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Converting Brix to OG

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Post Mon Mar 03, 2008 1:54 pm

Converting Brix to OG

I'm putting together a chart for my brewery to list the Brix-to-OG conversions at a glance, and I wanted to use the accurate calculation rather than the easy (but inaccurate) Brix times four shortcut.

I've found the following two formulas, which give very different results (especially at higher gravities):

As seen at http://byo.com/feature/1132.html and many other places:
OG = 1.000019 + ((0.003865613*B) + (0.00001296425*B) + (0.00000005701128*B))
Where B = measured refractivity in Brix

or, from http://www.economysizegeek.com/2006/04/ ... actometer/
OG = 1.000898 + 0.003859118*B + 0.00001370735*B*B + 0.00000003742517*B*B*B
Where B = measured refractivity in Brix

Does anyone know which (if either) is the correct formula to use? The second one seems suspect to me, as 0 Brix gives an OG of 1.001 (not 1.000 as expected), and gives much higher results across the entire range.
Brian Pylant

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Rand

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Post Mon Mar 03, 2008 2:01 pm

Can't help. However, I would buy you a beer if you sent me a copy of the completed chart...

Rand
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OskeeI

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Post Mon Mar 03, 2008 2:54 pm

Re: Converting Brix to OG

Brew.Drink.Repeat. wrote:I'm putting together a chart for my brewery to list the Brix-to-OG conversions at a glance, and I wanted to use the accurate calculation rather than the easy (but inaccurate) Brix times four shortcut.

I've found the following two formulas, which give very different results (especially at higher gravities):

As seen at http://byo.com/feature/1132.html and many other places:
OG = 1.000019 + ((0.003865613*B) + (0.00001296425*B) + (0.00000005701128*B))
Where B = measured refractivity in Brix

or, from http://www.economysizegeek.com/2006/04/ ... actometer/
OG = 1.000898 + 0.003859118*B + 0.00001370735*B*B + 0.00000003742517*B*B*B
Where B = measured refractivity in Brix

Does anyone know which (if either) is the correct formula to use? The second one seems suspect to me, as 0 Brix gives an OG of 1.001 (not 1.000 as expected), and gives much higher results across the entire range.


Actually at a Brix level of zero, neither would be exactly 1. The first one is a linear relationship, whereas the second one is non-linear. Having dealt with a little mathematical modeling during grad. school I would be inclined to use the second as few things in biology have a linear relationship.

Would be easy to punch in the formulas into Excel to come up with a conversation tool.
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MullerBrau

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Post Mon Mar 03, 2008 3:08 pm

MB has an Excel spreadsheet (free download) which you may be able to use to get the formulas derived from it.

http://morebeer.com/learn_vids/vids_refract
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Brew.Drink.Repeat.

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Post Mon Mar 03, 2008 4:07 pm

MullerBrau wrote:MB has an Excel spreadsheet (free download) which you may be able to use to get the formulas derived from it.

http://morebeer.com/learn_vids/vids_refract


Already done - they use the same formula as the BYO article.



Actually at a Brix level of zero, neither would be exactly 1.


Really? Why is that? I assumed (yeah, I know what that means) that zero Brix would be the same as 1.000... although when I increase the decimal places in the BYO forumula I see it's actually 1.000019... hmmmm...



Would be easy to punch in the formulas into Excel to come up with a conversation tool.


That's where I'm making the chart, and where I noticed the discrepancy between the two. For example, in the BYO formula 30 Brix comes out to 1.116; in the other it's 1.130.



However, I would buy you a beer if you sent me a copy of the completed chart...


If I ever get to Salt Lake City I might take you up on that... in the meantime when I get this done I will gladly post a PDF to my website so anyone can download and print it. Sharing is fun.
:D
Brian Pylant

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Post Mon Mar 03, 2008 7:12 pm

A little more info:

John Palmer's chart on pg. 266 of How To Brew, which is taken from the American Society of Brewing Chemists (but does not specify a formula) gives yet a third set of results. I did take into account that this chart is Plato to OG; my Excel sheet includes both Brix, and Plato (using Brix / 1.04 as the formula).

Perplexing... I'm sure that using any of these will put me in the ballpark, in the infield of the ballpark no less, but I'd like to use the most accurate formula possible, provided one exists. (Considering that no one hop utilization formula, be it Rager, Tinseth, Mosher, etc. is held as being the most accurate, I am willing to accept that this may be the case here as well.)
Brian Pylant

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TG

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Post Mon Mar 03, 2008 7:27 pm

Re: Converting Brix to OG

Brew.Drink.Repeat. wrote:I'm putting together a chart for my brewery to list the Brix-to-OG conversions at a glance, and I wanted to use the accurate calculation rather than the easy (but inaccurate) Brix times four shortcut.

