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# Point Of Diminishing Returns With Regards To Ski Length - Page 5

What are Ghost's numbers based on? Could we get an explanation please... sorry, I'm not a Phd. To me it sort of looks like he started with an end result and found a math equation that would spit it out. Forgive me if there was some science I missed in there, as I said, I'm not as smart as you guys.

Quote:
Originally Posted by SkiRacer55

This is different than I thought.  You are looking for a one size fits all all mountain ski that will also be just just peachy in a NASTAR course.  I gave you a specific suggestion, what I now think is that you are much better off using Ghost's formula, plugging in your stats, running the numbers, and finding a ski that delivers exactly those numbers...I'm sure you're gonna have a great season...

I don't know what it is about this thread that is making it so difficult for me to communicate my intent, so I will try again -

This thread is NOT about finding me an all mountain ski that will do well in NASTAR.

This thread is NOT about me trying to improve in NASTAR (at least not directly)

This thread is about trying to use math to figure out for how I (or anyone else) can determine the correct size ski; what would the length (originally just length and not TR) be, before it starts becoming more work for a particular event.  Over kill for the job at hand.

I never once asked for a recommendation on a ski.  I've been asking the whole time, how do you determine the ski's size you get, once you picked the event.

Ken

Edited by L&AirC - 7/21/11 at 8:29pm

easy answer? you start with what you want as an end result performance-wise from the ski, factor in your size, look at the ski size run (let's face it, modern skis only come in 4 or 5 sizes per model), decide where your size falls compared to 'averege' and voila, you get a ski length for the type of ski you are looking at.

The hard part is chosing a few skis to consider for the 'task at hand'.

Quote:
Originally Posted by L&AirC

All data is good, even when it tells you that you are wrong.

Uh, data are neither good nor bad, just relevant or irrelevant. And they don't tell you anything, even in mid-July after three brews. They need a hypothesis to test. Not support, but test. What's yours? Put another way, why don't you state what you want as "If I buy a ski of x characteristics, it will do y." OK, now notice that you cannot define y without skiing. It's a functional outcome. You can rewrite this, if you want, as y=dependent variable (performance outcomes) and x= independent variables (ski size, shape etc.) Looks pretty cool, huh?

Actually total b.s. The x's are all collinear, meaning they include some of each other's territory (not a good thing here), and unless you pick the right ones, their predictive value is weak sauce, and actually there are multiple y's, some being your anatomy (or maybe they're some of your x's, whadya think?), some being your subjective experience through a turn, and your skill set, and so on and so on. So it's called (maybe) a canonical correlation problem, with massive collinearity and poorly thought through causality on both sides, and you'll need to start with some factor analyses to settle on which variables are least intertwined with each other, and anyway your distributions are of unknown shape or variance, so that further limits your predictive power.

Or we could backtrack and go Bayesian on this, look at the impact of prior outcomes. Trendier but no more helpful, I bet. Or we could do an engineering model, elegantly simplified, rid of irritating real world noise or intermediate/hidden variables, and just assume actual humans using actual skis on actual snow will behave themselves in a manner a CAD would be proud of.

I could go on until your eyes get even glassier. If possible. But the point is, ski companies know all this. They employ very bright engineers, and statisticians who've forgotten more than I ever knew. And that's why ultimately they reach major economic decisions about which is the "right" ski to make in the right lengths and radii and flexes not by data or models, but by testing prototype skis with folks who know how to ski decently. Numbers, however deployed, give you a very large, very lumpy ballpark in which humans make weird and wonderful plays. Not to mention lots of errors.

So there is no "point" of diminishing returns, no magical moment of deflection - ideas which after all come from the same folks who so successfully predicted our economy over the last 20 years - no tables or formulas that will give you a "right" answer, if that means something that will correspond to what you'll feel on slope. I love numbers too, but as my 8-year old says, "get over it."

Edited by beyond - 7/22/11 at 12:12am
Quote:
Originally Posted by L&AirC

I don't know what it is about this thread that is making it so difficult for me to communicate my intent, so I will try again -

This thread is NOT about finding me an all mountain ski that will do well in NASTAR.

This thread is NOT about me trying to improve in NASTAR (at least not directly)

This thread is about trying to use math to figure out for how I (or anyone else) can determine the correct size ski; what would the length (originally just length and not TR) be, before it starts becoming more work for a particular event.  Over kill for the job at hand.

I never once asked for a recommendation on a ski.  I've been asking the whole time, how do you determine the ski's size you get, once you picked the event.

