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Equation 13 · Part 12 · The Logistics Tail: Sustainment as the Binding Constraint on Organised Force

Numerator: dS

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

What this part means

The complete quantity above the fraction bar.

Its job in the formula

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

The passage around this formula

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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Learn the underlying idea

A fraction a/b means a divided by b. The top number is the numerator; the bottom number is the denominator, and it cannot be zero.

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Sources cited in the article section

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