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# Definitions: Fall Line and Turn Radius?

Could someone explain to me what the following terms mean:

1.) Turn radius: how do you make sense of a ski's turn radius? For example, my new skis have a radius of 12. What does that mean? Could someone interpret that for me?

2.) Fall line: This month's issue of SKI has some excellent basic carving and powerder tutorials. The carving how-to begins with focusing on your fall line at turn initiation. What does "fall line" mean, exactly? My guess is it is the point at which your skis cross the mountain at turn completion, but that's just a guess.
Did you take high school geometry? No offense... but do you know what a turn is? Now do you know what a radius is? Not all arcs are the same correct? An arc being a part of a circle... Now lets say we have a round trampoline next to an 8oz drinking glass. They are clearly both circles, but not the same size the RADIUS is what defines these circles. The RADIUS is 1/2 the diameter or the cord from the center of the circle to the perimeter. Thus the TURN RADIUS is the arc (part of a circle) that your skis will make (naturally) when you are carving. If you still have no idea what im talking about then i will assume that you are a windsheild wiper turn person and will never need to know the meaning of radius or turn.

Now for fall line. This one i'll accept that you do not know... but it is a very common term used in skiing so i would assume that you would know it... or go to a dictionary to look it up. Essentially it is the natural straight line path down the hill. It also has a lot to do with slope at a given point and what direction the hill's tendancy is in, but based on the radius thing we are never going to be able to comprehend slope. So just go with the straight line down the hill.

Later

GREG
You have a ski whose characteristics favor a short radius turn. In a pure carve or camber turn, your ski will describe an arc with a 12m radius.

If you are straight running you are in the fall line. If you are at a stop on a slope, you are perpendicular to the fall line. We turn into and away from the fall line.
Rotofury,

Fall line means the line that shows the direction directly downhill. It's the direction that water would flow (on the surface) if you poured a bucket of water onto the slope. For a slope that goes downhill from the top of the slope to the bottom but also has a left to right tilt, the fall line would be down slope and to the right.
Nolo & the Rusty ... thank you both. You answered my question(s) just as asked. HeluvaSkier, perhaps you should change your name to HeluvaPrick. No offense, of course.
Well, since the software change at Epicski, that function has been disabled. Unfortunately you can no longer change your name here from day to do day. Thank you for the suggestion though. If the ability ever comes available again i will definitely take your suggestion into consideration.
Later
GREG
> If you still have no idea what im talking about then i will assume that you are a windsheild wiper turn person and will never need to know the meaning of radius or turn.

In my experience, it's possible to be a very, very good skier, while also being kind of dumb. It may even help.

If I had to guess, the average IQ of "windshield wiper" skiers is probably pretty high: all those doctors and dentists, for one thing.
Quote:
 Originally Posted by sjjohnston > If you still have no idea what im talking about then i will assume that you are a windsheild wiper turn person and will never need to know the meaning of radius or turn. In my experience, it's possible to be a very, very good skier, while also being kind of dumb. It may even help. If I had to guess, the average IQ of "windshield wiper" skiers is probably pretty high: all those doctors and dentists, for one thing.
Any particular reason for responding in riddle?
Quote:
 Originally Posted by HeluvaSkier Well, since the software change at Epicski, that function has been disabled. Unfortunately you can no longer change your name here from day to do day. Thank you for the suggestion though. If the ability ever comes available again i will definitely take your suggestion into consideration. Later GREG
Actually if that option opens up you better be a HeluvaTyper, otherwise it'll already be gone.
Fall-line: Roll a ball down a hill and wherever it goes is the fall line.

The only reason I bring it up is that many of our favorite slopes have double fall-lines, menaing they tilt on two axis.
Rotofury - if you're interested in another viewpoint, go to www.psia-e.org and click on SnowPro Fall 2004 Online (PDF version). Nick Brewster wrote an interesting opinion about ski radius on page 34 (Rotary Skill in Racing) that may give you further food for thought.

