In *Brewing Calculations*, we reviewed the calculations we learned last week for how much grain to use. However, that was a calculation that implied a single-grain mash, something that doesn’t happen very often. Luckily the formula for a multi-grain mash is identical, except that you make a separate calculation for each grain, multiplying the result for each grain by the percentage of the grist bill that the grain represents.

For example, if I’m making 50 litres of a beer that I hope will have an original gravity of 1.044 (11°P), in a brewhouse with an efficiency of 87%, using 60% pale ale malt (extract content of 80%, moisture content of 4%) and 40% Vienna malt (extract content of 78%, moisture content of 3%), our calculation would be

m = malt% x [(V_{litres} x s.g. x ° Plato) / (%extract x (1-%moisture) x %brewhouse efficiency)]

m_{pale ale} = 60% x [(50 x 1.044 x 11%) / (80% x 96% x 87%)]= 5.16 kg

m_{Vienna} = 40% x [(50 x 1.044 x 11%) / (78% x 97% x 87%)] = 3.49 kg

Of course, simple math allows us to rearrange the formula to solve for any of the variables, such as brewhouse efficiency:

brewhouse efficiency = (V_{litres} x s.g. x %° Plato) / (m x %extract x (1-%moisture))

So if we make 50 L of wort that has a specific gravity of 1.044 (11° Plato), and we used 8.6 kilos of malt that had 80% extract and a moisture content of 4%, the we can calculate our brewhouse efficiency as being

(50 x 1.044 x .11) / (8.6 x .80 x .96) = 87%

That being relatively simple, we then moved on to calculating finished beer colour (usually expressed in North America as SRM–the higher the number, the darker the beer) from the colour and quantity of malt used. However, this is more of a guesstimate than anything. Yes, we can calculate the amount of colour the malt will add to the finished product, and probably for darker beers, it will be a pretty accurate estimate. However, for lighter beers, colour may be more dependant on how long the wort is boiled, since heat and water plus amino acids causes the Maillard reaction that darkens beer. For example, a light-coloured wort might be 2.8 SRM before the boil and 5.6 SRM after the boil. Hops can also have an affect on lighter beer colour, as will the degree of oxidation of polyphenols drawn from the grain husks, the amount of carbonates (water softness) in the mash water, and the amount of nitrogen in the grain (since more nitrogen equals more amino acids which means more Maillard reactions which means more colour).

Ray Daniels, in his excellent book *Designing Great Beers*, gives the formula

MCU = (°L x m) / V

where

- MCU = malt colour units (a unit invented by Daniels — he does give a table for converting from MCU to SRM)
- °L = degrees Litner, a measure of the colour of the grain
- m = mass of grain used, in lbs
- V = Volume of wort in gallons

So 5 gallons of wort made from 8 lbs of malt with a colour of 2.5°L will have a colour of

(8 x 2.5) / 5 = 4 MCU

(You can calculate the colour of a multi-grain wort by doing a separate calculation for each addition, then adding the results together.)

Of course Daniels’ formula is in American measures. For those of you smitten with the metric system, I realized that using metric measures and then multiplying the result by 8.36 (2.2 kg per pound times 3.8 L per gallon) would give the same result:

[(3.6 kg x 2.5°L) / 19L] x 8.36 = 4 MCU

On to hop calculations. Last year in *Brewing Ingredients*, Kevin did teach us the formula for estimating the mass of hops needed to achieve a particular bitterness of beer:

m = (V x C_{g} x IBU) / U% x AA% x 1000

where

- m = mass of hops needed in grams
- V = volume of wort in litres
- C
_{g }= correction for specific gravity if it is over 1.050: (1+[s.g. – 1.050)/2]
- IBU = the number of bitterness units desired
- U% = utilization of hops (see below)
- AA% = the alpha acid content of the hops

The hop utilization table (U%) compared to boil time looks like this:

- Dry hop = 0% utilization
- 0-9 min boil = 6%
- 10-19 min = 15%
- 20-29 min = 19%
- 30-44 min = 24%
- 60 min = 30%
- >74 min = 34%

This year, Kevin took us a step further: calculating multiple additions of hops at various times during the boil–say we want a projected bitterness of 65 IBU for a 60L wort with a specific gravity of 1.050, and plan to use Magnum hops (10% A.A.) for 60 minutes, Cascade hops (6% A.A.) for 10 minutes and Simcoe hops (12% A.A.) for 5 minutes. The Cascade and Simcoe additions are for aroma, so we would add them in pre-planned quantities of grams per litre, depending on how much aroma we wanted. In this case, let’s say we’ll add 1 g/L of the Cascade (60 g) and 2 g/L of the Simcoe (120 g).

By flipping around the above formula to solve for IBU, and borrowing numbers from the hops utilization table, we get

IBU = m x U% x AA% x 1000 / V

*(Note that we don’t need a gravity correction factor since our s.g. is only 1.050)*

IBU_{Cascade} = 60 x .1 x .06 x 1000 / 60 = 9 IBU

IBU_{Simcoe} = 120 x .06 x .12 x 1000 / 60 = 14.4 IBU

Therefore the two aroma additions are going to contribute 9 + 14.4 = 23.4 IBU of bitterness. We then only have to solve for the mass of Magnum needed to produce the remaining 41.6 IBU:

m = 60 x 41.6 / .3 x .1 x 1000 = 83.2 grams of Magnum needed

We used the break between class to massage some feeling back into our calculator fingers, then it was on to *History of Beer*. Bill White led us down through the ages, looking at religion and beer, from ancient Sumeria and the goddess Ninkasi through ancient Egypt, Greece, Rome, the Bible, Aztecs, Mayans, Incans, African culture, Germanic tribes, the rise of mediaeval monasteries as centres of brewing.

Next week: beer moves out of the temnple and becomes a business.