How to Determine FG with refractometer measurement of beer and known ABV

[eric19312]

Hi all I'm trying to figure out how to do what is mentioned in the title. Thought maybe the math wizzes here might be getting tired of pH and spare a bit of mental capacity to help me with this problem.

I am thinking about in the situation where I have a sample of commercial beer with a labeled and presumed to be true ABV and want to determine the FG (and from that and ABV know the OG).

The usual way is to degas the sample and measure FG directly with a hydrometer. But that is not always practical. First it sacrifices a fairly large amount of the beer. I probably wanted to drink that beer... Second it is not always practical. Refractometer is portable. I've never tried this but could imagine checking a beer in a bar or brewery. Might have some explaining to do but I could at least imagine doing this.

I've not seen this on any brewing software and went to Sean Terril's equations. Those lost me. He provides a nice calculator but no clear way to turn the calculation around. Dug a bit more and found Petr Novotny's equations here. http://diversity-pivo.blogspot.com/2017/01/pocitame-nova-korekce-refraktometru.html

Using these equations I calculated FG from:

and then calculated ABW from the known ABV and calculated FG and this equation

and also calculated ABW using the lower of these two equations:

using an estimated Bxi and the measured Bxf

I then used excel solver to get the ABW from the two calculations to match by adjusting the estimated Bxi.

Looks like this:

So questions
Am I on the right track?
Is there easier way to do this? Beersmith or Brewers friend?
Shouldn't there be a wort correction factor involved here?

 

[balrog]

Yes, with those equations and those assumptions, you are correct with back-calculation.

My gut reaction however, is that you cannot ever assume that you have ABV, regardless of what they say/print, making whatever you back-calculated suspect.

I suppose if using a large sample is the issue, and you have unlimited cash, then one of these could be carried around and used.

 

[eric19312]

Yes, with those equations and those assumptions, you are correct with back-calculation.

My gut reaction however, is that you cannot ever assume that you have ABV, regardless of what they say/print, making whatever you back-calculated suspect.

I suppose if using a large sample is the issue, and you have unlimited cash, then one of these could be carried around and used.

I don’t see how this thing gets around the issue with measuring in presence of alcohol.

 

[balrog]

Dang. You're right. Never mind.

 

[Big Monk]

I don’t see how this thing gets around the issue with measuring in presence of alcohol.

Use the Excel Solver.

Type in the Terrill equation. Use 2 user inputs cells for OG and a guess at FG. Then calculate ABV. Now tell the solver to set the ABV cell to the desired ABV value by varying the FG cell. Viola.

EDIT: I see you already did that. You nailed it!

 

[eric19312]

just tested on a couple beers at local brewery. No issues and came up with different and to me more likely FG than the brewer had claimed. Schwarzbier labeled 6% ABV showed 7 brix on refractometer and calculated FG using solver and the Novotny equations as 1.011 FG. Very reasonable compared to brewers claim that the FG was on the order of 1.003. I'm thinking he may have meant 3 plato. The tripel showed 10.5 brix and claimed 10.1% ABV and this got me a FG at 1.014 again pretty much in expected range.

Sadly these came in to close to 50 carbs fo the 2 pints and I have a better understanding of what is not compatible with my low carb diet.

 

[ajdelange]

There is a way to get ABV (or ABW) from RI that's works well enough that breweries can do it for process control (but I think mist use Alcolyzers for that these days). The method involves measuring RI and then AE and ABV (or ABW) using distillation and plotting an ABV and AE vs RI on calibration curves. For a given beer in the brewery's portfolio the fit of the calibration curve is good enough. The fit over a family of similar beers (light lagers) may also be deemed adequate but if you try to span a brewery's entire portfolio you will likely come up short. There are several formulas that attempt to do just that. The problem is that you have no way to know when such a formula is giving you an accurate result and when it isn't unless you do a distillation analysis.

 

[eric19312]

Not sure I explained the question well enough. I’m willing to assume right or wrong that the labeled ABV on a commercial beer is correct. I want to use my refractometer and the known ABV to get a reasonably close estimate of FG. Reasonably close I guess would be within say .002 sg.

 

[ajdelange]

You would only be able to get that close with the calibration curve as described in #6.

 

[eric19312]

I continued this project and have built a small calculator in google sheets.

I ended up switching to Sean Terrill's linear equation for calculation of FG. Seems enough people are using it to be comfortable that it applies to a reasonably wide range of worts. Inputs are Brix of the beer sample, ABV of the beer, and refractometer correction factor (I'll use ST's default 1.04 until I can gather enough calibration data).

Here is a link to the sheet if you are interested. I plan to test on a future homebrew batches and see how accurate the OG and FG predictions are.
https://docs.google.com/spreadsheets/d/190BDuULGsOCP0LXS6VLFILID5kflqJoisbBH9p5K7y8/edit?usp=sharing