Good skiing!
Cool medmarkco! I'll check it out. After all, now that I know that a radius is half the diameter of a circle. Good thing I don't need to turn in a full circle, else I'd have to work Pi into the formula somehow!
Hmmm...sounds simple. But it's not quite that simple!

Turn radius does refer to the size of the turn, assuming that it is part of a circle. But few turns are actually circular, so the actual radius typically varies throughout the turn. Still, "short-radius turns" refers to "small" turns, "short" turns, or "tight" turns, as opposed to the larger, slower, turns known as "medium radius" or "long radius."

To me, the important difference is more one of timing than actual size. "Short radius turns" are typically quick and rhythmical, maybe an average of two seconds per turn. Few real "short radius" turns made by expert skiers are as tight in actual size as the turns most beginner skiers make, but at the slow speeds of beginners, it would seem odd to describe them as "short radius turns"--even though it might be accurate.

The "Fall Line" is, simply, "straight down hill" from any given point. It is the direction your parallel skis must be perpendicular to if you want to stand still on the slope. It is the direction a ball would START rolling, if you placed it at any given point on the slope. But it is NOT the path the ball would take all the way to the bottom. Think about it--if you roll a ball down a real slope, with bumps and rolls and such, it will take a curvy path, influenced by the "Fall Line." But it's actual path would be a function of the Fall Line at any given point, and the ball's momentum, and any obstacles that might also deflect its path. Sometimes it would even roll UP hill--up a mogul, for example, or up the side of a gully, all the while "seeking the Fall Line," but never actually going the direction of the Fall Line, except it's initial movement from a stop. (The only exception would be a perfectly smooth and flat slope, like a table tipped up at an angle, where the Fall Line is constant and at the same direction at every point on the slope.)

When we speak of the "Fall Line" part of a turn, we are generally referring to the moment you're traveling straight downhill. We've recently seen some people using the term differently here at EpicSki, but I think there is generally widespread agreement on this definition.

Sorry--things are rarely as simple as we'd sometimes like!

Best regards,
Bob Barnes

### that was me

Quote:
 Originally Posted by Bob Barnes We've recently seen some people using the term differently here at EpicSki, but I think there is generally widespread agreement on this definition.
yep - that was me (fall line meaning something totally different)

Bob, did anyone ever come up with a single concise term for the line bisecting the sine wave of the turns? (the line that happens to be parallel to the fall line as we turn on either side of this centerline) This imaginary line is also where transition from one curve in one direction changes to the other direction. Since skiing is much about how to manage this transition and things like when should a release occur, before, at, or after this line - this line should and probably does have a name.
Mea culpa, I was simplifying, but given the question, I felt erring to the side of simplicity was permissible. Most skiers don't need to know the math to turn a ski, but it's a blessing to have pros on the site like Bob and Physicsman who can give the rest of the story.
How could a line parallel to the fall line be called anything but the fall line?
If you were making rhythmical turns on a trail that had a side "camber" to it, (such as the middle section of the Kitzbuhel slalom hill), I can see a possible situation where John Mason's "centerline" (or should I say "centre line"!), linking the transition points, would not be parallel to the the fall line. But I don't know how perfect the "sine waves" would be...

### fall line

I agree with Nolo but i sometimes expand it to
"when the skis are in the fall line" to describe the point in time
when the skis are straight down the hill*

* assuming this hill is a single fall line, which many many green/blue runs are

at our school, we often talk about skiing our turns in a corridor,
say 1-2 snowcat tracks for short turn, and 2-4 tracks
for medium /long (if i remember correctly)

if your skis are 12 m, they will _tend to_ be happier in short
radius turn. when you take them along a flat catrack, you
may find they are happier on "edge"

### thus the problem

Quote:
 Originally Posted by nolo How could a line parallel to the fall line be called anything but the fall line?
Becuase when people say "fall line" in a ski turn, they mean when their skis are "in" the fall line, pointing that direction.

