HumanPoweredDesigner
Well-Known Member
I once alluded to this before, but now I'll through it out there to get some feedback, (since I no longer plan to use this design for other reasons):
Di = Cl^2*(a bunch of other stuff), says the books and years of testing.
I conjecture that Cl = Cl top + Cl bottom, and that Di actually is (Clt^2 + Clb^2)*(a bunch of other stuff), since the pressure on bottom can't possibly know what is going on with the pressure on top. I suspect that Di = Cl^2 because airflow is proportional to the square (I think I remember that right) of the pressure gradient with respect to spanwise distance, and induced drag comes from the spanwise flow of air. And we know how to minimize squares: try to get the same lift by making the bottom lift more or suck less so the top is not so big a gradient getting squared.
Look at two wings going the same speed with the same overall coefficient of lift:
Airfoil 1 is convex on bottom and has 13.5 pounds per square inch down there, compared to 14 pounds ambient, and 13 pounds per square inch on top, for a total lift of 0.5 pounds per square inch.
Airfoil 2 is flatter on bottom, and has 14 pounds per square inch on bottom, and 13.5 pounds per square inch on top, for a total lift of 0.5 pounds per square inch.
Airfoil 1 has twice the pressure gradient on top as airfoil 2, and also has a pressure gradient on the bottom.
One other thing I don't understand though is how air flows outboard under the wing and inboard on top, yet Orion says many times that there is suction under the wing that is just not as big as the suction on top of the wing. I suspect it really depends on the type of wing, and he is especially right about convex bottomed faster wings, but not about concave bottomed slower wings. Please correct me if I'm wrong.
Di = Cl^2*(a bunch of other stuff), says the books and years of testing.
I conjecture that Cl = Cl top + Cl bottom, and that Di actually is (Clt^2 + Clb^2)*(a bunch of other stuff), since the pressure on bottom can't possibly know what is going on with the pressure on top. I suspect that Di = Cl^2 because airflow is proportional to the square (I think I remember that right) of the pressure gradient with respect to spanwise distance, and induced drag comes from the spanwise flow of air. And we know how to minimize squares: try to get the same lift by making the bottom lift more or suck less so the top is not so big a gradient getting squared.
Look at two wings going the same speed with the same overall coefficient of lift:
Airfoil 1 is convex on bottom and has 13.5 pounds per square inch down there, compared to 14 pounds ambient, and 13 pounds per square inch on top, for a total lift of 0.5 pounds per square inch.
Airfoil 2 is flatter on bottom, and has 14 pounds per square inch on bottom, and 13.5 pounds per square inch on top, for a total lift of 0.5 pounds per square inch.
Airfoil 1 has twice the pressure gradient on top as airfoil 2, and also has a pressure gradient on the bottom.
One other thing I don't understand though is how air flows outboard under the wing and inboard on top, yet Orion says many times that there is suction under the wing that is just not as big as the suction on top of the wing. I suspect it really depends on the type of wing, and he is especially right about convex bottomed faster wings, but not about concave bottomed slower wings. Please correct me if I'm wrong.