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# CoM, BoS, Centrifugal G-Force, and "Inclination"

Before I got frustrated with and moved on from the "Discussions" forum in the members-only "Community" section of the PSIA National website, I posted a thread on Bumps (because personally I can’t ski, and the moguls prove it) and, in response to a video I linked, a member said that the bump skier was in the "back seat." Which intuitively I knew could not be true, because the video was of an Olympic or otherwise expert bump skier. To his credit a Level III (I will amend this post to include his name to give him credit) posted that while it looked like the skier’s butt was back, his Center of Mass ("CoM") was actually stacked over his Base of Support ("BoS") because the skier was going up the uphill face of the bump.

That got me thinking, that if you do your Movement Analysis ("MA") only with respect to "vertical" or to Earth Gravity ("EG"), or even with respect to snow slope, you could be missing the fact that when the skis move up the uphill face of a bump, or up the wall of a half-pipe, or laterally in a high speed carved arc, that MA must start by identifying the largest applicable Gravity ("G")-force.  Which at least Bob Barnes refers to as the "Resultant Force."  But I, personally, think I like G-force better.  Because there is only G-Force, which either is existent 1-G Earth Gravity or the 2or3-G's which "result" from centrifugal action in a turn.  But they are all G-forces.

So, the concept of adding "Where is the G-force" to my MA checklist I think would be very helpful.

[Edit:  Everything I said above is wrong.  But it was a good start for me to understand the truth, which as you will find below took me a long time to comprehend.]

Some of the pictures of GS racers in Mr.GolfAnalogy’s recent "Help with Counter thread" furthered my thought processes which I would like to discuss with you.

A GS skier in a high speed carved arc is not "inclined" at all.

The Herminator (i.e. Hermann Maier.)

True he is "inclined" with respect to the snow surface and with respect to EG, but these two things are irrelevant to the turn.

Rather, if you turn the above picture counter-clockwise 90 degrees, you will see that the skier is actually "standing" with respect to the largest applicable G-force. And standing with his skeleton stacked, which is the way the anatomy of us land-living animals is designed to deal with gravitational forces.

Above image from Paul Lorenz.  http://www.paullorenzclinics.com/

This is a break through in MA for me. So, in the spirit of exposing my ignorance for you all to help cure, I note that this has been covered before by some of the currently active members and by Bob Barnes who posted some really helpful pictures

and diagrams and even animations in the thread below:

http://www.epicski.com/t/82403/a-revival-of-the-steered-turn

Edited by Tim Hodgson - 9/16/16 at 10:12am

There is only one g force on earth and that is towards the earth centre at 9,81m/s2. When you stand on flat ground there is the g force acting upon your CoM pulling you down at Fg=9,81m/s2 but at the same time a contact force Fn of equal value acting in the opposite direction. All other forces must be viewed as separate forces and when you add all these forces into a diagram you will get a resultant force that will determine the outcome. For instance the bump will add a force acting on your CoM in such way that you need to compensate by leaning backwards.

tdk6:  10-4.  Thank you for replying.  No problem.  So that I can simply understand and simply explain them to my students, what should all these other forces be called?

Are they all just "resultant forces."  Or are they separately named.

For instance, carving a high speed arc certainly generates a resultant force called "centrifugal force."

Is going up the uphill face of a bump or up the side of a half-pipe not a "centrifugal force?"  But, rather, some type of force created by the skier's mass (CoM) slowing down?  Does that have a name?  (Preferably a name used in ski instruction.)

I am not arguing.  I am learning.  I would appreciate suggestions of the appropriate words so that I can think about these forces and so I can explain them.

Clearly one of the goals in skiing is to recognize and anticipate these (insert number here) forces and move the BoS to be between the force and the CoM.  No?