Ken

the human being is so incrediably adaptable and versatile that there is still isnt math that can determind this.

I look at ski length this way actually. How short can I go before I start doing more work because the ski is too short.

Quote:
Originally Posted by Whiteroom

easy answer? you start with what you want as an end result performance-wise from the ski, factor in your size, look at the ski size run (let's face it, modern skis only come in 4 or 5 sizes per model), decide where your size falls compared to 'averege' and voila, you get a ski length for the type of ski you are looking at.

The hard part is chosing a few skis to consider for the 'task at hand'.

"...factor you size..."

How do you do this? Everyone seems to be saying it's impossible yet it is part of how you earn your living. I would like to believe you didn't learn it as a "carnie" and you and all the others in your profession have something to base this on. Is it strictly from demoing skis, extracting from the customer how they " really" ski and trying to find the match? Of course you have the added burden of fitting their budget too.

Ken
Edited by L&AirC - 7/22/11 at 4:05am
Quote:
Originally Posted by BushwackerinPA

the human being is so incrediably adaptable and versatile that there is still isnt math that can determind this.

I look at ski length this way actually. How short can I go before I start doing more work because the ski is too short.

OK. How do you determine they are too short? That sounds as equally crazy as determining they are too long! According to everything else you and many others have posted, you can't.

Is it strictly experience? I'm sure that demoing and experience are the best way to determine what size ski to pick, but shouldn't it be possible to come close to picking a ski that you don't have to "adapt" to.

Ken
Quote:
Originally Posted by beyond

Uh, data are neither good nor bad, just relevant or irrelevant. And they don't tell you anything, even in mid-July after three brews. They need a hypothesis to test. Not support, but test. What's yours? Put another way, why don't you state what you want as "If I buy a ski of x characteristics, it will do y." OK, now notice that you cannot define y without skiing. It's a functional outcome. You can rewrite this, if you want, as y=dependent variable (performance outcomes) and x= independent variables (ski size, shape etc.) Looks pretty cool, huh?

Actually total b.s. The x's are all collinear, meaning they include some of each other's territory (not a good thing here), and unless you pick the right ones, their predictive value is weak sauce, and actually there are multiple y's, some being your anatomy (or maybe they're some of your x's, whadya think?), some being your subjective experience through a turn, and your skill set, and so on and so on. So it's called (maybe) a canonical correlation problem, with massive collinearity and poorly thought through causality on both sides, and you'll need to start with some factor analyses to settle on which variables are least intertwined with each other, and anyway your distributions are of unknown shape or variance, so that further limits your predictive power.

Or we could backtrack and go Bayesian on this, look at the impact of prior outcomes. Trendier but no more helpful, I bet. Or we could do an engineering model, elegantly simplified, rid of irritating real world noise or intermediate/hidden variables, and just assume actual humans using actual skis on actual snow will behave themselves in a manner a CAD would be proud of.

I could go on until your eyes get even glassier. If possible. But the point is, ski companies know all this. They employ very bright engineers, and statisticians who've forgotten more than I ever knew. And that's why ultimately they reach major economic decisions about which is the "right" ski to make in the right lengths and radii and flexes not by data or models, but by testing prototype skis with folks who know how to ski decently. Numbers, however deployed, give you a very large, very lumpy ballpark in which humans make weird and wonderful plays. Not to mention lots of errors.

So there is no "point" of diminishing returns, no magical moment of deflection - ideas which after all come from the same folks who so successfully predicted our economy over the last 20 years - no tables or formulas that will give you a "right" answer, if that means something that will correspond to what you'll feel on slope. I love numbers too, but as my 8-year old says, "get over it."

(heavy sigh)

It's hard. I get it. It will be impossible to be exact. I get it. I'm not stopping. Get over it.

Uh huh.  Sounds good, but I think it's time for me to return to the planet Earth. Knock yourself out, and, once again, have a great season....

Quote:
Originally Posted by L&AirC

I don't know what it is about this thread that is making it so difficult for me to communicate my intent, so I will try again -

This thread is NOT about finding me an all mountain ski that will do well in NASTAR.

This thread is NOT about me trying to improve in NASTAR (at least not directly)

This thread is about trying to use math to figure out for how I (or anyone else) can determine the correct size ski; what would the length (originally just length and not TR) be, before it starts becoming more work for a particular event.  Over kill for the job at hand.

I never once asked for a recommendation on a ski.  I've been asking the whole time, how do you determine the ski's size you get, once you picked the event.

