Wednesday, March 30, 2011

Board Outline Drawing

Excel Workbook to plot board outline, rocker and concave I started to put together an excel workbook to help plot certain parts of the board. I've got no plan to build in any fluid dynamics (largely cause I don't know how to), its purely a drawing project. However, the value I can see in it is that it will provide a way to accurately (mathematically) describe the outline and so the impact of changing them can be studied more systematically (less anecdotal). The first cut at it was just for board outline and used only second order polynomials to describe the curves separately on each side. This was pretty limited and made drawing the curved tips really difficult to do other than through Excel's solver function to nudge the circle into where the short and long side curves intersect.

A better alternative is to use cubic splines which are piecewise third order polynomials that gives a hell of a lot more control of the curve.

To use the splines you need to pick the points you wish the curve to pass through and then generate a spline for each set of 3 points. Ideally you would put some smoothness boundary conditions on the splines so that the spline 'pieces' fitted smoothly together. However, this added another level of complexity so I left it to joining them by eye. Here's a first cut at piecing 2 cubic splines together to create one quarter of the board outline. One for each of the short edge, rounded tip , long side (mezzanine) and mid section.

There are a number VBA macro out there that you can just cut and paste into an excel workbook. The one I pulled down could easily be tweaked to spit out the co-efficients so that the whole outline of the board could be accurately described with the collection of 6 co-efficients used to generate the outline. Some of the other things I'll add are calculating the radius of curvature for continuous rockers, determining center rocker lines needed to get the desired concave.

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