…trickle trickle…
Taking ‘force developed’ a bit further.
In the figure below are three strips, basically longitudinal sections through a flat bottom, a concave and a vee. I’ve also included suggestions as to the directions of the forces developed for a particular scenario. (See my last few posts in the thread Creative Drag:… actually I’ve left out a lot of descriptive detail, which is contained in the Creative Drag thread, and maybe elsewhere too.) I’ve only indicated the extremes - roof of concave, rails, area of apex of vee - perhaps you can fill in the rest – grading one into the other.
It’s all pretty crude, but it should provide a sense of what I wanted to point out.
In a nutshell, I’m inclined to believe that concaves offer a quality difference in the ride, as well as other points already mentioned in a prior post (fin area, etc.) and that quality difference is one of stability, or at least the sense of stability by the rider. The vee offering a more particularly more stable ride when up ‘on a rail’.
The propulsive forces developed will primarily depend on the surface area interacting with the flow, and the characteristics of that interaction. Just carving a contour doesn’t guarantee you anything – for example, what is being preserved, total surface area, or transverse (cross-sectional) width, and are the lateral walls, for the concave and vee, similar in the way they are developed relative to the average bottom plane.
With respect to contours in general, I see it as a matter of choice, loose a little lift in one direction, gain a little in another.
This is not to minimize how contours might impact certain maneuvers like pumping. The constrained flow of the concave is likely to enhance the pumping effect.
This whole approach introduces questions about a lot of other design elements, for example a role played by rocker. Here however, the approach has been in very general terms.
Shaping is wholistic. Analyzing individual elements is always risky.
kc
ps
This was done pretty quickly … Hopefully I got it right, but I reserve the right to correct any of my nonsense.