Hey Dave. I’m with you on your wanting a simple way to describe rail shape. I played around with a formua of my own a few years ago. It sounds complicated, but if you get past the underlying math it is a pretty easy concept. I basically used your formula plus an extra index value to describe the overall curvature of a rail.
For example you could say, at the midpoint, I want the vertical tangent line to be 65.45% of the thickness – which is in your illustration above. One foot off the tail you will probably want this percentage to be around 75%. When I made my board I just picked two points like this and fit a line between them. This allowed me to calculate the percentage at any point along the length of the board.
Here’s where the NERD ALERT bells start ringing (…or are they already going off?).
After calculating the above percentages, I used a Hyper Ellipse equation to adjust how much crown to add to the rail curves. I’m not going to go into the details of the equation here (you can read about it in my orher post http://www2.swaylocks.com/node/1028419#381880). In short I came up with a crown index parameter.
n = Crown Index (i.e., the amount of curvature in the rail)
n = 2 (thin rails and lots of crown)
n = 10 (Boxy triple cheeseburger rails)
The equation that I used has the disadvantage of only producing boxy looking rails. That was ok with me, but I realize most people dont want that. The whole concept of using the crown factor to describe the rail is nice though. Here is a hypothetical conversation that you could have with your customer.
Enlightened Customer: I want a board with 60/40 rails at the midpoint, and going to 75/25 at the tail. Make the midpoint deck curve n=4 and the bottom curve n=7. This will give me a moderate crown on top, and a nice tucked rail along the bottom. At the tail I want the deck curve at n=7 and the bottom curve at n=9.
Here’s an example of a pair of curves that I built in Excel. The blue curve on top is the deck curve, and the red one is the bottom curve.
Here is an illustration of the cross-sectional ribs that I created for a HWS using Hyper Ellispes. I crunched the numbers using a Perl progam that I wrote. The results were exported to a PDF file, and I printed it out on a big sheet at the copy place down the street.
