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Equation 7 · Part 2 · The Logistics Tail: Sustainment as the Binding Constraint on Organised Force

Symbol r

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

What this part means

the radius.

Its job in the formula

r occurs above the fraction bar. The numerator is divided by the entire denominator below it.

Where the article explains it

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}.

The passage around this formula

…to reproduce any historical campaign. A transport team departs a base carrying load L0L_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)=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…

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Learn the underlying idea

A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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Sources cited in the article section

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