Ken

The point I was going for is that different ski types will be sized differently, for the same person, depending on the 'task' they will be used for. There won't be one best ski size, there will be many- just like your 155cm SL and 176cm GS. You also have to consider that different ski manufacturer's products behave differently, some 'ski long' and some 'ski short', but this doesn't mean you can't tell what size you should ski without massive demoing. You can with a little intuition and common sense.

As for "How do you factor your size"... remember grade school gym class? Did you ever line-up by size, shortest to tallest? where were you? In the middle or at one end? Everyone knows where they are compared to 'average'... I think. If you're not sure just ask someone.

So you know you are in the lower half of adult male size (just spit-balling here, don't know your size) look at the ski sizes available for the model you are looking at- let's pretend a size run is 163cm, 170cm, 177cm, 184cm... are you starting to see what I'm seeing? I honestly think the size question is fairly straight forward, the hard part is deciding on the ski model you want to buy.

Of course if manufacturer A makes a 167cm and a 174cm and manufacturer B has 163cm, 170cm and 177cm it can get fuzzy if you let it... don't. The difference between brands will tell you what you need to know. The differences between what you want in ski behavior and in manufacturer characteristics will let you determine length without it becoming a clusterf***.

Quote:
Originally Posted by SkiRacer55

I'm 63, race Masters, Atomic has always worked well for me, I really like the D2s, here's what I use, all FIS (although some are women's FIS) legal:

- SL, I have two pairs of Atomic 165 D2 SLs, last year's.  They tweaked the ski some over the previous year's and I think it's a whole lot quicker and livelier.

-.

SR55, good to see confirmation of this form someone with much more experience of them than me.  i have a pair of 2010 and 2011 165 D2 and the 2011, although i haven't skied it much seemed much snappier, so much so that i am thinking of going back to 165 Sl next year.  (Although i also have a 155 D2 still to try).  Decisions, decisions.....

Quote:
Originally Posted by Whiteroom

The point I was going for is that different ski types will be sized differently, for the same person, depending on the 'task' they will be used for. There won't be one best ski size, there will be many- just like your 155cm SL and 176cm GS. You also have to consider that different ski manufacturer's products behave differently, some 'ski long' and some 'ski short', but this doesn't mean you can't tell what size you should ski without massive demoing. You can with a little intuition and common sense.

As for "How do you factor your size"... remember grade school gym class? Did you ever line-up by size, shortest to tallest? where were you? In the middle or at one end? Everyone knows where they are compared to 'average'... I think. If you're not sure just ask someone.

So you know you are in the lower half of adult male size (just spit-balling here, don't know your size) look at the ski sizes available for the model you are looking at- let's pretend a size run is 163cm, 170cm, 177cm, 184cm... are you starting to see what I'm seeing? I honestly think the size question is fairly straight forward, the hard part is deciding on the ski model you want to buy.

Of course if manufacturer A makes a 167cm and a 174cm and manufacturer B has 163cm, 170cm and 177cm it can get fuzzy if you let it... don't. The difference between brands will tell you what you need to know. The differences between what you want in ski behavior and in manufacturer characteristics will let you determine length without it becoming a clusterf***.

I agree that different ski types will be sized differently.  Once you pick the type, how do you pick the size of that type?  I don't think I could end up with a 'best ski size' but I should be able to figure out my starting point.

Going by what you posted, it's height.  There are 5 pages of posts in this thread saying it isn't height but weight - no it isn't weight but skill set, - no it's height; no it's....  WTF?  There's very few places you will find more experienced skiers posting in one forum so I figure that disproving this quest, if it's a fools quest, should be fairly simple.  So far the only thing this thread has proven is that it would be hard to figure out and their are a ton of variables.

If I want a cheater SL race ski, I pick the ski solely based on my height?  That means a 155 since I'm only 5'7" and that isn't in the lower half; that is the lower half of the lower half.  I have one of those and I always felt I would like it longer.  Why, maybe because my weight is closer to the top half of the lower half.  Seems reasonable to think that right.  Could be because my weight and the speed I want to go. so going longer is better.

I'm sure from reading reviews and research, a Fischer cheater SL 165 will feel differently to me than the similar ski from Elan or Atomic.  Lets say I walk in your store and tell you I really like the Elan's (pretend you sell them if you don't) but I'm not sure which size.  What do you do to figure out the best size for me?  Is it strictly from experience and talking to people about their experience and trying to match those up with what I tell you?

