Spuuut referenced some of your work in a prior post (at least I think it’s you.)
I’d like to understand the treatment that is being applied here (to hydrofoils.) Please, if you’re inclined, direct me to a reference, post, or URL of yours that explains your treatment? Also, is what I’ve diagrammed in figure 1, a reasonable start? And, are you willing to deal with a few more questions?
Thanks,
Kevin
(Edit: 09/21/06, Included legend for figure 1, KC)
Brett,
Are we going to get to see what a concave foil with winglets looks like? You seem to like it the best from what I have seen. Pretty interesting you making the foils out of sheet plastic.
Terry,
Are you still working on another design iteration of the HYPO, or have you arrived at a final design? I remember you saying it had neutral/no stability in roll. Hypothetically, how would you combat that? Would you change the front, rear, or both foils to have a righting moment for small deviations in roll (let’s say from someone who is not that agile)?
Thanks in advance,
JSS
The drawing is nice, and as far as 2D goes its fine. There is also velocity in the y direction though. this causes sideslip along the wing, and induces a roll moment. Now that moment could be countered by the surfer’s weight, but it would be innefficient. If you had an oblique mounted foil, (not like conventional sweep:looks like this: / instead of V. The foil could be oriented into the flow. Of course this would only result in no sideslip for the precise angle you are surfing down the wave at the time, and it would only be designed for going right or left, unless a trimming method was developed to allow adjustment.
……
Terry,
Are you still working on another design iteration of the HYPO, or have you arrived at a final design? I remember you saying it had neutral/no stability in roll. Hypothetically, how would you combat that? Would you change the front, rear, or both foils to have a righting moment for small deviations in roll (let’s say from someone who is not that agile)?
Thanks in advance,
JSS
Yes and no…I have arrived at a general final design (3 yrs ago), but as there’s lots of unknowns (or poorly knowns) involved in the response of the craft, I still need to continue to experiment with the details.
The board shown in the pic that Dale posted at the beginning of this thread was the original “proof-of-concept” version. Since that pic was taken, the forward foil shape–as viewed from the front–has been refined. Also the canard foil rigging angle adjustment rods (visible in the pic) have been incorporated into an assembly that allows the rider to select between a “flight” configuration and a “paddling” configuration while underway. This change substantially increased the max paddling speed that can be achieved.
Still to come are some (significant) changes to (hopefully) improve roll control and further enhance the maneuverability. Also the ability to disassemble the craft for transport. As noted above, the basic concepts of how these features will function have been chosen, but the (practical) details are still being worked out. Building this upgraded “patent pending” version of the craft will be one of my primary goals for this coming winter.
When I said it had “neutral/no stability”, I misspoke. I should have said it has “nearly neutral to no stability” (in roll). The main (fully submerged) foil carries between 90 and 100 percent of the (effective) combined weight of the surfer and craft and presently has no intrinsic stability in roll. However, when traversing across the face of a wave there is not only a slope to the sea surface along the pathline of the craft, but also transverse to the pathline. As a result only the tip section of the canard foil (on the wave side of the craft) is piercing the surface of the water. Calculation shows that when the craft is not banked in roll, or the bank angle is small, there is a small degree of stability–but the situation becomes unstable as the roll angle increases. The stability is small not only because of the geometry of the situation, but also because the weight being supported by the forward foil is small (10 percent or less, and maximum hydrodynamic efficiency is achieved at 0 percent). On the other hand, it is in part this feeble or absent stability that enhances maneuverability (just as with aerobatic airplanes or fighter aircraft like the F-16)–a desirable feature (and the primary design goal). The upcoming model is intended to keep approximately the same stability (to preserve maneuverability), but augment the control means so as to reduce the demands on the rider to keep the craft in balance.
FWIW, one of the more difficult things to do with the present board is to traverse across a section of broken wave while at the leading edge of the white water bore from the collapsed lip. In this situation, the board is moving both alongshore and onshore at the visual boundary between the blue water (shore side) and the surging motion of the “white water” bore moving toward shore on the (former) wave side. Since the main foil extends down below the bore and into the blue water the board tends to continue along its set pathline if upright. However if the bore surges into the side of the craft, that creates a torque that wants to roll the board toward the shore (i.e. counterclockwise if going right). That torque starts a rolling motion and the board responds by turning toward shore. If the rider then banks the board back toward the white water, the board responds again by turning in that direction. But it is difficult to be so precise as to avoid some contact with the white water again. So it again turns back to shore. I find it challenging to avoid this repeating sequence, which tends to produce a scalloped path across the white water section at a diminished effective speed. Hopefully this problem will be mitigated as a consequence of the upcoming stability/control changes as well.
Spuuut referenced some of your work in a prior post (at least I think it’s you.)
