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Ski Rebound and the mechanical properties of Snow

post #1 of 25
Thread Starter 

Jamt and company have really got me thinking about the energetics of skiing.

After making some measurements of ski elasticity I'm starting to come around to the view that a ski alone under a distributed load condition cannot store enough energy to get that "pop" you feel when you load your tails and suddenly release them.

A good scientist is always challenging their own BS so I'm really trying to understand what is going on here.

What has been neglected to date in this discussion is the visco elastic properties of the snow that supports the ski and skier.

If snow were made of rubber balls, a lot of energy would be transferred to the snow as a travelling elastic wave under the skier.

This energy storage mechanism could be important to understanding the energetics of skiing.

 

Snow isn't made of rubber balls but it is far more complicated than one thinks.

I don't yet have any conclusions about this but what goes on in the snowpack has to be considered in a correct description of skiing energetics.

So I'm doing some reading.

This is the best document on snow mechanics that I have yet found.

It is probably better to drink than read stuff like this but just in case you are interested, here it is.

http://www.dtic.mil/cgi-bin/GetTRDoc?AD=ADA330695

 

Snow is an amazingly complicated material.

No wonder the Eskimos have over 20 words to describe the different kinds. 

post #2 of 25

Since a Volkl Racetiger has a lot of pop and a K2 Recon has none, does that suggest that it is the ski that contains the dynamic pop.  Also, the injected ice race courses don't have a lot of give in the snow, and the pop is designed to perform well on them. Just going along with your train of thought.  

post #3 of 25
Thread Starter 

I took the stiffest ski i have and grabbed it in a vice at the center.

Volkl P40 F1 with three sheets of metal, 182.

It took a 17 pound point load at the tail to deflect it one inch.

I used a dial indicator and a fish scale to do this.

More work required, as usual.

I need to do some bigger deflections, the spring rate didn't seem linear.

post #4 of 25

I thought you were going to say you put it in a vice and flexed it back to use it like a catapult. If it lofts a 5 lb weight 84 yards it is has some good "pop".

 

You can check the force needed to produce the deflection which forms the ideal arc for the full turn.

 

I think we'll find the flex is progressive. Wonder if you'll see a difference with very damp skis?

post #5 of 25
Quote:
Originally Posted by dakine View Post

I took the stiffest ski i have and grabbed it in a vice at the center.

Volkl P40 F1 with three sheets of metal, 182.

It took a 17 pound point load at the tail to deflect it one inch.

I used a dial indicator and a fish scale to do this.

More work required, as usual.

I need to do some bigger deflections, the spring rate didn't seem linear.


Interesting...but try it again, and support the ski at tip and tail...then use the fish scale at the ski center (right on the boot center line would be ideal) and pull....that would be closer to what really happens in skiing.

post #6 of 25
Quote:
Originally Posted by davluri View Post

Since a Volkl Racetiger has a lot of pop and a K2 Recon has none, does that suggest that it is the ski that contains the dynamic pop

No.

post #7 of 25
Quote:
Originally Posted by Skidude72 View Post


Interesting...but try it again, and support the ski at tip and tail...then use the fish scale at the ski center (right on the boot center line would be ideal) and pull....that would be closer to what really happens in skiing.


Since I have always wanted flex numbers on the ski, I have thought about how to quantify that. I was going to use a  bathroom scale and a screw jack to push on the binding area of the ski (clamped on a rack, base side up).  You could also clamp it in the center top sheet up and push up on tip or tail I suppose.  I was interested also to see how much stiffness was lost after 100 days or so.

 

hdn, brilliant. and your theory is...... really apply yourself now.

post #8 of 25
Thread Starter 

I'm trying to find some pics of how racers really bend their skis.

The only pic I could find is of me on snow so soft you had to ski it on cat feet.

Anybody have any pics like this of a racer finishing a turn where you can see how the ski bends?

I think that the tail is doing all the heavy lifting when you do a sudden release and get popped.

Whatever the mechanism I do know that I can lift myself off the snow by rocking back and releasing.

I think race skis get their pop from their torsional rigidity..but I'm not quite sure why.

......

For some reason i can't upload the pic but it is a shot from the rear just as I clear a gate.

post #9 of 25
Quote:
Originally Posted by dakine View Post

I'm trying to find some pics of how racers really bend their skis.

The only pic I could find is of me on snow so soft you had to ski it on cat feet.

Anybody have any pics like this of a racer finishing a turn where you can see how the ski bends?

I think that the tail is doing all the heavy lifting when you do a sudden release and get popped.

Whatever the mechanism I do know that I can lift myself off the snow by rocking back and releasing.

I think race skis get their pop from their torsional rigidity..but I'm not quite sure why.

......

For some reason i can't upload the pic but it is a shot from the rear just as I clear a gate.

 

 

http://www.ronlemaster.com/

 

Click on "images"....pages and pages of them

post #10 of 25
Thread Starter 

A little more data.

I supported the P40 on triangular blocks at both ends of the running surface.

Rigged up a dial indicator to measure ski deflection near the center.

