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For reasons that I will probably post about some time I was looking at the specs on the Atomic Snoop Daddy and the Rossi B3.

the Rossi Dimensions are: 120-83-110 (for a 176 length)
the Atomic Dimnesions are: 127-88-113 (for a 174 length)

Both turn out to have a 16 cm sidecut. However the Rossi is listed as having a 17.3 m turning radius vs. the Atomic with a listed 20.5m radius. This makes no sense to me as with a shorter length the Atomic should have a shorter radius, if anything.

Is this inaccuracy common? If so, people should be careful to look at the sidecut specs as opposed to turning radius for comparison of skis (which I have pretty much always done, anyway).
I don't think it's inaccurate at all - they are different widths, so the radius will be different. (PhysicsMan can probably explain it properly)

Oh, and I think it's probably 16mm sidecut, not cm.
Likewise, I don't think it is inaccurate.

I do not think it has to do with ski width, so much as how each manufacturer chooses which points on the ski are used to specify ski length.

Tip-to-tip along the base?
Contact point to contact point?

What these variations would mean, in the context of PM's sidecut calculator, is to change the conversion factor between the "ski length" cell and the "effective edge length" cell.
I'm not sure the width would effect the radius. French measure along the curve, not chord length, which could explain the difference (the Rossi may actually be shorter than the Atomic).
Quote:
 Originally Posted by Wear The Fox Hat Check out this from PM...http://forums.epicski.com/showthread.php?t=2681
According to PM's equation points out the turning radius of a ski is only dependent on sidecut and "effective edge length," i.e. the curved edge length of the running surface. Nothing to do with ski width.

Telerod's point about the difference between measuring chord length vs. length along the curve may be valid (I'd have to do a calculation to check if that could make up the 3m turning radius difference).

I wonder if there are ski manufacturers who are using chord length to determine turning radius. Hope they all convert.
Quote:
 Originally Posted by Si According to PM's equation points out the turning radius of a ski is only dependent on sidecut and "effective edge length," i.e. the curved edge length of the running surface. Nothing to do with ski width. Telerod's point about the difference between measuring chord length vs. length along the curve may be valid (I'd have to do a calculation to check if that could make up the 3m turning radius difference). I wonder if there are ski manufacturers who are using chord length to determine turning radius. Hope they all convert.
Seems to me even running length isn't quite it. Wouldn't the relevant number be the distance between the widest spot on the shovel and the widest spot on tail?

I would hope the manufacturers are using more detailed models with info we don't have access to. The "effective edge length" is a fudge factor to soak up the difference between detailed and simple calculations.

As PM says in his documentation with the spreadsheet, the effective length formula was tuned
"so that the results of the sidecut formula agree on average with the sidecut radius for a variety of skis where the manufacturer actually published BOTH the sidecut radius and the three width dimensions."
Quote:
 Originally Posted by Wear The Fox Hat Oh, and I think it's probably 16mm sidecut, not cm.
A 2 meter turning radius! Now that's a responsive ski.
Quote:
 Originally Posted by mdf A 2 meter turning radius! Now that's a responsive ski.
OK! OK!
My edit window was expired by the time I noticed my error!
Either that or you just haven't experienced the 100+ cm wide skis that I have:
Don't forget about relative flex of each guys.
mdf makes a good point, the chord length will not be directly related to effective length depending on the shape of the shovel and tail.

