What does the term "Platform Angle" mean to you?

[Chris V.]

You may be misunderstanding the meaning of "center of mass." It has nothing to do with whether you're horizontal or vertical, balanced or unbalanced, leaning against a wall or not. It's the weighted mean of the locations of all of the points in your body that have mass. That doesn't change based upon orientation to the earth, or the direction in which the force of gravity is acting, or anything else.

It is perfectly well possible to get your COM outside the body by statically angulating in street wear, whether standing or lying down.

The "compensation" is for the purpose of remaining in balance while angulated--quite a different subject. But--an important one, getting back to your original musing, because to remain in balance while standing, yes, we have to use muscular exertion, and as I said before I expect greater exertion will be needed while angulated than while not angulated.

 

[François Pugh]

The Physics of Touching your Toes! | ScienceBlogs

Can you touch your toes? Seems like an easy thing to do for those of us who have the flexibility. Now, here's the challenge. Stand with your back and your heels pressed up against a wall, and now try to touch your toes.

scienceblogs.com

 

[cantunamunch]

You may be misunderstanding the meaning of "center of mass." It has nothing to do with whether you're horizontal or vertical, balanced or unbalanced, leaning against a wall or not. It's the weighted mean of the locations of all of the points in your body that have mass. That doesn't change based upon orientation to the earth, or the direction in which the force of gravity is acting, or anything else.

Nope, not misunderstanding. Just didn't think it was worth spending time on since a limp shoe lace or a letter C can have it's CoM outside itself.

 

[karlo]

Yes, I should have explained it in a proper way....

Thanks

One of my open questions for almost 20 years now, first posted on Epicski in relation to a similar picture: When the CoM is outside the body, does that necessarily involve more muscular effort - and therefore necessitate greater fitness?

Absolutely. Our bodies, from day to day activities are used to COM being inside. That and the lever. Think pregnant women and how they stand and walk

 

[cantunamunch]

Absolutely. Our bodies, from day to day activities are used to COM being inside. That and the lever. Think pregnant women and how they stand and walk

I am. But I am also thinking of @Bob Barnes' backpedaling animations.

When to pull back feet in bumps

In East, I can only practice bump on closed training course( basically ski zipperline) at my home mountain, there is no nature mogul hill, I am beginner bumper. I can manage skiing blue bump run at speed as it goes(not in controlled way), but move to black bump run, I could not stand the speed I...

www.pugski.com

Notice that the guy with excessive forward lean (pink) has no problem keeping CoM inside or close to the body, possibly for longer than the 'optimal' (black) skier but still exhausts himself significantly more than the 'optimal' guy.

So for that simple case we can argue that energy expended is more related to how far the CoM moves -within the moving frame of reference (crosshairs)- than to how far the CoM moves away from the body.

In case anyone thinks we're drifting far away from the original topic, they're mistaken. We're trying to define a proper set of cross hairs for the case of the turning skiers above - and platform angle naturally drops out of that.

 

[karlo]

I am. But I am also thinking of @Bob Barnes' backpedaling animations.

Oh. I was picturing myself with a 40 liter backpack. That didn’t go well.

 

[cantunamunch]

Oh. I was picturing myself with a 40 liter backpack

Been there, done that, hated it for days.

Notice that in the animations the crosshairs are defined by the center of the circle. The circle is the available range of motion of the BoS.

To apply similar analysis to turning platform angle, we need to re-draw the stick figure of post #46 in terms of how far the BoS can deviate from stacked and then look at the net CoM motion relative to the center of that BoS solution.

 

[karlo]

To apply similar analysis to turning platform angle, we need to re-draw the stick figure of post #46 in terms of how far the BoS can deviate from stacked and then look at the net CoM motion relative to the center of that BoS solution.

 

[Mike King]

One of my open questions for almost 20 years now, first posted on Epicski in relation to a similar picture: When the CoM is outside the body, does that necessarily involve more muscular effort - and therefore necessitate greater fitness?

Seems to be a simple answer. Sure. Because if the CoM is outside of the body, there is greater angles in the skeleton of the body. Greater angles means that when the ground reaction forces operate on the mass of the body, simplified as operating on the CoM, there's more leverage applied to the bones of the body. Since the muscles are attached to the bones, greater leverage implies greater muscular effort to resist the force.