When I was using the phrase "crossing the fall line", I meant a point in the turn where the skis are momentarily not turning but going straight. Not held in a traverse, but that turn transition point. You can't call this the "fall line" since that means something else to everyone. The skis, in fact, at this point, are least pointed to the fall line. But it's also where the skis are crossing a line parallel to the fall line. This non-fall line fall line, baseline to the sine wave the skis are moving back and forth accross, needs a name. Or it has one and I'd like to know it. I just don't think you can use fall line for both lines without confusion.

Thus the need for a precise term.
Quote:
 Originally Posted by medmarkco Rotofury - if you're interested in another viewpoint, go to www.psia-e.org and click on SnowPro Fall 2004 Online (PDF version). Nick Brewster wrote an interesting opinion about ski radius on page 34 (Rotary Skill in Racing) that may give you further food for thought.
Urgh.

First: the radius written on the ski is not the "turn radius," it's the radius of the sidecut itself! See Bob Barnes post above, and numerous posts in other threads, and the portion of the FIS rules that describes how the "radius" of a ski is determined (and note, as mentioned in several prior threads, that it is an approximation for various reasons and in various ways).

So a ski can (and, in a perfect geometric world, always does) carve turns smaller than its sidecut radius.

Second: Whatever the radius of the ski, ten 21-meter-radius turns -- even if they were perfectly circular (i.e. had a constant radius) -- would take you some distance down the hill, but it's not likely to be exactly 210 meters for two reasons, which make him wrong in two different directions:

(i) The author of the article seems to have mixed up radius and diameter. If you did 10 turns that were perfect semi-circles, each with a radius of 21 meters, you'd go 420 meters down the hill (over a quarter of mile, incidentally).

(ii) The radius of the turn doesn't tell you how far down the hill you go, unless you know what portion of a circle you're forming. Skiers, whether on the race-course or just skiing, don't ordinarily do a half-circle: they don't start a turn perpendicular to the fall line and finish perpendicular to the fall line in the opposite direction (i.e. they don't turn through 180 degrees of a circle). Just off the top of my head, it would be a lot more typical to turn through 90 or 120 degrees or so -- starting at a 45- to 60-degree angle to the fall line, and finish at a similar angle on the other side.
Incidentally, you would travel one turn-radius down the hill if you were doing 60-degree turns (starting at an angle of 30 degrees to the fall line and finishing at an angle of 30 degrees to the fall line ... oh, yeah, and incidentally: assuming the fall line is straight line).

The straight-line distance is 2R sin (theta / 2), where theta is the angle you turn through.

One more note: the relationship between lineal distance and carved-turn radius is further complicated, in that you don't necessarily initiate a turn just by rolling onto the edges with your skis oriented in the direction you're traveling. The turn can begin with the skis at an initial angle, as shown in Ron LeMaster's photo-series, and still be carved without significant skidding. In the pre-shaped ski era, that was more pronounced.
Quote:
 I meant a point in the turn where the skis are momentarily not turning but going straight.
I believe the term is "neutral."
Quote:
 Originally Posted by Bob Barnes/Colorado It is the direction a ball would START rolling, if you placed it at any given point on the slope. But it is NOT the path the ball would take all the way to the bottom.
Exactly.

If you want to get all theoretical, it's the path a ball that has weight, but no mass, would take.

### Thanks nolo

Still "neutral" is a point on the path the skis are taking. I was looking more for a definition of a line through which multiple neutral's occur. Perhaps there is no accepted word for that bisecting line.
John,

I would think that the name for the line you are talking about is (or should be) the "Average Path of Progression." It would be the integration of the path of the curves down the hill it is your progress. (Since all turns are not sinewaves and there might be some "hickups" in the path, I believe curves are a better description.)

The Average Path of Progression (APP) would not follow the fall line, although it could. It would normally slink across the hill as turn radius changed or the skiier advanced in a different direction. In a "Pain in the S Turn" the APP follows a GS turn while the skiier skis short radius turns around the APP.

The APP does not follow the Center of Mass line (CM) of the skiier. It could in a short radius turn sequence, but not in most cases.

Mr. Barnes, what do you think about that description?

