Flow is a rate, here it could be volume of water per sec, or even mass of water per sec, for purposes here lets say its volume of water per sec. (To convert to mass per sec, we’d just times it by the density of water.) It order to make sure we’re both talking about the same thing, lets do a flow calculation. (I don’t wish to imply that you wouldn’t know how, only to make sure we’re both talking ‘apples’, and not ‘apples and oranges’ kind of thing.) Say we have a pipe with a cross-sectional area of 3 sq inches, and we know that the fluid moving through the pipe is moving at a velocity of 5 inches per sec. The flow through the pipe is then, 15 cubic inches per sec. (That is 3 sq inches X 5 inches per second = 15 cubic inches per second.) Lets consider another pipe with a cross-sectional area of 2 sq inches, but with the same fluid velocity of 5 inches per second as the first. The flow would then be 10 cubic inches per second. Lets consider another pipe, its starts with a cross-sectional area of 3 square inches but then narrows after a distance to 2 sq inches in cross-section. Lets say that the fluid is moving in the direction from the 3 sq in to the 2 sq in pipe. And further that at the begining of the 3 sq in pipe the fluids velocity is 5 in per sec, so the flow at that end is 15 cubic in. per sec. Now the water moves through the pipe and comes out the other end, the pipes are assumed to be rigid and retain their cross-sectional area, so the flow coming out the other end must also be 15 cubic in sec. So, if the flow is 15 cubic in per sec coming out of the 2 sq in pipe, the velocity of the fluid in that part of the pipe must have increased, for 5 in per sec only gives 10 cubic in per sec. Algebra will give the value of the new fluid velocity, and its 7.5 in per sec. So, and here’s the Conservation of Energy bit, by constricting the flow have we generated Energy? The answer is no. Energy has been transformed or the balance between the different forms of energy has been shifted towards the kinetic, but no new energy is generated. Back to Newton… What I left out in the above is what is actually holding the pipes steady against the flow. In fact, I assumed that the flow somehow remains constant when this constriction is placed in its path. The fact is that upstream, the constriction will be seen as Resistance to the flow, and what ever pump is operating will actually have to work a little harder to keep the flow constant. (And the nuts and bolts holding the pipes in place will have to work a harder too.)These little considerations are often overlooked, (see my post to the … Rocket Science Contributors thread) and all to often only the increase in velocity is evoked when applying the principle, e.g. the Venturi effect. So consider, and this just amounts to an alternative view of what I’ve just described, in the example above, in the case of the 3 sq in cross-sectional pipe, lets say the the fluid simply poured out the end. This superficially looks like a rocket of some sort, and one might reason that surely the pipe wants to move in the opposite direction to the direction of the flow pouring out its end (again opposite and equal reactions.) So then consider the 2 sq in pipe, same flow pouring out the end, but now the water has a higher velocity! Will it want to move in the direction opposite to the flow with a greater force, perhaps at a greater speed? The answer is no. For in fluids the its about the flow, and here the flows are the same. Disturbing? But true. In the end, its a balancing act. Constrict the flow, and expect to pay, perhaps the cost is worth it. … but there will be a cost.
Newbalonie, In my posts I may not have directly addressed the consequences of concave or bottom contours in general. Its clear to me know that I should have made the arguments which I made in these posts before ranting on about Venturi. Thanks for the opportunity to get back on track. Also again you’re right (see postings) about not moving on until the point is clear, at least reasonably so. The lesson learned, I will go back and re-introduce the planing hypothesis, but this time with some more illustrations as to how it applies, and possibly some numbers. After which, I will give my take on the consequences of contours. (This approach will also allow me to re-use a lot of diagrams I was preparing for my next thread, they’re simply too ‘colorful’ to toss out…) Kevin
Think about this. A surfer who weight 80 kgs will need a support of > 80ksx9.81ms/s2 = 785kgm/s2. 1/2pv2 at 10m/s(36km/h, significant speed) > equals only 50kgm/s2. Bouyancy me be able to support much, but not all of > the riders weight specially on a shortboard.>>> So where does the rest come from? We need the rest of the equations! Only > then we’ll know if the pressure along the stagnation line or spray area or > whatever is significant. Also, since we’re working in two dimention(the > sprayline is spread out along the length of the board(turn) or across the > nose), the actual force is distributed over a larger area, not?>>> regards,>>> Håvard The formula you are using refers to a peak value, if you integrated over the surface area (using the appropriate curve, the one in the diagram representing a general case) you’d get the force, i.e. density times velocity squared is not force, but has the units of force per unit area. (That is, the formula is enough, for effects described in the diagram, you just forgot the integration.) The point of the diagram, was to introduce the planing hypothesis, how it works, how it might be applied in surfing. But trying some numbers is hard to resist - ‘numbers’ are surely part of the final test. Also, I agree, bouyancy does matter, it may not matter all the time, but there are surely some manuvers which rely on it, particularly during recovery from some stalls, and even during nose rides, especially those which seem to take place way out on the shoulder, at least pretty far from the curl. Kevin In the picture, taken from BruceJones.com, I think Brock might be getting a little help from bouyancy. Mind you there are some other interesting things going on.
