subscript

The passage around this formula

The structural consequence is a hard radius rather than a gradual decline. Consider a schematic model, offered to expose an assumption rather than to reproduce any historical campaign. A transport team departs a base carrying load $L_0$ , consumes f units of that same load per day for its own animals, and covers v units of distance per day. To reach a force at radius r and return, it is on the road for 2r/v days, so the load it can actually hand over is $P(r) = L_0 - \frac{2rf}{v}, \qquad r_{\max} = \frac{v\,L_0}{2f}$. Beyond $r_{\max}$ the convoy arrives having eaten everything it set out with. Adding a second convoy to supply the first does not defeat the limit; it recurses, and the tonnage required grows far faster than the tonnage…

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