Sidecut calculator reborn

[NateW]

Once upon a time I had a web site, which had a sidecut calculator.

Then the PC that was hosting the web site died, and that was the end of that.

After two decades, I finally got around to making a new calculator. Click here.

It's not pretty, but it works.

[SunSurfer]

I used and appreciated the old one.

That said, with variable radius sidecuts common on modern carving boards and a greater understanding of how board flex/bend influences turn shape as the board gets higher on edge, the average sidecut of a board doesn't tell as much as people once thought it did.

[ShortcutToMoncton]

Agreed. My Coiler has an 11.5m (?) sidecut, but when Bruce was showing me the numbers it was clear that 1) the sidecut at any given point on the edge varies quite considerably, 2) for these type of boards, the more important thing from a ride characteristic appears to be how the sidecut changes along the edge, and 3) board flex patterns can really emphasize these sidecut changes and work in parallel.

In comparison to my board’s 11.5m average, I think the actual sidecut is longer at the nose, much tighter at the front binding, a bit tighter at the rear binding, and way longer off the tail. 

So 11.5m is useful, but for boards with variable sidecut (which I think is most of them nowadays) it doesn’t explain how two boards with the same average number might act quite differently in practice. 

[NateW]

I sidestepped that issue by being disappointed in the only variable-sidecut board that I've tried so far.  It's a production Kessler GS board that I bought used a couple seasons ago, and just felt weird to ride a board that behaves like a long radius at low edge angles and shorter radius at high edge angles. I liked that idea in theory, but on the snow it just didn't feel right.

So I'm still using an old-school constant 13m sidecut for my custom boards, at least for now.

But I also want to try a more variable sidecuts, just out of curiosity, so that got me looking at (used) production boards, which got me wanting a calculator again. I'm trying to keep the approximate radius close to 13m, on the theory that whatever I get will behave approximately like a 13m board.

[SunSurfer]

@NateW Not sure if you saw this thread.

 

[NateW]

I hadn't, thanks.

[NateW]

On second thought, I have seen it before. But I only know that because it contains a reply with my name on it.  

Edited August 31, 2023 by NateW

[Jack M]

Thanks Nate.  I also enjoyed the original, glad to have it back.  In its absence I've looked for others but was always disappointed.  It is always useful to know the "average" sidecut radius of any board.  It will at least tell you the general size of turns the board will carve, and what boards are in the same ballpark.

[bobdea]

On 8/30/2023 at 6:55 PM, NateW said:

I sidestepped that issue by being disappointed in the only variable-sidecut board that I've tried so far.  It's a production Kessler GS board that I bought used a couple seasons ago, and just felt weird to ride a board that behaves like a long radius at low edge angles and shorter radius at high edge angles. I liked that idea in theory, but on the snow it just didn't feel right.

So I'm still using an old-school constant 13m sidecut for my custom boards, at least for now.

But I also want to try a more variable sidecuts, just out of curiosity, so that got me looking at (used) production boards, which got me wanting a calculator again. I'm trying to keep the approximate radius close to 13m, on the theory that whatever I get will behave approximately like a 13m board.

Duuuude, I can’t do radial anymore. In hardboots I’m not super comfortable with the contra/thirst thing either but on softboot wide boards I think it will eventually become the way everyone does it because it does grip well underfoot at low angle very well. 
those side cuts combined with the decamber makes the things so much more friendly but they absolutely do take some time to learn to trust….. 

the big kesslers are amazing but somewhat disconcerting. The 162s and 168s are ****ing insane… some day I’ll ride hardboots again!!!

[NateW]

My Kessler is 174. It basically rides like my Donek 170 / 13m board except that at low edge angles the SCR feels bigger, like 15 or 16m.

I might like it more if I hadn't been riding 13m radial boards for so long that anything else feels weird. At low speeds / low angles, where the sidecut acts like it's more than 13m it feels unresponsive. I'm pretty sure that if I had a board that rode like 11m in some conditions, then it would just feel twitchy to me.

