Why damping is so complicated -- WARNING: Physics!!!!!!!

[brianmwaters]

There is a ton of confusion on this site as to what damping actually is and what it does. It's a complicated topic. Lind and Sanders describe it as something that lowers the frequencies of vibrations of skis, lowers the amplitudes and causes the amplitudes to decrease with time.

To understand it, it helps if you've taken intro physics and remember your damped harmonic oscillator/RLC circuit stuff (remember the "dashpot," or the impedance concept, and how they changed the natural frequency and made the amplitude of the oscillations decrease logarithmically with time?).

Skis are even more complicated because, unlike those simple cases, they can support standing waves, so there are many modes (n = 1, 2, 3...). Each of these modes has its own wavelength with nodes/antinodes in different places. (It's similar to the case of a string vibrating under tension.) However, it's probably not easy to predict the natural frequencies and where the nodes/antinodes occur.

But, wait, it gets worse! A ski is not one-dimensional, it's three-dimensional! It therefore supports at least two types of vibration, longitudinal and torsional, each with many modes. This is starting to get into elasticity theory, which I know little about. However, it might be possible to model single modes as simple harmonic oscillators, if you assumed that the modes were decoupled and that amplitudes were small.

And for the final fork in the gears, the boundary conditions for ski vibrations are completely non-trivial. They vary with snow conditions, load, and who knows what else. The vibrations themselves probably even change the boundary conditions, when the skis bounce off the snow. The best solution here is probably FEM/FEA.

But then, even if we could model vibrations, how would we know how to use the information? Lind and Sanders describe damping skis as more of an art than a science, because different skiers will want skis with different damping characteristics.

For my two cents on that, I've been riding K2 (which are known for dampness) for a long time. The only time I've ever noticed a reduction of control is at super high speeds on choppy spring snow. They rip up everything else super-well. In fact, when people talk about a loss of "sensitivity" in damp skis, I have no idea what they're talking about. So I'm inclined to think that we should just damp the crap out of everything, unless we want a particularly poppy ride.

[bigKam]

If I remember correctly, damping does NOT change the natural frequency of a system. Recall the standard second-order system, with or without damping, wn does not change. What does change is the damped-natural frequency. Anyway, you can see this by looking at how the poles migrate in the s-plane when you change damping.

[brianmwaters]

i just went back to my old differential equations textbook, and damping does change the natural frequency. they use the undamped natural frequency as a parameter to calculate the damped natural frequency, which is what you might be thinking of.

anyway, for the underdamped case,

omega = sqrt(4km-c^2)/(2m)

where
omega = natural frequency
k = spring constant
m = mass
c = the damping constant of the viscous damper



thinking about it physically, the dashpot tends to slow down the motion of the system, because it exerts a force proportional in magnitude and in the opposite direction of the velocity of the piston in the dashpot.


and for the record i don't know anything about poles and s-planes.

[bigKam]

Yes, I agree that using a dashpot 'slows' the oscillatory motion. But technically, the natural frequency, w_n, only depends on mass and stiffness, i.e., m and k

w_n = sqrt(k/m)

http://personal.cityu.edu.hk/~bsapplec/natural.htm

So I think the confusion here is terminology.

[brianmwaters]

so i guess the term "natural frequency" specifically refers to the undamped natural frequency? didn't know that.

[bigKam]

3M makes a constrained layer damper (aluminum and visoelastic polymer) for aircraft and other applications. I have not used it yet but a colleague suggested I look into it for skis. It appears that the damping gizmo I've been putting in my skis is similar, but I'm not 100% sure without further investigation.

I heard rumors that nano-fibers (ultra-small size fibers) embedded into epoxy resin can improve the damping characteristics of the material by up to 3 orders of magnitude. I'm not sure if I believe this, but it sounded interesting. But of course using nano anything at this point is way beyond the reaches of my hobby ski-building radar.

I've been intrigued with damping of skis for some time now. About a year ago I started looking into a way to quantify the dynamic characteristics of a ski in an easy way. Some of my initial experimental results looked interesting but I set the project aside about 5 months ago. I'll try to pick it up again to see what I can come up with.

[brianmwaters]

actually west system makes an epoxy additive (they call it "filler") called 403 Microfibers. they say it improves bonding to wood, and still is good for wet-out... and in light of what you've just said it sounds pretty interesting. i bet the fibers would work in any other brand epoxy, too.

[carver]

I know less than nothing about the science but I do have a massive amount of on snow experience. IMHO some damping def. helps. To much will render your ski/board dead on arrival. Think of the difference between driving a luxury car and a sports car the luxury car isolates you from the road while the sports car makes you feel connected intimately with it. Tune your ski/board damping to match the use you have in mind. Err on the side of less than to much. Nothing sucks more than a dead feeling ski/ board.
Ski companys have tried all kinds of ways to dampen there product from simply gluing rubber blocks to the top sheet to embedding metal wire encased in rubber blocks in the core(the wire supposedly absorbs energy) and k2 went so far as to use peizeo electric(sp?) chips to burn off energy.

[knightsofnii]

we could use the chips to burn off K2, then the world will be a better place

[davide]

To keep it simple: low frequency vibrations (20-60 Hz) are bad, because edges loose grip. High frequency vibrations (KHz) are good, because they give a lively feelings (but it is a matter of taste).

To eliminate low frequency vibrations, the most effective way (used in World Cup downhill skis) is to attach an aluminium plate about 20 cm from the tip (around the node of the second mode), using two side tapes.
That is all.

Then if you want to have fun with FEM, analitycal models and new composites, good luck.