Wouldn't distance prove the point? With an adjustable daisy you raise yourself 1 foot for every 1 foot you pull down on the other side (1:1). With the 2:1 hauling ratchet, grigri/ascender/redirect ascending method, far-end hauling, you are moving the load 1 foot of distance for every 2 feet you pull down.
This is more about effort than distance: Say you had a 200 lb. crate on a concrete floor and you wanted to move it. (Kind of like hauling to Mammoth, but smoother and less steep). I guarantee it would be easier to move that crate hauling from an eye bolt fixed to the wall, going through a pulley on the crate, and the free end of the rope going to you, than it would be to have the rope tied to your waist, going through a pulley on the crate and the free end coming back to you.
In answer to your other question (edited), best pulley closest to the person hauling. Theoretical Mechanical Advantage (TMA) of 2.76T vs. 2.67T for the other way around.
Adjustable daisy definitely gives 2:1. If there is 10 lbf tension on the daisy, there is 20 lbf tension on you, because it's fixed at 2 points, to you. Of course Pete already said that, in a lot of words. Yeah there's frictional "losses" and stuff that do matter, but you get the point I hope.
Fish made a decent measure on one of his daisies a couple years back and concluded there are 60-70% friction loss for a net 1.3-1.4:1 mechanical advantage using Ankra buckles for daisies. Not worthless, but well shy of 2:1. In other words for a 200 lb climber to pull themselves up using only the daisy would require ~140 lbs of pulling on the strap.
Conclusion was a 1.3:1 mechanical advantage using adjustable daisies, so 153 lbs of pull to move a 200 lb climber up. The real advantage is more around capturing progress and being able to use two hands (i.e. not needing a free hand to fifi into the daisy).
Thanks for posting the other thread Moof. Most interesting. In the third to last post. It sounds like Russ and Pete aren't that far off from each other, just defining things differently in theoretical and practical terms. In the real world, I guess it's somewhere between a 1:1 and 2:1.
good luck on your adventure this june, , Im thinking on doing my first solo on, tangerine trip in september and know my pig will be heavy and was thinking on useing a 2;1, but have no really experance on anytinbg thing like that, Can you give me a quick run down of what i need and need to do to set it up? pictures? also im headed up the nose with a bussy and she is 130 lbs and think hauling wil be hard for her, so was thinking on setting up a 2;1 for her do you think thats nessary? any help would be great thanks
Squeezo...if you're in a position to set up the pullies, you're ideally situated to haul the bags. ;-)
I hate having two people on the same end of the haul line (although when the bag is going to stick a lot it's still the most efficient way.) It's hard to sync, and when I'm the bottom hauler, I feel like a rat on a wheel. It's so demoralizing to jug away and just keep sinking down.
My favorite alternative, which works best when the bags aren't going to stick and there is room at the anchor for both partners to be side-by-side is to have one person haul 1:1 in the usual fashion and have the other haul 1:1 on the loaded line (i.e. Run a piece of spectra cord from their harness through a high pulley back to an inverted ascender on the loaded line. Use a munter mule to dial in the distance to the jug.)
It's so easy to haul in sync when you're side by side (especially important if both partners' peak impulse is needed to get the bag to move), and having someone haul w/ their full body weigh on the bag-side of the line seems to help break the bag's friction better too. It can also a quick and easy way to help your partner finish a haul when you arrive at the anchor after cleaning a pitch.
We started doing this when I dropped the 3rd pulley on "blast day" (doh!) making 2:1 and 3:1 single-hauler systems impossible for the entire route. Tip for idiots like me...If you're using a pulley system that involves accessory cord, don't let the pulley whiz off the end of the cord. :-(