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Geometry and Sidecut Radius

Slow Eddie

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Hi All,

I was trying to figure out the sidecut radius of one of the boards I own. Here are what I thought to be the pertinent dimensions:

Nose Width (defined as widest point forward of center) = 233 mm

Waist Width (defined as narrowest point of board) = 188 mm

Tail Width (defined as widest point aft of center) = 229 mm

Distance between widest points of nose and tail, at edge = 1685 mm.

Making the assumption that the radius is constant, and the taper from front to back is a product of "rotating" the sidecut towards the rear of the board, rather than using two different sidecuts, the average "wide" width of the board was considered to be 231 mm, yielding a difference in width of 43 mm ("sidecut depth", in Burton lingo).

Those familiar with geometry can see where I am going with this one. The straight-line distance can be regarded as a chord of a circle with a radius of r. The sidecut depth can be regarded as the sagitta of said chord. According to the formula for determining the radius of a circle from these two pieces of information, which I found here...


...the radius of the circle that matches those dimesnsions is 33035 mm, or 33 meters! Now, even for a custom-built 185 cm board, isn't that a little excessive?

Perhaps there is a problem with my math. Does the equation seem to be a valid method to derive the number I'm looking for? I triple-checked my measurements, so I hope there's no error there.

Does anyone out there have a more reliable way of determining sidecut radius?


Eddie Plantilla

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I worked out the same equation myself a while back, and it matches the equation you found. But I get one half the radius you get when I plug in the numbers: 16.5 meters. Did you use half of the running length for d, and divide by twice the sidecut depth?

I've used the same equation to estimate sidecut radius on some of my boards and it seems to give believable numbers. I remember getting a little under 9 meters for my old 156 Burton Alp and somewhere around 12 meters for a 167 Factory Prime which sounds about right.


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The widest points of the board are actually not part of the sidecut. If you put your board flat on the floor, and slide a piece of paper under the nose until it stops, you'll see that the widest point of the nose/tail is off the ground. This is a result of having to end the sidecut somewhere, somehow, while maintaining continuity of the curve of the board. Therefore, at the point the sidecut ends, the edges are still flaring out from center.

If the widest points of the board were on the ground, that would mean that the last few cm's of board on the ground are not part of the equation of the sidecut.

And 33 meters has got to be a goof.


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I was, in fact, using the entire chord length for d, rather than one-half the chord length. But having made the corrections, now I'm getting an r value of 8.275 m - about half of what you got. Must be something else wrong on my end - the 16.5 m you got sounds about right for the feel of this board.

Good thing I'm not an engineer.

And in response to Jack's comments, perhaps I will try the paper-under-the-base method and redo my measurements.

Thanks to both for the input.


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I think maybe you're dividing by the 43mm number (aka 4.3 cm) that you called the sidecut depth. You should be dividing by half of that number because you want the sidecut on just one side of the board, not the difference in widths between the ends and waist.

Jack - I think you're saying that the length on which to base the sidecut radius calculation is a little less than the length between widest points? Another factor is that I read somewhere that most boards have a more complex curve to the sidecut than just a simple radius, so this is all approximate anyway.


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Wolfgang - thanks for the clarification. We're on the same page now.

Jack - I see what you mean about measuring between where the uncambered deck touches the floor, but when the deck is weighted and tipped onto its edge, wouldn't the widest points of the board define the endpoints of the running length/chord length anyway?


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Originally posted by Jack Michaud

The widest points of the board are actually not part of the sidecut. If you put your board flat on the floor, and slide a piece of paper under the nose until it stops, you'll see that the widest point of the nose/tail is off the ground.

While technically that is true for board with unequal nose & tail width, it will only throw off the measurements by a few mm - hardly a significant number. The big error comes from the fact that the side cut does not start and end at these points, but rather is blended so that it hits them smoothly (primarily on the nose - the tail is often a lot less smooth). One of the bad assumptions of the formula is that the sidecut starts and ends at those points, but that assumption is minor compared to the other ones it makes. The other bad assumptions include the waist being at the midpoint of the arc, and also that the sidecut is in fact circular.

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