Gravity equation?

ajdelange said:

It's simple to do if you do it by weight. Ten grams of sucrose in 100 grams of solution is 10 °P - the scale professional brewers use to measure the 'gravity' of solutions. Clearly 2 Oz of sugar added to 1 quart of water gives a solution of strength
2 Oz/( 100*(weight_of_1 quart_of_water_in_Oz + 2Oz) ) °P.

There is a table (published by ASBC) which relates °P to apparent (20/20) specific gravity for sucrose solutions. It's contents have been fit (by the ASBC) with a polynomial

°P = (((135.997*S - 630.272)*S + 1111.14)*S - 616.868)

so this polynomial, though not an exact representation, is, in the first place, very close and, in the second place, an industry wide standard. The catch is that you don't want °P as a function of S. You want S, the specific gravity, as a function of °P. The easiest way to get this is to plug the formula into a spreadhsheet and let the Excel Solver find the S that gives a desired P but no one seems to know what the Solver is or how to use it. You can also just try different values of S until you find the one that gives you a value close to P. This is what the Solver does but it does it automatically.

There are also approximate formulas such as the Lincoln Equation which will give you S as a function of P.

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ajdelange said:

Part of the problem is that I put the 100 in the denominator. It goes in the numerator:

100* 2 Oz/(32 Oz + 2Oz) °P

A gallon weighs 8.34 lbs = 133.44 Oz so a quart weighs 33.36 Oz. Thus

2/(33.36 + 2) = 0.0565 times 100 gives 5.65 °P.

This works in any consistent weight units (grams, pounds, shekels...)

As for the other equation: just copy and paste

= (((135.997*A1 - 630.272)*A1 + 1111.14)*A1 - 616.868)

into cell A2 of a spreadsheet. Then type specific gravity numbers into cell A1. Degree Plato values will appear in A2.

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