Calculating The Hop Amount

Here we will calculate the amount of hops needed for our Bourbon County Stout clone recipe from the previous post. This calculation is greatly simplified by the fact that we have only a single hop addition and we know the final IBU. As stated in the previous post, we will be using the Tinseth method for IBU calculations. Let's take a look at that equation (Information from HowTo Brew):

IBU = (AAU * U * 75) / Volume of Recipe

• AAU = Alpha Acid Units = (weight of hops in oz. * % Alpha Acid of hops)
• U = Utilization factor, which is a factor of the wort gravity and boil time
• Volume of Recipe = the batch size = volume in fermenter (V_fermenter)

Now let's take a look at the utilization factor. We said it is a function of both gravity and time. Therefore we can express the equation for utilization as:

U = f(G) * f(t)

I won't go into an in-depth explanation of why these functions are relevant except to say that the bigger the beer (higher gravity) the less effect the hops will have (the utilization factor decreases). The amount of time the hops are boiled also affects the IBU's.  The longer the boil, the more the alpha acids are isomerized (the utilization factor increases). The equation for each function is:

f(G) = 1.65 * 0.000125^(Gboil - 1)

f(t) = [1 - e^(-0.04 * t)] / 4.15

• Gboil = pre-boil specific gravity or specific gravity at time of hop addition if added later in the boil
• t = time in minutes that the hops are in the boil

We already know the IBU of the recipe,but we need to calculate the hop amount. Therefore we rearrange our IBU calculation to solve for the AAU:

AAU = (IBU * Volume of Recipe) / (U * 75)

Also, remember that

AAU = Weight of hops in ounces * %AA of hops

So far we have all the information needed to solve the equations except for the gravity of the boil (Gboil). Actually, Gboil should be the gravity at the time of the hop additions. In our recipe specifics from the previous post, we know that we are boiling for 80 minutes, and adding the hops with 60 minutes remaining in the boil. From the post on water amounts, we know that I lose 0.117 qt/min. For 20 minutes of boil time (counting down from 80 minutes to 60 minutes), we will lose about 2.34 quarts of wort. The pre-boil volume calculated in the previous post was 6.5 gal or 26 quarts. This means we will have a volume of 26 – 2.34 = 23.66 quarts (about 6 gal.) at the time we add the hops.

We now know our wort volume at the time of the hop addition, but we need to know the gravity at this time. For this, we use the fact that the sugar in the wort remains constant– it is the concentration that changes due to volume changes. This means that the gravity points multiplied by the volume at point 1 is the same as the gravity points multiplied by the volume at point 2. The equation looks like this:

G1 * V1 = G2 * V2

We know the gravity and volume in the fermenter, and we know the volume at the time of the hop addition. Therefore, we rearrange the equation to solve for G2 (point 1 represents the fermenter and point 2 represents the boil):

Gboil = (Gfermenter * Vfermenter) / Vboil

Plugging in the numbers:

Gboil = (130 * 3.25) / 6.0 = 70.4

Represented as specific gravity: 1.0704

In this manner, you can calculate the expected specific gravity values for various points in the process (namely pre-boil) and augment the recipe with DME as necessary in order to hit the expected original gravity. That exercise is for a future post. In the meantime, we now have all the data needed to plug into the IBU equation and find our needed hop amounts. Let's summarize the data we have:

Variable	Value
IBU	60
Volume of recipe (Vfermenter)	3.25 gal
Time in minutes (t)	60 min
Gboil	1.0704

Let's start plugging in these numbers.

Utilization Equations

f(G) = 1.65 * 0.000125^(1.0704 - 1)
f(G) = 0.876

f(t) = [1 - e^(-0.04 * 60)] / 4.15
f(t) = 0.219

U = 0.876 * 0.219 = 0.192

IBU Equation

AAU = (60 * 3.25) / (0.192 * 75)
AAU = 13.54

Hop Amount

Recall that AAU can be represented with the equation:

AAU = weight of hops in ounces * %AA of hops

Solving for the weight in ounces:

weight of hops in ounces = AAU / %AA of hops

Our recipe calls for Willamette hops, which have a %AA in the range of 3.5 to 6.0. For this example, we will assume that the %AA = 4.75 (average value). When I purchase the hops, I will use the %AA on the package and re-calculate the number of ounces needed. For now, we get a good ballpark value:

weight of hops in ounces = 13.54 / 4.75

weight of hops in ounces = 2.85

Summary

We calculated our utilization number,but we could have just used a simple lookup table found here. You will see that we are right in line with the table values. I do question whether or not the volume in the fermenter should be used, or if we should have used the volume after boiling. I'm not sure it matters since these equations are nothing more than estimates. It is more important that we solve for the equations in the same manner each time, and that we use the same equation each time (Tinseth as opposed to Daniels or Rager or Mosher or....). Through the consistent use of equations, we build up correlations between the IBU value and the hop profile sensed in the beer.