To be clear, I don't hate it - it's a fun change of pace, just because it's different. But when the novelty wears off it will show up in the classifieds.

*

[NateW]

On 8/31/2023 at 6:29 AM, Jack M said:

Thanks Nate.  I also enjoyed the original, glad to have it back.  In its absence I've looked for others but was always disappointed.  It is always useful to know the "average" sidecut radius of any board.  It will at least tell you the general size of turns the board will carve, and what boards are in the same ballpark.

You're welcome! 

[SunSurfer]

@NateW Just confirmed a suspicion of mine. Enter any SCR then put edge angle to 90 degrees and the calculator returns a turn radius of 0 (zero). 
The calculator is just returning the curve generated on a perfectly flat surface with nil surface penetration by flexing the board until all of the steel edge touches the surface.
Even on ice surface penetration occurs otherwise there is no grip. Ice skates penetrate the ice surface to form a groove the skater is supported by for any change in direction.

A calculator for the real world would have some way of calculating the resultant curve formed at the level of the surface by the combination of both sidecut radius and board flex. (Yes, I think that the Physics of a carved turn model is incomplete - https://arxiv.org/pdf/physics/0310086.pdf )

Thinking of it in 3 dimensions - X horizontal, Y vertical, and Z board's direction of travel.
X axis represents the sidecut curve
Y axis represents the flex curve
and the board rotates from X towards Y along its long axis as the edge angle increases.

A simple treatment could simulate the boards flex radius at 90 degrees edge angle matching the SCR at 0 degrees edge angle, (assuming also no torsion of the board) and produce a resultant base curve at the level of the surface.

If the flex curve radius was able to be varied then we could all see in an accessible way how board flex and SCR interact in forming turn shape.

My maths is not up to generating a calculator like this. Nate, how about yours?

PS: thinking about it more I suspect that it is probably beyond all but the most expert maths modellers.
 

Edited April 3 by SunSurfer
postscript added after mulling it over for a few more hours, and seeing Corey's reply below.

[Corey]

The most important question is: How long is a rope? 

I kid, but this seems like something that would be exceedingly hard to model in a pure mathematical sense. Knowing that a rider can change the turn diameter by loading the board, independent of edge angle, means it's going to be complicated. 

The Thirst sidecut design (and @johnasmo's subsequent open-source experimentation) gives a hint of this complication. 

My two Coiler Contras have absolutely become my favorite boards with a shocking versatility, so I'm a believer! 

[SunSurfer]

@Corey Agreed, incredibly complex. Flex radius changes as the board tilts, snow compresses, and the changing bending forces generated by the rider's direction change (both in vertical and horizontal planes). Riders mass and stance width are also variables.

The rider's loading doesn't change the board's sidecut, it just changes the board's flex radius.

For me, too many people accept the Calculator above as "truth", given that it has the peer reviewed published physics analysis underpinning it, and seem completely unaware of the contribution of the flex curve to final turn shape.

[Jack M]

15 minutes ago, Corey said:

The most important question is: How long is a rope? 

Very important.  The calculation of turn radius = sidecut radius times cosine of edge angle is just an approximation.  Cosine of 90 degrees is 0.  I think it describes the "projection" of the sidecut onto a flat surface.  But because the length of the snowboard does not change, and because it sinks into the snow some amount, and because of flex, it's not that simple.  I believe the actual radius is slightly tighter.  My maths aren't up to the task.

[Hug Masso]

Sorry to seem dumb, but I don’t see how this calculator works. I put the numbers in it and nothing happens, there is no “generator” or “calculator” button. How does it work? Is it my phone? 
 

Thanks in advance!

[SunSurfer]

@Hug Masso 

Try using a computer. When I tried using my phone the layout and text didn't align properly.

You enter the measurements (tip width, waist, tail width, effective edge) of your board first. Then it calculates an average sidecut radius with the board flat 0 degrees on a flat surface. 