It depends on your frame of reference.   If you have a fixed frame of reference, fixed to the ground, you have the gravity force added to the force acting on the skier at the ski-snow interface adding to the net force accelerating around a turn.  If you have a frame of reference moving around the turn with the skier, fixed to the skier, you have the gravity force added to the centrifugal force adding up to the resultant force that must be resisted by an equal in magnitude, but opposite  in direction reaction force at the ski snow interface so that the skier does not accelerate in this frame of reference.

Inclination is best left at being the angle the skis make with the snow surface.

Do a search for critical angle.  See especially post 17:

A resultant force is a force consisting of two or more forces. For instance when carving you have gravity pulling you down while the centrifugal force is pulling you towards the outside of the turn. That means that the resultant force is the diagonal force with both forces values added. The reaction force is the force acting in the opposite direction of the resultant force.

The centrifugal force is not a resultant force. Its a reaction force. It reacts to something.

I don't know what I would call a force acting upon me when running into a bump. I would not call it a centrifugal force but its certainly a reaction force. We are talking about fore aft balance here. I would not mention any type of force to my students.

Going up the side of a half pipe can be considered a centrifugal force.

I would not consider the goal in skiing to be recognizing the forces. However, its certainly not bad as a underlying theory. Keep up your good work.

Sept 12, 2016

E350 said:  (Anyone recognize the skier?  So I can credit him?)

The picture of the single skiier in question i.e. Yellow helmet,Atomic skis, Leki Poles and red/white Austrian national team uniform, I believe is the Herminator i.e. Hermann Maier.

More clear and detailed version of the Herminator (not the same race).

CP

ps: from Google Image searching on Hermann Maier.

CharlieP:  Thanks!  Attribution given.

Ghost:  My perspective is the skier's perspective, from the snow up. I will read your link and search for critical angle here.

tdk6:  I now know why Jules Vagner pm'd me on the PSIA forum and advised me never to talk about "centrifugal force."  And I undertand why you say it is a reactive force, because it is an outcome i.e., a reaction of the weighted ski carving an arc.  It would not exist but for the skis moving in an arc and the weight of the skier.  And I get that "resultant" force is the sum of all forces acting on the skier.  It is curious to me that the skier's resistance of the centrifugal reactive force is also considered a "reactive" "force."  But I guess it is a "force" created i.e., "reacting" to the equal and opposite centrifugal reactive force.

To All:  As you can probably tell I have never taken a physics class.   So, lets just consider this "Applied Physics (Skiing) 101."

O,K.  I've got some homework to go.

P.S.  I still am attracted to my "Instructor's Uniform Theory of G-Forces in Skiing."   But I stand corrected that it is not accurate as formulated.

Just one thing TDK, centrifugal force is not the reaction force, it means literally centre fleeing force.  It is the force we feel pulling us to the outside of a turn.  The force at the ski pushing us back in the moving frame of reference is not the centrifugal force; it is the applied centrepetal force that prevents us from accelerating in the frame of reference that moves with the skier that is the reaction force.    Equal in magnitude, but opposite in direction to the net (a.k.a. resultant) force.

The sum of all the forces, divided by the mass will give the acceleration.  This must be true no matter  what system of reference you use, even if your system of reference is itself accelerating around a corner (changing direction is acceleration just as much as changing speed is acceleration, acceleration is the rate of change of velocity.   Yet if a you go around a corner in a moving van with your system of reference laid out in the box of the van with a nice x-y axis, and a marble in the middle at the origin of your x-y axis, you will see the marble accelerate and start moving to the outside wall of the van's box.   How can this be?  What is the force acting on it to make it accelerate a=F/M.   Just like we deduce gravity from the acceleration of a stone toward the ground, we deduce centrifugal force from the acceleration of the marble in that frame of reference.

Quote:
Originally Posted by E350

tdk6:  I now know why Jules Vagner pm'd me on the PSIA forum and advised me never to talk about "centrifugal force."  And I undertand why you say it is a reactive force, because it is an outcome i.e., a reaction of the weighted ski carving an arc.  It would not exist but for the skis moving in an arc and the weight of the skier.  And I get that "resultant" force is the sum of all forces acting on the skier.  It is curious to me that the skier's resistance of the centrifugal reactive force is also considered a "reactive" "force."  But I guess it is a "force" created i.e., "reacting" to the equal and opposite centrifugal reactive force.

