Hans & Jameskiri - Firstly, and this is a little off topic, but I have to disagree with you both on the issue of pumping. I have spent many hours breaking down slow motion footage and I promise you that at no point is the board “Pushed sideways down the wave face”. Pumping, if done properly, should be a series of smooth, linked top & bottom turns, combined with a compression and expansion of the surfers body. The whole point is to keep the fins and rail engaged in the wave to generate forward speed, and so if the board slid sideways at any point it would destroy any forward momentum. If you doubt me, try going frame-frame on a video and watch the tail of the board, it will never move sideways.
Also I realise that tow is not obligatory, and I understand the Pros and Cons of having fins in line with the stringer. What I want to know is WHY this happens. I would love to try and draw a velocity triangle, but since this, like Reynold’s Number, can’t be done without actual numbers, which as yet no one has been able to provide, this does not help to answer my questions.
GTFD - There is a lot of data from sailing/powerboats out there that could be used for approximation, but unfortunately it’s all based on flat water and a major component of any equation would be the speed and direction of the water flowing up the face of the wave (see below!).
Obproud & Stoneburner - If I understand your points about the flow of water, I think you are talking about something similar to “Apparent Wind theory” in sailing, where you have the True Wind blowing over the boat and then the “Induced Wind” which is created by the boat moving forwards through the air. The Apparent Wind is a vector of those two and is what you actually set your sails by.
I’ve attached a diagram of this theory, altered for a surfboard on a wave. In Figure 1 the board is travelling across the wave with the “True Flow” of water up the face of the wave at 90 degrees to the direction of travel. If we assume that the board and the wave are moving at about the same speed (in reality the board would be moving faster) then the “Apparent Flow” would be at 45 degrees to the direction of travel, and the the angle of attack would be perfect for generating lift. In principle, I can see how this theory could work and make sense, but I have a few problems in my head, maybe you can help me understand:
1. If this is correct it means the effectiveness of your fins is directly related to your direction of travel on the wave. If you drop down the face of the wave, the “True Flow” and “Induced Flow” are in the same direction, and we still have a negative angle of attack (Fig. 2). While if the board is turned up the face of the wave the “True Flow” and “Induced Flow” are opposing, and would cancel each other out leaving no water flowing over the fins (fig. 3).
2. For this theory to be correct, the board would have to be sliding sideways on the face of the wave. On a boat the air flows uninterrupted over the deck, allowing the sail to affect the flow and create lift. However the rail of the board is designed to grip and re-direct the flow of water behind it, so that a board angled at 90 degrees across the face of a wave, will gently rise up and off the back (and we all know how it feels when the rail actually slips on a steep face) By my understanding, the use of concaves on the bottom of a board is to re-direct as much water out the back of the board as possible, this would mean that the flow past the fins is running nose to tail. Maybe I’m wrong, and despite the best efforts of rail, concave and fins, most of the “true flow” up the face of the wave does pass under the board and out the other side, in which case there is still the first problem that the effectiveness of the fin would be altered by your angle to the wave face. Again maybe this is the case, and as with a sailing boat, the fastest direction of travel is the equivilent of a “Beam Reach” when the Apparent flow is just right for your fin set-up.