Then you can enter different board angles and it calculates the curve as if the board could flex without limit so that the the whole of the steel edge touches the plane supporting the ends of the effective edge.

Edited April 3 by SunSurfer

[johnasmo]

Letting the calculator figure the radius is a good thing.  Calculating radius from sidecut depth and effective edge is a good way to take the sidecut shape out of the picture.  A VSR shape and a radial shape with the same depth will project to a plane with a similar curve depth, but the shape of the projection will differ, making that a design variable you can play around with.

A turn size calculator that doesn't take into account snow compaction won't be able to explain how straight skis turn.  Trench depth matters, but predicting it with a calculator would involve knowing rider mass, speed, and some tangible measure of compactability as a function of depth.  Yeah, that's when the math and physics get so complicated that making and testing prototypes remains more practical.

A calculator that took trench depth and board angle as input, though, could calculate your turn size without even knowing sidecut radius.

It's always going to be about both flex and sidecut.  My feeling is that sidecut radius is a good predictor on firm hardpack so long as the board isn't too stiff.  In softer snow, say leaving two or more inches of trench, it's more about the flex.  And like sidecuts, different core profiles produce different flex patterns, making that a design variable you can play around with.

[NateW]

My goal for this calculator (like the one before it) is to be able to answer questions like "is this board going to turn tighter or wider than my current board?" based on readily available information (tip / waist / tail measurements). 

I added the speed stuff because I was curious about what those speeds would be like in general, and also curios about how much the speed should vary with carve radius.

I don't think anyone is measuring their trench depth, and I don't think anyone really cares much about the actual specific length of their turn radius, so I'm not inclined (no pun intended) to figure out how to use the former to estimate the latter.

It might be interesting to model how much the board stiffness affects carve radius, but my guess is that it makes very little difference, so it's not a priority for me. It seems to me that stiffness affects feel much more than carve radius. By "feel" I mostly mean how sensitive the board is to edge-angle during skidded turns, and how much support the board gives me when my balance gets way off and I need to heave myself back toward the center of the board.

I don't use any of the info from this calculator while I'm riding, but I do use it when I'm considering whether or not I want to buy a particular board. That's another reason I think it's useful to use board dimensions for input, but not trench depth.

9 hours ago, Hug Masso said:

Sorry to seem dumb, but I don’t see how this calculator works. I put the numbers in it and nothing happens, there is no “generator” or “calculator” button. How does it work? Is it my phone? 

After you enter a number, tap on a different text-entry box.

I made this on a PC where I press the tab key after I enter a number.

But now you've got me thinking that I should just have it do the math with every keystroke... There will be some weird numbers in the output after you type the first digit of a two-digit number, but that's probably less confusing than the way it works right now.

[st_lupo]

6 hours ago, johnasmo said:

Letting the calculator figure the radius is a good thing.  Calculating radius from sidecut depth and effective edge is a good way to take the sidecut shape out of the picture.  A VSR shape and a radial shape with the same depth will project to a plane with a similar curve depth, but the shape of the projection will differ, making that a design variable you can play around with.

A turn size calculator that doesn't take into account snow compaction won't be able to explain how straight skis turn.  Trench depth matters, but predicting it with a calculator would involve knowing rider mass, speed, and some tangible measure of compactability as a function of depth.  Yeah, that's when the math and physics get so complicated that making and testing prototypes remains more practical.

A calculator that took trench depth and board angle as input, though, could calculate your turn size without even knowing sidecut radius.

It's always going to be about both flex and sidecut.  My feeling is that sidecut radius is a good predictor on firm hardpack so long as the board isn't too stiff.  In softer snow, say leaving two or more inches of trench, it's more about the flex.  And like sidecuts, different core profiles produce different flex patterns, making that a design variable you can play around with.

This!  I'm fairly convinced the flex profile of the board is at least as important as the sidecut for determining the realized turn radius.  But, what properties of the snowboard are really important to describe?  Two boards can provide the same theoretical turn radii, but how the board reacts on the way into that operating point determines if the board feels good or bad or if you can even reach the required degree of inclination. 

