Equation 13 · The Logistics Tail: Sustainment as the Binding Constraint on Organised Force
What does this equation mean?
Read the formula alongside the article passage below. Each part has a deeper page with its role in the equation, the supporting passage and nearby citations.
This equation states an equality: the expressions on both sides have the same value under the article’s assumptions. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.
Read it piece by piece
Symbol d
d is part of the quantity the equation computes from the expression on the right.
Symbol S
S occurs above the fraction bar. The numerator is divided by the entire denominator below it.
Symbol t
t occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.
Symbol T
T is one of the signed contributions combined to compute the quantity on the left.
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.
Symbol r_c
is one of the signed contributions combined to compute the quantity on the left.
=
The expressions on both sides represent the same quantity under the stated assumptions.
See an illustrated explanation →subtraction
Subtract the following term or group from the preceding one. A leading minus marks a negative quantity.
subscript
The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.
Denominator: dt
The complete quantity below the fraction bar; it must be nonzero for this division.
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.
What the article says around this equation
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 . Culmination is the radius 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…
Read the full surrounding passage
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 . Culmination is the radius 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 of the transport fleet.
Sources cited in the article section
These citations give research context. Read each source to check which claims it supports.
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