Refractometers and Brix Conversion

[Garrete]

Hello.

I use BeerSmith for brewing. I also have been using this Refractometer Conversion Table I found from Zymurgy Jan/Feb 2001.
It has the following formulas:
Brix*1.04 = Plato
(Plato/[258.6-[Plato/258.2]*227.1)])+1=SG

According to those formulas, a Brix of 20 is 20.8 Plato and 1.087 SG.

With a Blog from BeerSmith http://www.beersmith.com/blog/2010/11/02/how-to-use-a-refractometer-brix-and-beer-brewing, he walks you through the steps of using your Refractometer tool. However, the numbers do not match those from Zymurgy. Using BeerSmith, if you enter 20 Brix, you get 19.92 Plato, a BIG difference from Zymurgy. Has the formulas changed? This now makes me question any gravity readings I have taken. Can someone help clear this up for me?

Thank you in advance.

[ajdelange]

Brix and Plato are identical. They both represent the percentage sucrose by weight in an aqueous solution. A 10 Bx solution contains 10 grams of sucrose per 100 grams of solution. A 10 °P solution contains 10 g sucrose per 100 grams solution. Where they differ somewhat is in the specific gravity assigned (by respectively Brix and Plato's comission) to a particular concentration. The apparent specific gravity (20/20) of a 20.8 °P solution is 1.08665. But the apparent specific gravity (20/20) of a 20.8 Bx solution is 1.08660 (from the ICUMSA polynomial). Not much difference.

Approximate inversion of the Lincoln equation is available from

S = 1 + P/(258.6 - 0.8796*P) and exact inversion from

S = 668 - sqrt(668^2 - 820*(463 + P))/410

but remember that the Lincoln equation represents an approximation (though a good one) to the ASBC polynomial. Exact inversion requires finding roots of the ASBC polynomial.

[Whitebeard_Brewer]

Brix and Plato are identical. They both represent the percentage sucrose by weight in an aqueous solution. A 10 Bx solution contains 10 grams of sucrose per 100 grams of solution. A 10 °P solution contains 10 g sucrose per 100 grams solution. Where they differ somewhat is in the specific gravity assigned (by respectively Brix and Plato's comission) to a particular concentration. The apparent specific gravity (20/20) of a 20.8 °P solution is 1.08665. But the apparent specific gravity (20/20) of a 20.8 Bx solution is 1.08660 (from the ICUMSA polynomial). Not much difference.

Approximate inversion of the Lincoln equation is available from

S = 1 + P/(258.6 - 0.8796*P) and exact inversion from

S = 668 - sqrt(668^2 - 820*(463 + P))/410

but remember that the Lincoln equation represents an approximation (though a good one) to the ASBC polynomial. Exact inversion requires finding roots of the ASBC polynomial.

I think my head is going to explode!!!

[Bugeater]

There is one more factor that you haven't figured in. That is the problem of measurement error. If your refractometer plate is a little wet, or if the wort is not thoroughly mixed, temperature off, or any of a bunch of other factors your reading may be a bit off. In addition, the gradations on the scale are sometimes hard to read.

The point is that no matter how exact your computations are, you are starting from an approximate reading. Thus, even though you are close, you will not have the exact SG. For homebrewing purposes, you are close enough regardles of which formula you use.

Wayne

[Garrete]

...They both represent the percentage sucrose by...

But aren't we measuring maltose and not sucrose in out wort?

[LordUlrich]

Actually SG is a measure of density, and we are measuring the density or the refractive index of the fluid. BUT there is a relationship between the percent of different sugars and both the density and refractive index.

[ajdelange]

...They both represent the percentage sucrose by...

But aren't we measuring maltose and not sucrose in out wort?

We are measuring a spectrum of sugars of which sucrose is only a small percentage but the fact that we do not encounter much sucrose has but a minor effect. The apparent (20/20) specific gravities of 10 % w/w solutions (10 °P, 10 °Bx) of, respectively, sucrose, glucose, fructose and invert sugars are, respectively, 1.04838, 1.04785, 1.04886 and 1.04835.

A hydrometer responds to the density of the solution in which it is immersed but it is calibrated against sucrose solutions of controlled strength. A refractometer responds to refractive index. It's Brix scale, if it has one, is calibrated against sucrose solutions of controlled strength. The assumption is that, in both cases, the actual sugar spectrum will cause the instrument to respond in a manner close enough to that for sucrose that it is sufficiently accurate to assume that the sugars are sucrose. Perhaps instead of calling a hydrometer reading "original extract' we should call it "original sucrose equivalent" or something similar.

[Hammy2424]

After all those lessons my refractometer now reads in degrees Delange!!