I have some Tungsten Carbide blocks about 3" square and 1.5" thick that weigh 7 pounds.

After I got the indicator zeroed I piled the carbide blocks on at the boot center point.

Here is the data.

 

Blocks          Load(#)          Deflection(")

    0                   0                        0

    1                   7                       .29

    2                  14                      .59

    3                   21                     .87

    4                   28                   ~1.15

 

This plots out as a nice linear fit with a spring constant of 25 lb/in.

 

The ski isn't point loaded like this when skiing.

Clearly, the snow mechanics will affect the deflection.

On hard ice a ski will bend until it is geometric contact with the snow like the carpet experiment.

On softer snow the ski can bend much more because it is pretty much surfing on a surface with brittle, viscous and elastic properties.

On powder the snow density is so low that it acts much more like a fluid.

 

This line of thought makes me think you could get the most pop on snow that was soft enough to allow the ski to arc but firm enough to withstand the pressure imposed by the ski without flowing.

 

I had me some snow like that last week.

Powder packed hard by many ski and snowcat passes.

With just a touch of fluff for esthetics.

I was skiing with a friend who was on the PSIA technical committee and a senior examiner.

We were on a wide blue run where you could lay them over as far as you wanted without losing traction.

Ego snow!

I was skiing my 16m Kastle RX's and my friend remarked that I was carving turns with about a 8 meter radius and making nice rail tracks.

They were bending and popping.

Love it!

post #11 of 25

I've read that it's actually your muscles storing and releasing the energy.  If you've ever done heavy squats, you do realize your muscles will stretch and spring back (i.e. you can squat MUCH more starting upright than you can getting under the bar on a rack at the bottom position.  Still, I find it hard to believe this is the main factor.  As others have stated, some skis have more pop than others.

post #12 of 25
Quote:
Originally Posted by davluri View Post

hdn, brilliant. and your theory is...... really apply yourself now.

 

The "pop" or rebound a good skier experiences in a turn is a function of his rate of change of momentum, driven by the dynamics of the turn, specifically the virtual bump and vaulting effects. Different skis are capable of supporting more or less dynamic turns based on their construction and characteristics. So, "pop" is not inherent in the ski as such (think bow and arrow) but in the quality of the turns that ski enables a great skier to execute.

 

Brilliant, no? And I didn't really have to apply myself. This is elementary stuff.

post #13 of 25
Quote:
Originally Posted by goldsbar View Post

I've read that it's actually your muscles storing and releasing the energy.  If you've ever done heavy squats, you do realize your muscles will stretch and spring back (i.e. you can squat MUCH more starting upright than you can getting under the bar on a rack at the bottom position.  Still, I find it hard to believe this is the main factor.  As others have stated, some skis have more pop than others.

Minor quibble: I think it's actually your tendons that store most of the energy in this case, particularly the Achilles for calf movements... which loads like a spring. The muscles in some cases help get the spring loaded.

You can jump higher if you first load the springs from in a downward movement rather than from a still, down position.
post #14 of 25
Quote:
Originally Posted by justruss View Post


Minor quibble: I think it's actually your tendons that store most of the energy in this case, particularly the Achilles for calf movements... which loads like a spring. The muscles in some cases help get the spring loaded.

You can jump higher if you first load the springs from in a downward movement rather than from a still, down position.


Flexed boot shells restore energy too...

post #15 of 25

FWIW, tendons don't store energy. They don't have elastin in them like ligaments do, and tendons don't stretch much. Thankfully, tendons don't need elastin, because the muscle is able to store energy elastically, though only for a very short time.

post #16 of 25
Quote:
Originally Posted by Dave Cee View Post

FWIW, tendons don't store energy. They don't have elastin in them like ligaments do, and tendons don't stretch much. Thankfully, tendons don't need elastin, because the muscle is able to store energy elastically, though only for a very short time.

 

 

What about these, then?

 

 

Elastic properties of human Achilles tendon are correlated to muscle strength

http://jap.physiology.org/content/99/2/665.full

 

(Underline is mine)

 

"The Achilles tendon force at MVIP (F) was calculated from the MVIP torque and the Achilles tendon moment arm. There were no significant differences in either the F-ΔX or F-ε relationships between men and women. ΔX and ε were 9.8 ± 2.6 mm and 5.3 ± 1.6%, respectively, and were positively correlated to F (r = 0.39, P < 0.05; r = 0.39, P < 0.05), which meant that subjects with greater muscle strength could store more elastic energy in the tendon." 

 

AND

 

"THE ELASTICITY OF THE ACHILLES tendon provides an important mechanism: namely, the storage and release of elastic strain energy, which improves the economy and performance of motion (12625)."

post #17 of 25

And this one is pretty good too: http://www.ncbi.nlm.nih.gov/pubmed/12485689

 

Specifically this, from the abstract: "Secondly, tendons can recoil elastically much faster than muscles can shorten, enabling animals to jump further than they otherwise could."

post #18 of 25

Dakine, stumbled upon some interesting data in 3.3.2.2 of http://e-collection.ethbib.ethz.ch/eserv/eth:28070/eth-28070-02.pdf

post #19 of 25
Quote:
Originally Posted by Skidude72 View Post

Quote:
Originally Posted by dakine View Post

I took the stiffest ski i have and grabbed it in a vice at the center.

