Wing downwash calculcation
Hello,
I know that this might be something so easy that most of you don't bother, but here's my question: I have a given wing layout and the circulation/lift distribution over this unswept, untwisted, tapered, iow: "normal" wing. Now I want to calculate the induced drag, which requires the induced angle of attack/induced velocity over the wing. Looking at the formulas available, e.g. in Theory of Wing Sections, I know that for each location y0 I have to evaluate the integral for alpha_induced (from which I can get w_induced, which I need for the induced drag): alpha_i (y) = 1/(4 pi V) * INTEGRAL (-b/2, +b/2) [ dGamma/dy' * dy'/(y - y') ] My calculation is a very easy one, I have only few "check points" along the span and it's all discrete, in fact I use a simple Excel spreadsheet. So I have a row with the spanwise location I'm looking at, and a row with the lift at each of those locations. Of course, I don't want to integrate, but rather I want to do a summation instead of an integration over those spanwise locations. But when I do that, I seem to have a problem with interpreting the above integration equation. 1) If I use dGamma/dy * dy, it just gives me dGamma... so I'm not sure how to interpret this. I know dy is the integration "width", but it cancels out the dy I have to use for the dGamma calculation. So I'm already confused. Do I just use dGamma (current to next spanwise point) here? 2) I know that for each y0, I have to have y go over the whole span and sum up the inner part of the integral. But when I come to the point where y0 = y, and since y0 - y is in the denominator, I get a division by zero, and that can not be right. Do I instead have to use some really large number here? How do I bypass this problem? So, on the one hand I'm trying to keep this simple with a spreadsheet and all, but on the other hand I don't seem to have the brain power to get this thing done. Does this question make sense? Any help? If someone has a code in some recognizable programming language that does this, I would appreciate it if this could be shared. Also, any sources that could shed more insight, even though I fell that I covered most textbooks... Thanks. |
RE: Wing downwash calculcation
assuming your wing is close to ideal, you can use
downwash angle ( radians ) = 2 x lift coefficient / ( pi * aspect ratio ) The induced angle of attack is half this value ( momentum theory ) Then, your induced drag = lift * sin ( induced angle ) |
RE: Wing downwash calculcation
ORIGINAL: Mattokun ..........I don't seem to have the brain power to get this thing done......... |
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