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Center of Mass

post #1 of 15
Thread Starter 
This question is especially directed towards you engineers and physics-type people ....

Does one's center of mass move? By that I mean, if I locate my center of mass within my body right now, say somewhere above my navel, then will it be there no matter which way I bend and lean and fold and extend my body all the time while skiing? Or does it move depending on how I move my arms, legs, etc with respect to the snow and my skis and all that stuff?

And a related question: If I'm riding my bike and sitting firmly on the seat, is my center of mass higher up than if I stand up on the pedals without touching the seat?

You can see where I'm going with this. If that cm doesn't move, what an interesting thing it would be to imprint its position in my brain now. I've been doing a lot of envisioning this summer while dreaming of skiing, and finding and remembering that spot would be a great exercise for the next couple of weeks, if it exists. Then once the snow arrives I can work on placing that spot where I want it while doing different types of turns.

Of course, if the center of mass moves around, I still need to somehow "know" where it is, but it will be a feel-my-way-through-it sort of thing that will just have to wait till the slopes open.
post #2 of 15
Yes, the CM moves all over the place. It can even move outside your body.
post #3 of 15
Thread Starter 
Rats!
post #4 of 15
LF,

Here's a side view that has been playing around here for years...

Quote:
Originally Posted by Bob Barnes/Colorado
Bob also has some illustrations in his book showing the CM moving outside the body from the front ...I don't recall if he ever posted somethinglike that on Epic yet or not.
post #5 of 15
Anyone know how that centre of mass in the animation was arrived at, is it just someones idea of where the CofM is or is it calculated with some degree of accuracy?
post #6 of 15
Quote:
Originally Posted by Rich_j View Post
Anyone know how that centre of mass in the animation was arrived at, is it just someones idea of where the CofM is or is it calculated with some degree of accuracy?
I remember the PM (PhysicsMan) had discussed both CMG (COG/COM) as well as Centripetal/Centrifugal forces acting on the CMG. Here's a link to his post that links to some of his math.

BTW, we all decided that Center of Gravity and Center of Mass was the same thing in the end, not that one resides within the body and that the other moves about (as it does per Bob's graphic, on all planes as well).

Centrip/Centrif and COG/COM (CMG)

You may find more of his math on CMG there or by searching for posts by PhysicsMan
post #7 of 15
Thread Starter 
What prompted my question was an observation I made while trying to balance on a big exercise ball while doing fitness exercises. I discovered that if I focused on a specific spot in my body (which in this case surely is the center of mass), trying to keep that point over the center of the ball, then I could balance on it. After finding that point, I worked my knees, legs, and arms to keep that point centered over the ball, and when successful I could stay up on the ball despite its squishy- change-shape nature and its tendency to roll out from under me. This really works. If it works on a ball, then it's similar to skiing on uneven terrain while moving the body around, left and right, fore and aft.
post #8 of 15
I think he's trying to show the ideal; i.e. flex and extend to conform to the terrain so as to avoid the CM moving up or down. For example, if you got the CM moving upward (because you didn't flex) and didn't do something to counteract that at the top of each little hill you'd be getting some air.

The concept is that is steady CM is "good" and one bouncing around like one of those old-time song lyric balls is "bad".

But to answer more directly: close observation of the animation indicates that the CM is well-placed. For example, during full flex the CM is located outside the body; that rings true when you look at the position of the legs and chest.
post #9 of 15
Quote:
Anyone know how that centre of mass in the animation was arrived at, is it just someones idea of where the CofM is or is it calculated with some degree of accuracy?

It is precisely calculated, Rich, down to the micrometer.

Kidding--the animation is obviously just a theoretical stick figure representation of a typical skier. In a real skier, the actual location of the center of mass is determined by the unique proportions of the skier's body, as well as his or her body position at any given moment.

Typically, children, whose heads are larger in proportion to the rest of the their bodies than adults, have higher centers of mass than adults when standing upright. Adult men, with smaller hips and more massive torsos and arms, typically have higher centers of mass than women (in proportion to their height), again when standing upright.

And as Borntoski says, body position affects the location of the center of mass at any moment. Here is the illustration he refers to (I think):



Because balance requires that the CM be located above the base of support (the feet), at least when standing still, if the CM were, say, where the belt buckle is, the two figures on the left would fall over. As it is, because the arms and upper body have moved opposite the hips to compensate, the CM remains over the feet, and in these instances moves outside the body.

Many common objects have centers of mass outside of the mass itself. Hula hoops, boomerangs, tires, and donuts illustrate the point well. The center of mass is the point about which an object spinning freely in space will rotate. Clearly, in these examples, that point is not in the object. The center of mass of a donut, for example, is in the hole!

It's interesting to ponder that even as a high jumper's body passes cleanly and entirely over the bar, his center of mass may pass under it! With the deeply arched back and arms and legs stretched down low as the hips pass over the bar in the "Fosbury Flop" (see illustrations here), the center of mass remains as low as possible at the highest point of the jump.

