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Acceleration - Page 4

post #91 of 104
I think this is it. Knock yourself out:

http://www.citebase.org/fulltext?for...sics%2F0310086
post #92 of 104
An outcome of good turns is minimal acceleration of the skis throughout the turn. Unless of course, more acceleration is desired.
post #93 of 104
Quote:
Originally Posted by borntoski683 View Post
If you are interested in the physics, there was an attempt at a white paper made and a link to it is posted on this forum somewhere during the last year. The consensus I think was generally that the people writing the paper knew a lot about physics and little about actual skiing. Their understanding of skiing was somewhat limited and implied they were not high end skiers. So their analysis was a bit flawed in that way.
Not too surprising. I've had the dubious pleasure of teaching programmers to ski. While some are quite talented, a surprising number seem to have no perception whatsoever of what their various body parts are actually doing. Maybe that's common with other technical, desk-bound types, too.

I are an engineer, by the way. Although, as a civil engineer, I am generally not allowed to play with anything that moves.

Quote:
Originally Posted by borntoski683 View Post
Part of the whole point I was trying to make earlier is that while it may be somewhat intriguing for certain types of people to break down skiing into physics models....most of the time they are doing it either blatantly inaccurately or using some hypothetical simplified situation that is not a clear picture that will help anyone's skiing. There were some books written in the 70's that pretty much nailed the "how skiing works", and they don't require an engineering degree to understand.

That being said, its summer time and if you get off on calculus, then why the hell not. Enjoy yourself.
Indeed. Calculus is The Secret (TM). It can be bludgeoned into handling the singularities that tend to arise when some quantity under consideration (often a component of acceleration or velocity) passes through zero as it changes sign.

It suffers from the problem that many mathematical models consist of systems of partial differential equations that are too complex to have closed form solutions, even with many simplifying assumptions. If one was to develop such a model for skiing, the problems alluded to by others in this thread occur:
1. If it's complex enough to have more than a distant relationship to reality, even a numerical solution could be difficult.
2. If it's simple enough to have a closed form solution, it doesn't represent reality closely enough to be useful to anybody.

If number 1 occurs, the geeks will apply for a research grant to buy time on a massively parallel computer somewhere.

If number 2 occurs, a bunch of ski geeks on Epicski will complain that too much stuff got left out and the mathematical model really should look more like #1 if you want to accomplish anything.

We might also note that any model is further complicated by an enormous array of human variables which are difficult to quantify. Psiman shows one thing, but psiman with a nervous system shows something else. Individual perception and reaction will cause any skier, even a skilled one, to vary considerably from any model we might develop.

That, of course, is why we ski.
post #94 of 104
Quote:
Originally Posted by jhcooley View Post
Calculus is The Secret (TM). It can be bludgeoned into handling the singularities that tend to arise when some quantity under consideration (often a component of acceleration or velocity) passes through zero as it changes sign.

It suffers from the problem that many mathematical models consist of systems of partial differential equations that are too complex to have closed form solutions, even with many simplifying assumptions. If one was to develop such a model for skiing, the problems alluded to by others in this thread occur:
1. If it's complex enough to have more than a distant relationship to reality, even a numerical solution could be difficult.
2. If it's simple enough to have a closed form solution, it doesn't represent reality closely enough to be useful to anybody.

If number 1 occurs, the geeks will apply for a research grant to buy time on a massively parallel computer somewhere.

If number 2 occurs, a bunch of ski geeks on Epicski will complain that too much stuff got left out and the mathematical model really should look more like #1 if you want to accomplish anything.

We might also note that any model is further complicated by an enormous array of human variables which are difficult to quantify. Psiman shows one thing, but psiman with a nervous system shows something else. Individual perception and reaction will cause any skier, even a skilled one, to vary considerably from any model we might develop.

That, of course, is why we ski.
It's interesting that you bring up Psiman. That's a perfect example of how a simple model can illustrate a part of a much more complex process.

I don't think anyone here expects to be able to develop a comprehensive mathematical model of skiing. But it's interesting (to me, at least) and possibly instructive to think about the various components of skiing and see what parts of them can be modeled mathematically.

