A soldier requires a minimum of about 3 pounds of rations per day to maintain his strength and health. A soldier can carry about 80 pounds of equipment and supplies for an extended period, so ten days' rations is a reasonable maximum, assuming 50 pounds for arms and armor and other equipment. Infantry in large bodies can march about 12 miles a day, so infantry alone with supply wagons or packhorses might be able to cover 120 miles before running out of supplies.
A stall-fed packhorse might consume 10 pounds of grass and 10 pounds of grain (barley or oats) each day and carry a burden of 250 pounds. A stall-fed warhorse might carry a greater burden but would require a proportionately greater amount of fodder. Assuming that grass is readily available for grazing, a horse might consume as much grain as it can carry in twenty-five days. Of course, if a packhorse consumes its entire load then there is not much point in bringing it along.
A cavalrymen with 50 or 75 pounds of equipment might weigh nearly as much as a horse could reasonably carry. A second horse might carry ten days' food and fodder (250 pounds, with the rider and two horses consuming 23 pounds each day) plus serve as a spare mount in case the first horses was injured. Large bodies of cavalry could travel somewhere between 19 and 30 miles a day, depending on the likelihood of meeting the enemy and the degree of catuion required, or between 180 and 300 miles on ten days' supplies.
So, assuming that grass and water are readily available, an army could carry enough food and fodder for about ten days without much of a supply train at all. This is a rough estimate but a reasonable one... [bit about living of the land in heavily populated agricultural areas].
On the steppe, such an army woulds starve after ten days. It would have to turn back after five.
In the desert, the assumption that grass and water are readily available no longer holds, and the range of such an army drops precipitously. For each day in the desert, an additional 10 pounds of fodder would have to be carried for each horse, plus 80 pounds of water per horse and 5 pounds of water per person. This is why armies could not travel through the desert except along rivers or for very short periods of time. Infantry would have to turn back after just two days in the desert; cavalry, after just a single day.
Supply trains provide no simple solution. The men and horses in the supply train have to eat too. Pack horses consume 10 pounds each day and carry 250 pounds of supplies, or twenty-five their daily consumption. Porters who consume 3 pounds each day and carry 75 pounds of supplies would be equally efficient. Supply wagons are better; the driver and two horses would consume 23 pounds each day but the wagon might hold 1,400 pounds of supplies, or sixty times their daily consumption, depending on the efficiency of the harness and other factors. Supply wagons were restricted to relatively flat terrain, however. Ships and boats were far more efficient than even supply wagons, but they were more restricted in where they could operate.
Imagine a platoon of thirty infantrymen marching out onto the steepe with one large supply wagon. After ten days, they exhaust their rations and turn to the supply wagon for more. They will find that the driver and the horses have consumed 230 pounds of the load, and that another 230 pounds have be set aside for the driver and horses on the return trip. The remaining 940 pounds is just enough for each of the thirty infantrymen to fill his knapsack with the 30 pounds he can carry, and that in turn will last him just long enough to march back to where he started from.
Increasing the number of wagons quickly runs into the law of diminishing returns. One wagon will double the range of infantrymen from 120 miles to 240 miles, or rather 200 miles with one day of rest in six for the horses. (Horses become permanently incapacitated without periodic rest.) To double it again to 400 miles requires not two wagons, but actually six - one wagon for every five infantrymen, already the maximum likely to be found in practice. The number of wagons will reach thirty - one wagon, one driver and two horses for every infantrymen - before the range will double again.
So if there is one wagon for every five infantrymen, and enough grass and water along the march, then infantry can make a 400 mile round trip (i.e 200 miles in each direction). Take away the grass and water, and its range drops to one fifth of that. Natrually, these umbers are only rough estimates but they suggest and order of magnitude. To put them in perspective, Russian armies faced a 600-mile round trip from Kiev to the Crimea and back, and Chinese armies faced a 1,600 mile round trip from Beijing to Outer Mongolia and back.