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Published equation contexts

P(r)=L0−2rfv,rmax⁡=v L02fP(r) = L_0 - \frac{2rf}{v}, \qquad r_{\max} = \frac{v\,L_0}{2f}

Why this formula appears here

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 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 far faster than the tonnage…

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rmax⁡r_{\max}

Symbol r_max

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

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How to interpret it

With a fixed numerator, increasing a nonzero denominator reduces the fraction. Read it with the definitions, units, and assumptions supplied by the article.

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Published contexts (1)

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

Equation 7 · Security & Technology

The Logistics Tail: Sustainment as the Binding Constraint on Organised Force

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

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 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 far faster than the tonnage…

Meanings in this article

  • rr: the radius.
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