Malt extract brewers: after adding extract to your kettle, do you often find that your volume is too big and your gravity is too low? The reason why is because malt extracts contribute volume in addition to gravity. The good news is that you can compensate for it without math. You just need to heat less water than you normally would, dissolve your extract and top up the kettle with water until you reach your target volume. Done! That said, there are times when it's helpful to know your water volume. For example, if you want to treat your water.
In the case of extract beers, the solution is pretty simple. If you use dry malt extract, you can assume it adds 0.075 gallons per pound. If you use liquid malt extract, you can assume it adds 0.084 gallons per pound. The only complication is that your pre-boil wort volume will probably be measured hot while your water volume will probably be measured cold, and water expands when it's heated. To calculate the hypothetical cold volume of your pre-boil wort, you can use the following formula:
Cold Wort Volume = Hot Wort Volume x Hot Water Density / Cold Water Density
The density of tap water is around 8.33 lbs/gal and, if you stir your malt extract into near-boiling water, you can assume the hot water density will be 8.04 lbs/gal. From there, you can calculate your required water volume by plugging in your cold wort volume into the following equation:
Required Water Volume = Cold Wort Volume - (Malt Extract Volume Contribution x Malt Extract Weight)
It's not difficult at all, but we should drive the point home with an example. Let's assume your target pre-boil volume is 6.9 gallons and you'll be using 6.3 lbs of dry malt extract. Here's your required water volume in two easy steps:
Cold Wort Volume = 6.9 gal x (8.04 lbs/gal) / (8.33 lbs/gal) = 6.7 gal
Required Water Volume = 6.7 gal - 0.075 gal/lb x 6.3 lbs = 6.2 gal
Speaking of water treatments, I've read that malt extract batches should be brewed with distilled or RO water because water minerals survive the malt extract production. However, I've never seen any quantitative data to support the claim. Do extract manufacturers treat their water supplies to achieve optimal mash pHs? Are certain minerals retained more efficiently than others? If you're an extract brewer who's willing to measure your pre-boil pHs and provide some basic data on your recipes (brewing with untreated tap water is fine), give me a holler at the email address in my profile. If I learn anything useful, I'll done post it to this here weblog.
---------- This line separates the practical stuff from the geeky stuff ----------
Calculating the required water volume was pretty easy, but I had to figure out the malt extract volume contributions myself. Hey, maybe this website will become the go-to the place for people look up those values! That would be super cool. Anyway, I'm going to show you how I arrived at those numbers so you can figure out the impact of any adjunct on your required water volume. Here's a quick outline of the process:
-Figure out your ingredient yield.
-Calculate your the cold volume of your pre-boil wort.
-Calculate the total mass of your wort.
-Convert the target specific gravity of your wort to degrees Plato.
-Calculate the required mass of your ingredient.
-Calculate the required mass of water.
-Convert the required water mass to a volume.
-Calculate the volume contribution of your ingredient.
To illustrate the calculations, let's assume your target pre-boil volume is still 6.9 gallons. Instead of assuming a weight of malt extract, though, let's assume your target pre-boil gravity is 1.042 and you'll be using a dried malt extract called Briess CBW Pilsen Light.
Yield is the percentage of an ingredient's weight that contributes to wort gravity. Differences in yield are the reason why dried malt extracts result in higher wort gravities than equivalent weights of liquid malt extract (liquid malt extracts have more water than dry malt extracts, which contributes to weight but not gravity). There are a number of ways to figure out your ingredient yield. Sometimes you can look it up on the manufacturer's website. Often, you'll find data for a similar ingredient and decide it's close enough. Occasionally, you'll need to make a sample solution and do some math. In the case of our example, Briess provides a table that results in a yield of 97%*.
Figuring out your cold pre-boil wort volume is exactly the same as our earlier example. It's 6.7 gallons.
Since specific gravity is defined as density divided by the density of water, and density is defined as mass divided by volume, you can figure out the mass of your wort as follows:
Wort Mass = Specific Gravity x Cold Water Density x Cold Wort Volume = 1.042 x 8.33 lbs/gal x 6.7 gal = 58.2 lbs
If you have a problem with lbs as a unit of mass, feel free to use the gravitational acceleration at your local altitude to convert your known weights to slugs and back. I'll be drinking beer and laughing at you. Either way, the next step is to convert your target specific gravity to degrees Plato with the following equation (if you want to know why the conversion is different than other formulas you may have encountered, you can read my long-winded explanation here):
GP = ((116.716 x SG - 569.851) x SG + 1048.046) x SG - 594.914 = ((116.716 x 1.042 - 569.851) x 1.042 + 1048.046) x 1.042 - 594.914 = 10.5 P
Degrees Plato, the unit of gravity used by many commercial brewers in the US, is the mass percentage of dissolved sugar in wort. If you know the mass of your wort and the percentage of that mass that comes from dissolved sugar, you can figure out the total mass of dissolved sugar. The total mass of dissolved sugar is commonly called 'extract', which is easy to confuse with 'malt extract'. When a brewer says 'extract' and it's not obvious they're referring to an ingredient, they're probably talking about the mass of dissolved sugar. Once you know how much extract your wort should have, you can use your ingredient yield to figure out the required mass of your ingredient. After subtracting your ingredient mass from your wort mass, you'll be left with the mass of your water. Here are the calculations for extract, ingredient mass and water mass:
Extract = (GP/100) x Wort Mass = (10.5 P / 100) x 58.2 lbs = 6.1 lbs
Malt Extract Mass = Extract / (Yield/100) = 6.1 lbs / (97/100) = 6.3 lbs
Water Mass = Wort Mass - Malt Extract Mass = 58.2 lbs - 6.3 lbs = 51.9 lbs
Rearranging the definition of density will allow you to calculate your required water volume:
Required Water Volume = Mass / Density = 51.9 lbs / (8.33 lbs/gal) = 6.2 gal
To figure out how much volume the malt extract adds per pound, I subtracted the water volume from the cold wort volume and divided it by the mass of malt extract:
Malt Extract Volume Contribution = (6.7 gal - 6.2 gal) / 6.3 lbs = 0.079 gal/lb
Finally, I repeated the calculation for a wide range of target gravities to verify that it remained constant. But I used 0.075 gal/lb in the earlier example, right? It's true! The difference was caused by rounding errors that don't occur when you automate your calculations in a spreadsheet. For example, it would have been silly of me to claim your malt extract mass was 6.2812 lbs and your water volume was 6.2275 gallons. If you want to do the easy water calculations, 0.075 gal/lb is the number to use.
*Ingredient manufacturers often report their yields as either (a) the specific gravity of 1 gallon of wort made with 1 lb of the ingredient or (b) the weight of the ingredient, in lbs, required to make 1 gallon of wort at a certain specific gravity. In either case, Yield (% wt) = 100000*(SG-1)/Wt/46.2.