Like MTB: total suspension travel is one of the numbers that people get really hung up over (and it does, to an extent, describe the intention of the bike).  But factors such as progression rates, axel path, anti-squat, damping, length, reach etc, etc are going to have an even greater influence on the ride qualities that may inspire the confidence to really push the bike.  I'm sure there are some analogs between MTB and SB.  Damping, progression, etc in a SB are created by materials, camber and side-cut profiles.

If you really want to capture the dynamics of a full SB turn, there is a lot of factors that should really be taken in.  Snow deformation is an inherently nonlinear phenomenon (Ski-Snow Contact Mechanics), camber and side-cut geometries would need to be handled simultaneously, board flex, length, rider weight, COG, and torque inputs at the bindings, slope grade, board speed, etc, etc.  In the above discussions I'm wouldn't even be 100% sure that the assumption of uniform trench depth is valid (but maybe close enough).  At that point you might as well perform you simulations on the hill.

[SunSurfer]

@st_lupo Thanks for the snow penetration by skis reference above.

It's photos like those from the

topic that in many ways make the most convincing case for board flex being a major determinant for turn shape at high angles. But they also make the case for the calculator producing smaller than actual turn radii at high board angles.

take any 12m sidecut and run it through the calculator
45 degrees = 8.5m (rounded)
50 degrees = 7.8
55 degrees = 6.9
60 degrees = 6.0
65 degrees = 5.1
70 degrees = 4.1
75 degrees = 3.1
80 degrees = 2.1
83 degrees = 1.5
85 degrees = 1.1
86 degrees = 0.84
87 degrees = 0.63
88 degrees = 0.42
89 degrees = 0.21
90 degrees = 0

So understand its limitations. Absolutely it calculates the average sidecut. But take the board angle effects with several grains of salt!

Note also that the Physics of a carved turn maximum speeds merely note the speed at which snow spray starts to occur, not the point where the snow strength fails and the board slides out from under the rider.

Edited April 4 by SunSurfer

[Jack M]

11 hours ago, NateW said:

It might be interesting to model how much the board stiffness affects carve radius, but my guess is that it makes very little difference

I intended the Winterstick Squaretail Plus 170 to replace my Kessler 168.  I spec'd the sidecut at 9-12-11m, based on Kessler's published "sidecut range" of 8-12m.  The first 170 was too soft for me and turned much tighter.  At least as tight as my F2 WC163 (radius 9.8m) at the time if not tighter.  It held a great edge thanks to extra torsional reinforcement, but it was redundant with the 163 which was not the desired outcome.  I sold it and had another 170 made stiffer and I tweaked the sidecut a little and it was a success.

[SunSurfer]

@Jack M And there you have it. An example of the significant contribution that the flex radius of a board makes to turn shape independent of SCR.

Just come across this very recent and more complete look at ski performance and turn shapes for carved turns. I found it a little more approachable than some other papers, and full of little gems.

Amongst the gems, on snow testing with the Norwegian National Ski Team demonstrated that the turn radius with changing ski (board) angle, predicted by the equation behind @NateW's effective SCR calculator, is a reasonably accurate predictor up to about 70 degrees.

Balanced carving turns in alpine skiing. Sports Biomechanics, 22 (9). pp. 1209-1242 (Cover date Sept 2023)

https://eprints.whiterose.ac.uk/168379/1/carving.pdf

Edited April 4 by SunSurfer

[Jack M]

I suspect nobody is truly carving beyond 70 degrees.

[SunSurfer]

CARV ski technology has the ability accurately measure changes in ski (boot) sole angle from a zeroed calibration point. In the boots of some skilled hardbooters, it would provide a definitive answer to that question.

https://getcarv.com/ 

And Carv explains why Ted Ligety is so good.
https://getcarv.com/blog/why-its-almost-impossible-to-ski-like-ted-ligety
Note Ted gets edge angles up closer to 80 degrees in his turns.

Edited April 4 by SunSurfer