I’d like to understand the treatment that is being applied here (to hydrofoils.) Please, if you’re inclined, direct me to a reference, post, or URL of yours that explains your treatment? Also, is what I’ve diagrammed in figure 1, a reasonable start? And, are you willing to deal with a few more questions?
Thanks,
Kevin
(Edit: 09/21/06, Included legend for figure 1, KC)
Hi Kevin,
I’m not aware of anywhere on the web that I have discussed anything other than snippets of my treatment(s) of the motion of conventional or hydrofoil wave-craft on a wave. However (like the construction of my next version of my hydrofoil paipo board but with a lower priority) that is one of the projects that I am hoping to work on this coming winter.
In the meantime, and in reference to your figure…
Imagine looking down and from a fixed location videoing a surfer riding on a wave and who remains at the same position relative to the curl as the wave moves toward shore. You will find that his path (over the bottom) traces out a diagonal line consisting of the onshore and alongshore components of his motion. I’ll refer to his track as the “pathline” of his motion. Observation indicates that such a surfer, in trim, generates a path angle (the angle between his pathline and an axis paralleling the wave crest) that is typically between 30+ degrees and 45 degrees.
Now let’s look as some slopes. The slope of the face of the wave measured in a vertical plane perpendicular to the crest of the wave will depend on one’s location on the wave face. Observations suggest that for a surfer in steady-state trim, this slope will be about 1:1 (or 45 degrees). Just as a skier skiing diagonally across a ski slope experiences a slope that is less than if he went straight downhill, so too does the surfer experience a reduced slope along his pathline compared with the slope of the wave face. If the slope of the wave face at the surfer’s location on the wave is “Sw”, and the angle of his pathline relative to the crest of the wave is “theta”, then to a first approximation the slope along his pathline, “Sp”, will be:
Sp = Sw x sin(theta)
This slope directly relates to the force driving the surfer and board.
At the same time, there will be a transverse slope between the left and right sides of the board. To a first approximation, this slope, “St” will be:
St = Sw x cos(theta)
This slope can be important in determining the aspect ratio of the surfboard ( aspect ratio = max width of the wetted hull divided by the average wetted length of the hull). The aspect ratio plays an important role in determing the efficiency of a planing hull.
To see this, consider a rectangular flat plate measuring 6" in one dimension and 6’ in the other direction. If the plate is moved across the water with some non-zero angle-of-attack (AOA), water moving toward the plate will be deflected downward as it passes under the plate. Since this imparts a downward momentum to this water, the water (which had no downward momentum at the upstream end), by Newton’s Second Law (Force = time rate of change of momentum) and Third Law (equal and opposite reaction), there is a upward pressure force exerted on the plate (and perpendicular to its plane).
Since the pressure force is exerted normal to the bottom of the plate, and the plate is inclined relative to the horizontal (by the AOA), the pressure force has both a vertical and a horizontal component. The component perpendicular to the motion of the craft (and the sea surface) is the lift force; the component perpendicular to the lift force and directed downstream is the induced drag force.
FL = P x cos(AOA) (lift force)
FD = P x sin(AOA) (induced drag force)
…where the magnitude of P (the pressure force) is also proportional to the AOA.
The larger the AOA (within limits), the greater the pressure force, lift force, and the greater the induced drag.
However, not all the water moving toward the inclined plate need be deflected downward. Instead it can flow off to one side of the plate or the other instead. Since less downward momentum is now being imparted to the water approaching the plate, the pressure force exerted on the plate is diminished. In order to compensate (since some specific lift force is required to support the plate–e.g. the combined weight of the rider and board), the AOA of the plate must be increased to provide the required lift force. This, in turn, increases the incline of the pressure force, thus increasing the induced drag.
Obviously if the plate were now rotated 90 degrees, so that the distance between the upstream and downstream wetted edges were 6", instead of 6’, and the span of the plate perpendicular to the motion were 6’ instead of 6", a much greater percentage of the water approaching the plate would pass under it and not around it. Hence the downward momentum transmitted to the water approaching the plate would be increased, and the induced drag would be reduced in comparison with the first example (but still not as low as if the width of the plate were even greater (e.g. infinity).
If the aspect ratio is “AR”, then the reduction factor for the lift created by a plate with a finite wetted width “ARF”, relative to a width approaching infinity (but with the same wetted area) is approximately given by:
ARF = (AR)/(2 + square-root(4 + AR x AR))
Let’s get an idea of how big this factor might be for a surfboard by assuming that the wetted area when traversing across the face of a wave is approximated by a triangle with a max wetted width of 18 inches and an average wetted length of 24 inches (4’ max wetted length). The aspect ratio is then 18/24 = 0.75 and the aspect ratio factor is 0.18. Hence for a given wetted area, the AOA of the surfboard would have to be about 5.5 times greater than for the same wetted area of a very wide, but very short, shape. Thus the surfboard would have a high induced drag compared with a (very) wide board.