To All:  As you can probably tell I have never taken a physics class.   So, lets just consider this "Applied Physics (Skiing) 101."

O,K.  I've got some homework to go.

P.S.  I still am attracted to my "Instructor's Uniform Theory of G-Forces in Skiing."   But I stand corrected that it is not accurate as formulated.

E350 The force generated by traveling in a circle (arc) is Centripetal force.  Creating this force is what carving is all about.

Yes, many define Centrifugal force as the reaction force to Centripetal (Circular travel) .  But for many others (including me) it is really a phantom force  and what is really happening is that your mass is trying to return to an inertial (straight line) path.

Here is a link to argue my case.   Think about this in the context of why many can not complete their turns.  Could it be that they are not applying the right mechanics to continue the forming of the circle and generation of centripetal force?

Centrifugal force isn't a force.  But it is a sensation.  We feel ourselves pulled to the outside of a curved path.  Nothing is pulling us, though.  It's possible to rewire the brain to feel centripetal force as the pressure pushing back up under your boot sole, to think of centripetal force and make it replace centrifugal force.  Yes, that's possible.  Engineers are maybe good at that sort of thing.

When the skier miscalculates something and the ski slips away, and slides off downhill, that isn't a force sending the skier off in a slide.  It's an object (skier) continuing in motion in a straight line until some force slows or stops the object.  Gravity is also at work, complicating that "inertial" movement.  The slide of the skier is a combination of things, the continuation of the body in a straight line, and a free fall governed by gravity, with the snow interrupting the trajectory.  We can rewire the brain to feel ourselves obeying Newton's first law, with some gravity thrown in, if we try.  Yes, we can do that.  Engineers?

But it is functionally easier to think of the whole shebang being motorized by centrifugal force, resisted by the gripping ski, or not.

Edited by LiquidFeet - 9/13/16 at 6:11am

FIFY

Quote:

Originally Posted by JESINSTR

Quote:
Originally Posted by E350

tdk6:  I now know why Jules Vagner pm'd me on the PSIA forum and advised me never to talk about "centrifugal force."  And I undertand why you say it is a reactive force, because it is an outcome i.e., a reaction of the weighted ski carving an arc.  It would not exist but for the skis moving in an arc and the weight of the skier.  And I get that "resultant" force is the sum of all forces acting on the skier.  It is curious to me that the skier's resistance of the centrifugal reactive force is also considered a "reactive" "force."  But I guess it is a "force" created i.e., "reacting" to the equal and opposite centrifugal reactive force.

To All:  As you can probably tell I have never taken a physics class.   So, lets just consider this "Applied Physics (Skiing) 101."

O,K.  I've got some homework to go.

P.S.  I still am attracted to my "Instructor's Uniform Theory of G-Forces in Skiing."   But I stand corrected that it is not accurate as formulated.

E350 The force (generated by traveling) CAUSING YOU TO TRAVEL in a circle (arc) is Centripetal force.  Creating this force is what carving is all about.

Yes, many define Centrifugal force as the reaction force to Centripetal (Circular travel) .  But for many others (including me) it is really a phantom force  and what is really happening is that your mass is trying to return to an inertial (straight line) path.

Here is a link to argue my case.   Think about this in the context of why many can not complete their turns.  Could it be that they are not applying the right mechanics to continue the forming of the circle and generation of centripetal force?

Doc's frame of reference is fixed, not moving with the 8 ball.    In a non-accelerating frame of reference, there is no centrifugal force.  In an accelerating frame of reference there is.

