Imagine it’s late autumn of 332 BC. You’re Alexander the Great, and your armies are marching toward Egypt from Gaza. There’s just one little problem: you need to cross the Sinai peninsula - 150 miles of hot, barren desert. How will you carry food and water for the troops?

*Green triangle on the left is the Nile river delta in Egypt; green chunk in the upper right is Israel. The big desert peninsula between them is the Sinai.*

Option 1: carry it

A physically-active human needs about 3 lbs of food per day. (Modern hikers can probably find lighter calorie-dense foodstuffs, but we’re talking ancient history here.) Water requirements vary; 5 lbs is a minimum, but the US Army Quartermaster Corps recommends 20 lbs/day when marching through a hot desert. Alexander’s army crossed the desert in 7 days. Food might be reasonable, but to carry the water would mean 7*20 = 140 lbs per person, plus 50+ lbs of armor, weapons, etc.

When I go hiking, I aim for a 20-30 lb pack. US marines are apparently expected to be able to carry 150 lbs for 9 miles - quite a bit less than the 20+ miles/day Alexander’s army managed, and with no comment on how long the marine in question might need to rest afterwards. (Also, I’m not sure I trust that source - 150 lbs for 9 miles sounds unrealistic to me, and if it’s true then I’m very impressed by marines.)

Suffice to say that carrying that much water across that much desert is not a realistic option, even if we drink it along the way.

Option 2: horses

A horse consumes 20 lbs of food (half of which may be forage) and 80 lbs of water per day. In exchange, it can carry about 200 lbs (surprisingly, my source claims that horses can carry more than they can pull). Of course, that 200 lbs has to include the horse’s own food and water, plus whatever useful load it’s carrying. So, marching through a desert, a horse can only transport (200 lbs)/(80+20 lbs/day) = 2 days of supplies for itself, and that’s before whatever useful things actually need to be transported.

In other words, there’s a hard upper limit on how far goods can be transported by horse without refilling supplies along the way. That limit is around 2 days travel time without any refill, 10 days if there’s plenty of fresh water along the route, or 20 days if there’s both water and forage. At 20 miles/day, that’s 40, 200, or 400 miles. Realistically, if we want the number of horses to be reasonable,...

Coordination & Constraint