It's too bad SLC has given up on this topic - I think it's worth looking deeper into the importance of lift-induced drag in the strategy of gaining speed by stalling the wing. I have to admit that I found the idea to seem like voodoo the first time I heard about it, but I ran some numbers and I believe it's true. I also believe that induced drag is the critical factor in making this work.
Though my aero experience is informal, my understanding of drag on lifting surfaces was that it can be considered as the sum of three factors:
Skin friction, from shear forces acting parallel to the surface
Pressure or
Form drag, caused by incomplete pressure recovery on the suction surfaces (the back side), acting normal to the surface
and
Induced drag or more evocatively
lift-induced drag, caused by the span-wise circulation "tilting" the angle between the wing and the local flow and thus "tilting" the wing's lift vector backward from vertical. Crucially, this also manifests itself as a pressure differential (like form drag), which can make it somewhat academic to consider it separately to pressure drag.
Anyone with a degree in the matter can feel free to call me down from these claims, but I think they're representative and helpful in understanding the forces involved.
Authors (such as Katz) like to give the claim that unstalled wings (no flow separation) have "zero" form drag - muddle through d'Alembert's paradox to get the idea:
http://en.wikipedia.org/wiki/D%27Alembert%27s_paradox
When stall (turbulent boundary-layer separation) occurs, the form drag becomes nonzero and, in textbook airplane wings with long spans and low section lift (lift force per unit span), increase the drag. As SLC has reiterated, though, F1 wings are very different - very short spans with high section lift coefficients.
My thinking is that the short span is crucial, since the lift per unit span determines the lift-induced drag. The formula that demonstrates this is noncontroversial and pretty intelligible. You can reference it here:
http://en.wikipedia.org/wiki/Lift%E2%80%93induced_drag
I wrote an Excel spreadsheet to apply this formula (as well as the formula for lift), using some values for a 2010 rear wing, assuming a velocity of 80/s (almost 29kph), and a wing lift coefficient of 2.5. This is a ballpark guess based on examples from Katz and other sources – if anyone has intimate knowledge of a more representative number, I’m sure we’d all be thrilled to hear it. The other inputs you need are the dimensions of the wing:
Using these inputs, I ran into an issue with some missing terms:
The value "k" is an efficiency factor. It is the inverse of the Oswald efficiency factor "e" (
http://en.wikipedia.org/wiki/Oswald_efficiency_number)
It's a little more than one for most airplane wings, but for a wing with endplates it can be significantly lower - indicating a more efficient wing.
(
http://www-aa.stanford.edu/Reports/VKI_ ... r_Kroo.pdf)
I estimated k based on the height of the endplate and a simple equation from Katz. With this, the unknowns filled in and, with the lift equation, got a drag force and Lift-Induced Drag ratio for the wing:
As you can see, induced drag forces are significant. Note that I didn't include any factor to adjust for proximity to the ground or any other geometric influences besides the endplates. If anyone has a suggestion for a more representative value for e, I'm all ears.
For a stalled wing, I used a flat-plate equation and the geometric angle of attack to resolve the forces. Note that induced drag still applies because there is still a spanwise circulation and a trailing vortex sheet proportional to the vertical load.
As you can see, the back of my envelope shows a 24% drop in rear wing drag. Note that this is for a fully-stalled wing - more likely an F1 wing would have some attached flow and therefore a *partially* stalled wing, and so a smaller effect size.
I hope you're not all too worn down from intellectual struggle to weigh in on my numbers - as you can see, I rely on some assumptions about key values, and other people's empirical study. If I'm way off the plot I'd like to know, because my numbers show that induced drag is <b>critical</b> in making the stall work for us- not a minor factor.
I realize that I haven't included form and skin drags in my calculations of the unstalled wing. In support of this, I offer up this research, showing that the section L/D for a 40% chord single-flap wing at 2.5 Lift coefficient is over 20 (page 26):
http://aerade.cranfield.ac.uk/ara/1941/ ... rt-723.pdf
Section drag is a 2D effect and doesn't model the 3D spanwise flow that causes induced drag - only form and skin frictions. The short-chord F1 wing at a similar section load produces about 10 times as much drag - lift-induced drag dominates.