"Turning radius" may differ from sidecut radius depending on how it is defined. Maybe they take flex into account somehow, as Uncle Louie suggests.
Good point, Uncle Louie. Of course, the "sidecut radius" is traditionally measured with the ski not flexed. But the manufacturer may take the flex into account when designing the sidecut. From Volkl's 05/06 catalogue: "the ski's sidecut is designed in a virtual turn; flex, G-force and turn radius are simulated".
For all we know, the curve of the edge may not be part of a circle's arc, it may be part of a parabola or sine wave or something else weird, in which case the "sidecut radius" (ie. the radius of an imaginary circle formed by continuing the curve of the edge, when viewed from above) would be only an approximation.
I have often wondered the same thing as the original poster. I think differences in measuring "ski length" are part of the answer, but not necessarily the whole thing.
The only ski that takes flex into account is the Rossignol Mutix. In the 06/07 Rossi catalogue it gives the "dynamic radius" as 11m with the "short arms" and 15m with the "long arms". Of course, the sidecut of the Mutix does not change when you swap the arms, so what they're estimating here is some kind of "turning radius" based on softer ski flex and extra snow compression with the shorter arms.
By definition, I believe turning radius of a ski is based on a flat ski and not dependent on ski flex. It's just the radius of the circle prescribed by the shape of the ski. Of course that requires some approximation as the shape of the ski is not necessarily circular. Also, that's not to say that flex isn't an important characteristic.
That's the definition of sidecut radius. "Turning radius" might be used differently. Dynamic radius on the Mutix leads me to believe Rossi might consider flex when numerically describing turning radius. Bell's post saying only the Mutix uses such factor might be an assumption based on the fact that only the Mutix has more than one turning radius (hence "dynamic").
just because skis have the same width at certain points, it doest mean that the curve between those points is exactly the same.
Si, buy them both, ski them, and report back. It's the only solution. (Or better yet, get Phil "gearwhore" Pugilese to buy them. I hear he hasn't bought any skis in at least 12 hours... )
Sidecut radius is calculated using the length from the widest point of the tip to the widest point of the tail.

Width and flex have nothing to do with it.

It is very possible for skis with similar sidecut dimensions to have different radii. The key is the relationship of the sidecut dimensions.
Si - Excellent observation.

IMHO, even if done using the most accurate measurements and using a consistent computational technique, sidecut radii numbers are at best only good to about plus or minus about 5%.

As mentioned earlier in this thread, determination of the exact position of the front and rear contact points (and ski width at these points) is always a bit of an issue, but, in principle, this can be done quite accurately for hard snow. There is a minor problem in that the contact points move slightly fore and aft as the ski is edged and flexed, but this is a fairly small effect.

A more significant problem pertaining to contact length is whether or not a particular mfgr does something incredibly stupid like simply uses the maximum tip and tail dimensions (and the fore-aft distance between them) for their computation, even if the widest points occur in the upturned portions of the ski.

In my opinion, (and as also stated earlier), the major problem in determining an accurate sidecut radius is that the sidecut curve is not exactly a part of a circle, and thus, when you try to fit a circle (ie, radius) to it, you get different results depending on what procedure you use.

I've tried a few different procedures and they all give different estimates for the sidecut radius. Below are some of the procedures I've tried:

1a) A single curve fit to a circle knowing the sidecut dimensions, contact length, but NOT knowing the exact location of the waist. In addition, use the standard small angle approximations. This is the procedure given in many sources (eg, Physics of Skiing), and is the one I use in my published spreadsheet,

1b) Same as 1a but not using the standard small angle approximations. This is pretty obscure, and I was surprised to find a website in Sweden that discusses this approach. The computations are significantly more difficult and probably not suitable for the average user.

2) A single curve fit to a circle knowing the sidecut dimensions, contact length, but knowing the exact fore-aft location of the waist.

3) Knowing the sidecut dimensions, contact length, and exact fore-aft position of the waist, estimate one radius for the fore-body of the ski, and another for the rear of the ski and average the two radii. The two radii are often surprisingly (several meters) different.

Basically, given the above differences, as well as the effects of snow compaction, the small degree of skarving present in even the best "carves", and the effects of flex on the actual turning radius, I personally take sidecut numbers with a proverbial grain of salt that is anywhere from 0.5 m to 1 m wide .

If I'm really interested in getting an accurate comparison of some skis, I'll measure the skis myself and do the calculations for all the skis consistently by the same method (eg, my spreadsheet) instead of having to worry whether the mfgrs all used the same measurement and computation techniques. Even doing this, I'll mostly use the numbers I obtain to rank order the radii and get an idea of the spread in radii, and not take them as "Gospel".

