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Empirically Measuring and Calculating Alcohol and Extract

Content in Beer with a Reasonable Degree of Accuracy and Confidence

Michigan Craft Brewers Guild - Conference

Kalamazoo, MI -- January, 2014

Gary Spedding, Ph.D [FINAL CORRECTED VERSION]

Brewing & Distilling Analytical Services (BDAS) LLC

Theory behind alcohol production & determinations/Definitions.

Simple but powerful equations to relate SG or Plato determinations in the brewhouse to ABV and ABWt determinations. Methods to use.

Data and exercises for you - use those equations/get comfortable with. Relationships!

Interconversions of data. New Equations.

Use base data to get carbohydrate estimates, and calorie info. On-line tools and calculators.

Objectives Today

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“Alcohol Measurement in Beer and Useful Derived Data” via:

Hydrometers

Digital Density Meters [GC?]

Refractometers

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“Background Info., Key Facts and Definitions”

See handout for full details (Now added below – post-seminar delivery - to allow for

an integrated set of slides)

Alcoholic Strength: A measure of the amount of alcohol in beer. The alcohol content of a beer typically refers to the amount of ethyl alcohol (as opposed to higher or fusel alcohols). The analysis of beer for alcohol content is an important part of brewing laboratory work for quality assurance programs and for legal reporting purposes. Results, however, are subject to appreciable variation and under official methods the analyses are time consuming and expensive.

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Specific gravity (SG) or relative density: is an intensive property of a substance (be it solid or liquid) and is, historically, the ratio of the density of a substance at the temperature under consideration to the density of water at the temperature of its maximum density (4 °C). The actual density in theory – for the purposes of most discussions with respect to beer – is generally 20 °C/20 °C relative to water at unity though, elsewhere in the alcohol beverage world, it is typically expressed as at 20 °C/4 °C. The complexity of the temperature associations could not be presented in depth here - full details may be found in the literature (see the references). An SG value is numerically equal to the density in grams per milliliter (or Kg per liter) but is stated as a pure number (because the division by the water’s own density value leads to a cancellation of the units), while density is stated as mass per unit volume. Water has a specific gravity of 1.0000 at 20°C. Base and derivative density values form mathematical grounding in many of the formulas used in alcohol and extract calculations. The density value 0.998201 will be seen in the literature as pertaining to the formulas and conversions of alcohol density, specific gravity, and alcohol by weight and volume and while understood within this article is also not covered in any depth here.

Original Extract or Gravity: The initial SG of wort is known as the original extract (OE) or original gravity (OG) depending upon units implied by these terms (OE is in Plato, while OG is in numerical “gravity units” – see below and under “Plato”). OE is an expression of sugar content - grams of sugar per 100 grams of wort. [Equivalent to % weight/weight (w/w)]. In the brewing industry this is denoted as “degrees Plato” (0P) and to a first degree of approximation beer responds in the same way as the original solutions of sucrose and water used to derive the Plato scale. Brewers often determine or record and report this using numerical specific gravity values rather than in degrees Plato and it is this that is more correctly the OG value. OG represents the ratio of the density of wort at 20 °C to the density of water at the same temperature (see “Specific Gravity” above). Plato and SG values can, however, be inter-converted using appropriate formulas as illustrated in the text (example, for our purposes here, 12.00 °Plato is an SG of 1.04838 – actually 1.048311 at 20°C/20°C). See Plato in this table. When reading the literature and interpreting equations it is important for the reader to understand the differences in units applied to OE and OG terms as this can otherwise cause some confusion as to which values to use in the equations. OE = (RE + 2.0665 x ABW)/ (1 + 0.010665 x ABW). A fundamental formula not covered in the text but which can be used to test derivation of formulas and cross-check values.

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Apparent and Real Extract: Brewers measure changes in density as sugars are consumed and converted into alcohol. Measurements are obscured (the true gravity is “hidden”) by alcohol (of lower density than water, sugar solutions or beer) causing “buoyancy effects” with hydrometers for example. Thus false or apparent readings of gravity are made when instruments measure beer (containing water, sugars and alcohol); hence “apparent extract”. The real extract is a true(r) measure of remaining sugars - and proteins etc., to be exact about the nature of the extract - as determined in the absence of alcohol (removed via distillation or boiling) or compensated for the actual alcohol content via its determination and/or via algorithms in instrumentation. Such equations are described and discussed in the text. When yeast has finished fermenting the brewers wort, or the brewer terminates the fermentation, the final gravity reading is sometimes also called the terminal gravity (this will also be in “apparent” or “real” terms depending how measured or calculated). RE is real extract in grams per 100 grams of beer (Plato).

