Well then snowpro - ya might get real
dizzy shakin yer head at this next
I think it's Kinda nice when people question the nature of such well established images. I too have always disliked this particular representation of Forces sans qualification
. I see it as being accurate in a general sense
for rigid objects - but not sufficient to describe detailed skier dynamics (for which I suspect it was never intended
My own particular gripe is that the arrows shown assume a Rigid Body
where arms and legs are all rigidly attached to (and unmoving in relation to) the torso. If the image were to be qualified with “The arrows drawn are a generalization of summed forces” - then I think it works nicely for many discussions. Without such a qualifier, Spindrift’s observation and many other objections are likely to come about.
To explore it further: What if the skier shown (in the original image) is actually morphing
their body in some way at that exact moment? Say Maier is actively lifting his Left Arm
upward and/or actively articulating his waist such that his shoulders are actively being ‘leveled out’… then what?
Any such muscular induced accelerations of attached Masses will undeniably change the Magnitude
of the Force Arrows drawn; maybe only a little, but probably a lot - certainly enough to skew the Green Arrow. If the skier is
lifting that left arm in the moment documented by the image the skier would be accelerating that attached Mass upward
and this would change the magnitude of the Yellow Arrow. The skier would momentarily experience an increase in downward Force at their CM thus skewing the Green Arrow also.
Another consideration is that the diagram might actually be
accurate - but not complete. As just mentioned we are not rigid objects and each individual Arrow drawn is actually a summation
(or resultant) of other Arrows that were not drawn.
What if Maier is neither ‘lifting’ nor ‘standing on’ that Left Leg - meaning he is *not* supporting any portion of his upper-body with it? We could then consider “Maier’s Relevant
Mass” to be everything except
his Left Leg. In this case the only Mass relevant to the Arrows drawn would be the Mass that is actually supported by his Right Ski
It is entirely possible that only the Mass of Maier’s Left Leg
is being supported by his Left Ski in that image. That Left Leg may represent perhaps 20% of his overall Body’s Mass - certainly sufficient Mass to bend that Inside-Ski as shown - yet *not* participating in any way at bending his Right Ski. This suggests the need for a second set of arrows representing the Forces acting independently on the Mass of his Left Leg.
If this seems far-fetched - try it some time. At the end of the season I skied a great deal with no option but to do just this. In early March I pulled my right calf muscle apart while teaching. It was ugly. It’s a Very
unpleasant feeling to have one’s body part tear slowly apart.
I finished out the last hour of that lesson by teaching one-ski skiing since it’s all I could do. I found it quite a strain to hold that useless right leg up off the snow all the time so I quickly learned to continually ‘rest’ that leg on the snow - but with no other weight on it besides its own weight. I also kept that foot slightly forward at all times. While my right calf still took a beating from the lumpy snow it really wasn’t all that hard to do. I managed quite a few more runs down groomed black terrain before going in. (Never say die when skiing
A week later I had the opportunity to train with a couple of National Alpine Team members. No way I was going to pass this up so I signed up despite the still-healing injury. On my first run that morning I booted-out at abundant speed. During my gyrations to recover, my left ski was stripped off and I fell heavily onto the front of my right ski - tearing my right calf apart even more fully than before… Nauseating sensations I must say.
Unwilling to forgo this time with Demo Teamers I insisted on continuing on with the group. I stayed with them all day by keeping my body weight primarily on my left leg and continuously balancing over the left ski. Most of the time my right leg had only to support its own weight. Even so, looking at the video later on I could clearly see the right ski throwing up snow and even carving cleanly in both directions when Dynamic Parallel was employed. I got quite good at ‘feathering’ that bum leg - much like the feathering the prop of a bum engine on a multi-prop airplane. That leg didn’t contribute very much and stayed mostly out of the way.
The bottom line is that readers should not take any such diagrams as the Full and Complete All-Encompassing Literal Truth. Such diagrams are merely conceptual representations of basic ideas.
Discussions with Technical Analysis of Skier-Motion frequently break down in translation between parties because participants use ‘generalizations’ (like the Maier diagram) to support their own precise
descriptions of relationships-in-isolation.
Heck, even the concept of ‘Center-of-Mass’ (CM) breaks down when we realize that multi-jointed, multi-segmented biomechanical beings have many individual CMs
that add up to the oft-described skier-wide CM.
Each individual body-Joint
separates two independent body-Segments
. Each body-segment has its own CM that can operate independently from every other body-segment’s CM. When two such segments are momentarily held rigid with respect to each other - they effectively become a single segment with a new (temporary) CM location that includes the Mass of both. When we discuss skier motions we often imply with unintended precision
the motions of the “Skier’s CM”. We do *not* generally take into account the many independent CMs and their potentially dramatic impact on our proposed idea.
I realize such infinitesimal detail is way more than most of us care to consider but it is
the reality with which we are dealing in Technical Discussions whether we choose to recognize and incorporate the ‘dynamic individuality’ of body parts or not.
When Technical information is presented without consideration for the obscure details these 'unaccounted for' detais behind our generalizations leaves us with gaping holes in our proposal - holes that others are sure to try and fill or contest. Sometimes with accurate information; more often with equally incomplete (and contrary) rebuttal. This leaves the floor wide open for emotional expressions of highly dogmatic convictions in place of the comprehensive reasoning that might otherwise properly connect the dots.