this also depends on what sort of winder you are putting it on and what method.......
if you hold the winder in one hand and wrap with the other then you are putting twists into the line. if it is a yoyo and you roll it on it will not be twisted....
On a card winder wrapping in a figure 8 keeps the twists out, but when you're throwing the spool on the ground to fly a glider type kite that seems to tangle more then a straight wrap. I'm trying to get away from the hoop winders, I don't roll but wrap so there are always twists and they just take up too much space in the bag. just need to get on the jig saw and cut out a few dozen large 8 winders. I have a couple Gators & homebuilt fighter kite spools like the Gators I'll keep around though for the gliders and fighters.
Heh, you guys pretty much described the way I do things-- throw the yoyo on the ground, let line out, pull line in, then wind it back up. I do get some twisting, but so far it's been okay. At Ripon I went to help Jim (ozonejim) wind in a kite and he took the hoop from me (heh) and wound it himself, using that rolling method. It would be nice to use the rolling method, but man, it takes a loooong time to wind just one kite. I'd be there all day winding line for all the kites I want in the air.
Mike, I know what you mean about how much space these hoops take up. I was fighting it-- bought several of those Carey III winders. I would bring the kite down (line squiggled on the ground), then find myself a seat, wind the line around my leg once for some slight tension and go to town winding that sucker up. Hardly took any time at all and I didn't have a problem with the twists. In the end, I finally gave up and found a discounted piece of wheeled luggage that's big enough for several 8" hoops and a bunch of smaller ones. I got it at that Tuesday Morning store-- not sure you have one of those in your area.
You and Gibian are making a good case for wooden line winders, for all kinds of reasons.