(I think we are starting to get esoteric here, however, it is a good term for ski instructors to have in their vocabulary. I wouldn't want to use it with a lot of my students though.)
Quote:
 Originally Posted by sjjohnston Urgh. First: the radius written on the ski is not the "turn radius," it's the radius of the sidecut itself! Second: Whatever the radius of the ski, ten 21-meter-radius turns -- even if they were perfectly circular (i.e. had a constant radius) -- would take you some distance down the hill, but it's not likely to be exactly 210 meters...
First and foremost, the side cut radius is indeed the maximum theoretical radius of a perfectly scribed circle of a non-decambered ski. Once reverse camber distance, slope inclination, and leg inclination are factored in, the ski has an infinitely variable radius which makes any attempt at comparison virtually impossible. For the sake of discussion some variables must be fixed. Nick clearly stated he was "simplifying the issue".

As you correctly point out, the math is incorrect. Ten 21 meter circles intersecting at a common tangent do equal 420 meters of vertical drop. Which by the common course setting rules equals 46 direction changes - not 23 - further supporting Nick's postulation that more than sidecut alone is needed to successfully navigate an FIS/USSA course. Theoretical side cut radius accounts for only 10 direction changes. (Notice too that Nick is talking vertical drop and not measured distance- another simplification).

Therefore, additional skills are needed to make the requisite number of turns. Actual turning radius will be effected by the varying inclinations of the race course and the skier's ability to get the ski up on edge, both of which affect the distance of reverse camber. Add to that a distorted "J" arc by pressuring the front of the ski and the radius (measured vertically) gets even tighter.

Current thinking in GS is to complete 65-70% of the direction change prior to reaching the gate. In practice that means the skier is coming back at the gate when he reaches it, rather than turning around the gate. This prevents deceleration and ski "chatter" caused by excessive centrifugal force in the lower half of the turn. Therefore turn initiation starts very high in the arc.

Nick's primary point of the article is that rotary skills are still needed (in addition to edging and pressure skills) and often not receiving enough focus in light of all the talk about carving perfect arcs. Adding the complexity you and I have interjected takes sidecut radius to a more involved level than I think the original poster intended. I just thought he might want to think about ski radii from another perspective- not become entangled in a mathematical hornet's nest solving complex and infinitely variable equations.

### Da Math.....

Quote:
 Originally Posted by nolo Mea culpa, I was simplifying, but given the question, I felt erring to the side of simplicity was permissible. Most skiers don't need to know the math to turn a ski, but it's a blessing to have pros on the site like Bob and Physicsman who can give the rest of the story.
Nolo,
This is truly Karmataious!
Just this afternoon my curiosity led me to search out the formula I would need to take Tip/Waist/Tail dimensions and calc a skis static turn radius. I built it into a spreadsheet so I could compare skis that do not list that spec. Next I'll calc edge angle effect.

In ski terms radius math could be expressed as:

Radius = ((contact length sq'd) + (4 x sidecut sq'd)) / (8 x sidecut)

Using: Sidecut = ((Tip +Tail)/2 - Waist)/2
with tip/tail measured at flat ski contact points.

So, the math effect of what Bob aluded to would be:

When a ski is tipped onto edge and flexed into reverse camber, the straight line distance between contact points shortens, increasing the effective sidecut as the waist moves further from that line, netting a shorter turn radius.
:
Oh, and I thought the falline was the most direct path from head to point of impact?
Bob B,

With each post, you reaffirm the decision I made to join your ETU! Thanks for your insight and explanation. Like Steven Hawking said, It's one thing to figure out the mysteries of the universe, it's something else entirely to explain them to the masses.
Quote:
 When a ski is tipped onto edge and flexed into reverse camber, the straight line distance between contact points shortens, increasing the effective sidecut as the waist moves further from that line, netting a shorter turn radius.
I would expect nothing less from a man of your nomenclature.

Since many manufacturers do publicize this number, is it a meaningless marketing ploy or an important characteristic of a ski?
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