Sunday, June 10, 2012

Dry measures are actually measurements of weight at constant density

Dry measures are most commonly used for measuring grain, and the most relevant statistic of grain is its weight. Historically, weighing big containers of grains was difficult, so people ended up estimating weight indirectly, from volume. The actual system of commodity baskets used in the United States now is quite complicated, but the general principle is that a "bushel" is a measuring basket intended for estimating the weight of a particular commodity.

US commodity bushels are too intimidating to actually use. But a fantasy world, being a fantasy world, allows us to simplify. So let's go ahead and assume that the people of that world classify bushels by the density of the material they're meant to measure, and choose the right sized one so that it will measure out approximately 50 compromise pounds (A "compromise pound" is just a name I came up with in a previous post for a nonspecific pound somewhere in the order of magnitude of one metric pound).

Bushels would presumably be classified by inches, that is, the depth in inches of a bushel with a one square-foot floor (I don't know of any historical source that does this, but it makes sense). This number is just twelve times the specific volume (cubic centimeters per gram, or pints per pound). For example, if you have a substance half as dense as water (1/2), its specific volume is double (2), and uses a 24-in (2 x12) bushel.

The common hulled grains (wheat, rice, and cracked corn), are all around 4/5 as dense as water, which gives of bushel depth of about 15 inches. This translate into 1.25 cubic feet, or 35 liters, which is very close to the official American dry bushel of 1.24 cubic feet, unless I've gotten my math wrong.


Chart 1: Approximate volume of 15-in "dry" bushels and related measures

1 ton = 10 cmb = 40 bsh (= ca. 50 cu ft, 1400 L)
1 quarter ton  =  10 bsh (= ca. 12.5 cu ft, 350 L)

1 dry coomb =  4 bsh (= ca. 5 cu ft, 140 L)
1 dry streck =  2 bsh (= ca. 2.5 cu ft, 70 L)
1 dry bushel = 4 dry pecks = 100 dry cups (= ca. 1.25 cu ft, 35 L)
1 dry peck = 1/4 dry bushel = 25 dry cups (= ca. 540 cu in, 8.75 L)
(subunits from here on are the same as fluid measures. Follow the example of the dry cups)


Chart 2: Bushels of weight and related measures

1 ton = 10 cmb = 40 bsh (= 2000 co lbs, 1000 kg)
1 quarter ton  =  10 bsh (= 500 co lbs, 250 kg)

1 coomb =  4 bsh (= 200 co lbs, 100 kg)
1 streck =  2 bsh (= 100 co lbs, 50 kg)
1 bushel = 4 pecks = 100 dry cups (= 50 co lbs, 25 kg)
1 peck = 1/4 bushel = 25 dry cups (= 12.5 co lbs, 6.25 kg)
(subunits from here on are the same as fluid measures. Follow the example of the dry cups)

No comments:

Post a Comment