**Evaluation of The Method:
Comparing Estimated and Measured %ABV**

**© **James M.
Gossett (March 31, 2012) Questions/Comments?

Stoichiometry of Ethanol Production From Maltose

Contribution of Ethanol to Apparent Brix

Measurement of %ABV Using Brix Refractometry

Derivation of Calculator Equations

Evaluation of The Method: Comparing Estimated and Measured %ABV

My refractometer-based **method** for estimating
%ABV from pre- and post-fermenation Brix was evaluated using a dataset of 12 beers. Results were compared to
experimentally **measured** %ABV data.
Note that most of my brewing is of fairly high-gravity beers –
Northern Ale, Double IPA (DIPA), Honey Malt Ale, Belgian Tripel; consequently, the dataset is skewed
towards the high end of %ABV. There
is also one apple cider among the set.
Two of the samples (DIPA-1a and 1b) were actually of the same beer,
sampled months apart.

**%ABV**

Figure 1 presents comparison of
Brix-estimated vs. measured %ABV.

Figure
1. Comparison of Brix-based modeled
vs. measured %ABV for a dataset of 12 brews.

The summary statistics are: mean difference = 0.1 %ABV; sample
standard deviation of the difference (n=12) = ±0.4 %ABV. Thus, one can reasonably
expect to estimate %ABV, for home-brewing purposes, with the Brix-based
calculator. Commercial brewers
would likely feel the need for more accuracy.

The mean difference and
sample standard deviation of the difference reflect some combination of
imprecision and inaccuracy – in both the model-based estimates and in the
experimental measures of %ABV. We
are comparing the model-based estimates to imperfect measures of Òactual
%ABV.Ó As reported **earlier**, the
standard deviation of the method used here for measuring alcohol content is ±
0.2 %ABV. And imprecision in reading
the Brix scale affects model estimates of %ABV, just as it does experimental
measures of %ABV: the refractometer
cannot be read more precisely than to ± 0.1 Brix. That sort of imprecision in reading
the Brix scale propagates to an imprecision in model-estimated alcohol values
of about 0.1% ABV. Putting these sources together,
itÕs not hard to understand why imprecision in the difference between
Brix-estimated model and measured alcohols would be as high as ± 0.4% ABV.

**Residual Real Extract**

Figure 2 presents Brix-based
calculator estimates of residual Real Extract (P_{f}) versus ÒmeasuredÓ
values.

Figure
2. Comparison of
Brix-based modeled vs. ÒmeasuredÓ residual real extract.

What I am referring to as
ÒmeasuredÓ residual RE is not quite that.
ItÕs not based on specific analysis of carbohydrates, via HPLC or some
wet-chemical technique (e.g. anthrone reagent). As presented **elsewhere**, it is based on Brix measurement (B_{f}
_{aft boil/reconst}) of the beer after boiling off 75-80% of its volume (to remove EtOH)
and replacing it with distilled water.
If we assume that the factor of 1.04 between initial Brix (B_{i})
and initial extract (P_{i}) in pre-fermented wort represents
non-carbohydrate constituents that contributed to initial Brix; and that these
remain after fermentation; then

residual RE _{ÒmeasÓ}
= B_{f} _{aft boil/reconst} – (B_{i} –B_{i}/1.04)*(OG/SG_{f}
_{aft boil/reconst})

The factor (B_{i}
–B_{i}/1.04) represents the grams of non-carbohydrate
contribution to original Brix (B_{i}) and the ratio (OG/SG_{f} _{aft
boil/reconst}) corrects for the difference in specific gravity between
original, pre-fermentation wort (when the B_{i} measurement was made)
and the specific gravity of the post-fermentation beer after
boil/reconstitution (when the B_{f} _{aft boil/reconst}
measurement was made). It is
necessary because the reference on which weight% is based has changed. The same mass of nonfermentable
carbohydrates in 100 g of original wort at (for example) SG = 1.050 will
contribute a greater extent of weight% to a post-fermentation beer, after
boil/reconstitution, with (for example) SG =1.010.

The model-estimated residual
RE compares reasonably well with the ÒmeasuredÓ residual RE.

**Final Brix, After Boiling/Restoration**

For those who would prefer to
model the final Brix measured on the post-fermentation beer, after boiling off
75-80% of its volume and restoring with distilled water, I present Figure 3.

Figure 3. Comparison
of Brix-based modeled vs. measured residual Brix (after
boiling/reconstitution).

**Comparison With Hydrometer-Based Methods
of %ABV Estimation**

There are many
hydrometer-based methods to estimate %ABV in finished beers. I chose only four of them for
comparison to my Brix-based method.

__Standard SG-Drop Method__

From the FermCalc website

http://web2.airmail.net/sgross/fermcalc/fermcalc_alcohol.html

ÒÉDescribed on pages 79-80 of *First Steps
in Winemaking* by C. J. J. Berry (1987). It estimates the alcohol content by
dividing the drop in specific gravity by the constant 0.00736,Ó or:

sg - _{i}sg)
/ 0.00736 _{f} |

where

*a _{v}* = alcohol
content, % by volume

__Miller__

From Dave Miller
(*The Complete Handbook of Homebrewing*,
1988, Storey Communications. Miller
uses the same formula as the Standard, SG-Drop Method above, except the factor
in denominator is 0.0075.

__Duncan and Acton__

From the FermCalc website

http://web2.airmail.net/sgross/fermcalc/fermcalc_alcohol.html

ÒThis method is
described on pages 64-66 of *Progressive Winemaking* by Peter Duncan and
Bryan Acton (1967).Ó

sg
- _{i}sg) / [7.75 - 3.75(_{f}sg - 1.007)] _{i} |

__Realbeer.com__

http://www.realbeer.com/library/beerbreak/archives/beerbreak0301.php

Gives %ABW

ABW = 76.08(OG-FG)/(1.775-OG)

which
I then converted to %ABV by %ABV = %ABW*FG/0.794, where 0.794 is the density of
EtOH at 15ûC.

I
used each of the four hydrometer-based methods to estimate %ABV in the 12
finished beers. Because my FG
hydrometer measurements were made on finished, bottle-conditioned beer, I added
0.0036 to OG (pre-fermentation) hydrometer measurements to include the effects
of 5 oz/gal bottling sugar.

Figure
4 presents the results, with both my Brix-based, model predictions and measured
%ABV shown for comparison.

Figure 4. Comparison of Brix-based method and four
hydrometer-based methods with measured %ABV,

If the measured %ABV values are to be believed, the
Brix-based method appears at least as accurate as any of the hydrometer-based
methods.

The data are presented in an alternative way in Figure
5.

Figure 5. Scatter plot of estimated vs. measured

The four, hydrometer-based methods tend to
over-estimate %ABV. As presented
earlier, the mean error (from measured %ABV) of the Brix-based method was +0.1
%ABV, with sample standard deviation (n=12) of ±0.4 %ABV.

It is, of course, up to prospective users whether this
level of accuracy and precision is sufficient for their needs. However, consider that similar analysis of most hydrometer-based
methods is not readily available.

**Derivation of Calculator Equations **