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Published equation contexts

dSdt=T(r)−C,T(rc)=C\frac{dS}{dt} = T(r) - C, \qquad T(r_c) = C

Why this formula appears here

The concept is routinely taught as a matter of judgement. It is more usefully written as an identity. Let C be the consumption rate of a force in the field and T(r) the sustained throughput that can be delivered to it at distance r from the last high-capacity transfer point. Stock at the front then evolves as dSdt=T(r)−C,T(rc)=C\frac{dS}{dt} = T(r) - C, \qquad T(r_c) = C . Culmination is the radius rcr_c at which delivery equals consumption. Beyond it the force draws down accumulated stock and the clock is set by how much was accumulated, not by the enemy. Every term is estimable in advance: consumption from the force’s composition and expected tempo, throughput from transfer capacity, road and rail condition, and the self-consumption…

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tt

Symbol t

t occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

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CC

Symbol C

the consumption rate of a force in the field and T(r) the sustained throughput that can be delivered to it at distance r from the last high-capacity transfer point.

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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)

A symbol can carry a different meaning in another article. Each occurrence keeps its own guide and term definitions.

dSdt=T(r)−C,T(rc)=C.\frac{dS}{dt} = T(r) - C, \qquad T(r_c) = C .

Equation 13 · 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 concept is routinely taught as a matter of judgement. It is more usefully written as an identity. Let C be the consumption rate of a force in the field and T(r) the sustained throughput that can be delivered to it at distance r from the last high-capacity transfer point. Stock at the front then evolves as dSdt=T(r)−C,T(rc)=C\frac{dS}{dt} = T(r) - C, \qquad T(r_c) = C . Culmination is the radius rcr_c at which delivery equals consumption. Beyond it the force draws down accumulated stock and the clock is set by how much was accumulated, not by the enemy. Every term is estimable in advance: consumption from the force’s composition and expected tempo, throughput from transfer capacity, road and rail condition, and the self-consumption…

Meanings in this article

  • rr: the distance.
  • CC: the consumption rate of a force in the field and T(r) the sustained throughput that can be delivered to it at distance r from the last high-capacity transfer point.
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