JESINSTR:  OK, I have no idea whether tdk6 or Ghost or you are right, but I like your Inertia idea the best because it supports my "Instructor's Uniform Theory of G-Forces Mass in Skiing."  Why?  (Because you explained it with a video? Very important, but no.*)

Because it explains the "force" that we feel when absorbing while collapsing into and skiing up the uphill face of a bump AND its explains why if we hit a patch of ice or otherwise lose an edge while carving a high speed arc we slide away from the arc AND it explains how a skier can stay glued to the vertical wall of a half-pipe.

From the video I surmise that "Inertia" is the property of a moving mass "trying" to move in a straight line (even if it is hemmed in and redirected by one of those round wooden crochet racks once the rack is removed).

So, I proclaim:  Neither Centrifugal force nor Centripetal force exist.

Only Mass, Movement and Inertia exist, and the possibility to Accelerate the Mass by increased application of an external force.

SO INTERTIA IS THE "INSTRUCTOR'S UNIFORM THEORY OF MASS IN SKIING."

Da!  Da!

* JESINSTR, I think you should watch your video, I don't think it supports your proposition.  But it turned a light on in my dim brain from which the unified theory sprung.

P.S.  And of course LF is right.

from xkcd

Quote:

Originally Posted by Ghost

E350 The force (generated by traveling) CAUSING YOU TO TRAVEL in a circle (arc) is Centripetal force.  Creating this force is what carving is all about.

Doc's frame of reference is fixed, not moving with the 8 ball.    In a non-accelerating frame of reference, there is no centrifugal force.  In an accelerating frame of reference there is.

First sentence is interesting....might be semantics or Frame of Reference.  In skiing there is no prebuilt circular frame to follow and it is up to the skier to form and continue that circle. That is why I use the word generated.  It is offensive in nature.

Re Sentence two. Why would a skier base his/her technique on a defensive feeling that many hold in question vs  the forward looking creation of a force that is universally accepted and guarantees a specific result?   Fear of being pulled to the outside and movements to address this "feeling" is why so many fail to advance.

Quote:
Originally Posted by LiquidFeet

Centrifugal force isn't a force.  But it is a sensation.  We feel ourselves pulled to the outside of a curved path.  Nothing is pulling us, though.  It's possible to rewire the brain to feel centripetal force as the pressure pushing back up under your boot sole, to think of centripetal force and make it replace centrifugal force.  Yes, that's possible.  Engineers are maybe good at that sort of thing.

When the skier miscalculates something and the ski slips away, and slides off downhill, that isn't a force sending the skier off in a slide.  It's an object (skier) continuing in motion in a straight line until some force slows or stops the object.  Gravity is also at work, complicating that "inertial" movement.  The slide of the skier is a combination of things, the continuation of the body in a straight line, and a free fall governed by gravity, with the snow interrupting the trajectory.  We can rewire the brain to feel ourselves obeying Newton's first law, with some gravity thrown in, if we try.  Yes, we can do that.  Engineers?

But it sure is functionally easier to think of the whole shebang being motorized by centrifugal force, resisted by the gripping ski, or not.

LF,  I guess I am a rewired skier.  I have found that it is a lot more fun trying to building turns than worrying about busting out of them.

Quote:
Originally Posted by JESINSTR

Quote:

Originally Posted by Ghost

E350 The force (generated by traveling) CAUSING YOU TO TRAVEL in a circle (arc) is Centripetal force.  Creating this force is what carving is all about.

Doc's frame of reference is fixed, not moving with the 8 ball.    In a non-accelerating frame of reference, there is no centrifugal force.  In an accelerating frame of reference there is.

First sentence is interesting....might be semantics or Frame of Reference.  In skiing there is no prebuilt circular frame to follow and it is up to the skier to form and continue that circle. That is why I use the word generated.  It is offensive in nature.

Re Sentence two. Why would a skier base his/her technique on a defensive feeling that many hold in question vs  the forward looking creation of a force that is universally accepted and guarantees a specific result?   Fear of being pulled to the outside and movements to address this "feeling" is why so many fail to advance.