Quote:
Originally Posted by SkiRacer55

Uh huh.  Sounds good, but I think it's time for me to return to the planet Earth. Knock yourself out, and, once again, have a great season....

poo poo me if you like, but it seems odd to me that we spend months debating the physics of a ski turn, have books written entirely on the physics of skiing, spent last summer knee deep in the physics with the virtual bump and rebound threads.  PSIA has a 7M download at their site with 160 pages on the physics of skiing but there is NO physics involved in picking a ski?  Seriously?   Should we do the Harry Potter and let the ski pick us?  (Sorry.  Just saw it today - Good flick if you get a chance btw). Demoing is the only way yet thousands of skis are sold without anyone ever demoing them.

Surely with your credentials, you can post more about what to consider.  Even in your first post you stated there are guidelines.  What are they guidelines?

I'm not being obstinate.  Look at how many people are viewing this thread compared to the other threads.  It's fairly active.  I've received PM's telling me to keep at it.  Why is that?  Are will all aliens or do we all want to learn something and now seems like a pretty good time.

I've even found a link to another site where you put in your ski profile and they will list skis that people with similar profiles tested and liked.  Guess what?  For me, it kept recommending skis in the same range the Ghostilator did.  Coincidence?  Most of the testers were close to my size.

Moderators - is it OK for me to post that link?  I can PM it to one of you if you like.

Ken

Sizing Algorithm for the non-mathematically inclined, along with rational.

Skis come in an assortment of sizes.

The top size is for the biggest heaviest hardest charging skiers.

Skiers who lack skill will have a harder time fighting a ski made to satisfy strong skilled skiers.

So for a skilled strong skier:

Step 1) Choose the longest ski available

step 2) Drop down by one if you do not want the ski for hard charging or if you are not in the heavier half of the population of skiers.

step 3) Step back up one if you want the ski for hard charging and are among the top 3 fastest skiers on the hill on most days out.

For an unskilled skier with strength:

Step 1) choose the 2nd longest ski available.

Step 2) drop down by one if you do not want the ski for hard charging or if you are not in the heavier half of the population.

For a skilled skier who lacks strength

Pick the 2nd largest size.

For all skiers, drop down by one from the above if you are incredibly light.

L&AirC:

I bought skis built for heavy, charging men and used them last season.  They were a lot longer than anyone would recommend for me (I'm a woman, average in size).  When I went back to my old shorter skis at the end of the season just to see how they felt, they were so squirrelly I found them actually dangerous.  I had gotten thoroughly used to the longer ones (174s compared to 160s).  I also raced faster on the long ones - stirring confirmation that something was going right with the new length.  The shorter ones were too much work, not the longer ones.

I understand your desire for a clear explanation of which length goes with which skier.  But I think there is no answer waiting to be revealed.

Perhaps people who are working on increasing their skiing skills will adapt their skiing habits to match their new ski's attributes.  Perhaps there is no perfect or right ski length for a particular person at a particular skill level.  Perhaps just trying a different ski and seeing if we can learn to ski it is a great way to build a new skill set.  And if it doesn't work out, we can sell them on eBay and get another pair.

That process may sound inefficient, but I think it's exactly the opposite.  Learning by trial and error, on snow, is a great way to progress in understanding how different skis behave.  Yes, it costs money, and yes, it takes time.  But if the learning process doesn't take time and effort and if it doesn't involve the risk of failure, it probably isn't worth doing.

Uh huh...well, things just got a lot more complicated, because the FIS in its infinite wisdom, just decided to mandate a minimum of 195 cm and 40 meters sidecut for WC GS...which can only mean that this will all trickle down to the 10,000 current skis you are now considering...which will all change considerably...so I strongly recommend that you continue to dither between your 155s and 176s for another year...which I'm sure will be productive (Have a great season!),,,and then in 2012-2013, I think your obvious choice is... a pair of 125 cm, 37 meter sidecut skis..plus a hamburger, and a flashlight...can't lose, guranteed...

Quote:
Originally Posted by L&AirC

poo poo me if you like, but it seems odd to me that we spend months debating the physics of a ski turn, have books written entirely on the physics of skiing, spent last summer knee deep in the physics with the virtual bump and rebound threads.  PSIA has a 7M download at their site with 160 pages on the physics of skiing but there is NO physics involved in picking a ski?  Seriously?   Should we do the Harry Potter and let the ski pick us?  (Sorry.  Just saw it today - Good flick if you get a chance btw). Demoing is the only way yet thousands of skis are sold without anyone ever demoing them.

