“Gravity Frustration” or “Why you should read Chapters 5 and 6 of Designing Great Beers.” or “Dr Strangelove or: How I learned to barely scratch the surface of a deep topic.”

I recently sent out an email the KROC mailing group regarding “preboil gravities” that are computed in ProMash, which is a good piece of software with lots of features.  Unfortunately it is getting dated (the website shows 2003 as the last update) and I have never heard of an ingredient update.

There was a lot of good advice regarding checking the grain crush, mixing the wort in the kettle, cooling the wort sample, taking hydrometer readings among other recommendations.  I won’t repeat the entire discussion thread here, please ensure you are signed up to get KROC emails if you missed it.  I want to actually introduce a means to predict what the gravity of the wort you will have in your fermenter based on what you start with.  It might get geeky, and as our friends in the UK say – there might be some maths involved.

First off – what do brewers mean when the talk about gravity?  The acceleration of objects on the surface of the earth towards the center at 32 feet per second squared?  No.  We are discussing specific gravity.

Specific gravity is the ratio of the density of a substance to the density (mass of the same unit volume) of a reference substance.  Said another way, SG is the ratio of the density of wort to the density of water.

Specific gravity, as it is a ratio of densities, is a dimensionless quantity. Specific gravity varies with temperature and pressure; reference and sample must be compared at the same temperature and pressure, or corrected to a standard reference temperature and pressure.

Specific gravity can be measured using a hydrometer.  Operation of the hydrometer is based on Archimedes’ principle that a solid suspended in a fluid will be buoyed up by a force equal to the weight of the fluid displaced by the submerged part of the suspended solid. Thus, the lower the density of the substance, the farther the hydrometer will sink.

The “Plato scale” is an empirically derived hydrometer scale to measure density of beer wort in terms of percentage of extract by weight. It was developed in 1843 by Bohemian scientist Karl Balling as well as Simon Ack, and improved by German Fritz Plato. The scale expresses the density as the percentage of sucrose by weight (grams of sugar per 100 grams of wort), so a wort measured at 12° Plato has the same density as a water−sucrose solution containing 12% sucrose by weight, denoted as 12% Brix. For the brewer, it has an advantage over specific gravity in that it expresses the measurement in terms of the amount of fermentable materials. Degrees Plato are more popular in central European brewing, and occasionally feature in beer names.

Given that background information, the questions remain – given a pre-boil sample of wort, can I predict what my Original Gravity will be in the fermenter?  What is the 60 minute mark for hop additions?  Will I need to add water or boil longer?  These are knowable details, but we need to take a few measurements first.

What is the volume of wort collected in the kettle?

What is the “density” – or the percentage of “sucrose” by weight (% Brix)?

A couple of points to consider:

• the collected wort will be hot, usually around 165F, so the density will be lower.

• the wort in the fermenter will be cool, usually around 68F, so the density will be higher.

• the boil will condense the wort by boiling off the water (somewhat obvious.)

Useful formulas:

SG -> Brix Equation:

    Brix = (((182.4601 * SG -775.6821) * SG +1262.7794) * SG -669.5622)

(Source: http://en.wikipedia.org/wiki/Brix)

Brix -> SG Equation:

    SG = (Brix / (258.6-((Brix / 258.2)*227.1))) + 1

(Source: Brew Your Own Magazine)   

Gravity Units

Ray Daniels introduces the concept of Gravity units.  They’re pretty easy to use, so I’ll follow his lead.  If you have a hydrometer, it’s easy – the gravity units are the last two digits of the SG – e.g. 1.050 is 50 GU, or mathematically GU = (SG – 1) * 1000.  If you are using a Brix refractometer, plug the Brix to SG equation into a spreadsheet or just look for a calculator online that will do the conversion, then use the GU formula (hint: it’s the last two digits).

So lets say a brewer named Rick decides to brew a nice ESB one day.  He reads a recipe in the Brewing Basic Styles, plugs the numbers into ProMash, buys his grains and gets set for a brew day.  Because I’m “batch sparging” (which Bob Z rightly points out is a misnomer) I have been adding a couple extra pounds of base malt to grind.  I ended up with some wild numbers – about 8 gallons of wort collected for a 5 gallon batch and measurement of about 11 Brix.

Assuming a boil loss of 15%, you will lose 1.2 gallons per hour, or 0.02 gallons per minute.  Using  (GU*original volume)/(original volume – time in minutes * loss per minute) you can estimate the GU’s at any point in time.  Obviously these measurements would have to be tested for accuracy!

Sparge yield of 8 gallons (use a measuring stick customized for your kettle if you don’t have a liquid level indicator).  Preboil density measured at 11 Brix.  Target ~5.5g-6.0g at 1.060.

Using the GU -> SG -> Brix calculations, we have a OG in the fermenter of 14.76904% Brix