HTH,

Tom / PM
Nice post, Tom. Thanks.

I'd like to clarify one thing, though. In the manner that ski manufacturers use the term "Sidecut Radius," the relative hardness of the snow and the inability to achieve the pure carve ("skarving") confuse the issue.

Sidecut radius is simply a circular approximation of a usually non-circular sidecut on a new, untuned, unflexed ski when it leaves the factory.

This term gets confused when people interpret it to mean "turning radius," something they believe indicates the size turn the ski will naturally make in the snow. For the reasons outlined by many posters above, this is nearly impossible to determine, because flex, snow hardness, etc, do obviously play a role. This is why most manufacturers stay away from this terminology.

On a side note, don't try to do your own radius computation using the manufacturers published sidecut dimensions - they are never accurate enough to give you an accurate result. The published dimensions are usually the dimensions of the mold, and hence the finished product is smaller once the edges are finished. As as Tom says, you need to know the distance that widest parts of the tip and tail are from the center.
Quote:
 Originally Posted by Wear The Fox Hat Si, buy them both, ski them, and report back. It's the only solution. (Or better yet, get Phil "gearwhore" Pugilese to buy them. I hear he hasn't bought any skis in at least 12 hours... )

Well, that is kind of happening. I am purchasing a pair of Snoop Daddy's (174) for bc and as a compliment to my Metron B5's. I just learned yesterday that I had won a pair of Rossi B3's (Skiing Magazine special edition) in a 186 (hmmm, is that cm or mm ). I don't see a need for the Rossi B3's really, however, they have significance to me as representative of a letter to the editor that I wrote (see this thread). So, I may decide to mount them up, leave them at Solitude (I can't travel with 3 skis), and occasionally ski them in memorial.
If the side curves change radius along the length of the ski, and you can't actually measure the total curve lengths, two skis can have the same sidecut and quite different turning radii.

Also, FWIW, I've found that PhysicMan's radius calculator can give significantly different estimations of turning radius than those at manufacturer's sites. For instance, Volkl gives far shorter radii for its fattest skis than the spreadsheet. Could be that some assistant at Volkl typed in the wrong numbers - the 177 Mantra and the 176 Gotama are given the same radii, highly unlikely - or it could be that the complex curves actually used are not covered by the spreadsheet's assumptions.
BTW, unequal radii in the forebody and aft sections of the ski and other sidecut shapes that are not one pure segment of a circle have their advantages -- Done correctly, they give the ski more versatility.

OTOH, if you have one radius in front of your boot, and another radius in back of your boot, Oh, dear, just how are you ever going to make perfect RR tracks.

Tom / PM
PS to the above ...

I don't have the time to look this up at the moment, but if my memory serves me, doesn't the B3 have more of a semi-twin tail and the Atomic more of a traditional flat tail?

Of course, my memory could be completely wrong, but if so, that would reduce the effective contact length of the Rossi and hence reduce its sidecut radius. My spreadsheet is intentionally very simple-minded. You have to "fool" it to take such subtleties into account.

Tom / PM
Quote:
 Originally Posted by PhysicsMan OTOH, if you have one radius in front of your boot, and another radius in back of your boot, Oh, dear, just how are you ever going to make perfect RR tracks. Tom / PM
The very fact that you are leaving tracks indicates that "snow compression" has taken place. And so the amount that the ski flexes has played a role. Therefore the purely geometrical calculations of turning radius, based purely on sidecut radius and edge angle, are no longer totally accurate.
(I only know all this from plowing through many classic PM posts!)
Quote:
 Originally Posted by Martin Bell ...I only know all this from plowing through many classic PM posts! ...
Hopefully, you didn't wear out too many of these guys in the process.

BTW, in my previous message, I forgot to mention the measurement / computational technique that is probably the most meaningful to actual skiing for determining the effective sidecut radius of a ski, but which is also the most difficult to do in practice, and impossible to do from just the published sidecut numbers.

