The Union Armies carried a lot more "camping and comfort" equipment than a Napoleonic era army.
Ingalls kept about half the wagons loaded with animal feed. Organised as a large flying column this allowed the AoP 10 days operations away from a supply base, although this was feeding the animals at 14lbs/day, causing much wastage (Sherman advocated 20lb/day)*.
If they'd manage to forage to the same level as Napoleon, which is prettymuch an impossibility (the richest farmlands of the west would only support a static force of 20,000), this could be brought down to about 25 wagons/ 1,000 men
Sherman's Atlanta campaign was slightly different. He had 2,500 wagons (ca 25 wagons/1,000 men), and they carried their own forage, and their own load. He formed special foraging parties (of his best troops) to scour the countryside for forage etc. acting much like one of Napoleons campaigns. This was possible due to comparitively rapid movement, and the time of year (and the fact that Georgia was unscathed).
* See Chapter 25 of Sherman's Memoirs at http://www.gutenberg.org/files/4361/4361-h/p4.htm#ch25
The numbers don't always reflect the dynamic element of warfare. For example Sherman may have had 2500 wagons on the roster, but they never moved off at the same time. I'd suggest the high point of supply would be soon after the opening of the campaign, but every day, emptied wagons would be turning back to be reloaded. At some point, defined by distance from depots, one third of the wagons would be loaded and available to the troops, one third empty and returning, and one third at the depots either disabled or reloading.
With reference to foraging, how much time is lost by a combat formation if they must collect their own supplies from the land? Since wagons move much slower than troops, either marching or mounted, there must have been a trade-off between waiting for wagon supplies to arrive vs commandeering on the march. Perhaps less critical for infantry formations except when forced marching.
How much supply, especially forage, did ACW cavalry carry when moving quickly? There must be a comparison somewhere between the time taken to allow animals to graze (lost time from the march) and feeding them as much grain as their digestions could handle, and losing less marching time.
Kester