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# "the fall line"

So i've been skiing about once a year for the last five years, but the past couple of years i've skiied more, and also become more interested in skiing itself. I want to learn more about the technical side of skiing. Which leads me to this: What is the fall line?
The fall line is the elevation gradient vector, the direction of steepest decent, the direction a stationary ball would roll in, the fastest way down.
While everything that Ghost said is correct, the best way I've heard it described is if you were to set a ball on top of the hill and let it go, the path it would take is (more or less) the fall line.

Then there are double fall lines which I have yet to hear a good explanation for. The best way to describe them is to see them, and I don't have a picture handy.
The only thing wrong with the ball rolling down the hill is that the fall line can change direction quicker than the ball can because of the balls inertia. Double fall lines are when the trail does not follow the local fall line which can lead you off the trial into the bushes.
Quote:
 Originally Posted by Korporal While everything that Ghost said is correct, the best way I've heard it described is if you were to set a ball on top of the hill and let it go, the path it would take is (more or less) the fall line. Then there are double fall lines which I have yet to hear a good explanation for. The best way to describe them is to see them, and I don't have a picture handy.
the fall line is the path a ball would roll if placed on the ground at that point (so that inertia isn't a factor). If the trail doesn't go that way, you have a double fall line.
Fall line: The direction the slope falls away from you. Otherwise known as directly downhill. The direction a ball would roll, or that water would flow. While skiing it is the direction gravity will pull you if you let it.

### What to do about the fall line

Quote:
 Originally Posted by k2josh So i've been skiing about once a year for the last five years, but the past couple of years i've skiied more, and also become more interested in skiing itself. I want to learn more about the technical side of skiing. Which leads me to this: What is the fall line?
The fall line is where it's at. Using the fall line is central to skiing.

Practice going straight down a slope. Make sure it's almost flat. Find the natural and most direct line down the slope. Practice your turns and stay in the fall line. Do this very slowly and do it as a drill.

Try to establish were the fall line is when ever you are skiing. For the most part, all turns are based on how you want to use the fall line. Turns made off fall line are usually more dificult than those made with the fall line.
The fall line is that thin line between skiing and falling. Once you cross it then you are falling. If you never cross the fall line you will never fall, some people never learn though and just slide on their butts all the way down the hill.

How are those 360's going?
Quote:
 Originally Posted by teledave The fall line is that thin line between skiing and falling. Once you cross it then you are falling. If you never cross the fall line you will never fall, some people never learn though and just slide on their butts all the way down the hill. How are those 360's going?

Double fall line is probably a misnomer in a sense, since there is in theory only one fall line. But a good example is a trail which falls off to the skier's left or right in addition to falling to the bottom of the hill. So the trail might be kind of cut along a diagonal to the true fall line. Or you're skiing along a descending ridge vs straight down it.

So typically in that situation you're fighting to keep from ending up on the low side of the trail as you descend. Magic Mtn Lucifer is a nasty double fall line that always comes to my mind. I remember skiing that one in powder and crud conditions a couple of years ago and I just seemed to always end up in that gutter on the left side of the trail .
Remember that your eye will decieve you and that is the trap that others have mentioned with "double fall lines".

Your eyes are telling you one thing; your are looking straight down a trail toward the bottom of a hill and the "break of the hill/fall line is something different. You wil be skiing from the "visual cues" and your body will be fighting the "true fall line".

Look carefully and "listen" to the cues your feet are providing.

Never look at a hill as an "inclined plane" like a sheet of plywood tilted at an angle. On a hill that breaks .... say ... from high on the right (low on the left), you will be making more turns and edging harder to the right.
If you need to find the fall line just flatten both skis and let gravity pull you.
Quote:
 Originally Posted by justanotherskipro If you need to find the fall line just flatten both skis and let gravity pull you.
But first, point your bellybutton up hill. Yeehaaa!----Wigs

### Just to provoke a little thought....

Given the bowling ball theory, where is the "fall line" on these shapes?

or

or

or

What about a surface like this...

Or this,

or this...

or this

OK, let's hear it.
i'm just gonna go ski...
Like I said just take the derivative....

