Thanks. It would be nice to have more than basic text and graphics, but I won’t complain as Swaylock’s is free – and free is free?
I though I might provide you with my approach. Hopefully, if you’re so inclined, you will resolve your vectors in terms of those in figure 2, and then again, perhaps not.
My approach may not be as immediately as practical as your approach, but I’m sure, as you’ve indicated, in the end one will be able to move from one to the other with the correct transform.
In figure 1, the plane of the bottom of the surfboard is represented by a normal (a unit vector in the direction perpendicular to the plane of the bottom of the surfboard) and the motion of the fluid, by a vector in the direction of the motion of the fluid. The angle of attack is found by using the dot product of the two vectors.
Conceivably you could then go on to define different angle-of-attacks as in figure 2. I realize this may not be standard a standard approach, nor useful to parse up the respective angle-of-attacks in this manner. (I somehow doubt it makes much engineering sense to do so. It’s not really something I’ve done.)
Nevertheless, given my approach, which tends to view a surfboard ‘when in motion’ as planing on multiple planes –i.e. not just the standard horizontal plane used by naval architects, it’s the best approach I’ve been able to muster so far. The need to do so comes from my interpretation of where the thrust is coming from. In particular, that planing in one direction provides the thrust in another, if the bottom is oriented correctly. This however is my problem, and I’ve offered it not so much as a counter argument or to start a controversy, but just as an explanation as to why I’ve tended to take the approach I have. (In my prior Dynamic threads, I referred to thrust as propulsion, though there is no assumption, nor expectation that you have read those.) You need not comment on my interpretation of the mechanisms of thrust, it’s the resolution technique that will hopefully allow you to answer my questions.
Anyway, thanks,
Kevin
(Edit, 09/25/06. Added diagram and additional notes. KC)
Figure 3 may be of some help.
Though here, tau and lambda look wrong, the geometry would show they are the same angles as referred to in the prior post. Both these angles are resolvable using the ‘cosine angle’ treatment as indicated in figure 2. Similarly for theta.
(Edit, 09/25/06. Additional notes. KC)
Also above, I actually have used the dot product approach to resolve flows, it just that at this point I haven’t attempted to use the full Lift/Drag treatment for each. I have no idea at this point how useful such an approach would be - I’m not an engineer and have little experience with these kind of lumped parameters