The rope does not need to be any determined length. Just no that the longer the rope the harder and farther you can cut outside the wake which then allows you to cut hard back at the wake and get lots of air. A shorter rope will give you much more control though.
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A good start to size up a ski for yourself is to stand up without boots on, and check the length compared to your body. Eye height is a good length to start skiing with, including for children.
Skiing with shorter skis makes learning harder, not easier.
If you are buying Twin Tips get (minimum) head height.
If you ski powder an even longer ski is advisable.
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These are all too long.
To start skiing the skis should be between your chin and nose.
For the general skiing population between the nose and eyes is good.
Twin tips you can figure your buying the equivalent of around 5cm shorter of regular skis so you want to adjust how long the skis are.
Skis shouldn't go above your head unless your buying twin tips, then it is barely taller than you, and expert skiers.
Skiing with shorter skis is actually easier. I've used long and short skis, shorter was much easier. Also, think back to the 80's when everyone skied with skis 10cm taller than them, think how much harder it was back then. If you don't ski or you didn't ski then watch skiing videos from then and now, you can see now the skiers are a lot better.
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Ah, the 80's where everyone had really long skis, and then the 90's where everyone had really short skis. It's now 2010 and we've reached a happy medium.
If you buy (if you're a borrowing/ renting beginner or first timer, very short is fine for a while) skis shorter than eye height you will have a lot of difficulty progressing beyond beginner, since carving skis benefit largely from a larger area of ski edge to help you turn, and keep control at high speeds. It might feel like it's easier when they're shorter, but only if you have bad technique, which is a bad habit.
If you're getting off-piste twin tips go at least a few cm over head height.
Skiiers in todays ski movies have skis much longer than head height.
But, obviously, opinions are divided ;)
An average rope length is about 60 ft. It could be anywhere between 50 and 100, though.
The height of your hands (from your feet) when your arms are bent at a 90o angle from your elbow. About 3/4 of your body height.