But yes, skiing is too complicated to model. So is the weather. So is physiology. No one should ever try.
post #95 of 104
Thread Starter 
Quote:
Originally Posted by michaelA View Post
Assuming the fog prevents much depth perception and that Harald only Banks his turns, then yes, he probably would look a bit like a pendulum swinging back and forth (with a bit of added up and down motion).
If the upper body is kept stable can't the legs turn back and forth under it such that they look like a pendulum from the front?
post #96 of 104

Numerical solution of idealized problem

In this idealized problem, I chose the following assumptions and inputs:
1. You are a cylinder of water with diameter of 2 ft.
2. You are at an altitude of 7000ft at 30 degrees F.
3. Coefficient of friction is 0.05 (taken from a table at some website).
4. Drag and friction coefficients are independent of speed.
4. Initial velocity is zero and initial direction is straight down the hill.
5. Incline is 23.5 degrees.
6. Calculation is run through ten half-circle turns at constant turn radius R.
7. Magnitudes of linear (al) and centripetal (ac) accelerations are plotted in units of g.
8. Speed (v) and time (t) are given in dimensionless units as shown. For an 18 meter turn radius, speed units are about 30 mph and time units are about 1.4 seconds. That is, a speed of 2 on the graph is about 60 mph and a time of 15 is about 20 seconds.


No friction and no drag

http://eightsisters.wordpress.com/20...on-and-no-drag


1. You can tell where you are in the turn by looking at the magnitude of linear acceleration, which is maximum (and less than one g unless you are traveling down a cliff) when you’re pointed downhill and zero at transition points. Each cusp in the linear acceleration is a transition point.
2. The rate of change of linear acceleration is zero when you are pointed downhill (ie constant acceleration) and maximum at transition points.
3. Without drag or friction, you are never slowing down (ie the magnitude of linear acceleration is never negative).
4. If you were not turning, the speed vs time curve would be a straight line with slope equal to the constant acceleration of g*cos(incline), which is its value at time zero.
5. In the case of centripetal acceleration, what is plotted is the absolute value of the magnitude of the acceleration. This means that it does not tell you when you are turning to the left versus when you are turning to the right. This was done to make it easier to put all three curves on the same plot. To account for this, all you have to do is change the sign of the centripetal acceleration at each transition point, alternating between positive and negative. At each transition point, the magnitude of the centripetal acceleration is therefore instantaneously zero as you instantaneously transition from turning left to turning right, or vice versa.
6. Since your turn radius is constant and you are always speeding up except at transition points, the absolute value of the magnitude of the centripetal acceleration (v^2/R) is also always growing except at transition points.
7. With no drag, your speed after ten R=18 meter turns is a frightening 120mph, you are pulling an unhealthy 16 g’s, and also you are dead. Or at least you fell down well before your tenth turn.



Friction but no drag


http://eightsisters.wordpress.com/20...on-but-no-drag


1. The effect of friction is to decrease linear accelerations. Peak values are about 11% lower, and you are now slowing down a bit at each transition.
2. Still, your terminal velocity is infinite and your speed and the magnitude of centripetal acceleration increase with each turn.
3. You still end your tenth turn at over 100mph pulling 13 g’s, and you are still dead.



Friction and air drag

http://eightsisters.wordpress.com/20...n-and-air-drag


1. With air drag, we now have to specify your turn radius (or at least the ratio of your turn radius to your body-width. I choose R=18 meters for my 2-foot-wide cylindrical bag-o-water person.
2. You now have a terminal velocity, but it is the human freefall velocity of about 120mph (within the parameters used in this model) and you still make it up to 90mph at your tenth turn.
3. If you’re still holding that 18 meter carve, you are still pulling an superhuman 9 g’s.



