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Equation 7 · Part 6 · The Logistics Tail: Sustainment as the Binding Constraint on Organised Force

Symbol r_max

P(r)=L0−2rfv,rmax⁡=v L02f.P(r) = L_0 - \frac{2rf}{v}, \qquad r_{\max} = \frac{v\,L_0}{2f}.
rmax⁡r_{\max}

What this part means

rmr_max appears in the objective or constraint used by the optimization on the right.

Its job in the formula

rmr_max appears in the objective or constraint used by the optimization on the right.

The passage around this formula

…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)=L0−2rfv,rmax⁡=v L02fP(r) = L_0 - \frac{2rf}{v}, \qquad r_{\max} = \frac{v\,L_0}{2f}. Beyond rmax⁡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 delivered. This is why the practical answer for two millennia was not better convoys but…

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