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excellent thread gents
so is MTB a hit and run artist? did i really read his lengthy mathematical post or just gloss over it?
so…what is FLEX?
technically, FLEX is an inadequate term as it relates to mechanical objects…
so to clarify…
undampened flex with strong return is a spring
undampened flex with weak or no return is compliance
flex with a combination of both is a dampened spring (classic spring/mass/damper mechanical vibrations model)
when you look at modern shortboard surfing from the 70’s vs today, one of the key differences is that lighter equipment allows the surfer to use his legs more effectively as a spring (the pump)…
so legs are the spring, the board is the mass, the water under the board is the damper…
the lower the mass (lighter board) and the lower the wetted area (smaller shortboards), you have reduced the mass and damper and thus faster stronger spring oscillation is facilitated (faster springier leg pumps - classic cause and effect of the spring/mass/damper model)…combine that with todays dampened springed poopees and you can see the effect in action…
as far as velos kneeboards…from the sound of it they benefit more from compliance than a standup surfboard…the feeling on intimacy with the wave must be epic…
mtb here, on the rebound…(sorry for the delay in responding, but I also have other things to do which place demands on my time)
Please keep in mind that my post was addressing only the commonly expressed concept that energy stored in the (presumably longitudinal) flexing of a surfboard might result in an increase in speed due to the momentum imparted to the water as the energy associated with the flexing of the board (the spring in the system ) returns to its equilibrium position.
To summarize and/or restate the points I tried to make in my previous post…
What one has is not an energy conserving system, but rather a highly damped system (as indicated by the power required to drive the board at representative speeds–e.g. approx 4.3 hp at 19.5 mph). Hence to maintain a speed, the craft must constantly be resupplied with new energy. Rates of energy input (and dissipation) constitute (and are defined as) power. When the propulsive power matches the rate of dissipation of energy (power loss), the craft travels at a constant rate of speed. To go faster either:
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More power must be supplied to the craft–e.g. riding a faster moving (e.g. typically bigger) wave, or riding higher on the wave face (to increase the wave face slope angle), or…
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The power dissipated must be reduced (e.g. by riding a hydrodynamically more efficient craft), or…
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Additional energy must be supplied to the system (on a continuing basis).
The primary source of propulsive power is the force of gravity acting in concert with the sloping face of the wave. The only possible additional source of energy (apart from an external input…such as being pulled by a towline to a PWC) is the potential energy stored in the rider (e.g. via ATP) and subsequently expressed by extensions and contractions of various elements of his body (e.g. arms, legs, etc.). In the present case, the rider’s legs pumping up and down would be analogous to pistons extending and contracting to transfer energy to the spring (surfboard).
The point of the earlier post was to demonstrate that the energy stored in a (longitudinally) flexed surfboard, and the rate at which that energy can be supplied via flexing the board (i.e. the power associated with the flexing board) is small compared the rate of power dissipation due to drag. Hence the increase in speed resulting from this additional power input is small–even if the efficiency of the transfer mechanism is 100 percent.
[An aside…
As regards the comment that a 4 inch flex is not representative of the longitudinal flex (flex rocker?) in a shortboard, that is true. But as is evident from the flexural equations in that post, the stiffer the board is (for a given surfer’s weight), the less energy that can be stored in the flex of the surfboard (i.e. the “spring”). Hence “pumping” a stiffer board up and down to transfer energy to the flexing board will, all other things being equal, be even less of a factor. Hence by choosing what is clearly an exaggeration in the flex, I could demonstrate that even with that favorable (but unrepresentative) quality of the board, the energy transfer was too small to make a significant difference. While it is also true that with a smaller degree of flex the rider may be able to complete a flex cycle more frequently than for a greater flex, that certainly isn’t what appears to be the case when observing real rides with pumping. ]
Therefore, if flex (and the rider’s use of flex) is to significantly increase the speed of a board, that increase must result from:
(1) allowing the board to continue to operate efficiently at positions on the wave face with a greater wave face slope (as to where this occurs on the face of the wave obviously depends on the shape of the wave as it breaks), or…
(2) the flex must be used to improve the hydrodynamic efficiency of the hull (as I alluded to in my earlier comments about “natural rocker”), or…
(3) both (1) and (2).
As I noted above, my earlier post addressed only whether energy stored in the flexing of a board could substantially increase speed–and my conclusion was that it could not. Note, however, that I did not address in any detail the potential role of flex with regard to items (1) and (2) (immediately above). Not surprising, since the question I addressed could be answered with some simple and pretty defensible calclulations and assumptions combined with basic laws of physics, whereas (2) and (3) get into the nitty-gritty of the specific hydrodynamics of the interaction between the wetted area of the board and the wave, plus the details of the compound-curved, 3-d flow field within face of the wave in the immediate vicinity of the board. Both are very difficult problems to solve–even with the current state-of-the-art computational fluid dynamics programs and modern computers.
However, it would seem conceivable, and perhaps even highly likely, that the energy (and power) that can be produced by the rider, combined with an appropriately designed craft, could collectively be sufficient to dynamically modify the shape of a (planing) hull so as to expand the scope of conditions over which a hull will maintain some degree of hydrodynamic efficiency. And by so doing, expand the region of the wave face over which the hull will operate efficiently–in particular, riding where the slope of the wave face is increased. Either in a “static” fashion (as in maintaining a constant position), or through some near optimum dynamic path (e.g. a series of “skating/pumping” motions that traverses some vertical region of the wave face in the vicinity of the craft) so as to produce a substantial increase in propulsive power while minimizing the loss of hydrodynamic efficiency.
Similar considerations can also be applied to minimizing the speed lost while executing turning maneuvers. It is this consideration, rather than pure speed, that was one of the primary motivations for my ongoing experiments with my hydrofoil paipo (“HYPO”) board. Also, as has been commented on by several in this thread, flex can also considerably alter the “feel” of a board board, thus allowing the builder/rider to find the combination that he perceives to be the best for his style and desires.
My present impression is that in general it is much easier to make a board “feel” different than it is to substantially alter its speed performance (although the performance may be perceived to be substantially different). While no one who has ridden my flex kneeboards has described them as “slow”, for me it is largely this “feel” factor–especially during maneuvering–that has driven the design of them.
mtb