A possible example of the effect of width on induced drag is the speed potential of a fish, which is typically much wider than say the typical thruster for the same length.
But there is a complicating factor in that to take full advantage of the lower drag associated with a wide board, that width has to be wetted (not counting spray). But if one rolls the board toward shore so as to match the transverse slope angle (along the board’s pathline) in order to wet the full width, the pressure vector now also has a component perpendicular to the pathline and directed somewhat toward shore. This reduces the magnitude of the lift component (by the cosine of the transverse slope angle) and, if not balanced in some other way, will accelerate the rider and board away from the face of the wave and toward shore (resulting in him progressively getting lower on the wave). Lower on the wave means less wave face slope, which in turn means less pathline slope, which in turn means a reduced driving force. These opposing considerations are probably (intuitively) one reason for the limited banking of the typical surfboard in roll when traversing across the face of a wave. The steeper the wave face slope, the greater the transverse slope, and the lower the aspect ratio of the wetted area of the surfboard. Too steep a slope and the reduction in hydrodynamic efficiency associated with aspect ratio more than offsets the increased driving force otherwise associated with an increased wave face slope. This balance and trade-off may relate to where skilled surfers choose to trim for maximum speed on the face of a wave.
Now…as to a hydrofoil…
A typical hydrofoil is characterized by a chord (leading edge to trailing edge) dimension that is substantially smaller than it’s span. So the aspect ratio is increased, and the induced drag can be substantially reduced. In addition, for a fully submerged foil, there is no need to bank the board in roll to increase the wetted span (it’s already wet). Once again this decreases the induced drag relative to that of a typical surfboard. This is part of the motivation for choosing a fully-submerged main foil on my hydrofoil paipo board.
However, that’s only part of the total equation. Nothing has been said about parasitic drag. Within limits a conventional surfboard can, to some extent, be trimmed to vary the wetted area and hence the friction (parasitic) drag. In contrast, the wetted area of a fully-submerged foil (and the wetted area of the supporting struts) is fixed…and what is optimal at some speed, may be excessive at some faster speed. Hence, depending on how the hydrofoil is “optimized” as to function (e.g. speed vs maneuverability) it is possible that the hydrofoil will be the more efficient at some speeds, while at other speeds the planing hull of a conventional surfboard may be the more efficient.
A surface piercing foil lies somewhere inbetween. It’s lift generating capability is less than that of an equivalent fully-submerged foil due to ventilation, wave-generation, and reduction in pressure force when within two chord lengths of the sea surface (but may still be improved over the typical planing hull). But they can also be designed so that the wetted area decreases as speed increases, thus potentially reducing the parasitic drag relative to a fully-submerged foil.
Since my design goal was enhanced maneuverability (which includes carrying more speed through a maneuver), the greater efficiency (with regard to induced drag) of a fully-submerged foil, relative to that of a surface-piercing foil, is the motivation for the main foil on my hydrofoil paipo board supporting 90-100 percent, and the canard foil 0-10 percent, of the combined weight of the rider and board.
However, that’s only part of the total equation. Nothing has been said about parasitic drag. Within limits a conventional surfboard can, to some extent, be trimmed to vary the wetted area and hence the friction (parasitic) drag. In contrast, the wetted area of a fully-submerged foil (and the wetted area of the supporting struts) is fixed…and what is optimal at some speed, may be excessive at some faster speed. Hence, depending on how the hydrofoil is “optimized” as to function (e.g. speed vs maneuverability) it is possible that the hydrofoil will be the more efficient at some speeds, while at other speeds the planing hull of a conventional surfboard may be the more efficient.
