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# Brewery Math

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## Matthew Peetz

on 12 March 2017

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#### Transcript of Brewery Math

Brewhouse Efficency
What: How to calculate what % of the available sugars were extracted from the grain.
Malt Calculations
Why: In order to determine how much malt I should be adding to the mash.

How: Determine your desired starting plato, your final volume, what percentage of each grain you want to use, grain PPG, and Brewhouse Efficiency.

PPG: Points/Pound/Gallon

Equation: # grain = points / PPG / brew house efficiency
Equation: points = gallons * SG

Example : Brewing a 7 BBL batch of Dunkel with 50% Munich malt, 48% Vienna malt, and 2 % chocolate malt. Brewhouse Efficiency is 87% with a starting plato of 14.8

Solution: Get everything into SG units and Gallons
SG = 259 / (259-14.8)
SG units =1.060 - 1.000 * 1000
SG units = 60

Gallons = 7 BBLS * 31 gallons
Gallons = 217 gallons

Total = 217 gallons * 60 SG units
Total SG units = 13020

Munich Malt = 13020 * 50%
Munich Malt = 6510 points

Vienna Malt = 13020 * 48%
Vienna Malt = 6250 points

Chocolate Malt = 13020 * 2%
Chocolate Malt = 260 points
Conversions
Plato and Specific Gravity
Plato = A scale used to determine how much sugar is present in beer. Based on weight as a % of sucrose. 15 Plato means 15% of the weight of the solution is sucrose.
Specific Gravity = A density reading
P = 259 - (259/SG)
SG = 259 / (259 - Plato)
Brewery Math
Problem: I have an 8 BBL brewhouse with water that has 9 ppm calcium. I want to have 100 ppm and have a bucket of CaCL2 hexahydrate (18% calcium by weight). How many pounds should I add?
Why: To determine if you are leaving too many sugars behind.
How: Measured Points

Theoretical Points
Theoretical = Grain Points * Weight lbs
Measured = (Specific Gravity) - 1.000)) * 1000 * vol gals
Example Problem: 5 BBLs of 1.064 SG wort. Brewer used 265 pounds of grain at 40 ppg
Solution: 5 BBLS * 31 gallons/BBL = 155 gallons wort
(1.064) - 1.000)) * 1000 * 155 gallons
64 * 155 gallons =
9920 Measured Points
Theoretical = 40 ppg * 265
Theoretical =
10600 Theoretical Points
Brewhouse Efficency = 9920/10600
Brewhouse Efficency =
93.5 %

Class Problem:A brewer used 135 pounds of 2-row at 40 grain points, 30 pounds of caramel malt at 35 grain points, and 5 pounds of chocolate malt at 25 grain points. He brewed a 3 BBL batch and ended up with a final gravity of 1.058. What was his brewhouse efficency?
Solution: 40 grain points * 135 pounds = 5400
35 grain points * 30 pounds = 1050
25 pounds * 5 pounds = 125
5400 + 1050 + 125 = 6,575
(1.058 - 1.000) * 1000 = 58
58 * 3 * 31 = 5394
5,394/6,575 =
82%
BBLs, Kegs, Sixtel, Gallons, Liters
1 BBL = 31 gallons
1 BBL = 2 kegs (15.5 gallons)
1 BBL = 6 sixtels (5.2 gallons)

1 Keg = 15.5 gallons
1 Keg = 165 12oz Pours

1 gallon = 3.785 Liters
1 Liter = 1000 mL
1 mL = 1000 uL

Example = How many L are in 7 BBLs?
Ls = 7 BBL * (31 gallons/ 1 BBL) * (3.785 L / gallon)
= 821 Ls
Example : 15 degree Plato
SG = 259 / (259-15)
SG = 1.061
Problem : 12.2 degree Plato reading, what is the SG?
Solution
SG = 259 / (259-12.2)
= 259 / 246.8
= 1.049
Conversions
Brewhouse Efficency
Malt Calculations
IBU Calculations

Use the points to determine grain in pounds

6510 points Munich
6250 points Vienna
260 points Chocolate Malt

Munich = 35 PPG
Vienna = 35 PPG
Chocolate = 28 PPG

Munich Pounds = 6510 points / 35 PPG / 87%
= 213 pounds
Vienna Pounds = 6250 points / 35 PPG / 87%
= 205 pounds
Chocolate Pounds = 260 points / 28 PPG / 87%
= 9 pounds

Why: Certain styles of beer are best produced with distinct water profiles. Some water profiles are unsuited to produce certain styles of beer due to inadequate buffering capacity or other mineral issues.
How: Determine current water profile and how much mineral is needed.

Example: I have 34 ppm of calcium in my water, I need 100 ppm for proper enzyme activity. I have a 7 BBL brewhouse and will be adding CaSO4.
Remember: ppm is mg/L, so our answer will by in mg and we need to convert the volume to liters.

How: Determine total volume in Liters, amount of calcium needed in ppm, and percentage of calcium by weight in CaSO4 (23% by weight).

