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# Just for fun question.

All things being equal,

Clean carve.
clean initation
Weight distribution
Length of transition
Consistant pitch
Consistent snow condition (assume firm pack groomed)
Equipment Ski/boot length and tune
Wax
ETC

What shape shaped turn will get you down the hill fastest.

C shaped (arc to arc)
J Shaped
upside down J shaped.
Z shaped

(Bob or those of you that have read his book need not reply, just yet)
shaped skis or straight skis?
I'll bite: upside down J.
Turns that look like rounding off a corner would be my guess with the radius at the corner being the shortest the skier could possibly ski. I guess this is sort of an off-set J looking thing.
Quote:
 Originally Posted by dchan Consistant pitch Consistent snow condition (assume firm pack groomed) What shape shaped turn will get you down the hill FASTEST.
Ummm, a straightline? Guess thats not really a turn though.
S shape - less of the C, or flat horizontal, so, not "completing" the turn.
C shape, (I think)
The problem is........what I imagine I am doing is not necessarily what I AM doing.
Can I choose "none of the above"?

I think of all the letters and punctuation marks - and aside from the number "11" - it's got to be parentheses. Why finish a turn if you don't have to?

(
.)
(
.)
The shape that gets you down the most vertical soonest without skidding. Ie. if this were typed on a vertical piece of paper,
A
|
|
|
.\
...\
.....\
.......B

is faster than
A
.\
...\
.....\
......|
......|
......|
......B
given the choices, "C" arc to arc. All the others imply a braking component (at least they do when I do them ).

However, I'm with WTFH and Bob and anyone else that said you don't need to "complete" or "finish" the turn to be fast.
Quote:
 Originally Posted by Ghost The shape that gets you down the most vertical soonest without skidding. Ie. if this were typed on a vertical piece of paper, A | | | .\ ...\ .....\ .......B is faster than A \ ..\ ....\ .....| .....| .....| .....B

Actually, I think I disagree with you, (but I could well be wrong!) because if you are travelling slower at the point of transition, then you will not lose as much speed in the turn, i.e:
|
.\

is not faster than
.\
..|
and I think it might be slower - certainly in car racing, it is better to be slower into a turn and be able to get the power on early, than be fast into the turn and slower out.

(but I could be wrong)
I stand corrected!
Notice I said "without skidding". It's basically the sooner you build up your speed, the more ground you cover at speed. It's also totally terrain dependent. If the offset is such that you have to cover a lot more ground following the fall line deeper into the turn you lose the advantage. I suppose we could set up a spreadsheet and calculate the ideal path for each race, but I doubt even PM could do the calculations on the fly. That's what makes racing an art.
figure 11s is what I would use.

I have never read the book but I would think Z shape on a very flat ski would be the fastest, but since when has anyone wanted to do that. Z shape turn while a very important part of skiing and something any "expert" should know just arent fun. Last time I checked though all that really matters is fun........
OK, let's say that the object is accelerating at 4m/s^2, the distance is 6m, and the angle is 45 degrees.
For your first scenario, I get a time of 1.62 seconds, for the second I get 2.15.

You are correct, and it's back to school for me!
Sorry, forgot the argument:

The fastest turn will have the least pressure on completion. The C/J/Z turns have the highest turn forces at completion. The upside down J (or comma) as the least.
assuming shaped skis, "C's"
Quote:
 Originally Posted by BigE Sorry, forgot the argument: The fastest turn will have the least pressure on completion. The C/J/Z turns have the highest turn forces at completion. The upside down J (or comma) as the least.
but a Z turn has defined "straight" in it, ski racers use a more z shaped turns. Also in in autoracing; I instruct and have been taught that in cars with enough horsepower (think STI or Zo6) a angled Z shaped turn is faster.

I am now actual curious on what the answer is....
I don't have that much HP!
Let's not forget the shape of the ski's turn and the shape of the CM's turn need not be the same. As to force, you should try to only push sideways; never push yourself uphill (force acting on you up; force acting on snow down), unless it cannot be avoided. Of course pushing downhill is allowed, but you will have to pull your skis back under you.
(C turn) A pure carved turn when if done properly is the fastest way to ski
but may not get you to the bottom of the slope the fastest. There is no skidding, and the slope determines the speed you are going. When a ski is going in more than one direction at one time you are losing speed.
Quote:
 Originally Posted by dchan What shape shaped turn will get you down the hill fastest. C shaped (arc to arc) J Shaped upside down J shaped. Z shaped
You missed out "sinusoidal curve"
Cycloid.

Brachistochrone problem details here
hmmmm

instructor always insisted more than twice as far down hill as across.... shrug - not that bad as a rule of thumb thingy then....
Quote:
 Originally Posted by Martin Bell You missed out "sinusoidal curve"

Martin, you can get decongestants to treat that... (oh, and have you replied on the DMSS site yet?)
THIS is why I stay out of this section
It is apparent that once again this thread shows bias and illustrates the closed minds of Epic; proof positive of your slaved relationship to PSIA and the USSA and their never ending propoganda machine.

How could you leave out "flatboarding".

Just another testimony of your mutated ego!
Quote:
 Originally Posted by comprex Cycloid. Brachistochrone problem details here
Ding ding ding ding...

Winna... it would be closest to the J shaped turn..

Reminder I mentioned all things being equal....

type of ski, if both skiers were on the straight skis, the answer is still the same.

if both skiers didn't "finish the turns" but different shaped turns, Cycloid still wins.

If you could (and I suspect there are some skiers strong enough to carve a cycloid turn with minimum amount of skid) pure carved turns shaped like a J would be the winner again.

Ghost has the right idea too..

Now you can argue all you want about the technical side.. I just though it might be a fun Summer exercise..
According to your argument, J and upside down J are equivalent.
Quote:
 Originally Posted by dchan Ding ding ding ding... Winna... it would be closest to the J shaped turn..
What do you mean by J shaped? Literally shaped like the letter J? So starting by facing straight down the fall-line, and then turning more and more across it?

I liked this:
http://mathworld.wolfram.com/Cycloid.html
(reminded me of Bob Barnes' bumps animation...)

So comprex and dchan, please excuse me but I've forgotten all my calculus years ago. Are you saying that PhysicsMan is wrong to base his ski track geometry on sinusoids and should instead have based it on cycloids? I sense a mathematical duel coming on...protractors at dawn...
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