Fear's got nothing to do with it.  You are best to view it in a fixed frame of reference, from the point of view of the camerman standing still on the slope, filming the skier.  Skier remains in an unchanging state of motion until acted on by a force,  Sum all the forces acting on the skier, divide by skier's mass and you get acceleration.  Skier would go straight, but the net force including gravity and the ski-snow interface force add up to a strong, non-zero force pushing him around a turn. Simple.   Force applied at the ski makes the skier turn.

But from a first person point of view,  camera is  attached to helmet.   Skier feels centripetal force pulling him out of the turn, and stays in the turn (not accelerating with respect to the camera going around the turn) because his net force including gravity, ski-snow interface force and centrifugal force add up to zero.   It is much more complicated physics, especially if radius of turn is changing, but it is also closer to what we feel as we accelerate around a corner.

KEY thing, use one or the other frame of reference/point of view; don't try to use both at once.    No centrifugal force in a non-accelerating frame of reference.

E350 - Yes, its all about the frame of reference. And you will encounter people like me not having an issue with either one. I find that as an instructor I need to be able to quickly change frame of reference in order to live up to my red G jacket.

I like the way you grabbed at the Inertia theory. A great way of describing forces in both slamming into bumps and carving high G turns.

Here is a diagram I've made way back in time that tries to explain the effect of gravity on our skiing and why everything feels so light at the top of the turn and heavy at the bottom. The red force vector, lets call it inertia, is acting on our CoM towards the outside of the turn, the green force vector is gravity pulling us down towards earths centre and the yellow is the resultant force vector consisting of the red and green vectors added to each other. The reaction force vector is not drawn in this picture. From this picture its easy to see that at the top of the turn while inertia and gravity is working somewhat in the opposite direction the resultant force vector is not acting on our CoM with great magnitude the way it does as soon as we pass apex and gravity swings around at us and both inertia and gravity are pulling in the same direction. The steeper the slope is the more significant this effect will be. The flatter the slope is the less significant this effect will be. Also, the higher the inertia is the less this effect will be experienced. Lots of things we can learn from this. For example, gravity will help us incline and tip for higher edge angles at the top of the turn, as we come around apex we need to give it all we've got in means of edge angles and CoM placement, to reduce the impact gravity has on us past apex we need to try to create as big a turning-force above apex as we possibly can, at the bottom of the turn the resultant force will help you un-tip and release your CoM into the new turn. This is why Ted said: I start my turns earlier and end them later. Now you know why

When I ski I am a body in motion. I have placed a tool on my feet that allow me to use that motion to generate reactive forces that I can then use to change the direction of of my body in motion. No  discussion about centrifugal or centripetal forces needed. I just tell my students to let their feet push them around.

fom

Quote:
Originally Posted by JESINSTR

Quote:
Originally Posted by LiquidFeet

Centrifugal force isn't a force.  But it is a sensation.  We feel ourselves pulled to the outside of a curved path.  Nothing is pulling us, though.  It's possible to rewire the brain to feel centripetal force as the pressure pushing back up under your boot sole, to think of centripetal force and make it replace centrifugal force.  Yes, that's possible.  Engineers are maybe good at that sort of thing.

When the skier miscalculates something and the ski slips away, and slides off downhill, that isn't a force sending the skier off in a slide.  It's an object (skier) continuing in motion in a straight line until some force slows or stops the object.  Gravity is also at work, complicating that "inertial" movement.  The slide of the skier is a combination of things, the continuation of the body in a straight line, and a free fall governed by gravity, with the snow interrupting the trajectory.  We can rewire the brain to feel ourselves obeying Newton's first law, with some gravity thrown in, if we try.  Yes, we can do that.  Engineers?

But it sure is functionally easier to think of the whole shebang being motorized by centrifugal force, resisted by the gripping ski, or not.

LF,  I guess I am a rewired skier.  I have found that it is a lot more fun trying to building turns than worrying about busting out of them.

Now that's downright nasty.  But you have a point.

