Zodiac and Late Roman Army Organisation

[Flavivs Aetivs]

(By the way, everything I have seen says that transport costs increased linearly with distance in preindustrial societies, not exponentially. A yoke of oxen eats the same amount of fodder whether its been walking for three days or three weeks).

I suspect the costs calculation has something to do with whether the draft animals have to pull their own feed-stuffs or get it supplied en route. If they have to pull their own as well as the kit and food of the soldiers there is a limit as to how far they can go before all they are pulling is their own food.

I am pretty sure that would only be the case for a campaign in hostile territory, or a deserted part of the empire. Moving through friendly country, I think the soldiers would collect new supplies every few days or weeks, and the smaller the force the shorter the distance supplies would have to be brought to each collection point.

If I derived it correctly, the size of a baggage train required to carry a fixed amount of supplies, plus its own food, for x days increases something like 1 / (1 - cx) for c a constant based on the ratio between the weight of a day's supplies and the capacity of each animal or bearer or wagon in the train.

You're math seems to be accurate (it's obviously right). As the cost increases at a decent rate.