Specific Gravity, Plato, and other Saccharometer Scales

Let's start out with some definitions, and then move to a practical example.

Specific Gravity

This is the one which is easiest to explain. Specific Gravity is the relative density (mass per unit volume) of a liquid, relative to that of water at a specified temperature. So, if your hydrometer is calibrated for 68°F (20°C), distilled water should read 1.000. A liquid twice as dense as water would have a specific gravity of 2.000, and so on.

The abbreviation SG is often used for Specific Gravity.

Plato, Balling, Brix

These three saccharometer scales are all very similar, and one often sees them used interchangably. There are differences between them, but I donít get too hot under the collar over them. I sometimes like to think that the biggest difference between them is who uses them: Plato by brewers, Brix by winemakers, and Balling by folks with old saccharometers.

These scales correspond to the percent sucrose in a pure aqueous solution (i.e., just table sugar and water), on a weight (or mass) basis. Thus, a solution consisting exclusively of 100 grams of Sucrose and 900 grams of water will be 10° Plato (or Brix, or Balling).

A brewer says that the saccharometer reading of a wort in degrees Plato has that many percent extract, even though the wort contains other sugars besides sucrose, to say nothing of dextrins, proteins and protein fractions, hop components, etc. It works for them close enough to get the job done.

Allen, Oeschle Scales

Have you ever taken a specific gravity measurement, say, 1.048, and dropped the ì1.î part to come up with 48? Seems intuitive and makes a lot of sense, doesnít it? Well, thatís the basis of these saccharometer scales.

°A = °Oe = 1000 x (SG - 1)
SG = 1 + 0.001 x °A = 1 + 0.001 x °Oe

Belgian Scale

Used to identify some wonderfuly tasty Belgian ales, such as Rochefort 10. The ì10î is the initial extract of the wort, expressed in Belgian degrees. Itís an awful lot like the Allen and Oeschle scales, except the decimal point is shifted one fewer places ó only two for the Belgian scheme. Thus, 10° Be is 100° A (or 100° Oe). Thatís a pretty hefty wort, nas çest pas?

°Be = 100 x (SG - 1)
SG = 1 + 0.01 x °Be

Watch out for °B (degrees Balling or Brix) vis-a-vis °Be (degrees Belgian). Itís a thicket!

Baumé

This is actually two scales. There is a Baumé scale for liquids denser than water (Bh, for Baumé high, the one weíre most interested in), and a Baumé scale for liquids less dense than water (which may be interesting to wine- and mead makers for measuring their products after the fermention is essentially complete). We concentrate on the Bh scale, which is often used for Maple Syrup.

Bh° = 146.78 x (SG - 1) / SG
SG = 146.78 / (146.78 - Bh°)

Tralle

(I donít know nothiní about this scale!)

Potential Alcohol

Some saccharometers have a so-called ìPotential Alcoholî scale. Putatively, this scale shows how much alcohol a solution would contain if it should ferment totally to dryness, if all the extract fermented entirely into carbon dioxide and ethanol. If one subtracts the initial and terminal ìPotential Alcoholî measurements, in theory, one obtains the percent alcohol (by weight or volume?). Itís a tricky nut to crack, however, because a wort or must (what winemakers call their worts, which arenít worts, theyíre musts) which has fermented completely must have a terminal specific gravity less than one (ethanol is less dense than water; an admixture of water and ethanol is likewise less dense than water alone), so a fully-fermented wort or must must have a negative PA reading, because the PA reading for water must be zero, sure as God made little green apples. It sort of reminds me of a puppy chasing its tail.

Some practical examples

Example One: How much extract do I need?

Solution ó  Step One: Assume the extract is all sucrose. Yeah, I know it sounds goofy, unless youíre really brewing lighter fluid or a Sterno-like liquid, but it is actually quite close. If you take this leap of faith, you have got it made.

Step Two: Compute the equivalent measurement on the Plato scale to obtain the percent extract, by mass (or weight, if you prefer). For our example, an SG of 1.048 (at 68° F) is 11.9° Plato, or 0.119 Kg of extract for every Kg of wort.

Step Three: Multiply the SG by the extract fraction. Thought we were going to throw away one and keep the other, eh? Not so fast! The Plato scale tells us how many grams of extract are in 100 grams of wort, but, once weíve added the extract, 100 milliliters of wort have more mass than 100 grams. In fact, the Specific Gravity tells us exactly how much more. So, we multiply 1.048 (which is expressed in Kg wort / liter) by 0.119 (which is Kg extract / Kg wort) to get 0.1247 (expressed in Kg of extract / liter), to four significant digits.

Step Four: Multiply this product by your volume in liters. Okay, 20 liters times 0.1247 Kg / liter yields 2.4940 Kg. Ta-da! Youíve got to add 2.494 Kg of sucrose to enough water to make 20 liters to obtain a Specific Gravity of 1.048. Wasnít that easy?

If you insist on working with three barleycorns to the Kingís knuckle, and twelve of his knuckles to one of his feet, four farthings to the penny, usw, hereís what you can do: Before you start, convert the number of US gallons you want into liters by multiplying by 3.78 (close enough for us). When youíre done, multiply the number of Kg of extract by 0.4536 to get pounds of extract.

Note that this procedure tells you how much extract you need in solution ó it doesnít tell you directly how much of that gooey syrup in the tin can (or magical powder in the bag labeled ìDMEî) to use. However, if you happen to know your DME is, say, 94 percent extract, or your malt extract syrup is 68 percent extract, or that you can squeeze 0.561 Kg of extract from every Kg of that two-row (grain) malt (see the section on ìEfficiency and Brewhouse Yieldî for information on this), you can do the simple division.

If youíre using a DME which is 94 percent extract (YMMV, as they say), youíd need 2.494 Kg / 0.94 = 2.653 Kg of DME.

If youíre using a syrup which is 68 percent extract (could be higher or lower), youíd need 2.494 Kg / 0.68 = 3.668 Kg of syrup. Two 3.3# cans, plus a little more. (Golly, this seems to work!)

If youíre using grain malt from which you can wring 59 percent extract (your brewhouse yield), youíd need 2.494 Kg / 0.59 = 4.227 Kg of grain, or just about 9 1/3 pounds.