Originally Posted by E350

So, I proclaim:  Neither Centrifugal force nor Centripetal force exist.

Where'd you get MY picture?

About those pictures with the arrows on them. A static representation in two dimensions of a dynamic process taking place in four dimensions (time happens). What could go wrong?

fom

Quote:
Originally Posted by fatoldman

About those pictures with the arrows on them. A static representation in two dimensions of a dynamic process taking place in four dimensions (time happens). What could go wrong?

fom

I wonder how many dimensions there are on this computer

Quote:
Originally Posted by Ghost

Fear's got nothing to do with it.  You are best to view it in a fixed frame of reference, from the point of view of the camerman standing still on the slope, filming the skier.  Skier remains in an unchanging state of motion until acted on by a force,  Sum all the forces acting on the skier, divide by skier's mass and you get acceleration.  Skier would go straight, but the net force including gravity and the ski-snow interface force add up to a strong, non-zero force pushing him around a turn. Simple.   Force applied at the ski makes the skier turn.

But from a first person point of view,  camera is  attached to helmet.   Skier feels centripetal force pulling him out of the turn, and stays in the turn (not accelerating with respect to the camera going around the turn) because his net force including gravity, ski-snow interface force and centrifugal force add up to zero.   It is much more complicated physics, especially if radius of turn is changing, but it is also closer to what we feel as we accelerate around a corner.

KEY thing, use one or the other frame of reference/point of view; don't try to use both at once.    No centrifugal force in a non-accelerating frame of reference.

No arguments....   I think we may be on different wavelengths.   sorry

I Proclaim:  That this common definition of inertia is misleading:

"Q: What is the law of inertia?

A:  Quick Answer:  The law of inertia states that an object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force.

However, as shown by JESINSTR's most excellent video, an object in motion stays in motion with the same speed BUT NOT IN THE SAME DIRECTION !!!

Rather, an object in a circular motion when released from the friction which keeps it moving in an arc, juts off its circular path of travel on a STRAIGHT LINE !!!

And NOT in the "same direction" as stated by the stupid dictionary definition of inertia.

That stupid dictionary definition of inertia has been the cause of confusion in my little brain since I heard it and thanks to JESINSTR's, again, most excellent, video we have the knowledge and ability to correct it.

So, for all you Ski Scientists, I am going to modify the law of inertia in Applied Ski Physics to state as follows:

THE LAW OF INERTIA IN APPLIED SKI PHYSICS STATES THAT AN OBJECT AT REST STAYS IN THE BAR, AND AN OBJECT IN MOTION STAYS IN MOTION WITH THE SAME SPEED AND IN A STRAIGHT LINE UNLESS ACTED UPON BY AN UNBALANCED FORCE!

So, again, I am sticking with my "INSTRUCTOR'S UNIFORM THEORY OF MASS AND INERTIA IN SKIING."

Of course, modified by the fom corollary.

P.S.  I Proclaim:  That this and likely all of my future threads can be subtitled:  "Fun with stupidity!"

P.P.S.  And more importantly I Proclaim:  Snow at Kirkwood!

Edited by Tim Hodgson - 9/13/16 at 9:10am
The law of applied physics need tweaking. The physics nerds at rest stay in the bar. Kids with no formal physics training whatsoever stay outside making turns...
:0
Quote:
Originally Posted by E350

To All:  As you can probably tell I have never taken a physics class.   So, lets just consider this "Applied Physics (Skiing) 101."

O,K.  I've got some homework to go.

This may be problematic, but not without remedy.  I recommend you read up on "Free Body Diagram."  It is essentially what you are trying to draw.  If you can understand the concepts behind a Free Body Diagram, you are well on your way to understanding Physics 101 and you can apply to skiing.

Predicting and understanding motion is a big component of introductory physics.  The first step is typically to draw a "Free Body Diagram."

Quote:
Originally Posted by E350

I Proclaim:  That this common definition of inertia is misleading:

"Q: What is the law of inertia?