Surely with your credentials, you can post more about what to consider.  Even in your first post you stated there are guidelines.  What are they guidelines?

I'm not being obstinate.  Look at how many people are viewing this thread compared to the other threads.  It's fairly active.  I've received PM's telling me to keep at it.  Why is that?  Are will all aliens or do we all want to learn something and now seems like a pretty good time.

I've even found a link to another site where you put in your ski profile and they will list skis that people with similar profiles tested and liked.  Guess what?  For me, it kept recommending skis in the same range the Ghostilator did.  Coincidence?  Most of the testers were close to my size.

Moderators - is it OK for me to post that link?  I can PM it to one of you if you like.

Ken

Quote:
Originally Posted by LiquidFeet

L&AirC:

I bought skis built for heavy, charging men and used them last season.  They were a lot longer than anyone would recommend for me (I'm a woman, average in size).  When I went back to my old shorter skis at the end of the season just to see how they felt, they were so squirrelly I found them actually dangerous.  I had gotten thoroughly used to the longer ones (174s compared to 160s).

So this sounds like you adapted to the longer skis but didn't adapt back to the shorter ones .  I noticed that when I went to different skis, I sometimes had to make a run or two if I hadn't used them in a while.

I also raced faster on the long ones - stirring confirmation that something was going right with the new length.  The shorter ones were too much work, not the longer ones.

Would you still say that if you went to a 183 or 188?

Longer always seems to be faster but there seems to be a point where it becomes too long.  Case in point, my race friend that is 5'6" and usually gets his weight up to 175 or 180 for ski season (165 in the summer), skis a 188 FIS Fischer WC even in weekend NASTAR on turny courses.  He can't bend the ski on all the turns so he adapts by taking a step across the hill with his inside leg as he comes out of the gate.  Seems to me if he had a softer ski with less TR he wouldn't have to do this.  I would like to say he would be faster too, but even with his stepping across the hill, he'll typically have the fastest time on the hill and quite often beats the pace setter.  When I asked him why (he didn't get a shorter ski), he said "Who can afford to buy so many skis!"  So he buys skis for the races he cares about and adapts it's use other times.  His short ski is a 183 FIS Fischer WC.

I understand your desire for a clear explanation of which length goes with which skier.  But I think there is no answer waiting to be revealed.

Perhaps people who are working on increasing their skiing skills will adapt their skiing habits to match their new ski's attributes.  Perhaps there is no perfect or right ski length for a particular person at a particular skill level.  Perhaps just trying a different ski and seeing if we can learn to ski it is a great way to build a new skill set.  And if it doesn't work out, we can sell them on eBay and get another pair.

I'm fine with getting another pair.  It's the selling them I have a hard time with .

That process may sound inefficient, but I think it's exactly the opposite.  Learning by trial and error, on snow, is a great way to progress in understanding how different skis behave.  Yes, it costs money, and yes, it takes time.  But if the learning process doesn't take time and effort and if it doesn't involve the risk of failure, it probably isn't worth doing.

I love learning.  That's what I'm trying to do right now.  I have learned much in this thread, though not what I originally sought out.

So epicski you have worn me out.  I'm not giving up, I'm just giving up here.  Time to go study on my own.  Be back when I'm smarter.

Those that posted, thanks for participating.  Those that read only, hope you enjoyed it as much as I did.  It was educational and maybe someday I'll be smart enough to prove this one way or another - either is perfectly fine.

Thanks,

Ken

Edited by L&AirC - 7/24/11 at 6:40am
Quote:
Originally Posted by L&AirC

Longer always seems to be faster but there seems to be a point where it becomes too long.  Case in point, my race friend that is 5'6" and usually gets his weight up to 175 or 180 for ski season (165 in the summer), skis a 188 FIS Fischer WC even in weekend NASTAR on turny courses.  He can't bend the ski on all the turns so he adapts by taking a step across the hill with his inside leg as he comes out of the gate.  Seems to me if he had a softer ski with less TR he wouldn't have to do this.  I would like to say he would be faster too, but even with his stepping across the hill, he'll typically have the fastest time on the hill and quite often beats the pace setter.  When I asked him why (he didn't get a shorter ski), he said "Who can afford to buy so many skis!"  So he buys skis for the races he cares about and adapts it's use other times.  His short ski is a 183 FIS Fischer WC.