In this technique, instead of including the entire ski in the computation, you just (mathematically) fit the best circle to the center third or so of the ski. Since for most modern skis, this is the section that by far produces the highest snow / edge loadings, and contributes the most force to changing the direction of the skier in turns, the sidecut shape in the center of the ski is more important than the sidecut shape at the very tip and tail of the ski.

Another benefit of concentrating on only the middle third of the ski is that the circular arc approximation is vastly better over smaller distances so the various formulas I mentioned in my earlier post all produce more tightly grouped results. Unfortunately, this technique requires extremely accurate (say +/- 0.05 mm) measurements of the ski width to get reasonable accuracy in the radius determination.

Tom / PM
What I have done in the past, with good results, is assume a cubic polynomial fit through the ski, then use calculus to get the radius of curvature at the center of the sidecut. This gives:

Radius = L^2 / (2*Tip + 2*Tail - 4*Waist)

Where:

Tip is the tip width
Tail is the tail width
Waist is the waist width
L is the linear distance from the Tip to Tail (where the respective width points are measured).

Note that L is measured along the ski axis, not along the sidecut.

Be sure to use the same units for everything. As an example, take a Fischer RX-8 180cm with these dimensions:

Tip=115mm
Waist=66mm
Tail=98mm
L=165.5cm=1655mm (mm to be consistent)

Radius = 1655^2 / (2*115 + 2*98 - 4*66) = 16907.6 mm = 16.9m

The Tip, Tail, Waist dimensions are according to spec here, but L was measured on my workbench last season (and is subject to my memory since the pencil marks are pretty much gone now). The 180cm RX-8 is really 178.5cm tip to tail and 165.5cm from the tip width point to the tail width point. That 165.5cm is where my memory is not so clear, so a re-measure is in order.

The main benefit of using this simple formula (besides that it's based on Calculus, which is well accepted) is that you can directly see the contributions of each geometrical parameter and how they are weighted in the calculation. For instance, the waist has double the weight of the other width dimensions, with a negative sign -- so decreasing waist has twice as much effect as increasing tip/tail width on reducing the radius. And so on; even if you don't run the numbers, the formula itself has some great rules of thumb built in.

Craig
Quote:
 Originally Posted by skier219 What I have done in the past, with good results, is assume a cubic polynomial fit through the ski, then use calculus to get the radius of curvature at the center of the sidecut. This gives: Radius = L^2 / (2*Tip + 2*Tail - 4*Waist)
Hi Craig - Great to see a fellow geek on Epic, and a double for your work. It's always great to derive something from basic math concepts.

But ... the only problem is that your formula is absolutely identical to the standard formula that I quote in my original message: http://forums.epicski.com/showpost.p...16&postcount=1

You will see this immediately by substituting the formula for sidecut:

sidecut = 0.5 * ( 0.5* (Tip + Tail) - Waist)

and then plugging that into the formula at the beginning of the message I cited.

Tom

PS - Your comments on the value of seeing the effects of each variable on the final result are right on the mark.
Ok, since you all obviously have too much time on your hands,scan the ski get about 100 points along the running surface and do a least squares regression to find the best fit radius.
Quote:
 Originally Posted by PhysicsMan Hi Craig - Great to see a fellow geek on Epic, and a double for your work. It's always great to derive something from basic math concepts. But ... the only problem is that your formula is absolutely identical to the standard formula that I quote in my original message: http://forums.epicski.com/showpost.p...16&postcount=1

Ah, well that's a good kind of problem to have! I feel better that we both have arrived at the same formula. I looked back in my notes and saw some other interesting facts. Even though I assumed a cubic for convenience (so derivatives were straightforward) you can get the same formula just by assuming any smooth concave curve exists fitting the sidecut dimensions, which is kind of cool. It really does boil down to those "point" dimensions. Anyways, I should go back and read your previous topics in detail.

Now if we could only find a formula telling me how to stay out of the backseat all the time, I'd be golden....
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