Friction and enhanced drag

http://eightsisters.wordpress.com/20...-enhanced-drag


1. Note that in the previous case we included air drag but have neglected drag due to the snow, which must be very significant - particularly in high-speed turns.
2. Terminal velocity is now just under 60mph, and is approached after about seven turns.
3. Once terminal velocity is approached, you get to spend about as much time slowing down as you do speeding up.Linear acceleration is still greatest in magnitude when moving downhill and smallest at transition. The peaks in speed, however, occur slightly after turning away from straight downhill, and the speed minima occur slightly after each transition point. The same is true for the magnitude of the centripetal acceleration, since it is proportional to speed squared.
4. Maybe there’s someone with a frame that can sustain the ~3.8 g’s at ~56 mph, but I’m sure I would have had to break out of the carve long before that point.




There’s a lot of information in these plots that I’m sure I haven’t processed yet, and many more variations that could be tried. I’ll try to answer questions if something is not clear and would be interested to hear ideas of other tweaks that might be fun to look at.
post #97 of 104

Fixed link?

Some of the links don't seem to work. Try this one for all four plots.

http://eightsisters.wordpress.com/2008/06/05
post #98 of 104
Also the order of the plots in the corrected link is oposite the order in which they are described in the text.
post #99 of 104
Quote:
Originally Posted by amiles View Post
Some of the links don't seem to work. Try this one for all four plots.

http://eightsisters.wordpress.com/2008/06/05
FANTASTIC!



You could repost this under a separate thread entitled "Why carving ALL the time ain't necessarily a good idea."
post #100 of 104
Quote:
Originally Posted by amiles View Post

Friction and enhanced drag

2. Terminal velocity is now just under 60mph, and is approached after about seven turns.
3. Once terminal velocity is approached, you get to spend about as much time slowing down as you do speeding up.Linear acceleration is still greatest in magnitude when moving downhill and smallest at transition. The peaks in speed, however, occur slightly after turning away from straight downhill, and the speed minima occur slightly after each transition point.
4. Maybe there’s someone with a frame that can sustain the ~3.8 g’s at ~56 mph, but I’m sure I would have had to break out of the carve long before that point.


There’s a lot of information in these plots that I’m sure I haven’t processed yet, and many more variations that could be tried.
This is an accurate desciption of what is sensed in bringing a carving ski up to speed. At 4 turns at 18m speed control is cleary the issue as suggested above. Cool.

And now to contemplate on becoming "a cylinder of water with diameter of 2 ft." ohm.

Thanks amiles.
post #101 of 104

Correction and qualifier

Sorry for the string of posts - I should've taken more time to check before posting the first...

In the text accompanying the "no friction no drag" case, I mistakenly typed cos instead of sin for the downhill component of gravity. This was just a typo in the text - the term is correct in the calculations.

In the "Enhanced drag" section, there was also a qualifier that I appear to have accidentally deleted before submitting. Since it was the one where I actually told what I did, I should probably add it. As a pretend fix to the neglected snow drag, all I did was artificially multiply the air density by a factor of five. This put it at one half of one percent of water density (of order 1/20 "typical" snow density?).
post #102 of 104
thanks amiles, I bow to your superior knowledge and graphs.
post #103 of 104
Wow amiles, awesome process you have articulated & demonstrated there. I can totally get numerous visuals and images on how this applies in real life skiing ! Thanks. What I understand from this is there are numerous varieties of forces influencing our speeds and acceleration rates. In skiing a mountain those forces are ever changing. The many influences a skier has changes as well. With our choices, tactics etc. Not possible to get the same turn each time with the same forces as they will not be the same every inch down the mountain. Except for the gravity part. I can get a great visual and feel in that for myself. It also explains why a 1st time skier taken to the top by a well meaning friend has the inevitable ending when frozen in terror "being the cylinder of water on skis". Thinking of one described where the inevitable was quite a distance down hill from where they started & at ahuge gain of speed.

I can also see the value for ski jumpers and designers when it comes to a ski ramp, ski's etc. Ski jumping is probably a better application for this than general mountain skiing. A few more constants for a few more feet.
post #104 of 104

Gravity is the curvature of space

32ft/sec/sec. Changing velocity, Speeding up, slowing down, turning. Intention, inertia, attitude.
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