Hydrofoils and Lift

Benjamin,

Your perspective, and logical clarity of thought, is a refreshing addition to Swaylocks!    Welcome aboard.

It might just be a typo. If you look at the equation that he has, as P increases, L will also increase. Which is true.

Lift is created when an object changes the direction of the fluid. As the velocity of the fluid (relative to the object) increases the lift increases. As the velocity of the fluid increases it takes less area to lift an object of the same weight. The more surface area of the object is in contact with the water the more drag it will create.

As you go faster on a surfboard (increasing the relative velocity of the fluid to the board) the board lifts out of the water, and less surface area of the board in creating drag, and velocity is increased.

So, he is right that as the surfboard moves faster it is lifted out of the water, reducing the surface area in contact with the fluid, decreasing drag, and increasing top speed.

BenjaminThompso wrote:

...(snipped)...

I don't think Dan's reasoning is sound.  This is not criticism of Dan because I can't explain the hydrodynamics of surfing, myself.  So, I think we should give him some credit for trying.

Let me try to reason some things out conceptually:
(as always, if you know better than me, Please! correct me)

1)Dan's claim:  If you decrease surface area, pressure drops which means velocity increases. I wasn't sure if he was referring to width of the board decreasing or thickness of the rail decreasing, or both.  But either way, if you drop the pressure below the board or along its rail, that should effectively pull the board into the water.  And if the board is deeper in the water, there is more resistance to movement.  You can't increase velocity and displace more water because that would mean your doing more work on the water.  The universe is lazy, it will always choose the path of least work.  Does this mean that bernoulli and dan are wrong?  Bernoulli's equation is a derivation of physical law, which means that it can't be wrong---however! it can be misapplied/misunderstood/misused.  Same for Dan's lift equation, which I don't think is bernoulli's???


2)I think Bernoulli's equation essentially says that, if you push 1 gallon of water in one end of a pipe, 1 gallon of water must come out the other end of the pipe, water can't just disappear.  If you have a CLOSED SYSTEM, the in-flux and the out-flux have to be the same (flux is change in volume over time).  So if you take a pipe, where the entrance is twice as large as the the exit.  The velocity going in must be 1/2 the the velocity going out, so that the flux is the same.

"Closed System" is the key phrase.  When looking at a physical phenomenon, you have to draw a boundary around the subject (enclose the subject) then define the conditions on the boundaries (scientist call these boundary conditions).  In my experience, 90% of error comes from people drawing the wrong boundaries and defining the wrong boundary conditions (academic engineers say "trash in = trash out").  Enclosing a surfer on a wave (drawing the boundaries and defining boundary conditions) is more difficult than any engineering problem today, I'm not kidding or exaggerating.  That's why the Millennium Prize was created for whoever makes gains with the Navier-Stokes equations.   It's easy to identify which boundary conditions are wrong, but quite difficult to say what conditions are right.  It's easy to say Dan is wrong, but much more difficult to say what is right.

3) Back to Dan's Lift equation.  I think he made the wrong assumptions.  The equation may apply better for a foil moving through a homogeneous fluid like air.  But, a surfboard is traveling on the boundary of two fluids, water and air.  To make things worse! one fluid is 800 times as dense as the other, AND one likes to cling to itself while the other repels itself.  So pressure diffusion will be different in all directions...or water will move in some directions easier than others.

That's about as far as I can go at this point.  I'll think about this for the next few years and get back to you guys.

There exists a numerical model of the hydrodynamics of surfing for the case of a surfer traversing across the face of a wave at a steady speed equal to the the speed of the advancing curl (so the flow conditions remain steady-state). It was initially developed in the 70's, presented in an Ocean Engineering seminar at Scripps Institution of Oceanography in the 80's, and updated into the early 90's. It quantitatively predicts the following parameters as a function of where the board is positioned on the face of the wave and how the board is trimmed by the surfer:

1.  Speed "over the bottom".

2. Wetted length of the bottom of the board.

3. Average wetted width of the bottom of the board.

4.  Wetted area of the bottom of the board.

5. The location of the center-of-mass of the surfer on the board.

The output from an example simulation is illustrated in the attached figures.  (EDIT: Unfortunately the figures are presented in the reverse order from the listing above)

Note that the model predicts that for this particular simulation (i.e. wave height, board width, etc.) the maximum speed (23 mph) will occur when the board is positioned so that the slope of the wave face is 48 degrees, and the board is trimmed so that the angle-of-attack it makes with the water surface is 11 degrees. These values are in reasonably good agreement with direct measurements of speed, "end on" photographs of boards trimmed for speed, and visual estimates of the AOA based on the depth of the trough in the water just aft of the tail block.

