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Published equation contexts

c(z)=c0(zz0)−bc(z) = c_0 \left( \frac{z}{z_0} \right)^{-b}

Why this formula appears here

The formal relationship goes back to Theodore Wright’s 1936 observation that aircraft manufacturing labor hours fell as a power-law function of the number of airframes already built, and Way et al. build their entire forecasting method on a stochastic version of it, fitted to more than fifty technologies’ historical cost and production records [ 1 ] . Written in its cleanest form, cost c at cumulative production (experience) z relates to a reference cost c0c_0 at reference experience z0z_0 by: c(z)=c0(zz0)−bc(z) = c_0 \left( \frac{z}{z_0} \right)^{-b}. where the experience exponent b sets the learning rate LR = 1 - 2^{-b} , the fractional cost drop for every doubling of z . Way et al.'s working version of the same relationship is…

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z0z_0

Symbol z_0

z0z_0 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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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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c(z)=c0(zz0)−bc(z) = c_0 \left( \frac{z}{z_0} \right)^{-b}

Equation 5 · Technological Evolution

The Metabolism of Civilization: Energy to 2100

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

The formal relationship goes back to Theodore Wright’s 1936 observation that aircraft manufacturing labor hours fell as a power-law function of the number of airframes already built, and Way et al. build their entire forecasting method on a stochastic version of it, fitted to more than fifty technologies’ historical cost and production records [ 1 ] . Written in its cleanest form, cost c at cumulative production (experience) z relates to a reference cost c0c_0 at reference experience z0z_0 by: c(z)=c0(zz0)−bc(z) = c_0 \left( \frac{z}{z_0} \right)^{-b}. where the experience exponent b sets the learning rate LR = 1 - 2^{-b} , the fractional cost drop for every doubling of z . Way et al.'s working version of the same relationship is…

Meanings in this article

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