreadsheet using an NACA 2412, some generic GA-like wing-plan numbers, and some Cd numbers from XFOIL (a 2d aerodynamic performance estimation code), and it seemed to correlate pretty well.
Quote:
Originally Posted by GenKreton
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.
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I'm not (or no longer am) familiar with "secondary flows"... is this relating to the inherent difficulties of predicting 3-dimensional flows (of which bodies of rotation {like a trike body} are)? I think codes like XFOIL would help bring the numbers predicted by the "Drag Scaling Equation" closer to "the ball-park" without the need of windtunnel/model testing.
Quote:
Originally Posted by GenKreton
A quick example would be if you had an airplane airfoil that is 3x larger than you want for your car you do something like the following:
(1/3 scale factor) * (23.77/7.382 average density at sea level divided by 35,000 ft, scaled) * (60/600 grossly estimated traveling speeds) * (drag on airplane airfoil) = drag added to your car
Also if you only scale, preserving geometric relationships, then the coefficient of drag will not change on most of the sizes we would be discussing. Since you are considering scaling down size AND speed it is especially true. As you decrease speed the secondary layer flow decreases - the area where the fluid sheers off a surface, slowing down. This explanation is probably more than necessary I now realize  |
Yes, the boundary layer is affected by "scaling down size AND speed"; but I feel that the "Drag scaling equation" doesn't properly account for the laminar/turbulent transition location which is generally determined by Re, maximum body thickness, and the length where maximum body thickness occurs. Although, your assumption that this 'transition location (and thus drag) is negligible considering the Re range being considered' is probably sufficient for 'napkin' estimates.