Decoupling Plate Design - sliding movement requirement calculation

[SunSurfer]

This will probably only be of interest to people with a technical interest in decoupling plate design.

At the sliding end of the plate, how much movement will occur as the snowboard reverse cambers / decambers in the deepest part of a carving turn?

The geometric answer is the length of a chord, connecting the two ends of the arc that represent the plate attachment points on the board, subtracted from the distance separating the attachment points. The sagitta is the maximum distance between chord and arc.

I was playing with my prototype decoupling plate mockup by decambering the board and was surprised to see how little slide movement appeared to be occurring. If I actually worked through the geometry rather than just making a lazy guess what would be the result.

r = radius of decamber curve

x = known arc length (attachment point distance)

c (circumference) = 2*Pi*R

a (arc angle) = x/c*360

L (chord length) = r*sine(a/2)*2

s (sagitta) = r - square root((r*r)-(L/2*L/2))

When the math is done, if the distance separating the attachments was 700mm, and the board decambered by a sagitta of approx. 15mm between those two points, the chord connecting the two attachment points arc is now approx 699mm long i.e just 1mm different! The decambered curve of the board at this point matches the edge of a circle with a 4 metre radius!

Using the same math calculation however, a separation distance of 500mm, bent to the point of approx 159mm radius, produces a circle of circumference 1000mm, an arc angle of 180 degrees, a sagitta of 159mm, and a chord length of 318mm. The values are clearly consistent, just by looking at them.

I had thought that the slide movement required would be an order of magnitude larger and had built that kind of allowance into my own plate design. This result is leading me to reconsider how I allow for the sliding movement!

I've sat down and done the math and saved it as an attached, zipped, spreadsheet for anyone who wants to check the math or plug in their own figures.

SunSurfer

Arcs Chords & Sagitta.zip

[Chris Houghton]

Didn't look at your math, but I can say that the Silberpfeil with a Conshox plate has a lot more movement than 1mm. Maybe it has to do with the fact that the conshox has camber built into it?

[scrutton]

15mm sounds very little. I'd expect that when the board is pushed through a turn, the board is bending a lot more than that. Just my opinion though.

[SunSurfer]

15mm sounds very little. I'd expect that when the board is pushed through a turn, the board is bending a lot more than that. Just my opinion though.

Remember, I'm talking only about the amount of decambering between the 2 attachment points, not the amount seen along the whole running length of the board. The same spreadsheet can be used to calculate that by slotting in the running length of the board instead of just the distance between the two plate attachment points.

A board with a 160cm running length would decamber by around 8 cm if the same 4 metre radius curve was applied.

SunSurfer

[www.oldsnowboards.com]

Travel distance can certainly make a big difference. I can tell you most travel less than you are calculating. Some systems have a hard stop, this can work to your advantage, again, it is largely what works for a particular rider.