Another reason is that it serves as a form of “short-hand” and thus reduces (often substantially) the space required to say the same thing using words.
Among the reasons that I like to model surfboards is that I may discover something unexpected, or find a reason for something which you have observed but don’t understand or haven’t identified the cause.
By way of a couple of examples, consider the numerical surfing simulations that were shown earlier in this thread.
Each graphic is the result of numerous individual simulations–one for each pairing of trim angle and wave face slope angle. The solution to the equations is obtained using a successive approximation (or iterative) method. In this method, a trial value for an unknown variable (e.g. the speed of the flow) is chosen, and then vector equations for each type of force are calculated. The resulting vector forces are then added together to see if the resultant force vector equals zero. If that is the case, then a solution has been achieved.
However, that’s virtually never the case for the first guess. So a new guess is chosen for the speed of flow and the calculations repeated (note: things like wetted area, aspect ratio, etc. have to be updated at each time step as well). At the completion of each iteration step, the error (residual force of the vector summation) is noted, and the next guess for the trial value is chosen to come closer to providing a solution. This repeats until an acceptable error is achieved or a limit for the number of tries is reached… When a successful solution has been obtained, the speed of the flow, the wetted area, etc. are calculated and stored into their proper place in their corresponding matrices (1 matrix per variable of interest). If the limit for the number of tries has been reached without obtaining a solution, the value for that parameter is stored as zero (as a flag to indicate that a solution was not achieved). Once simulations for every matrix element have been computed and stored, each matrix of values is contoured (to interpolate values between the pairs of points), and thus yielding the graphics presented earlier in this thread.
However, a problem was encountered each time one calculated one of these types of plots–no matter how clever one tried to be with guessing a better new value for the flow speed during the iteration process there was always a region in the matrix where it was not possible to converge to a solution. Every matrix generated was found to contain zeros in some of its cells. One interesting characteristic of the matrix was that the locations of the zeros in the matrix were along a relativel thin, gently curved line of zeros lying mainly in the upper left hand portion of the matrix. So when the matrices were contoured, they resembled a gorge cutting through a hilly landscape.
Initially I concluded that I just wasn’t clever enough to devise a way to provide a suitable new guess that would solve the force equations–even when I tried making only very tiny changes at each step. But I figured that nature would be able to accomplish what I could not. So my ad hoc decision was to obtain an estimate of what I was unable to calculate, but should be there, by writing a special interpolation program to smoothly contour these “probable real values” across the gorge of zeros. That’s basically how the graphics presented earlier in this thread were generated.
But I wasn’t very happy with that approach. For example, perhaps some of the value pairs of wave face slope and trim angle (e.g. along the gorge) the equations were just chaotic and would not converge. Buy I wasn’t very happy with that explaination either. Finally it dawned on me that perhaps there really is no solution along the “gorge” because in those simulations the motion was not steady-state (as had been assumed in developing the model). In that case, each time one estimated a new trial value, while it may have been appropriate for the previous “environment” (i.e during the previous iteration), it might not be appropriate for the current iteration step.
I further noted that the gorge was more or less confined to the middle to upper left portion of the matrix–a region characterized by large trim angles (rider well aft on the board), but small wave face slope angles. And it dawned on me that those conditions are typical of the environment that can lead a planing hull to start “porpoising”–a situation where the nose of the board begins a series of large up-ahd-down cycles. Anyhow, that feature was something that I had not forseen might happen, so it was a bit of a surprise and encouraging.
Another example…
In the simulation model, all the computed forces computed lie in a two-dimensional vertical plane that passes through the centerline axis of the board. None of the forces have a component that lies outside this plane. But I noticed that in the real world, when the rider is racing across the face of the wave (as in the simulation model), the shore-side rail of the surfboard is almost always a little lower than the wave-side rail.
That was a bit of a puzzle as that rotation (about the centerline of the board) introduces components of the pressure force vectors that are no longer confined to the two dimensional plane–and there were no obvious other force vectors that could balance these “out of plane” forces. If this situation were real, one would expect that the motion would not be steady state and the surfer and board would be changing position on the face of the wave. That does happen, but from watching surfing (and videos) it is apparent that there still are lots of times when that isn’t the case and steady-state conditions assumed in the model formulation remain.
So, the questions for the reader become:
What is balancing out these apparent “out-of-plane” pressure forces…and what implications does this have for board design and installation?