Factors included in the simulation include:

1. Dynamic pressure (the pressure force associated with the change in the momentum vector as the water approaches and passes under the board)  Note: This is essentially Dan's pressure force equation, but since a surfboard has a small aspect ratio (max wetted width/avg wetted length), it is important to explicitly include the effect of the aspect ratio on the lift coefficient. Also in the calculations, Dan's lift coefficient (CL) is broken down to explicitly include the angle-of-attack (AOA) and the lift slope coefficient (CL*) where  CL = CL* x sin(AOA), or for small AOA  CL ~ CL* x (AOA in radians).

2. Buoyancy (the pressure force associated with the "static" displacement of water).

3. Skin friction drag (a retarding force tangential to the wetted surface of the board).

4. Gravity (a vertically downward force equal to the combined weight of the surfer and board).

5. The geometric factors altering the effective slope of the face of the wave along the pathline of the board as a function of board speed and wave speed.

The resulting equations are too complex to solve in closed form as a change in virtually any factor affects most of the others. For example if the surfer shifts his center-of-gravity forward or aft, that will change the angle-of-attack (AOA) that the bottom of the hull makes relative to the (inclined) surface of the water). That change In AOA then directly changes the magnitude of the dynamic pressure force, causing the board to rise (for an increase in the AOA) or sink (for a decrease in the dynamic pressure force) thus causing the wetted area to change. When the wetted area changes, so does the magnitude of the pressure force, causing an additional change in the dynamic pressure force. To complicate matters even more, when the wetted length and width of the board change it also changes the aspect ratio of the hull. This, in turn, also changes the magnitude of the dynamic pressure force through a change in the lift coefficient (Dan's CL). Any change in the dynamic presssure force also results in a change in the buoyancy (as it affects the displaced volume of water).

Nature quickly reacts to change to the new state of the board's motion that solves the hydrodynamic equations (for steady-state, the vector sum of all the forces = 0). Man, however, is not so capable. Hence the new state of the board's motion must be computed by iteration (essentially guessing an answer, then seeing if a solution is obtained...and if not, then improving one's guess until eventually a solution is achieved). (An aside: typically this requires around 500 iterations before the equations are adequately "solved" for each value of the AOA and the slope of the wave face that is to be simulated).

Clearly simulating the hydrodynamics of a surfboard is a major challenge. Even the method outlined above is only a first order approximation. There are many other (generally lesser) factors that need to be included to improve and/or extend the predictive capability of the model. For example the inclusion the change in the curvature of the wave face between the beginning of the wetted area of the bottom of the board and the tail affects the trim of the board about its roll axis and the effective AOA of the flow past the fins. The latter, in turn, also affects the drag associated with the fins. Also the present version of the model assumes sharp edged rails along the entire wetted perimeter of the board, so the effects of more rounded rails is not currently simulated.

BenjaminThompso wrote:

I didn't intend to imply that the equation is wrong, especially since I have no idea what S stands for and I would only guess that C stands for the speed of sound in the fluid.

However, I was assuming that Dan's opinion is what he stated in a video:  quoted without the umms

"with bernoulli's principle it's saying that when an area of an object is decreasing...for example, with my board I had a decreasing area..a gradual decrease, not a rapid decrease like you might find in a thruster, which with the flow around that gradual decrease, the speed will increase and the pressure will decrease with the velocity increase... so stated by bernoulli"

To me, he's saying that as you pull fluid flow through a smaller area, the velocity increases and the pressure decreases.  This is true, but I don't think this applies in the way he's stated, and if it does apply, it would pull the board down, not lift it.

I wasn't saying that you were implying the equation was wrong. I was saying that his description contradicts the equation, so maybe his discrption is a typo. I didn't see the video with the "umms".

BenjaminThompso wrote:

Obproud says "Lift is created when an object changes the direction of the fluid."  This is also true but I think Obproud is refering to Angle of Attack (orientation of object), whereas there is another type of lift created by the geometry of the object, which is what Dan was referring to.

What Obproud is saying about lift is true, but doesn't it apply the same way for all surfboards--as you go faster, the board lifts more.  This isn't the debate.  The debate is how the shape of a surfboard can increase speed...which is what everyone wants to know.

I really don't want to put Dan on the spot, but if his claims are correct, that's huge!

I don't think that there are different types of lift created by the geometry of the object and the angle of attack. AOA and geometry are both variables that determine the amount of lift created, because they both effect how the object turns the fluid. Lift is a function of AOA and geometry (along with velocity, weight and other variables).

What I am saying is that, maybe Tomo's analysis is incorrect, but his conclusion is correct. Here is why.

As the speed of the fluid, relative to the surfboard, increases, the board is more out of the water, the stagnation line is shifted aft, and less surface area is in contact with the fluid. Since there is less wetted surface area there is less drag, and the top speed is increased.

So, TOP SPEED is a function of wetted surface area; the less wetted surface area the higher the top speed possible.

