All of the standard equations for drag still apply. There are two types of drag. 1) Form drag which occurs due to a difference in pressure across a body. If you think of a sphere, there is high pressure at the front stagnation point and lower pressure on the aft end which will typically separate. This delta P causes a net force against motion. 2) Skin friction drag is what you're trying to modify. This drag is caused by viscous drag in the boundary layer. The boundary layer is caused by the relative motion of the fluid to a wall. Now, in your case, you're attempting to keep the relative motion as small as possible. So, the equations still (and always) apply, however your essentially attempting to reduce the effect of viscosity in the reduced boundary layer. Do note that, for most blunt objects, the form drag (#1) is typically much higher than the skin friction drag. So, while you're idea is plausible, the gains may be negligible.
This pic is from the top of the page from the "drag (friction)" Wikipedia. If I can interpret it to mean that 90% of the total drag on a streamlined body is due to skin friction (since form drag has been minimized), then I think it would be interesting to see what would happen if this concept was applied to such a body. I wonder also what portion skin drag plays in an aerodynamic body with a larger surface area than normal, like with those solar cars, or a long fuselage of a passenger plane. I guess I'll end up bothering someone at a campus with a college of mechanical and aerospace engineering department, to see if they can shoot down this concept and/or elaborate on it some.
I agree, the issue is that the figures you drew (car and boat) are very much not a streamlined body. They have much more in common with the circle. If you truly want to test this concept then I would suggest starting with a flat plate or other shape that would be easier to test and analyze.
I would imagine the total drag from skin friction in this case is probably closer to 50%. For example, skin friction accounts for roughly 50% of the drag on a typical commercial airliner, slightly more on a more streamlined business jet. Of course, this would assume that whoever designed these vehicles didn't make them have square backs as drawn here. I am just assuming that this concept would be applied to a typical car or boat shape, which has more in common with an airplane than a sphere or a flat plate. Other than that, the concept would theoretically reduce the drag on the body. If you could make the moving surface move at the same rate as the vehicle in the opposite direction, you could eliminate quite a bit (not quite all) of the friction drag on the surface in theory, but it would be extraordinarily impractical. For starters, you would likely use up as much energy rotating the surface as you would save due to the drag reduction if not more. It also would mean more parts that can break down. Also, how would you then have doors, windows, windshields etc if there is essentially a conveyor belt around the vehicle? You would have so many openings in the moving surface that the benefit would be even more negligible (or the penalty would be greater if that is the case).
For another, the drag of that conveyor belt would be many times greater than the drag of the air travelling over non-conveyored wings. It might make sense if you were attempting to tunnel through sand, however...
mugaliens, given the setup mentioned, that isn't true. Drag comes from skin friction, which comes from the shear stress in the fluid. This shear stress comes from the fact that the boundary layer profile is curved near the surface. The greater that curvature, the higher the shear stress. In the above system, the "conveyor" system would move with the flow an therefore approximately eliminate the no-slip condition and thus the boundary layer. With no curved profile, there is no shear stress and no drag. The limiting problem here is a practical one, not a theoretical one. Additionally, the different in drag between say a sheet of Teflon and sandpaper moving through the air is negligible assuming laminar flow. The only reason rough surfaces really create more drag is that the cause earlier transition. Again, in this situation, there is no boundary layer and thus nothing to transition to turbulence, so that isn't an issue either.