My point is; I don’t think that the spoon/flow and planing models are compatible (at least the bottom of the spoon-in-the-flow configuration). I agree with your rant on bonzer bottoms. Newbs
My point is; I don’t think that the spoon/flow and planing models are > compatible (at least the bottom of the spoon-in-the-flow configuration). I > agree with your rant on bonzer bottoms.>>> Newbs My apologies. Below is a diagram of two possible situations (of many.) The view is from the top. The thin blue line represents where the upward flow of water is contacting the board. The big blue arrow represents the flow. I tried to make the angle clear, if its not let me know. In the first case the intersection is almost half way back, the surfer likely to be surfing the board more towards the tail. In the second case the intersection in much more forward, the surfer likely surfing the board much more forward, towards the nose. The oval on the surfboard is meant to represent a scoped out area, a concave nose. (Admittedly its not the only way to concave a nose.) I have exaggerated the concave in order to make the point that the line of intersection changes. Please note: The flow is not directly from nose to tail, but across and back. The point of the diagram is not to indicate what happens to the flow after it intersects with the board, but just how and where the flow intersects with the board, at least in the two cases shown. Next post…
Return to the original planing diagram. All else constant, if you increase the rise, or Tau in the diagram you will increase the upward force on the plane. You’ll also increase the drag. The concavity increases the tau, relative to the rest of the bottom of the board. As a result, in the area of the concave both the upward force and drag is increased, at least that is my interpretation. There’s also a lot to said for recapturing the flow from the spray root. Reality check of sorts,… next post 
Here’s an interesting pic of a nose ride borrowed from BruceJones.com. I have no idea if the board has a concave, but the characteristic spray root is pretty evident. Notice how the water in the spray root, particularly up at the nose, is being thrown out away from the wave face and a little forward, that is, it is in the expected direction, if the flow intersecting the board was something similar to my previous diagrams. You might, while on the nose, say from the surfer’s point of view, think it was also being throw back, and it might be to some degree, but for the most part it isn’t (at least from the wave’s point of view.) Next post… 
Regretably, I’ve got to go. (Evident from how sloppy this last diagram is.) I will try and finish this tonight. Hopefully you see where I’m headed (in the next diagram I add a concavity.) …and then there’s rear concaves and vees… and channels? There’s also some forward tracking effects going on, but in my opinion, also explainable from the stand point of planing. This ain’t gospel, but it doesn’t require evoking much other than an appreciation of planing (see diagram.) Also, though I would have hoped to have made it clear in previous posts, planing in surfing, from the surfer’s or surfboard’s perspective is sort of an angled planing. From the waves perspective, its straight out planing at a high tau value. Later… Kevin 
What the hell is happening on the tail??? Newbs
USE THE FORCE LUKE! Toes on the nose, full trim,…Who knew skywalker was a surfer! Looks like he’s surfing next to one of those transporter thingy’s.
(That is, the formula is enough, for effects described in the diagram, you > just forgot the integration.) No I didn’t. I asked for the equation for it. It’s really that equation that show how the pressure is distributed.>>> In the picture, taken from BruceJones.com, I think Brock might be getting > a little help from bouyancy. Mind you there are some other interesting > things going on. Yup. He’s got about half a ton of water over his board holding the tail down. He’s on a springboard. regards, Håvard
The concavity increases the tau, relative to the rest of the bottom of the > board. As a result, in the area of the concave both the upward force and > drag is increased, at least that is my interpretation. I think of a concave more as a way of focusing lift while keeping drag to a minimum. Think of it as a satelite dish focusing all the forces into a point(or in this case a vector). Also, a surfboard is normally convex(rocker). Why would a concave create more drag the the convex of the rocker? regards, Håvard
What the hell is happening on the tail??? Newbs Please see the new thread, Rocket Science: Flow Across the Tail. I’m not sure what’s up here, but this thread seems to have been altered, at least the posting which I originally responded to seems to have vanished. I also thought I posted a big rant on Newton’s Third Law and the Conservation of Energy. I could be mistaken, anyway I get into tail contours in the thread mentioned above. Kevin