Actually the "fall line" features leather topskins, and matching boots.
It is where your socks go when they show up missing from the dryer.
is it true that if you know the fall line and you also know that the fall line is your friend then you dont fall ?
Lonnie,
As complex as the graphics appear at first, the fall line is simply the direction gravity would pull you. As you move across terrain the fall line does change directions but it is always the direction gravity pulls you.
As we ski that constant gives us the opportunity to either exploit or resist the pull of gravity. Which I suspect is why the term Gravity line has replaced fall line in most manuals.
I can't draw the fall line on your diagrams, because the location of the fall line is relative to where you are. On the imaginary "perfect" slope shaped like an inclined piece of plywood, the fall line points the same direction for everyone. For a "saddle" slope (probably the easiest to ski), the fall line points vaguely down the hill and toward the center of the slope. At the center, it just points down.

I can't believe nobody's said it -- the fall line is the direction you'll slide after you fall.
According to one person I know, the fall line is "over there, by those snow making pipes" Two fractured tibias proved his point.

I think k2josh has the answer in the posts above that he needs.

RW
It is the path defined by the steepest downward pitch. This can be determined by finding the path on which the second derivative is zero subject to the condition that the third derivative is uniformly positive. It is also similar to the path water would follow were it poured on the slope, excpet that once water has forward velocity it may very slightly from the fall line at any point on its path. Note- figuring out third derivatives while skiing rapidly can be hazardous to your health.
Quote:
 Originally Posted by FOG It is the path defined by the steepest downward pitch. This can be determined by finding the path on which the second derivative is zero subject to the condition that the third derivative is uniformly positive. It is also similar to the path water would follow were it poured on the slope, excpet that once water has forward velocity it may very slightly from the fall line at any point on its path. Note- figuring out third derivatives while skiing rapidly can be hazardous to your health.
Nope, the fal line is given by the gradient:

The second derivitave will only be zero if the surface is a plane, and the second derivitive cannot stay zero unless the third is also zero.
Quote:
 The direction of is the orientation in which the directional derivative has the largest value and is the value of that directional derivative. Furthermore, if , then the gradient is perpendicular to the level curve through if and perpendicular to the level surface through if .
The directional derivative noted in your reference, quoted above, is the first derivative of the surface function. The directional derivative is optiimized where its derivative (the second derivative of the initial function) is equal to zero. The steepest slope will be the most negative, or minimum. To test that an optimum is the minimum, test the second derivative to see if it is uniformly positive. The second derivative of the directional derivative is the third derivative of the original function.
Quote:
 Originally Posted by FOG The directional derivative noted in your reference, quoted above, is the first derivative of the surface function. The directional derivative is optiimized where its derivative (the second derivative of the initial function) is equal to zero. The steepest slope will be the most negative, or minimum. To test that an optimum is the minimum, test the second derivative to see if it is uniformly positive. The second derivative of the directional derivative is the third derivative of the original function.

Ah, I see the problem. I'm talking local, your talking global. So it is the ball and water analogies that are inaprropriate, as a (iinertialy) massless ball's path will be defined by the local properites of the surface no the golbal properities

This one reminds me of Spiderman.
Quote:
 Originally Posted by FOG The directional derivative noted in your reference, quoted above, is the first derivative of the surface function. The directional derivative is optiimized where its derivative (the second derivative of the initial function) is equal to zero. The steepest slope will be the most negative, or minimum. To test that an optimum is the minimum, test the second derivative to see if it is uniformly positive. The second derivative of the directional derivative is the third derivative of the original function.
Quote:
 Originally Posted by monkeyboy Ah, I see the problem. I'm talking local, your talking global. So it is the ball and water analogies that are inaprropriate, as a (iinertialy) massless ball's path will be defined by the local properites of the surface no the golbal properities
Opps, I knew I shouldn't be posting before the morning coffee. What you are suggesting will yield the SINGLE STEEPEST POINT on the surface. If you want to find the global fall line, you need to use variational calculus, not simply a point wise extrema test.

In any event, all physics is local, so the gradiant is what you want.
I see a new product marketing opportunity. The "builtin directional derivative calculator". Maybe one of the highend ski companies could market it - Volkl or something. All the magazines would love it
Quote:
 Originally Posted by learn2turn This one reminds me of Spiderman.
I was just thinking that!
As you can see, the gradient vector is the direction you must take to maximize in a negative sense (minimize) the substantive derivative of the Elevation function (F). Note the first term is only a factor during heavy snow storms.
Also note, in the above over simplification, the affect of the gradient on skier velocity (u) is left to the interested student.
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