Mike

 

[cantunamunch]

Seems to be a simple answer. Sure. Because if the CoM is outside of the body, there is greater angles in the skeleton of the body. Greater angles means that when the ground reaction forces operate on the mass of the body, simplified as operating on the CoM, there's more leverage applied to the bones of the body. Since the muscles are attached to the bones, greater leverage implies greater muscular effort to resist the force.

Mike

I thought that too at first, but Bob Barnes' animation implies that it can be the other way - greater net motion of the CoM relative to static stacked stance can be more exhausting than allowing the CoM to be outside the body so long as net CoM motion is minimised.

Not sure I'm comfortable settling on any definite answer just yet.

 

[Mike King]

I thought that too at first, but Bob Barnes' animation implies that it can be the other way - greater net motion of the CoM relative to static stacked stance can be more exhausting than allowing the CoM to be outside the body so long as net CoM motion is minimised.

Not sure I'm comfortable settling on any definite answer just yet.

Except that the further the CoM travels away from the centerline of the body, the greater the force from leverage. Bob's graphic is an analogy -- it isn't a real world measurement of force or even range of motion. Further, keeping the CoM moving in a flat plane down the hill through moguls sho result in less force than allowing it to rise and fall. So looking at range of motion of the body doesn't necessarily equate to effort (e.g. force).

 

[cantunamunch]

Except that the further the CoM travels away from the centerline of the body, the greater the force from leverage.

For the single force acting through the BoS - yes, we are completely in agreement there.

We've spent 8+ posts asserting that, and we still haven't addressed whether that assertion still holds true in an accelerated frame of reference such as a turning skier? such as the one diagrammed in post #46 of this thread?

Bob's graphic is an analogy -- it isn't a real world measurement of force or even range of motion

Certainly it is an inexact visualisation - but a useful one. We need a second, similar visualisation for the multiforce platforming situation.

Further, keeping the CoM moving in a flat plane down the hill through moguls sho result in less force than allowing it to rise and fall.

Mostly in agreement there BUT
a) we are not talking about just force, rather force through swept distance to represent energy expenditure - work or effort - which is where the distance the CoM moves really becomes significant.

b) If we are talking about work or effort rather than force, you have painted yourself into a conflicted corner. If the CoM is outside the body but stays on the flat plane, is that more or less work than lifting the CoM up and down while keeping it in the body?

(We can even ask by analogy - what is more work - a person squatting with their CoM aligned or the dancer doll in @François Pugh 's post?)

So looking at range of motion of the body doesn't necessarily equate to effort (e.g. force).

No, but it is the first step in figuring out which motions cause the CoM to move, and which don't.

 

[François Pugh]

A couple of thoughts. Work is the force applied times the distance moved in that same direction.
When skiing through a series of bumps keeping our CoM travelling along in flat plane, gravity does work on us which increases our speed as we descend, friction does work on us which eventually limits our speed, but more interesting is what work do we do. We do have to push our feet into the troughs so there's that, but we let the crests push our feet back up. If we resist our feet being pushed back up we work harder. In fact, we push our centre of mass higher into the air. Even though that force moving us is the ground reaction force, we are supplying the force pushing the snow away from us so same-same (I'm too lazy these days to get rigorous with the physics ).

 

[GlacierNovesia]

The problem with street shoe scenarios is that it is brutally difficult to get one's CoM far outside the actual body.

Well, I am no circus artist too so maybe for you and me it will be impossible. But regarding the plattform angle it doesn't matter. The plattform angle ψ depends more or less only on the question if CoM and your legs are inline or not. In this case ψ will become 90°. When you lean your hips towards the center of the curve (or roll your ankles in the same direction), ψ will become less than 90°. But for an plattform angle of more than 90° you have to move your hips towards the valley (!). So from my point of view the plattform angle is a mandatory but not sufficient requirement to prevent the ski from slipping. It is a very trivial condition. Like when you say that the wheels of a car have to touch the ground for the steering wheel to work. But there are also many other influences that decide whether to slip or cut the snow.

When his CoM is outside the body he falls over.

As long as gravitation and centrifugal force respectively the resulting components in the parallelogram of forces are in balance this will not happen.