Apparent Attenuation and Real Degree of Fermentation: The expression of the percentage reductions in the wort’s specific gravity caused by the transformation of the sugars (higher specific gravity than for water) into alcohol and carbon dioxide and yeast biomass. Real and apparent values exist for the reasons discussed under Apparent and Real Extract. It is simply a measure, in percent terms, of the amount of original extract which has been consumed or converted. The Real degree of fermentation equation: RDF = 206.65/ (2.0665 + RE/ABW), is a fundamental equation also underpinning the theory behind many equations as presented here (see also Original Extract or Gravity).

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Plato – (see also Original Extract or Gravity). The typical way brewers report extract in wort and beer (as weight percent). Plato values may be obtained directly from hydrometers calibrated in degrees Plato, by means of specific gravity measurements as related to standard Plato (or extract) tables and (to varying degrees of approximation) by calculation – some equations seen in the presentation. The Plato scale and tables are themselves approximations for complex physical-chemical reasons but have stood the test of time for most brewing purposes.

Alcoholic Strength: A measure of the amount of alcohol in beer. The alcohol content of a beer typically refers to the amount of ethyl alcohol (not higher or fusel alcohols).

Alcohol Content: Important for brewing laboratory work for quality assurance programs and for legal/consumer reporting purposes.

Results - subject to appreciable variation.

Official methods - analyses time consuming/expensive.

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Specific gravity (SG)/relative density -intensive property ( solid or liquid) - the ratio of the density of a substance at the temperature under consideration to the density of water at the temperature of its maximum density (4 0C?).

SG value - numerically equal to the density in grams per milliliter (or Kg per liter) STATED as a pure number (division by water value -- density > cancellation of the units), while density is stated as mass per unit volume (g/mL or Kg/L).

Initial SG of wort is known as the original extract (OE) or original gravity (OG). Expression of sugar content - grams of sugar per 100 grams of wort. [Equivalent to % weight/weight (w/w)].

Brewing industry - denoted as “degrees Plato” (0P).

Plato and SG values can be inter-converted using appropriate formulas.

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OG (tech. OE) often held as an indirect indicator of alcoholic strength of a beer. A higher OG (implying the higher the fermentable sugars) indicates a higher potential for conversion to alcohol.

But this DEPENDS upon how fermentable the extract is - yeast can only consume the simple sugars glucose, maltose and triose. E.G. If 65% ( typical) of OG is converted > simple sugars (mashing) alcohol content, as % weight, is roughly the OG divided by three.

1 gram of alcohol requires 2.0665 g of fermentable extract or 2.0665/0.65 = 3.2 gram of total extract when the real degree of fermentation (RDF) is 65.

The gram “alcohol from fermentable sugars” conversion? Theoretically, 1 gram fermentable sugar will yield 0.51 gram of ethanol and 0.49 gram of carbon dioxide. [Some sugar needed = cell growth.] Realistically, the ethanol yield is more likely 0.46 gram, and carbon dioxide 0.44 gram from 1 g sugar.]

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>Alcohol is generated relative to the amount of fermentable sugars in beer wort.

>Is related to both wort specific gravity (SG) and wort RDF (Real or “true” degree of fermentation).

>Accepted - 1 gram of alcohol requires 2.0665 g of fermentable extract.

[As originally determined: 2.0665 g sugar yields 1 g ethanol, 0.9565 g CO2 & 0.11 g yeast. Note: for equations below, 0.9565g & 0.11 g sum to 1.0665 extract NOT converted to alcohol.]

>Above values used in published equations to det. alcohol strength.

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“Using the above facts in formulas and calculations of alcohol determinations”

Solving for alcohol determination by weight determinations – drop in wort gravity (Karl Balling):

> [ABW: alcohol by weight (as w/w, grams of alcohol per 100 grams of beer). OG, original gravity & RE real or present extract.]

)100/0665.1()0665.2()(OE

REOEABW

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Brewers using a hydrometer - real extract can be approximated using OG and AE (orig. Balling):

RE, % w/w = (0.1948 x OE) + (0.8052 x AE)

(AE = apparent extract or attenuation – value determined when alcohol present) NB: this is only an empirical observation & applies only to traditionally fermented beers near 65 % RDF.

The last formula (based on assumptions, mineral content and physical chemical interactions of solutes) is based on a relatively constant ratio:

(OE – RE)/(OE – AE) = 0.8052 +/- 0.0012

[95% confidence]

(Over range of OE 9-18 Plato and RDF 58-70%).

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Substituting into the above formula:

No RE immediately needed!