Yes and a few observations: 1) Once a fully submerged foil has achieved sufficient speed to lift hull and rider out of the water, then any further increase in speed will be achieved with more than the minimum necessary foil area and a loss of efficiency 2) Thus, as you have said, a submerged foil will have an optimum speed at which it operates most efficiently. . . . and that is the speed at which it lifts the hull out of the water. 3) The ‘catch 22’ with submerged foils which are designed to lift the board and rider 100% is that if less foil area is used in order to obtain the required lift and maximum efficiency at a higher speed, then the board might not be able to reach the speed at which ‘lift off is achieved… . . . and if more foil area is used to get the hull out at lower speeds, then futher increases in speed will obtained with an increasingly heavy drag penalty due to too much foil being in the water. I realised that this was the case back when building our early foils in the 90’s, and, given that foil based lift is used as a means of achieving high speeds (rather than just for novelty value or a smooth ride) then I believe I have found an answer to the ‘catch 22’ regarding parasitic drag mentioned above. 4) The solution (again assuming that speed is the goal of hydrofoil surfing) is to use less foil area. … . to use an area which will only provide enough lift to support 100% of the weight of board and rider at very high speeds. . . . . and to design the foil to work in conjunction with the planing hull. As you have pointed out (and as I have been saying for years!) the planing hull is able to reduce wetted surface area and drag as speed increases. My approach is that as the foil based lift increases, the hull is used progressively less, and this, combined with the fact that the smaller foil will increase its efficiency until it is able to lift board and rider completely. . . (and we set that goal at a high speed ) means that the setup INCREASES its efficiency the faster it goes. . . . both planing hull and foil increase their efficiency as they go faster, and they work together. This approach means that there is no ‘hump’ in terms of hull based drag to overcome prior to ’ lift off’ and no ‘topping out’ of foil efficiency at or below achievable surfing speeds. 5) Regarding maneuverability, my approach has been to design the foil so that it does not impede maneuverability at all. . . and nor does it provide stability. . . .stability is provided by the hull. . . . and the hull is able to be used less and less as speed increases (less hull is needed for stability as speed increases). 6) It is apparent that hydrofoil surfboard designers tend to assume that the goal of foil based lit is to make rider and hull airborne. . . this is undersandable because ‘flying’ a foil based craft is an exciting and spectacular event. . . … there is however and underlying assumption that this foil based ‘flying’ is done with the goal of drag reduction and increased speed. . . . … . . if ‘hydrofoil’ surfboard designers are really intent on increasing speed via foil based lift then in my opinion (based on the points above) they would do well to look beyond the goal of 100% foil based lift, and use this lift as outlined above as a means of adding to hull based lift rather than completely replacing that hull based lift. 7) Designing according to this principle means that foils must operate at angles of attack very close to that of the hull in the area around the foil, and they must not extend far below the hull. 
Neighbor, have you tried Roy Stewart’s coffee yet? Well, then you’re not FLYING! You simply don’t know what you’re missing–LIFT like you’ve never, and TONS MORE DRIVE, that’s all!
Friend, you’d do yourself a favor to get right down to your grocer and DEMAND that he stock ROY STEWART’S PREMIUM ORBULATOR-STEWED PREMIUM NEW ZEALAND COFFEE–in the distinctive white resin tin!! You never felt anything like THIS, friends and neighbors, of that we’re sure!! Look for the man in the orange suit–and if it doesn’t say STEWART’S, it’s not VORTICULATED!
Now back to our program…
(bit o fun, RS–no offense/harm eh?)
Thanks for responding.
Your point regarding the need to consider all three dimensions is well taken.
I’m just trying to get up to speed on how this is being approached. In particular, how much can actually be attributed to a classical low angle of attack hydrofoil application, and how much to something else.
Traditional Lift/Drag analysis makes sense when the free surface of the liquid is horizontal, in particular when ‘lift’ is ‘up’ and ‘drag’ is parallel to the motion of the fluid. It’s a little more difficult to apply, perhaps just appreciate, when the free surface can be close to vertical as in surfing. In surfing, though relative motion of the foil craft with respect to the free surface may still be more or less parallel to the of the free surface, absolute motion is generally not (though it can be.) But the problem here isn’t just a matter of terminology.
All I’ve done in figure 1 is to resolve the classical Lift/Drag treatment (though still in two dimensions) so that the angle between the vertical and the tangent to the relative flow, here beta, shows up in the equations. On a wave beta can get pretty small, in fact that’s where the fun part of the wave tends to be – the ‘wall.’ For a small beta, cosine terms will dominate, and sine terms will tend to become negligible; the opposite for beta approaching 90 degrees. I believe Roy mentioned something about how we should interpret Lift and Drag, perhaps this is what he was referring to. Still this is just two-dimensional, but moving to three however won’t make this kind of thing go away.
Anyway, I’m sure someone has done this type of treatment somewhere, but I haven’t found anything on the Net yet. And though I can see the argument (the classical Lift/Drag treatment), I actually I don’t think this is what is going on here a lot if not most of the time, and I don’t think it’s just a matter of moving to three dimensions either, though that will be important. I think the initial assumptions regarding the flow are wrong, and therefore most of the time the angle of attack is generally very high, so high as to be operating in the classical ‘stall’ region. But then what does ‘stall’, for that matter ‘drag’ mean when the free surface is close to vertical. (At some point it might be worthwhile for me present my interpretation of what is going on, but its not really important now.)
Nevertheless, I do think there is a hydrofoil application here, and I’d like to understand the approach that’s been taken. If you want to throw some more my way, it would be appreciated.
Thanks,
Kevin
Thanks for responding.
I think I may have to read a few more times, but so far it’s been pretty helpful.
As I wrote in my response to Lasersailor I may have some disagreement with the treatment, but it’s unimportant at this point. Right now, I’m satisfied with any insight into the design of these crafts that I can get.
Thanks again,
Kevin
Thanks, I will have to sit down and take an our to work through it this weekend. The angles are the main thing I wasn’t sure about, as to the towards shore/ along shore angle, as well as the face ange of the wave and the velocity of the flow up the wave. And the velocity of the board wrt the wave. Ha so basically I have no clue what any of the variables are, but I should be able to come up with a solution in those terms.