Posted with Blogsy

Recipe Formulation

This post is going to be all about formulating your own recipe.  Sure, there are plenty of recipes out there for you to brew, but there is a feeling of accomplishment when you brew a beer that is of your own making.  I think you gain a greater understanding of the process as well.

Before going through the steps, I need to point out that I use an iPad app for brewing called iBrewmaster.  This software allows you to create recipes and store them, track batches and share information.  The app also comes with a large database of existing recipes you can use and tweak.  The software is important to mention because I use it for refining the recipe initial estimates, which I will go over later.

Create a Recipe

Step 1: Determine the malts and hops that should be used

In this step, we want to determine which grains will be used and the percentage of each grain for the mash.  We also want to find which hop(s) to use and how long they should be boiled.

I like to leverage the work others have performed.  Some day I hope to be smart enough to immediately know which grains to use for a particular style, but right now I am not that smart. So I will go to our friend Google and perform a search for say "Northern England Brown Ale Recipe".  By the way, all the different style names can be found in the BJCP Style Guidelines.

Anyway, I will go through a dozen or so different existing recipes and keep track of the grains and hops used and their quantity (as a percentage of the total).  Reading the BJCP guidelines for the style will also help in determining the ingredients.  Once I have chosen the most popular grains and hops, I like to go read the grain descriptions and possibly modify the grain bill based on flavors I am looking for.

Once you know the style you are brewing, we can list our known parameters:

• Target Original Gravity: 46 gravity points
• Vfermenter: 6 gallons
• Brewhouse Efficiency: 70% (just use it, we will cover this in a later post)
• Recipe grains, percentages and maximum gravity points:

Grain	Percentage	Gravity Points
Maris Otter	66%	38
Crystal 60	13%	34
Brown	10%	32
Carapils	08%	33
Chocolate	03%	34

Step 2: Determine the amount of each grain needed

In order to find the amount of each grain, we must first calculate the total extract from the grains.  Total extract is calculated with the following equation:

Etotal = GU x V

GU: Gravity units
V:    Volume

The total extract remains constant in the wort.  So, for example Etotal prior to the wort being boiled is the same as Etotal after the boil.  We happen to know the gravity and the volume post-boil (our known parameters above).

Etotal = 46 x 6.0 = 276

Now that we know the total extract from the grains, we can calculate how much each grain contributes to this total extract amount by multiplying the total extract by the percentage of each grain:

• Maris Otter = 0.66 x 276 = 182.16
• Crystal 60 = 0.13 x 276 = 35.88
• Brown = 0.10 x 276 = 27.6
• Carapils = 0.08 x 276 = 22.08
• Chocolate = 0.03 x 276 = 8.28

With the extract provided by each grain, we can now calculate the amount of grain needed to achieve the extract amount.  This is calculated with the following equation:

Grain Amount = grain extract total / (brewhouse efficiency x grain gravity points)

• Maris Otter = 182.16/(0.7 x 38) = 6.8 lbs = 6 lbs 13 oz
• Crystal 60 = 35.88/(0.7 x 34) = 1.5 lbs = 1 lb 8 oz
• Brown = 27.6/(0.7 x 32) = 1.2 lbs = 1 lb 3 oz
• Carapils = 22.08/(0.7 x 33) = 1.0 lbs
• Chocolate = 8.28/(0.7 x 34) = 0.35 lbs = 0 lbs 5 oz

Step 3: Refine the results
It seems we should be done now that we have the grain amounts, but the values need further tweaking.  Also, we have done nothing with hops to this point.  For this, I use the iBrewmaster iPad app.  The grains, grain amounts, hops and hop amounts are input into the iBrewmaster app.  The target volume and boil time are also input.  One of the coolest features of this app is that I can now set the appropriate style for the beer (Northern England Brown Ale) and check all the parameters against this style:

• ABV
• IBU
• Original Gravity
• Final Gravity
• SRM

If the beer is outside the BJCP range for any of these values, the app will let you know.  Here is an example where all the ranges are good:

If I choose a different style - Dry Stout, for example - you can see that I am not within the proper ranges (yellow means you are close; red means you are way off):

Typically, I seem to run into issues with the SRM value and I end up lowering the amounts of the dark grains.  Here also is where I refine my hop amounts and/or hop varieties used.

So this final step is really just about tweaking values until I am within the proper ranges.  Of course, no one says that you must be in these ranges.  Go ahead and brew whatever you want and feel free to experiment.  But, if you plan on entering your beer into a competition, you probably want to stay within the proper style specifications.

The technique outlined in step 2 was taken from Designing Great Beers by Ray Daniels.