)100/0665.1()0665.2()(8052.0

OEAEOE

ABW

If SG has also been determined for beer then alcohol by volume - ABV- can be determined w/a correction to account for the specific gravity of the beer:

[Where, sp. gr: specific gravity, e.g., for the beer or pure ethanol.] [But need SG beer – later…]

CCalcoholethylgrspbeergrspwtbyalcohol

volAlcohol

20/20@..

...%,.%,

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Which simplifies to:

Variant eq’ns available but alcohol should be reported both % by weight (wt.) & by volume (vol.) to two decimal places. For reporting purposes brewers are allowed a tolerance of +/- 0.3% alcohol by volume. [0.7907]

791.0...%,

.%,beergrspwtbyalcohol

volAlcohol

Some questions we now need to address.

If using SG hydrometers how to get Plato Values? Or Plato to SG?

If you obtain Density values how do you obtain SG values and vice versa?

Then: What can you do with those values?

Who or what is Tabarie ? ……and……

Should we care?

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Resolve an issue here (Assuming you have Plato OE and AE {or RE} Values).

To Compute ABV as above we need the current beer SG in gravity units!

Note: SGBeer = the Appt. Gravity!

Solve that using two equations (Lincoln derivatives)

Now Two Equations for Interconverting Plato and SG values. (AE or other Plato value to SG):

11.227

2.2586.258

PP

SG

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And to Convert SG to AE (or other Gravity units to Plato Value)

Plato Extract = [(SpG)2 (-205.347) + (668.72)(SpG) – 463.37]

[cf. Goldiner –Europe/Tables.]

From above we can see we can get SG and Plato Values interconverted

But What if you are obtaining Density Values instead of SG’s?

Use simple density (“rho”) relationships for water, extract and alcohol solutions

SG x 0.998201 = and /0.998201 = SG

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“Some other neat formulas and manipulations”

What if we have or need the alcohol SG and the methods used/instruments did not give us this? [Can be done via distillation] But, Can we avoid that?

Enter Mr. Tabarie and his relationships!

SGAlc = SGBeer - SGRE +1SGBeer = SGRE + SGAlc -1

SGRE = SGBeer - SGAlc +1

[Perfect - normal strength beers (ca. 3-7% ABV and Typical ca.2.5-7.5 Plato Real Extract)] Keep below 10-12% ABV beers!

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Now from all above if we have the SG for the alcohol (or its obtained via distillation and measurement) we have an alternative approach to determining ABV and ABWt – Use of OIML Tables! (at 20 °C) using density values.

Density values are taken to the Tables not as 0.98705 (example) values but as 987.0 as seen below.

OIML Table Vb for ABVOIML Table Va for ABWtInterpolation may be required between tabulated and actual density values.

We can now use OIML (Legal Metrology) Tables to look up ABV and ABWt at 20 °C from Density and then convert as needed to SG. Or use AOAC/ASBC (52.003) Tables to obtain ABV at 60 °F from SG.

Or a Quick ROT: ABV from 20 °C to 60 °F:

ABV(20 °C) x 0.9972 - 0.0069 = ABV (60 °F)

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For normal strength beers an (adequate) equation can be used that even obviates the need for the OIML Tables. Measure ABWt:

ABW = 517.4 x (1-SG) + 5084 x (1-SG)2 + 33503 x (1-SG)3

[note it uses SG Alcohol values not Density! Unlike OIML Tables.]

Use when beers expected less than 12% ABV(pers. observations). Convert to ABV from ABWt above using standard equations.

Note Caveats: Not Covered Here Today.Another complexity to this.If using distillations to obtain the alcohol SG.Are you using gravimetric or volumetric distillations?If gravimetric the SG alcohol is for weight of alcohol. Volume values obtained from tables need to be corrected back for beer SG. If volumetric ( may only need volume at this point –OK ) – but the weight of alcohol from tables needs correcting back to the SG of the beer.Contact us for details on this.If using a DMA5000/Alcolyzer and you ask it to print out the alcohol SG be aware that it is for weight of alcohol and not volume. This complicates back-calculations.

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To see how well we could use individual pieces of information - as obtained from various methods - run examples to see how well the equations might work for us. (Close but not official of course).

Examples >>>>

“Data and Tables”

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Anton Paar Data.Typical PrintoutFrom a DigitalDensity Meter/Alcolyzer.

OIML Density /ABV/ABWt Tables – Parts of.

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OIML Density /ABV Table – Portion of.

OIML Density /ABWt Table – Portion of.

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AOAC Alcohol Table

“Example Calculations and Exercises”

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Test Calculations – I

Exercises

Assuming you can carefully obtain the OG and the AE for beer using hydrometers. Then taking the AE (and OG) equation you can prove (use the Anton Paar Data) the ABWt, then the ABV values (in the example) Anton Paar Printout.