Solution: Ls = 7 BBL * (31 gallons/BBL) * (3.785 Ls/gallon)
= 821 Ls

ppm needed = 100 ppm desired - 34 ppm current
= 66 ppm needed

CaSO4 to add = 66 ppm / 0.23 (% of calcium by weight) * 821 Ls
=235,591 mg CaSO4
= 235,591 mg / (1 pounds / 453,592 mg)
= 0.52 pounds
Solution
Total Volume in Ls = 8 BBLS * 31 gallons * 3.785 Ls
Ls = 939 Ls

ppm to add = 100 - 9
= 91 ppm / .18 * 938.68 Ls
= 474554.89 mg
= 474554.89 * (1 pounds / 453,592 mg)
= 1.05 pounds
Hop Calculations
Why: To know how many hops to add!!!
How: Determine Hop Alpha Acid, Utilization, and Final Volume
Equation: Predicted IBU = Utilization * Alpha Acid * oz hops * 7490
gallons (final)
Example: IBUs from 2 oz of Galena at 60 min, 1 oz of Galena at 30 min, and 1 oz of Ultra at 5 min. Galena (13 % AA) Ultra (2.75 % AA) ( 13 % AA). Wort is 1.080 SG. Brewing 9 gallons.

IBU 60 = (20 % * 13 % * 2 oz * 7490) / 9 gallons
IBU 60 = 43.27

IBU 30 = (15 % * 13 % * 1 oz * 7490) / 9 gallons
IBU 30 = 16.22

IBU 5 = (3% * 2.75 % * 1oz * 7490) / 9 gallons
IBU 5 = 0.68

IBU Total = 43 + 16.22 + 0.68
IBU Total = 60.18
Equation: ozs Hops = Vol gallons * IBU
Utilization * AA% * 7490
Example: I want 24 IBUS in my 5 gallon pale ale at 1.040 SG from the 60 min addition.
ozs Hops = (5 gallons * 24 IBUs) / (23% * 5% * 7490)
ozs Hops = (120) / (86.14)
ozs Hops = 1.39 ozs
POP Quiz!!!!
Putting it all Together
Brewing a 10 BBL batch of Russian Imperial Stout.
Starting Plato: 18
Water Profile Currently: 58 ppm Calcium
Water Profile Desired: 270 ppm Calcium
Use CaCl2 at 23% Ca by weight
Malt: 73 % 2 row Malt @ 38 PPG
17 % Brown Malt @ 37 PPG
10 % Black Malt @ 22 PPG
Brewhouse Efficency is 86%
Hops: 58 IBUs for a 90 addition of 5% AA Fuggles
6 IBUS from a 15 min addition of 4% AA Hallertau
Utilization @ 90 mins = 25%
Utilizatoin @ 15 mins = 2%
Tell me...
how much calcium to add (pounds)
how much of each malt is needed (pounds)
how much of each hop is needed (pounds)
This is a given value that will be explained latter on
This is the theoretical
This is the measured
This tells me
total sugar I need,
what I am calling
"points"
This gives me
total sugar for
each grain.
This is simply converting mg to pounds.
Quiz Solution
First, convert plato and BBLs to gallons, liters, and SG

SG = 259 / (259-18)
SG = 259 / 241
SG = 1.075

Gallons = 10 BBLs * 31 gallons
Gallons = 310

Liters = 310 * 3.785
Liters = 1,173 Liters

Now you can work on the pounds of calcium
First, determine how much calcium to add
calcium needed = 270 ppm - 58 ppm
calcium needed = 212 ppm

Now figure out how much calcium to add
calcium to add = calcium needed / % by weight * Ls
calcium to add = 212 ppm / .23 * 1,173 Ls
calcium to add = 1,081,200 mg
calcium in pounds = 1,081,200 mg / 453,592
calcium in pounds =
2.38 pounds

Malt Calculations
The easiest way to figure out how many
pounds of malt you need is to first calculate
how much total sugar you need in terms
of SG units.
SG units = (1.075 - 1.000) * 1000
SG units = 75
SG total units = SG * gallons total
SG total units = 75 * 310
SG units = 23,250

Now you can determine how many units
you need from each grain.
2 row = 23,250 * 73%
2 row = 16,973

Brown Malt = 23,250 * 17%
Brown Malt = 3,953

Black Malt = 23,250 * 10%
Black Malt = 2,325

Quiz Solution
Now that you know how much SG units
is needed from each type of grain calculate
grain in pounds.
pounds of grain = SG units / PPG / Brewhouse Efficiency

Pounds 2-row = 16,973 / 38 PPG / 85%
Pounds 2-row =
519 pounds

Pounds Brown Malt = 3,953 / 37 / 85%
Pounds Brown Malt =
124 pounds

Pounds Black Malt = 2,325 / 22 / 85%
Pounds Black Malt =
122 pounds
Hops
oz of Hops = ( vol of beer in gallons * IBUs) / (Utilization * AA % * 7490)
oz of Hops 60 min = (310 gallons * 58) / (0.25 * 0.05 * 7490)
oz of Hops 60 min = (17,980) / (93.625)
oz of Hops 60 min = 192 ozs
pounds of Hops 60 min = 192 oz / 16 oz per pound
pounds of Hops 60 min = 12 pounds

oz of Hops 5 min = (310 * 6) / (.02 * .04 * 7490)
oz of Hops 5 min = (1,860) / (5.992)
oz of Hops 5 min = 310 oz
pounds of Hops 5 min = 310 oz / 16 oz per pounds
pounds of Hops 5 min = 19.4 pounds
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