Please don’t waste too much time if something I’ve done is unclear. It was done quickly. For one thing, I could have labeled things better (like that curved blue line which is the wave face.) Please just ask if something is unclear.
By the way, in the diagram x is towards the beach, as in the direction of propagation of the wave, and z is just up, as in the direction opposite that of gravity. Also, the diagram is still only in two dimensions.
And best of all, you are not required to reply. Maybe you’ve got something better to do, like surf or sleep? That’s basically my approach, and I expect nothing more from others.
Thanks,
Kevin
Bit of fun to you maybe, and sure I can take a joke, but I am actually contributing in a sensible and logical way to this thread, and your continuous trolling is a drag, man, it’s too boring . . . compared with the real subject, i.e hydrofoils. . . . so please tell me, do you understand the points I made in my last post about using low area horizontal area wings ?
And I didn’t read the abusive posts which Hicksy deleted, but I would have thought you would have improved your manners since then
Pisses me off actually (slightly). . … whereas a reasoned response would have been sweet, even if i didn’t agree with it.
But Ok, ha ha, now got anything real to say ??
.
Neighbor, have you tried Roy Stewart’s coffee yet? Well, then you’re not FLYING! You simply don’t know what you’re missing–LIFT like you’ve never, and TONS MORE DRIVE, that’s all!
Friend, you’d do yourself a favor to get right down to your grocer and DEMAND that he stock ROY STEWART’S PREMIUM ORBULATOR-STEWED PREMIUM NEW ZEALAND COFFEE–in the distinctive white resin tin!! You never felt anything like THIS, friends and neighbors, of that we’re sure!! Look for the man in the orange suit–and if it doesn’t say STEWART’S, it’s not VORTICULATED!
Now back to our program…
(bit o fun, RS–no offense/harm eh?)
Janklow !! Trust you to crack me up ! again! I was just perusing pertinent information from my peers here and you go and drop in a Stewarts Coffee Ad.
A bit of a laugh after a lesson is always in order, thanks.
Roys cool with that ? Id be stoked to know people were giving out that kind of good- natured attention to me.
Regards, Brett.
Neighbor, have you tried Roy Stewart’s coffee yet? Well, then you’re not FLYING! You simply don’t know what you’re missing–LIFT like you’ve never, and TONS MORE DRIVE, that’s all!
Friend, you’d do yourself a favor to get right down to your grocer and DEMAND that he stock ROY STEWART’S PREMIUM ORBULATOR-STEWED PREMIUM NEW ZEALAND COFFEE–in the distinctive white resin tin!! You never felt anything like THIS, friends and neighbors, of that we’re sure!! Look for the man in the orange suit–and if it doesn’t say STEWART’S, it’s not VORTICULATED!
Now back to our program…
(bit o fun, RS–no offense/harm eh?)
Roy wrote: Yes and a few observations: 1) Once a fully submerged foil has achieved sufficient speed to lift hull and rider out of the water, then any further increase in speed will be achieved with more than the minimum necessary foil area and a loss of efficiency 2) Thus, as you have said, a submerged foil will have an optimum speed at which it operates most efficiently. . . . and that is the speed at which it lifts the hull out of the water. 3) The ‘catch 22’ with submerged foils which are designed to lift the board and rider 100% is that if less foil area is used in order to obtain the required lift and maximum efficiency at a higher speed, then the board might not be able to reach the speed at which 'lift off is achieved… . . . and if more foil area is used to get the hull out at lower speeds, then futher increases in speed will obtained with an increasingly heavy drag penalty due to too much foil being in the water……
I’m sorry Roy, but this is simply not true. The drag of the board (and rider combination) is a minimum when the individual sources of drag (e.g. induced drag, parasitic drag, form/pressure drag, intersection drag, etc.) are added together and the result is the minimum value. In any decent design this is not when the threshold speed to raise the hull out of the water occurs (due to the large induced drag).
The induced drag diminishes with increasing speed and varies approximately as 1/(V^2); the pressure/form, parasitic, and other sources of drag tend to increase with speed and vary as (V^2). As a consequence, a plot of the total drag from all of the contributions creates a roughly parabolic curve–high drag at low speeds due to the induced drag; high drag at high speeds due to the parasitic and other drag sources; and a minimum drag somewhere inbetween.
For a typical airplane design, the design minimum drag typically occurs at a lift coefficient between about 0.2 and 0.4. The lift coefficient for a typical vanilla wing section (no lift enhancing devices such as leading edge or trailing edge flaps) is around 1.5-1.6. Thus for the airplane, the optimum speed will be roughly twice the lift-off speed (generally it will be a bit faster since a plane is typically optimized for minimum fuel consumption rather than minimum drag).
