In a message dated 2/18/2005 9:11:49 AM Central Standard Time, [email protected] writes: Changing aspect ratio with a fixed span does not affect induced drag (if we ignore that the weight of the structure changes). Induced drag is proportional to the span loading squared (the formula below is obtained by manipulating the one above Cdi=Cl^2/(Pi*AR)):
D = (W/L)^2/(Pi*q), where q = rho*V^2/2 ******** Oleg, This does not seem to be dimensionally correct. In english units D is in lbs., V is in ft/sec, W/L is in lb/ft^2, and rho (density) is in slugs/ft^3 (gotta love those english density units!). Converting from density to weight (density * g ) gives the left side in lbs and the right side in lbs/ft^2. I believe the missing term is the average chord (Cavg^2). Absent that, I'll generally be in agreement with your comments with a few caveats: Assuming the following is correct (my derivation of the same manipulation you've done using the equations Lift = q * Cl * A, Drag = q * Cd * A, where A is the wing area): D = (Cavg*W/L)^2/(Pi*q), where Cavg is the wing average chord. A number of things trade off. As aspect ratio goes up, Cavg goes down while W/L goes up (both numerator effects). Meanwhile, V^2 goes up (denominator effect) as W/L goes up for a relatively constant Cl (assuming the plane maintains approximately the same AoA at min sink or max L/D, whichever you choose). So which term dominates is not completely clear without running through a bunch of numbers and making some estimates of weights, planforms, etc. And then there's profile and parasitic effects to confound the overall result. And Cl doesn't really stay completely constant as you go through these variations since Cdi is changing and that changes the total drag bucket which changes the Cl at which you hit the max L/D point. That's why I prefer to put the whole thing into a complete polar analysis, provide the inputs and then see where it goes. There are just a lot of things trading off against a lot of other things and that's the safest way to sort it out. It's handy to use engineering scaling equations now and again but when you look at the whole package, sometimes various scaling terms trade off against each other to provide a non-intuitive result. Better to do the full Monty on a PC. It only takes a few milliseconds. Based on polar analyses of 2M and up (and some DLG designs), I'm still comfortable with my comments. As always, I'm open to any improvements in my thinking on these subjects. However, in these cases (2M and up), the local Re does not get much below 60k so, for a well designed airfoil, Re effects are not the dominant term. However, for the case of the science fair project that started this, and assuming we're talking about a hand toss glider size (foam or balsa) with a flat plate wing, it's easy to get below 20,000. For a flat plate, the only real data (UIUC) ends at 100k and doesn't show much Re effect. But a whole bunch of things are likely to be happening below where the data ends. Unfortunately, a flat plate in X-Foil isn't real stable. Or if you taper the LE and TE, it's more stable but the results are sensitively dependent on how you did it. So there's not much hard Re guidance down in the range of this project. After looking at the conditions a little closer, I'd guess that Re effects are likely to be a significant factor for this case. - Dave R RCSE-List facilities provided by Model Airplane News. Send "subscribe" and "unsubscribe" requests to [EMAIL PROTECTED] Please note that subscribe and unsubscribe messages must be sent in text only format with MIME turned off. Email sent from web based email such as Hotmail and AOL are generally NOT in text format