Perhaps longer is not too long, but rather, faster has become too fast.

An exercise-based way to choose your ski radius, or More fun with math:

Decide how much of a work out you want to get, that is do you want to be doing 2g turns or 3 g turns or say 3.5 g turns.  Whatever, just pick one.

The resultant force of gravity pushing down and your turn force will be at an angle from straight down (0 degrees for no turn, approaching 90 degrees for as turn force approaches infinity)

Now in order to be just balanced with the forces going directly 90 degrees through the base of the ski, you will have to tip that ski up on edge to a given angle from the horizontal.  For example, choose to make sustained 2g turns.  The tangent of that angle is 2g, (tangent is opposite over adjacent), so that angle is arctan(2), call it theta.  Note: note the actual total force on your legs is the vector sum of the down force and horizontal turning force, or leg force will be  2g/sine(theta)

Now in order to pull a sustained 2 "g"s in a turn, consider that the centripetal acceleration is given by a= V^2/r, where V is velocity and r is the radius of the turn.  So the radius of that 2g turn your making is given by r= (V^2)/a  put simply, r = (V^2)/2g.  (or you could use 3g or whatever multiplier you choose).

We all know that on a hard surface, the turn radius made by the ski is roughly given by the sidecut radius of the ski, R times the cosine of  tipping angle (theta), so r=Rcosine(theta) gives the radius of the ski is  R= r/cosine(theta)

Put it all together and you have R= ((V^2)/2g) / cosine(arctan(2))  Remember to use consistent units (eg, m/s and 9.81 m^2/s for g).

 Example g = 9.81 (m/s/s) Turn force is 2 "g"s theta = 1.107149 (radians) leg force is 2.236068 "g"s mph m/s r (m) R (m) 20 8.9408 4.074307 9.110428 25 11.176 6.366105 14.23504 30 13.4112 9.167191 20.49846 35 15.6464 12.47757 27.90068 40 17.8816 16.29723 36.44171 45 20.1168 20.62618 46.12154 50 22.352 25.46442 56.94017 55 24.5872 30.81195 68.89761 60 26.8224 36.66876 81.99385

Note that you can certainly use a longer radius and tip it more to get the same turn, but if you tip a shorter radius more at that speed, it won't carve cleanly because it will try and dial up a turn too sharp to hold.  Similarly if you try and go faster without tipping the ski any more the force will push you out of the groove.

Could someone please check the math?

Quote:
Originally Posted by Ghost

Sizing Algorithm for the non-mathematically inclined, along with rational.

Skis come in an assortment of sizes.

The top size is for the biggest heaviest hardest charging skiers.

Skiers who lack skill will have a harder time fighting a ski made to satisfy strong skilled skiers.

So for a skilled strong skier:

Step 1) Choose the longest ski available

step 2) Drop down by one if you do not want the ski for hard charging or if you are not in the heavier half of the population of skiers.

step 3) Step back up one if you want the ski for hard charging and are among the top 3 fastest skiers on the hill on most days out.

For an unskilled skier with strength:

Step 1) choose the 2nd longest ski available.

Step 2) drop down by one if you do not want the ski for hard charging or if you are not in the heavier half of the population.

For a skilled skier who lacks strength

Pick the 2nd largest size.

For all skiers, drop down by one from the above if you are incredibly light.

This makes a lot of sense, and is compatible  with what Whiteroom said above.  Notice, however, that we are modeling the intent of the ski designers, not the physics of the skis.

So, to get to a physics based question, maybe we ought to ask how designers decide how long to make skis.  Unfortunately, I would bet the only rules are relative and evolutionary -- take what worked before, change something, and if it works do more of whatever it was.

Any absolute, physics-based equation would only work for one design family, and would be invalidated when the design changed (compare, for example, length recommendations in 2011 and 1981).

That said, I think the hypothetical question is still interesting.  Suppose you freeze most aspects of a design and vary the length.  When does it get too long, and what starts to go wrong to enforce that limit?

Ok, so I just read Ghost's algebra post.  The logic seems reasonably sound, but it must be incomplete because it does not have a place for ski stiffness to change things.  I think the r=Rcosine(theta) is the suspect step.

Argh, I wasn't going to do this, but now I have to go away and figure out the curvature of the ellipse formed by the intersection of a cylinder and a plane.

Edit-

Ok, I'm back.  Assume the hape of the sidecut is a segment of a circle of radius R.

The interesction of a cylinder of radius R and plane at an angle theta is an ellipse whose semimajor, minor axes are R and R/cos(theta).