The same general principles apply to hydrofoil craft, but the design optimum speed will depend on the design objectives (e.g. speed vs maneuverability) and the operating environment.
In my earlier comments comparing a fully-submerged foil with a planing hull (or a surface-piercing foil), I only considered the differences in parasitic drag associated with a fixed vs a variable wetted area. But as noted above, there are other sources of drag the must be considered as well. For example, in comparing a fully-submerged foil with a surface-piercing foil it is important to remember to include additional sources of drag that are associated with a surface-piercing foil, but do not occur (or are minimal) for a fully-submerged foil. Among these are: the loss of lift resulting from ventilation of the portion of the foil (immediately below the sea surface) , a loss of lift from a portion of the foil operating within two chord depths of the sea surface (apart from any loss due to ventilation), and the loss of lift due to a reduction in aspect ratio as the foil rises to reduce the wetted area. There is also an increase in drag due to wave generation by the emerging foil through the sea surface.
All of these effects occur on a horizontal sea surface. Unless specific design criteria are met, there are also additional losses of efficiency when operating a surface-piercing foil on a sloping sea surface–such as the face of a wave. Collectively it can be seen that a fully-submerged foil can remain more efficient than a surface-piercing foil in some region of speeds around the optimum design speed. Obviously the range of speeds for which this will be true will depend on the details of individual designs.
First off, I love this idea! How much fun would that be!! As for some of the others, ie; foils on the noseriders, “adjustable” push down foils etc. interesting ideas how about toying with the onld Cheyne Horan/Ben Lexan star fin (winged keel) ?
Thanks for responding.
Your point regarding the need to consider all three dimensions is well taken.
I’m just trying to get up to speed on how this is being approached. In particular, how much can actually be attributed to a classical low angle of attack hydrofoil application, and how much to something else.
Classical “low AOA” hydrofoil application is all that’s required as long as you “do” the hydrodynamics in a coordinate system in which the x-axis corresponds to the intersection of a vertical plane passing through the pathline (see earlier post) of the craft with the local sea surface. The z-axis is lies in the same vertical plane and is orthogonal to to x-axis, and the y-axis is orthogonal to both the x and y axes (i.e. in a horizontal plane and transverse to the longitudinal axis of the craft). In this coordinate system “lift” retains its classical definition (referenced as normal to the free stream flow (i.e. perpendicular to the local sea surface), as does drag (parallel to the free stream flow…i.e. along the x-axis).
The special case of a path angle of 90-degrees (going “straight off”) would seem to correspond to your illustration. I didn’t look carefully at your equations as its not the coordinate system in which I’m used to working (a rotation around the y-axis, followed by a rotation around the z-axis would transform either of our coordinate systems into the other). But I’m guessing that they are correct. So more generally, it would seem that your illustration and equations would seem to be OK for the more general (3D) case, provided you interpret your x-axis to lie along the pathline).
Traditional Lift/Drag analysis makes sense when the free surface of the liquid is horizontal, in particular when ‘lift’ is ‘up’ and ‘drag’ is parallel to the motion of the fluid. It’s a little more difficult to apply, perhaps just appreciate, when the free surface can be close to vertical as in surfing. In surfing, though relative motion of the foil craft with respect to the free surface may still be more or less parallel to the of the free surface, absolute motion is generally not (though it can be.) But the problem here isn’t just a matter of terminology.
It’s still OK. In the coordinate system described above everything remains referenced to the (local) sea surface. When the sea surface becomes vertical, the required lift for equilibrium becomes zero and the drag and gravitational forces become colinear (neglecting the offset between the center-of-mass of the rider and board and the drag force on the bottom of the board) and opposite directed.
All I’ve done in figure 1 is to resolve the classical Lift/Drag treatment (though still in two dimensions) so that the angle between the vertical and the tangent to the relative flow, here beta, shows up in the equations. On a wave beta can get pretty small, in fact that’s where the fun part of the wave tends to be – the ‘wall.’ For a small beta, cosine terms will dominate, and sine terms will tend to become negligible; the opposite for beta approaching 90 degrees. I believe Roy mentioned something about how we should interpret Lift and Drag, perhaps this is what he was referring to. Still this is just two-dimensional, but moving to three however won’t make this kind of thing go away.
In my coordinate system, alpha would be the AOA and beta would be the compliment to the pathline slope angle. What’s the problem with alpha going to zero as beta goes to zero? …that’s what one would expect.
Anyway, I’m sure someone has done this type of treatment somewhere, but I haven’t found anything on the Net yet. And though I can see the argument (the classical Lift/Drag treatment), I actually I don’t think this is what is going on here a lot if not most of the time, and I don’t think it’s just a matter of moving to three dimensions either, though that will be important. I think the initial assumptions regarding the flow are wrong, and therefore most of the time the angle of attack is generally very high, so high as to be operating in the classical ‘stall’ region. But then what does ‘stall’, for that matter ‘drag’ mean when the free surface is close to vertical. (At some point it might be worthwhile for me present my interpretation of what is going on, but its not really important now.)