A:  Quick Answer:  The law of inertia states that an object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force.

However, as shown by JESINSTR's most excellent video, an object in motion stays in motion with the same speed BUT NOT IN THE SAME DIRECTION !!!

Rather, an object in a circular motion when released from the friction which keeps it moving in an arc, juts off its circular path of travel on a STRAIGHT LINE !!!

And NOT in the "same direction" as stated by the stupid dictionary definition of inertia.

That stupid dictionary definition of inertia has been the cause of confusion in my little brain since I heard it and thanks to JESINSTR's, again, most excellent, video we have the knowledge and ability to correct it.

So, for all you Ski Scientists, I am going to modify the law of inertia in Applied Ski Physics to state as follows:

THE LAW OF INERTIA IN APPLIED SKI PHYSICS STATES THAT AN OBJECT AT REST STAYS IN THE BAR, AND AN OBJECT IN MOTION STAYS IN MOTION WITH THE SAME SPEED AND IN A STRAIGHT LINE UNLESS ACTED UPON BY AN UNBALANCED FORCE!

So, again, I am sticking with my "INSTRUCTOR'S UNIFORM THEORY OF MASS AND INERTIA IN SKIING."

Of course, modified by the fom corollary.

P.S.  I Proclaim:  That this and likely all of my future threads can be subtitled:  "Fun with stupidity!"

P.P.S.  And more importantly I Proclaim:  Snow at Kirkwood!

As shown in the video the direction of the 8-ball keeps changing.  That is because the walls of the loop in contact with the ball are pushing it with a contact force.  At any instant in time, the direction of the ball is tangential to the circle.  Remove the loop and the ball keeps going in that direction.  For example when the ball is at the 9 o'clock position, it is moving straight up, but the wall pushes it towards the centre of the circle (centripetal force) so it changes direction, and keeps changing direction, turning to the right as it moves along the wall.  By the time it has reached 12 o'clock, it has changed direction enough that it is moving to the right of the page, but changing it's direction to be more downwards than straight to the right.

When a skier boots out in the middle of the turn he continues straight forward in the tangential direction. He is not flying outside perpendicular to the tangent of the circle but straight forwards in the direction of the tangent. Just like the 8 ball.

Ghost:  Right.  That is part of my epiphany.  That inertia travels in a straight line and only in a straight line.

Only by the application of an unbalanced force (i.e., air resistance on the seams of a spinning baseball, edges of carving parabolic skis, turned vehicle tires, opposing airplane ailerons, terrain features of all types on land, standing waves including diagonals in rivers, round crochet racks with 8 balls in them) will a moving object (i.e., Mass) NOT travel in a straight line.

That is the fom "redirection" corollary.

The "INSTRUCTOR'S UNIFORM THEORY OF MASS AND INERTIA IN SKIING" explains why we edge with angulation, and then maybe angulation with counter and then maybe even inclination alone to add an unbalanced force to our CoM, which without that unbalanced force our CoM would always continue in a straight line in its current direction of travel.  (Which of course without the addition of unbalanced forces would be down the fall line, powered by the one true force of Gravity.

I am sorry, I don't see centrifugal or centripetal "forces" adding anything to our analysis.  And, in fact, these latter "forces" have always confused me.  Thus, I Proclaim that the "Unified Theory of Mass and Inertia In Skiing" along with the fom redirection corollary replaces and entirely obviates the concepts of centrifugal and centripetal forces and, thus, makes Bob Barnes' diagram in the first post of this thread unnecessary and, I dare say, invalid.*

* I am just trying to draw Bob Barnes out of the woodwork in the event that he is still reading things on this forum.   I have the utmost respect for all the work he has done here.  And before I ever posted on this forum, I searched on this forum for all of his posts, and I am slowly reading them all...

P.S.  But don't blame Bob Barnes if I haven't learned anything...

P.P.S.  Dang, why do I feel an "oops" coming on?

Edited by Tim Hodgson - 9/13/16 at 3:14pm
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