The radius of curvature of that ellipse at the relevant point is R*cos(theta), as advertised.

[Math available on request.]

But notice that I derived this based on a sidecut which is an unchanging cylinder.  If the ski bends, the radius of curvature will get smaller.

Edited by mdf - 7/22/11 at 9:21pm

I have to jump in and add something that everyone has overlooked in this equation. Now when I buy a new pair of skis I don't only think about skis, I want to know exactly what bindings I'm going with, NOT JUST SKIS!!!

Makes no sense to continually go with "fixed" bindings on all your skis. Yes, I'm talking my old Tyrolia RFs and my newer Schizos, You'll learn to ski better, and have a better understanding of ski mounting points.  I only have one pair of "fixed" bindings in my 3-ski quiver, and they are mounted at +5 on a pair of Hellbents.

Adjustable bindings can make all skis more versatile in a variety of conditions, and they have really improved IMHO since my original pair of RFs....prolly getting the latest Head/Tyrolia offering this year.

I do have one saying when it comes to ski length:" There are few excuses for short skis, but many reasons for long ones "

ALL-MOUNTAIN SKIS RULE!!!

Quote:
Originally Posted by L&AirC

OK. How do you determine they are too short? That sounds as equally crazy as determining they are too long! According to everything else you and many others have posted, you can't.

Is it strictly experience? I'm sure that demoing and experience are the best way to determine what size ski to pick, but shouldn't it be possible to come close to picking a ski that you don't have to "adapt" to.

Ken

pick a model out ski every lenght you can find.
to short will vary for where you are at as well.

for instance 177 cm "the ones" are not to short for stowe, but even the 184cm "the one" are to short for snowbird.

Quote:
Originally Posted by mdf

Ok, so I just read Ghost's algebra post.  The logic seems reasonably sound, but it must be incomplete because it does not have a place for ski stiffness to change things.  I think the r=Rcosine(theta) is the suspect step.

Argh, I wasn't going to do this, but now I have to go away and figure out the curvature of the ellipse formed by the intersection of a cylinder and a plane.

Edit-

Ok, I'm back.  Assume the hape of the sidecut is a segment of a circle of radius R.

The interesction of a cylinder of radius R and plane at an angle theta is an ellipse whose semimajor, minor axes are R and R/cos(theta).

The radius of curvature of that ellipse at the relevant point is R*cos(theta), as advertised.

[Math available on request.]

But notice that I derived this based on a sidecut which is an unchanging cylinder.  If the ski bends, the radius of curvature will get smaller.

Thanks for doing the check.

The ski bends to conform to the imposition placed on its edge by the plane,  r=Rcos(theta).  The equation is only approximate; ski sidecuts are not perfect circles, they have taper, snow has give and skis have torsional flex.

Ski stiffness, as you surmise, is another can of worms.  Forces need to be sufficient to bend the ski to that radius, but in general ( and especially if your pulling a couple of "g"s) they are.  There is a limit though, so you won't be carving any 3-m turns on a pair of SG skis.  If you make a GS ski soft enough to make tight SL turns (eg my old Völkl P50s), they will be a little too easy to fold up for comfort at higher gs speeds, but what are you gonna do?  You have to compromise high speed charging stiffness to make a general purpose ski for varied conditions.

Quote:
Originally Posted by BushwackerinPA

pick a model out ski every lenght you can find.
to short will vary for where you are at as well.

for instance 177 cm "the ones" are not to short for stowe, but even the 184cm "the one" are to short for snowbird.

True.

I've found 165 SL ski is great at a little 200' hill, but a 208 cm SG is more fun at a 1500' + hill.  The hill affects how you ski, one of the main variables of how you ski that is affected by the hill is speed, which I have used in my model above.

I know everyone's been up all night wondering what I finally settled on for skis this year .  With the help of this agonizing thread (agonized in brain cell consumption from learning so much) and willingness to sell more skis to make room for new(er) skis, I think I only have one more purchase.  I was using four different skis last year and this year I'm going to see if I can get down to two.  I've sold one pair, have another on the market and will decide on the third later in the season after I race beer league a couple times.

If I remember right, I originally wanted a ski that would be fun for free skiing, would help me train for L2 (including learning bumps) and would do OK in nastar.  I started the thread because I was noticing people change their technique in different terrain.  Wasn't a bad thing but it was usually because the ski was too long or too stiff for what they were doing.  They could still do it well, but it might not be as pretty.  So I knew what too short was for me.  I just needed to figure out what was too long, and that really turned into what is too big of a turn radius for the turns you want to make at the speed you're going.  The fastest turns I make in racing are in nastar and beer league so 18M (nastar spec is 18-22M) is good.