Best regards,
Bob Barnes
post #10 of 15
I should point out, before this gets sticky, that the animated stick figure is not quite 100% accurate--there's a little bit of a fudge factor built in to reflect that reality of actual bump skiing. If the skier were truly absorbing the bump 100%, the bump would cause no change in speed, the pressure on the skier's feet would remain constant, and the CM would move in a flat trajectory at a constant speed (as it does in the illustration), with the feet always directly underneath.

In real bump skiing, this theoretical 100% absorption rarely if ever happens, nor is it particularly desirable. If you look closely, the CM does not remain directly over StickMan's feet. As he skis up the uphill side of the bump, his feet move ahead of his CM, which reflects the reality of a balanced position in a skier who is typically decelerating slightly at this point. Likewise, as he dives down the back side of the bump, his feet are behind him, similar to a racer charging down the steep start ramp.

To be truly accurate, StickMan would either have to keep his feet directly beneath his CM (which is not realistic, and not even possible with skis and stiff boots) as he absorbs the moguls 100%, or else the CM should move slightly up and down and fore and aft in the animation, reflecting the slight resistance of the legs as he skis up the bump's frontside and the slight variations in speed as he slows going up the bump and speeds up down the backside.

While no one has ever mentioned this little inaccuracy, I thought I'd better point it out here, before anyone tries to dissect StickMan too finely! (Hey CGeib--if you run out of things to do, try making yet one more StickMan animation, with the CM moving in a very small circle in the opposite direction of the circle of the feet. It actually wouldn't be too hard, since Stickman's movements are accurate, and the only thing that needs changing is the slight movement of the CM. I didn't do this with the original animation to keep it simple, but if you want real accuracy. . . . Have fun.) (Sorry, Lori.)



Best regards,
Bob
post #11 of 15
Quote:
Originally Posted by Bob Barnes/Colorado View Post
While no one has ever mentioned this little inaccuracy
Well, I 'sorta' mentioned it not too long ago...

Quote:
Originally Posted by cgeib View Post

Quote:
Originally Posted by ssh
...What would each of those stickmen look like trying to backpedal in bumps? Furthermore, what would their bodies be doing if they were guiding the skis properly?

How do you do that with so many variables? And how do you compete with "stickman"? That guy is just living right! Beautiful moguls that perfectly match his perfectly balanced full range of flexion and extension, plus he's able to peg a constant velocity of his CM that allows him to maintain perfect ski to snow contact without deflecting his CM.
post #12 of 15
Oh my, Bob, quite the edit! Ya want I should do a revision for every version of stickman?

Mods, can we revise Bob's edit capability to restrict posting any additional work for me!!!!!!!
post #13 of 15
Quote:
Originally Posted by LiquidFeet View Post
What prompted my question was an observation I made while trying to balance on a big exercise ball while doing fitness exercises. I discovered that if I focused on a specific spot in my body (which in this case surely is the center of mass), trying to keep that point over the center of the ball, then I could balance on it. After finding that point, I worked my knees, legs, and arms to keep that point centered over the ball, and when successful I could stay up on the ball despite its squishy- change-shape nature and its tendency to roll out from under me. This really works. If it works on a ball, then it's similar to skiing on uneven terrain while moving the body around, left and right, fore and aft.
Liquid, In the case of the ball, I think you do in fact need to keep the CM directly over the north pole of the ball. But the question is does your body need to be there? You could have your butt sticking out behind you and your head in front of you..and that location in airspace would not necessarily be occupied by any part of your body, yet you would be able to balance on the ball. You can also find positions where some part of your body does occupy the same space as the CM does.

Remember also that when you are focusing on a point inside your core, you are partly doing this to engage certain muscles in your core. However, your core does not necessarily need to be located exactly at the same place where the CM or balance point is, directly above the ball. You should use your core to hold your various body parts in such a way as to maintain balance or adjust it.
post #14 of 15
LQ,
I would caution you to not equate balancing on a ball so directly with skiing. The balancing actions are similar but profoundly different at the same time. Mostly because the ball is not sliding down a hillside and the sum of the forces involved are so different.
Even if we limit our perception to a first person point of view, we need to remember that we are moving through space and that our actions have a specific intent. That intent is to control and change our trajectory. It is not to seek, or maintain a static (or nearly static) balance point on the skis.
Use the ball to develop your balance on an unstable yet relatively static platform. That skill translates to balancing on skis but it is not an all inclusive simulation of balancing on skis once they start sliding across the snow.
post #15 of 15
Thread Starter 
Thanks for the comments on balance, and especially the responses to the ball balancing. It's just difficult to work on skiing when there's no snow, so I'm struggling to find some way to make what I'm able to do now while it's brown outside relate to the upcoming white season. Biking on obstacle-filled single tracks was admittedly closer, but with the foliage gone the single tracks have disappeared. The ball was a stretch.
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