I think that of the most important factors in surfboard design, and is part of what Tomo is trying to get at, is the transition between Hydrostatic lift (bouyency) and Hydrodynamic lift (plaining). If your board is wider it will transition from hydrostatic lift to hydrodynamic lift faster than if it is narrower, but a wider board will have a lower top speed, because of the drag created by the wetted surface area. A balance between these has to be created for an optimal design.

Nice post! what is your source?

I still would like to know what those variables represent.

I think its interesting...his use of science, when its common knoweldge that boards with wider tails are generally faster, average speed, in common surfing conditions and speeds. Wider tails (less aft curvature) have more lift and thus less resistance at everyday surfing speeds.

But I suppose saying that would be too simple and dull. Gotta have that mystical equation with the undefined variables.

I think if youre gonna sell using ("objective") science, you should at least give a basic description of the science behind the science, so that people can decide with some objectivity. Otherwise, its just more of the same ol surf smoke.  

Btw, I believe people like Greg Griffin and others like him have been applying these theories for almost four decades.  

Its also my opinion, that most surfboard outlines work this way. The difference between fast boards and slower ones is the total design, not just one element like planshape. I dont doubt his boards work well, I would just like to know the science behind the equation. Knowing the variables would be a nice start, thanks. I'd also like to know if DT is a degree'd engineer. That would be nice to know too. But if not, thats okay.  

BenjaminThompso wrote:

I didn't intend to imply that the equation is wrong, especially since I have no idea what S stands for and I would only guess that C stands for the speed of sound in the fluid.

The referenced equation (see below) is obtained from Newton's 3 Laws of Motion.

The variables are:

L = dynamic pressure or lift force (a vector quantity)

V = velocity of the flow relative to the body (a vector quantity)

(Note: The equation, as written, is in error in that it should read V(squared) rather than V(sub2). It's kind of interesting the only other place I've seen this error is in a picture of Simmons. So I'm wondering if that was Dan's source).

(Edit/Update (11/14/2009): Referenced picture of Simmons and Lift Eqn. attached)

V-squared  = dot product of V with itself

S = surface area (a vector quantity with the direction of the vector normal to the surface)

p = density of the fluid (a scalar quantity - normally represented by the Greek letter "rho")

C(subscript L) = the "lift coefficient" - A scalar coefficient that essentially is a measure of what fraction of the mass of water molecules moving towards the hull or foil are deflected by it, and to what degree the deflection occurs. Its value is commonly obtained from lab or field studies for anything but surfaces with simple geometry.

The equation derives from Newton's Second Law  (i.e. Force equals the time rate of change of Momentum) and is independent of whether there is energy dissipation or not. Alternatively, it also follows from Bernoulli's Equation if there is no energy dissipation.

For small angles-of-attack (AOA), say 15 degrees, or less, a new lift coefficient (CL*) is often defined by the equation:  

CL = CL* x AOA  where AOA is measured in  radians      (or CL = CL* x sin(AOA) for AOA in degrees).

CL* is the "lift slope parameter" and is a measure of how much the lift force is increased per unit change in the AOA.

But there is still an additional complication. Water flowing toward the hull (or a foil) doesn't necessarily have to be deflected so as to go under the hull and out the back. Instead, it can divert its path to one side or the other of the hull or foil. In that case, not as much momentum is deflected downward per unit time, and so the lift force is reduced. Hence the hull (or foil) has to operate at an increased AOA to make up for this loss. But doing so substantially increases the drag. Minimizing this reduction in lift is the primary reason why gliders (and commercial air carrier aircraft) have such a big wing spans in comparison with their chord (distance from leading edge to trailing edge of a foil or hull). For a competition glider, the aspect ratio of the wing ( = square of the span divided by the area) can be 30 or more. By contrast, the wetted portion of the bottom of a boat or a surfboard will commonly have an aspect ratio of 1, or less. Indeed, the effect of aspect ratio is one of the reasons that (within limits) wider planing hulls generally plane more efficiently than do narrower hulls.

The effect of aspect ratio is greatest when the aspect ratio is small (as in the case of a surfboard hull). Thus its effect on the ability of the hull to generate lift must be taken into account when assessing the hydrodynamic properties of a boat or surfboard hull. Various methods have been developed to estimate these effects and can be found in the literature (all the methods give essentially the same result for the purpose of calculations, but they are not exactly identical).

Here's the interview with Tomo on Down the Line Radio

http://a1135.g.akamai.net/f/1135/18227/1h/cchannel.download.akamai.com/1...

Not really technically pressing, but more input from the designer.

He won best in show at Sacred Craft...lots of people are gaga about his shit, but as pointed out, he seems to be referencing the same thing that Griffin has been quietly toiling on for a while...surface area reduction and edge release for improved speed, life and responsiveness.

AFOAF wrote:

...surface area reduction and edge release for improved speed, lift and responsiveness.

  

Where have I heard that before??