I also had to understand (didn't happen until recently) that for what I wanted, I didn't need to add to my quiver but give it an overhaul.  So I recently decided to get two skis.  I have one - Atomic D2 GS 174cm with a 17.8M TR and I'm now in hot pursuit of a 165cm SL race ski.  I picked the latter based on how I like to ski and what I'm going to be doing this year.  The Atomics I bought new and the SL I hope to find a good deal on old or used.  I'm not looking for it for racing SL but several instructors use this size ski and it works great in these parts.  I'll also be working nastar here and there and it will be fine for that.  The 155 SL ski I have is a blast but I always felt it should be longer, especially when setting gates and toting a gate bag so it's on the market.

I'm considering selling my 21.2M gs skis but I'm not sure yet.  Beer league is longer and steeper than weekend nastar so I might end up preferring those over the atomic's 17.8M TR.  Below is how things should end up.

I'll hang on to the Metrons for teaching beginners (ski backwards a lot) and early and late season.

Anyway, I wanted to thank everyone for participating in this thread again.  I really did learn a lot about skis in the thread or because of the thread.  I'm sure you'll all sleep easier tonight.

Thanks,

Ken

Great choice, Ken..

BTW there were a couple of pairs of  D2 Race SL on NEmasters.... Good price/some of them , even in plastic....Check them out..

I have been watching their site.  Good prices but I'll end up sleeping on the couch if I spend that much.  As it is I'm going to be \$3k lighter before the first snowfall if I include getting my daughter set up for J3 this year.

In my next life I'll have to make sure my wife is a skier .

Ken

L&AirC:  I still believe science can be applied, even though we don't know what it is yet.

Actually science will always be difficult to apply to your very specific question because some of the variables are not measurable scientfically. And of course, I am referring to the skier. Skier skill, strength, age, style (power, finesse, aggressive, relaxed) are all variables that would make one individual be more comfortable than another individual on a specific ski with a given length. Even when 2 skiers are on the Demo Team and of similar size/weight, it is reasonable to expect that their style might be different enough to have one like the length while the other prefer something shorter/longer. Formulas are great (I am an engineer too ) but likes, dislikes, preferences and comfort are rather hard to measure.

Quote:
Originally Posted by TomB

L&AirC:  I still believe science can be applied, even though we don't know what it is yet.

Actually science will always be difficult to apply to your very specific question because some of the variables are not measurable scientfically. And of course, I am referring to the skier. Skier skill, strength, age, style (power, finesse, aggressive, relaxed) are all variables that would make one individual be more comfortable than another individual on a specific ski with a given length. Even when 2 skiers are on the Demo Team and of similar size/weight, it is reasonable to expect that their style might be different enough to have one like the length while the other prefer something shorter/longer. Formulas are great (I am an engineer too ) but likes, dislikes, preferences and comfort are rather hard to measure.

You left out boot fit and flex, binding and binding location.  Cant forget functional movement either.

I get it, but those are desires or preferences that people are drawn to or adapt to.  Take those variable away and you should be able to say "Start here." then move up or down in length because of preferences.  Even in your example above, you will eventually get to a size that neither can ski no matter what their preferences are.  That was really my point.  At what length (or TR) do you have to start adjusting your technique because the ski is too big.  Same as all the griping about the FIS changes.  The TR and length are going to be so big, that people will have to change their technique to get through the course, they will have to change the course, or the skis will have to change somehow (early rise?).

For me based on my racing desires/preferences, a 18M TR should be just about perfect.  NASTAR is set with 18 - 22 meters between the gates and a 4- 8 meter off set (or something close to that and depending how skilled/attentive the course setter is).  A 27M TR ski can get you a platinum in nastar but you are going to have to adapt your style (i.e step uphill to change your line).  Beer league (where I ski) follows the same spec but is longer and steeper (gates tend to be further apart once you get going) so my 21M ski should better.  In both of those courses, in one ski model, the difference between a 174cm 18M ski and a 176cm 21M ski should be negligible.  This is pretending that the two skis I have are the same.  I would bet the 18M ski is more versatile since the length is so close. I highly doubt I will be able to tell the difference but I'm not selling the 21M's until I test it out .

Ken

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