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SCALING Y THE SIX-TENTHS HULE

his photo shows a Portland cement plant in Devil's Slide,Utah. The first operation on this site began production in1907. Its capacity of 110,000 metric tons per year (m.t./

yr) was tripled with an expansion in 1948. A third factory, theone shown here, was completed in 1997 (635,000 m.t./yrcapacity). According to a 1909 letterhead, company capitalat the time was $2.5 million. Using that as a basis, assum-ing a size-capacity exponent equal to 0.8, and escalating forinflation [Equation (/ /)], the 1948 estimated grass-roots fixedcapital would have been $2.5 million X 30.8 x (80/12) =$4 0 m illion. Similarly, the 200 4 value extrapolated from these

numbers would be $40 million X 20.8 X (400/80) = $350million. According to local tax records, the 2004 evaluationis slightly greater than $100 million. Tfiis reveals the dangerof extrapolating over large time periods with no correction forimproved technology. For a more realistic estimate, o 2 millionm.t./yr cement plant in the northeastern U.S. was reported tocost $3 00 million in 19 98. Based on this number, the calculatedgrass-roots value of the Utah plant would be $300 million X(0.635/2)0.8 X (400/390) = $120 million. (Photo courtesyJohn Sommers of Holcim [U.S.], a wholly owned subsidiary ofHolcim Ltd., Switzerland. Used with permission.)

TABLE 1 . TYPICAL EXPONENTS FOR EQUIPMENT COSTAS A FUNCTION OF CAPACITY*

Agitators

Blowers, centrifuga l

Centr i fugal pumps

Compressors, reciprocating

Beit conveyors

Crushers

Drum dryers

Dust coliectorsBag filterMulticycione

Eiectrostafic precipitatorsEvaporato rs, failing-fiim

Fiiters, plate an d fram e

Heat exchangers , f ioat ingh e a d

Jaciceted vesseis

Eiectric motors

Refrigeration units

Vibratory screens

TanksFloating roofSpherical , 0-5 barg

Size

r a n g e1-200

50-8.0000.01-27010-2,000

10-5010-1,000

2-100

2-1,1000.1-40

5-1,20030-3201-170

10-900

1-80010-8,0005-10,000

1-130

200-70,00050-5,000

Capacity

uniti

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