Nevertheless, I do think there is a hydrofoil application here, and I’d like to understand the approach that’s been taken. If you want to throw some more my way, it would be appreciated.
Three dimensions is important for at least a couple of reasons:
Consider a coordinate system in which the y-axis is directed onshore (perpendicular to the crest of the wave) and lies in the horizontal plane; the x-axis is perpendicular to the y-axis and also lies in the horizontal plane; and the z-axis is vertical (perpendicular to both the x- and y-axes). The transformation from the sea surface based coordinate system to this one is a rotation about the y-axis, followed by a rotation about the z-axis). The pathline is the diagonal track representing the motion of the craft and rider “over the bottom” as viewed looking down on the x-y plane when traversing across the face of a wave. The path angle is the angle between the pathline and the x-axis. In a steady-state condition in this coordinate system, where the surfer maintains a constant position on the face of the wave and relative to the moving curl, the component of the surfer and boards motion parallel to the wave crest is Vx, and the onshore component is Vy. The pathline angle is then atan(Vy/Vx). For small Vx, the craft moves almost directly onshore; for large Vx (relative to Vy), his path is nearly parallel to the wave crest. Since the surfer maintains the same position on the face of the wave, his Vy must be equal to the wave speed over the bottom (Vw). So the path angle becomes atan(Vw/Vx). Since Vw essentially remains constant (for a uniform rate of breaking) as the surfer’s speed increases, Vx increases, Vy remains equal to Vw, and so the path angle decreases. This reduction in path angle reduces the slope of the wave face along the pathline of the craft. Since that slope is related to the driving force, it means that the faster you go, the less driving force available to propel you. It is this negative feedback between board speed, slope, and driving force that makes it difficult to achieve big increases in speed (without any active intervention by the rider, such as by pumping).
If you think about things in these coordinate systems I think you will find that there’s no requirement for large AOA angles–everything works out fine with reasonable values for the AOA, etc. For example, I have an old computer simulation model of the (steady-state) motion of a surfer on a wave on an “idealized” surfboard. On a reasonable size wave it predicts that the maximum speed attained (without any pumping by the rider) will be about 23 mph and the corresponding optimum position on the face of the wave is where the local wave face slope is 47 degrees, and the board is trimmed to an AOA of 10 degrees. These numbers are close to the speeds measured by GPS, the slope estimated from pictures, and the AOA based on the trough present immetiately behind a surfboard as it crosses across the face of a wave. Of course if the forces are not in balance, the whole situation becomes more complicated since accelerations are involved, resulting not only in changes in velocity, but in the characteristics of the wave face as the rider and craft move closer or farther from the curl, and/or up or down the face of the wave.
One of the major uncertainties in my opinion in simulating these motions is estimating the magnitude of the flow of water past the board (say in the sea surface referenced coordinate system), i.e. as the evidence I have seen (from analysis I have done using a wave breaking simulation by Grilli) would seem to indicate that there are significant changes in the speed of the flow related to position on the face of the wave.
Hope this helps,
mtb
I really do like this idea, and its directly applicable to some of my classes right now (in stab control we are on constant heading sideslip) , so its more like doing extra homework. This weekend, I’m just going to try to develop the equations of motion for the hydrofoil surfboard, and just leave all the angles and everything as variables for now. I’ll start with the steady state case of going left. As to having better ways to spend my time, due to a recent knee injury I can’t surf, so this is the next best thing.
Also, what did you use for the simulation? I was thinking about starting a matlab file this weekend. In your program did you factor in the sideslip that occurs if the foils are mounted inline with the stringer instead of inline with the flow?
I need to figure out a way to incorporate a bunch of pressure sensors into a board with some sort of onboard data logger. It would be awesome to actually have some solid test data. The main thing I have no idea of is the ballpark amount of sideslip in steady state. I guess that depends on the waves slope. The oceanography part of this is what eludes me, as far as what is actually happening in a breaking wave.
Then you might like this. (More math latter.)
Hydro Bug?
Ignorance is bliss.
I’ve search around on the Net, and I’ve waded through a lot of the Swaylock’s archives but I not yet found something similar to what is illustrated in Figure 1.
If previously, somebody has proposed such a device, or you know of such a machine, my apologies, and it would be greatly appreciated if you let me know.
Given this was Dale’s thread, which usually means at some point matters will tend towards the pneumatic, which to me means ‘flexible’ I thought that a flex solution to a surf hydrocraft might be worth exploring. (The full pneumatic treatment comes a little later.)