Volkl P40 F1 with three sheets of metal, 182.

It took a 17 pound point load at the tail to deflect it one inch.

I used a dial indicator and a fish scale to do this.

More work required, as usual.

I need to do some bigger deflections, the spring rate didn't seem linear.


Interesting...but try it again, and support the ski at tip and tail...then use the fish scale at the ski center (right on the boot center line would be ideal) and pull....that would be closer to what really happens in skiing.

No, you're doing it right.  If you find pictures with lots of pop, or if you can recall incidents lot's of pop, the tips are in the air, and when they are still on the snow, but providing a little pop, look at where they are in relation to the turn and what they are doing at the time.  

 

Do you feel an elastic  "pop" when going straight over a kicker in a balanced position?  I don't; I feel a push.  How about if you re skiing on your tails when you go over a kicker?  How about if you rock back on your tails just as you tails go over the kicker?

 

Substitute the virtual bump for the kicker; throw in a bit of vaulting, as opposed to swallowing (- the french have a different word for this ;) ) the VB if you want, just for good measure.  

 

Snow does not have enough rebound.  If you deform it enough, it stays deformed, and if it's too hard to deform much, it doesn't bounce back,  You don't get much energy back from the snow; all you can do is bruise it and slow yourself down. 

post #20 of 25
Quote:
Originally Posted by Jamt View Post

Dakine, stumbled upon some interesting data in 3.3.2.2 of http://e-collection.ethbib.ethz.ch/eserv/eth:28070/eth-28070-02.pdf


Give us the Cole's Notes - Reader's Digest condensed book version;  I'm a llttle pressed for timesmile.gif.

post #21 of 25
Quote:
Originally Posted by Ghost View Post


Give us the Cole's Notes - Reader's Digest condensed book version;  I'm a llttle pressed for timesmile.gif

Chapter 3 is "Detrmination of Snow Resistance to the Ski" and 3.3 is Measurement Devices, so that is promising.  Looks fun to build, actually - a frame with a press pushing an edged ski.

 

And the conclusion in 3.5:

The mean resistance pressure p in the ski-snow interaction is a function of the penetration

depth D and the edging angle θ. The penetration speed has a negligible influence on the snow

resistance pressure. Since the penetration resistance arises from fractures in the microstructure

of the snow the penetration resistance curve exhibits a very strong hysteresis between loading

and unloading (see Figure 53):

Figure 53. The penetration resistance of snow as a function of penetration depth, which

exhibits a hysteresis between loading and unloading.

 

Doesn't look like he attempted to see how the parameters change for different types of snow.

post #22 of 25
Thread Starter 

It would be very hard to get well characterized and repeatable snow in such an experiment.

 

I have a small data logger and am looking for some decent, inexpensive accellerometers.

That and some linear potentiometers to measure camber and i might have something.

Thinking about building an instrumented ski.

We have plenty of theory floating around in this very interesting discussion.

I hope to bring some data to it next season.

Stay tuned.

post #23 of 25
A ski is a system with roughly the behavior of a damped spring. Snow properties only matter to the extent that they dynamically present an anchor and also add forcing functions to the system, when viewed from the skier's frame of reference. The entire skier's body acts as a complex system of forced damped springs. The action of a skier's leg extension combines with the modest spring action of the ski to produce levels of rebound that vary from ski to ski and with all the other variables in the turn.
post #24 of 25

This is my first time on this site.  I love that idea that the ski's involvement in rebound is in the properties of the ski which enable a more or less dynamic turn.  As an former aerospace engineer I have been fascinated by the lift or rebound I feel in some turns and where it comes from.   My learning about this is a work in progress.  This winter I will be investigating whether my ideas about turn radius are valid.

 

The physics I am working with now is that the leg muscles are "loaded" in response to the centrifugal force of the turn.   If the turn is ended gradually...i.e. the radius  of the turn is relaxed toward the end of the turn, the rebound will not be great.  If the radius of the turn is maintained right up to when the edges are released, the rebound is significant.  In the turn, the forces had been in balance; the downward force of the turn plus downward force of gravity had been balanced by the upward force of the tension held in the legs like a compressed spring.  When the force of the turn is suddenly released, the balance of the forces changes: the tension in the leg muscles is more than needed to resist gravity alone; the excess of the force in the legs beyond the force of gravity alone is the force which raises the body as a "rebound".

 

I was talking with a figure skating instructor and described what I was experiencing on skis.  She lit up and said that in skating the same effect is called the "lilt".   As skates do not flex like skis, and as the ice is not elastic, that similarity supports the idea that the main energy storage is in the musculature.

post #25 of 25

I don't know squat about the physics of skiing but I'll take issue with the OP's statement that the Inuit have over 20 words for snow. Check out the wiki.

http://en.wikipedia.org/wiki/Eskimo_words_for_snow

Americans do seem  to have a lot of words for "Eskimo", though.

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