Other calculations can follow (see below).

Test Calculations – II

Exercises

Supposing you can obtain accurate SG or Density measurements (Maybe hand held digital units) of from SG hydrometers you can now calculate from these values the OG, AE, and (if de-alcolyzed or distilled beer) the RE in Plato.

Hand calculate (Excel sheet?) from the “AE to SG” Equations the SG for the beer, the OG and the Real Extract from the Anton Paar data. (You are given the SG sample = the AE!). If Density readings convert to SG as shown above.

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Test Calculations –II (cont..) ExercisesHave SG for beer 1.00961 (AE).

OG 10.71 (Calc. as SG = 1.04298)RE 4.06 (Calc. as SG = 1.01592)

AE 2.46 (Calc. as SG = 1.00959 - NB: very close to 1.00961 from the A-Paar printout.)How to get the Alcohol SG? – Try Tabarie!

[SGAlc = SGBeer – SGRE +1] = 1.00961 – 1.01592 + 1 = 0.99369.Convert to Density (to use OIML Tables) = 0.99190 (or 991.9 for Tables).

Test Calculations –II (cont..) ExercisesNow we have the SG for Alcohol – Use OIML and AOAC Tables to Determine ABV’s and ABWt. {or alt. eq if below ca. 12% ABV.}

[SGAlc = 0.99369 to Density {0.99369*0998201} = 0.99190 (or 991.9) From the OIML Tables (next) –we obtain 4.38% ABV @ 20 °C (close to 4.35% A-Paar Data) and 3.48% ABWt (a little off but quite good?). ERROR HERE (See next slides)

[Using the AOAC (60 °F) Tables (data not shown here) gives us 4.33% ABV (@ 60 °F) – About right for this 20 °C ABV figure! Typically 0.02% higher @ 20 °C!]

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Addendum (Correcting an Error!)Last slide: From the OIML Table we obtained 4.38% ABV @ 20 °C (and stated close to 4.35% A-Paar Data) and 3.48% ABWt (a little off but quite good?).But (Go back to Caveat slide):-The ABWt value of 3.48% is derived from an SGalc that represents the value as if in pure “alcohol/water mixture”, So…

We need to correct the ABWt value here, accounting for the SG of the beer itself.

From earlier:-

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Correcting ABWt from (“water/alc soln.”) to SG of the beer.

Much closer (using the calculated Beer SG) to the Anton Paar Value. 3.42 or 3.43% (rounded) vs. the AP – 3.41% ABWt! Even better overall for us using such calculations!

SGsampleorBeerSGAlcwtbyalcohol

wtAlcoholcorr

..%,%,

%425.300959.1

99369.0%48.3 ABWt

Now we have determined all the relevant data and can confirm its closeness to the original AP printout data for this beer sample.This correction for the ABWt completes the basic data and reminds us that the SG for ABV and ABWt (from Tabarie derivation in this example set) gives us the correct ABV (just like for a volumetric distillation – for explanations not fully covered in the seminar) but a value for ABWt that needs to be back-corrected to account for the beer SG.

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OIML Density /ABV/ABWt/ For Exercise II

Calculations and Exercises: ConclusionArmed w the set of equations and tables defined above - if you can obtain either Plato Extract Values or SG Values for Original Extract (Gravity) and Terminal (Apparent) Extract Gravity – as well as Real Extract (by computation or by de-alcoholyzing/distilling a beer sample) via use of hydrometers or simple digital density meters - you can get quite close to true alcohol results for beer.

Remember to get a final official check for any legal needs though!

BUT WAIT … THERE IS more…

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“Introducing the Scandinavian

Beer Calculator”

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Finally: Try plugging some values including those from the Anton Paar data shown here into the Scandinavian Beer Calculator and see how that works for you.

Hopefully this gives you a good start to dealing with brewery and brewing lab calculations with benefit to you, legal authorities and your consumers!

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Brewing and Distilling Analytical Services, LLC. 1141 Red Mile Road, Suite 202, Lexington, KY 40504.

Tel: 859-278-2533.

www.alcbevtesting.com

gspedding@alcbevtesting.com/https://facebook.com/BDASLLC

Blogs:

http://alcbevtestingnews.blogspot.com/

http://alcbevmosaic.blogspot.com/

NOTE: THIS TALK FORMED THE BASIS FOR A PAPER WHICH IS FREE ON-LINE IN THE INAUGURAL (RESURRECTED) ISSUE OF THE BREWERS DIGEST.