What I meant to illustrate in Figure 1 is semi-flexible frame with four rigid hydrofoil feet attached. I don’t know if its possible to build such a device, but if I was to, I would tend to lean towards carbon fiber, with a strategy of using tubular structures, whether elliptical or otherwise. The only truly rigid pieces are the feet, the immediate stem connections to the feet, and parts of the main frame. In figure 1, the rigid parts are indicated by gray. The possible flexible motions are indicated using circles with arrows.
Why the flex? Control. In particular, the longitudinal flex will offers the surfer an opportunity to differentially orient the foils in the direction of motion, the transverse flex may assist the surfer in holding a position on the face while moving laterally (down-the-line as opposed to just forward towards-the-beach.) by differentially orienting the foils on either side, if not all differently. It’s assumed of course that the surfer would be able to manage all this control using his prone body, similar to using a surf mat. (By the way, I curved the dome of the boogie board so that some ‘squeeze’ could be applied with the legs, see Figure 2.)
Also, the option exists to literally couple both rear and forward parts of the frame using a simple joint allowing for a transverse type of flex (in the plane of the craft.) I’m inclined to think that this would even be more helpful in maintaining a position on a face, it would definitely make turning a lot more interesting.
As for flotation, two ways come to mind immediately: use a boogie board, see Figure 2, or you could go the full pneumatic way and make some interesting bladders.
As for dimensions, I’m not really sure at this point. I had hoped to get a feel for what might be required in terms of total foil surface area by looking at what others have done, but few if any offer dimensions (we live in a proprietary world, a.k.a. capitalism.)
My assumption has been that construction would be based on a carbon fiber composite, and together with a very light flotation device would basically keep the thing pretty light. This would hopefully kept torsion forces at a manageable level, but like I’ve said I’ve never build such a thing, hell, I’ve never even worked with carbon fiber.
As for the feet, they would of course be rigid but their actual design is a point of interest. I would tend towards the individually light concaves, flaring (becoming less concave) as they progressed towards the trailing edge, thought the effect would be extremely modest.
Also the possiblity might exsist to allow one to adjust the level of flex using cables and tension knobs all inside the tubular structure, so the surfer could fine-tune the beast at the beach.
In closing one of the interesting things about this approach is that the right surfer may actually be able to get up on it, at least get a knee on it.
Anyway, please if somebody has considered such a design having rejected it or otherwise, or maybe you’ve just seen this ‘hydro bug’ somewhere else, I would be interested to know about it. Personally I’m little skeptical of my ‘Swaylock born’ ideas. At any given time (at least in the past) there can be a lot of ideas being tossed around on Swaylocks, and I’ve learned that claiming any originality should only be done with great caution.
But please, even if it’s complete unoriginal, any criticism from a hydromechanical, design, structural, etc. would be welcome.
Thanks,
Kevin
By the way, though I was hoping not to actually reference my Dynamics – The Trim equation thread, it actually is relevant here, if only the mathematical approach, i.e. the treatment using the standard cosine angles and relating them to pitch, roll and yaw.
Regrettably, though surfers usually have some appreciation as to what is being referenced, the language used is far from standardized.
In the thread, the propulsion vector is actually normal to the surfboard. Of course it doesn’t have to be a surfboard, it could have easily have been a hydrofoil. The force (normal) is then resolved using the standard cosine angles which are then related to pitch, roll and yaw (it may not be completely trivial, but it can be done.) All Lift, Drag, etc. are are forces which are resolved along more convenient axes, so you can always work backwards, as I did in the prior post to incorporate beta, the vertical angle (which I believe will eventually play a major role in all of this.)
Side slippage would occur when the appropriate component or combination of components suggests that it might. To say more would require some experimenting, but that should stop the analysis.
As for actually collecting data, I’m “Mr. Theoretical” (or worthless to you would be a less kind why of putting it), mostly because I simply don’t have the resources available to me at this time. As you consider what and how, make sure you got some idea of what has been done, I’d start with Paine’s thesis, but the more interesting paper is the one by Hornug and Killen, ‘A Stationary Oblique Breaking Wave For Laboratory Testing Of Surfboards’, J. Fluid Mech. (1976), vol 78, part 3, pp. 459-480, which should be available in the stacks or online at some local university, if not your own school. (I lost all my research a while back, but thanks to a curious post by Oneula I was able to recover much of what I had lost, and hopefully will eventually be able to replace the references. But it won’t be anytime soon.)
Nevertheless, the Hornug and Killen paper is experimental. It deals with surfing proper, but the approach is worth understanding –i.e. waves. I don’t recall if they used pressure sensors, and it was done prior to the development of microsensor devices whaich are currently available. That said, I have not done a proper search of the literature for years now. (By the way, I thought both Paine and Hornug and Killen got it wrong, and still do, how’s that for arrogance. Their works are however very important. I believe a couple of surf parks use their technique for generating waves.)
Anyway, let me know if I can be of any help. I actually like this stuff.
Thanks,
Kevin
