Does a salt-free diet equate to salt-free urine?

No, but the naturally occurring salts in urine probably would be the limiting factor in how much to use.

Any ideas on how to calculate how much to add to the pile? Estimate it's around 450 cubic feet.

If you turn the pile (once a week or so)-
With that much material (16+ yards), IMHO you will not overdo it adding 1 gallon per day. There will be a point that you will want to finish the compost by letting the pile sit for a month or preferably longer - I do this when the freshly turned pile looks like dark shredded mulch - stop and start a new pile.

If you do not turn the pile-
I would make the pile, apply what you have at the time, and pretty much let it be - maybe a sprinkling now and then.

The link below discusses the NPK of urine used as fertilizer.
Best of Luck!

Here is a link that might be useful: http://forums2.gardenweb.com/forums/load/cornucop/msg0404052211211.html

Thanks, Cheapheap. Your post is helpful. Since the leaves were dry, I'm hoping as long as the pile does not freeze, the liquid may percolate down and help with the moisture requirement. This is the first year we've added urine and I'm looking forward to seeing if the pile works any faster. First time for last year's compost added in as well. I generally use a 12 - 15' snow fence circle, fill it up in the fall, then just leave it and let it take 1 to 2 years to do its work.

(If you use compost as a mulch, you can use it in a slightly unfinished state, by the way.)

My dogs and I add our pee to the pile regularly and all it does is help it heat up faster, thus breaks down faster. You would have to add a lot of urine, more than your body could make on a daily basis to matter much in a pile that size.

I would observe temperature and aroma and use that to monitor. If it starts smelling like ammonia and stale pee, you've got too much.

The pile still smells as fresh as a daisy, been adding a gallon a day for at least 90 days. Thanks for the guideline toxcrusadr, sounds logical.