I've found the following two formulas, which give very different results (especially at higher gravities):

As seen at http://byo.com/feature/1132.html and many other places:
OG = 1.000019 + ((0.003865613*B) + (0.00001296425*B) + (0.00000005701128*B))
Where B = measured refractivity in Brix

or, from http://www.economysizegeek.com/2006/04/ ... actometer/
OG = 1.000898 + 0.003859118*B + 0.00001370735*B*B + 0.00000003742517*B*B*B
Where B = measured refractivity in Brix

Does anyone know which (if either) is the correct formula to use? The second one seems suspect to me, as 0 Brix gives an OG of 1.001 (not 1.000 as expected), and gives much higher results across the entire range.

The first formula looks wrong to me. I bet the second "B" should be B*B and the 3rd should be B*B*B. Probably a typo.
Tom
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ontap78

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Post Mon Mar 03, 2008 8:04 pm

I printed off a conversion table off Brewrats some years ago. It's a nice vertical chart that I taped together and laminated.
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OskeeI

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Post Tue Mar 04, 2008 4:57 am

Got bored so played around, here is what the two formulas plot out to. The top one is the second formula and the lower line is the first BYO formula,

Image

OG on the Y and Brix on the X axis.

As the brix gets higher the second formula results in higher OG readings and the difference between the two formulas increases.

Here is a simple Excel spreadsheet I did plugging in each formula.

http://www.oskee.org/convert.xls
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AiredAle1

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Post Tue Mar 04, 2008 9:24 am

Call me lazy, or simple-minded, but I just multiply my Brix readings off my refractometer by 4, which gives me the approximate gravity reading. My reasoning is that my hydrometer reading is +/- 2 units since it's an estimate where the meniscus hits the scale, and my refractometer measurements are also +/- 0.25 unit estimates, so why sweat it?

More useful would be to calibrate both devices against carefully made sugar solutions, and this I have done.
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Brew.Drink.Repeat.

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Post Thu Mar 06, 2008 4:58 pm

AiredAle1 wrote:Call me lazy, or simple-minded, but I just multiply my Brix readings off my refractometer by 4, which gives me the approximate gravity reading. My reasoning is that my hydrometer reading is +/- 2 units since it's an estimate where the meniscus hits the scale, and my refractometer measurements are also +/- 0.25 unit estimates, so why sweat it?


The only reason I'm even bothering is because I've seen other brewers (pro and home) that keep these lookup tables nearby, and I thought it was a really good idea. I didn't think it would be a big deal to Google the formula and plug it into Excel, but now I have four options to choose from (BYO, BYO with the modifications suggested by TG, the one from Economy Size Geek and the table in How To Brew).

Oy!
:?

I'm going to post to the AHA TechTalk list and see if anyone has any clarification on this...
Brian Pylant

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When in doubt, think of your old hippie friend Acid Al.
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azeeb

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Post Thu Mar 06, 2008 5:23 pm

The first equation doesn't make much sense to me the way it is written here. Since everything inside the parenthesis is multiplied by B, you could just add the three terms together.

OG = 1.000019 + ((0.003865613*B) + (0.00001296425*B) + (0.00000005701128*B))

Is the exact same thing as

OG = 1.000019 + (0.00387863426128*B)

Since I can't imagine why someone would write it the first way, it would lead me to believe it is incorrect. Most likely it is also supposed to be a nonlinear equation, and the first term is multiplied by B, the second term by B*B and the third term by B*B*B, similar to the other equation.

My guess would be, this equation originally had squared (^2) and cubed (^3) superscripts, and the formating got lost when the article was published.
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Brew.Drink.Repeat.

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Post Thu Mar 06, 2008 5:33 pm

azeeb wrote:My guess would be, this equation originally had squared (^2) and cubed (^3) superscripts, and the formating got lost when the article was published.


That is my guess as well, unfortunately both BYO and More Beer are using it!
:cry:
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Kaiser

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Post Thu Mar 06, 2008 8:06 pm

After fixing the obvious typos in the BYO formula you can pick any of the formulas. Or keep searching to find even more to choose from :)

These formulas are basically a cubic approximation of the SG <-> Brix relationship that has been measured empirically: create solutions of varying but known extract/sugar percentages (Brix scale) and measure the specific gravity. Then find a linear, quadratic or cubic formula that best matches the data points. This formula can then be used to get a SG - Brix conversion for any point in between or within a given range. B/c these formulas are based on different experiments, they will slightly differ b/c of the unavoidable error.

BTW, the quick way of SG = 1 + Brix * 0.004 is a linear aproximation.

Kai
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Post Fri Mar 07, 2008 8:52 am

Makes sense... I just wanted to be sure that the differences were acceptable due to the process, and not simply a matter of one or more of them being outright incorrect (typos not included, of course).

Thanks!
Brian Pylant

It's pronounced ass-ih-tal-duh-hide.
When in doubt, think of your old hippie friend Acid Al.
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