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n the following article I will develop
equations to describe many different
facets of homebrewing. In each section, I first give
an equation that is as accurate as possible, including the ef-
fects of all of the important parameters. This equation is some-
times rather complicated, but the idea is to program it into a
computer spreadsheet and never look at it again. Then, where pos-
sible, I simplify the equations using appropriate assumptions so that
calculations can be made on the fly in the brewery or kitchen.
One thing I should explain at the outset is curve fitting. There
are many occasions when a functional relationship for a set of da-
ta is needed but not available. Curve fitting (also called regression
or least-squares fitting) is nothing more than a mathematical way to
draw the best curve through a set of experimental data points. In
this article I use quadratic (a + bx + cx2) and cubic (a + bx + cx2 +
dx3) functions to draw the curves.
Specific Gravity
Specific gravity is defined as the density of a substance relative
to the density of water. This is not quite sufficient as a definition be-
cause the density of water varies with temperature. Above 39 de-
grees F, water expands as it heats up, making it necessary to spec-
ify the temperature when indicating a specific gravity.
The most common way for a homebrewer to measure specific
gravity is to use a hydrometer. A hydrometer measures the den-
sity of a fluid in units of the density of water at some reference
temperature (the temperature at which the hydrometer is cali-
brated). In other words, the measurement you get from your hy-
drometer is really
Measured SG =
density of wort at temperature T
density of water at reference temperature
Z Y M U R G Y S u m m e r 1 9 9 5
54
Brew By the
Numbers —
Add Up What’s
in Your Beer
Have you ever wondered just how much wallop your favorite homemade
beverage packs, alcoholwise and caloriewise? Have you ever heard your
brewing buddies talk about apparent extract and real attenuation and wondered
what