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.

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Recipe Formulation with Water Calculations

In this post, we will formulate a new recipe and calculate the needed water amounts at the same time. This is not a big deal since the only real water change is the amount of water absorbed by the grains. Because we do not yet know the amount of grains we will use, we calculate the water from the target batch size back until we get to the water absorbed by the grains. At that point, we are able to calculate our grain amounts and then complete the water calculations. Rather than just talk about this process, I want to demonstrate the steps needed so that it serves as a complete example for reference.

Before moving on, I feel I need to make something clear: The Original Gravity (OG) and Final Gravity (FG) measurements are both taken from my fermenter. The OG is measured prior to adding the yeast for fermentation, and the FG is measured after fermentation has completed. This is important, and I did not make this distinction previously which could lead to some confusion when talking water amounts used in calculations.

OK, I am excited about this recipe because it is a first attempt at cloning my favorite beer: Goose Island's Bourbon County Stout. In this post, I do not want to get into my feelings towards the InBev purchase of Goose Island, so I will just summarize that my initial optimism and acceptance was turned sour by the discovery/learning of the unscrupulous InBev corporate views of the craft beer industry and their unethical business practices. So, all the better if the beer can be replicated at home. On to the recipe....

As I mentioned, I am excited to try and brew this beer, but the recipe guidelines are not from me. The grains and hops used are from the Goose Island description linked above; The gravity values used are from a post in the HomeBrewTalk forums (using the 2007 version of the beer); The grain percentages used are also from a post in HomeBrewTalk. Here are the specifics we are using:

Recipe Parameters

Parameter	Value
Batch Size (fermenter volume)	3.25 gal.
Target Original Gravity	1.13
Target Final Gravity	1.042
Color	Black ~100 SRM
IBU	60 (assume Tinseth method)
Length of Boil	80 min.
Mash Steps	Single infusion 152°F for 60 min.
Brewhouse Efficiency	70%

Grains

Grain	% Used	Max Extraction	Color (°L)
2-Row	34	37	1.8
Munich	30	34	10
Chocolate	14	34	350
Crystal 60	10	34	60
Roast Barley	10	25	300
Debittered Black (Briess Blackprinz)	2	25	500

Hops

Willamette 3.5% to 6.0% AA @60 min. ~4 oz. (TBD)

Yeast

Safale US-05 Dry Yeast 3 packets

STEP 1: Calculate Initial Water Amounts

Remember that the constants used in finding water amounts are specific to my system. Your values may be different. In some cases they are just guesstimates waiting for me to collect more accurate information

• V_final = 3.0 gal (amount in bottles or keg)
• bottling losses: ~ 0.25 gal.

• V_fermenter = 3.25 gal.
• Transfer and trub losses: ~0.75 gal.

• V_post-boil = 4.0 gal.
• Temperature shrinkage: 4% ~ 0.2 gal.
• 80 minute boiloff: 2.34 gal.

• V_pre-boil = 6.5 gal.

This is as far as we can get without knowing the grain amounts.

STEP 2: Estimate Grain Amounts

To summarize the values of interest here:

• Original Gravity: 1.13 (130 Gravity Points)
• V_fermenter : 3.25 gal.
• Brewhouse Efficiency: 70%

     ► Total Gravity (GT)

GT = Gravity Points * Volume

GT = 130 * 3.25

GT = 422.5

This is the total number of gravity points in our fermenter that we need to be contributed by the grains.

     ► Individual Grain Contributions to Total Gravity

Here we use the percentage of each grain used to determine the amount of gravity points each individual grain contributes.

Grain	Percent Calculation	Grain Contribution
2-Row	0.34 * 422.5	143.6
Munich	0.30 * 422.5	126.7
Chocolate	0.14 * 422.5	59.2
Crystal 60	0.10 * 422.5	42.25
Roasted Barley	0.10 * 422.5	42.25
Blackprinz	0.02 * 422.5	8.5

     ► Grain Amounts Needed to Achieve Gravity

Now we use the individual gravity contributions, the maximum gravity that can be extracted from the grain and our brewhouse efficiency to find the grain amount. Here is the equation used:

Grain Gravity Contribution / (Brewhouse Efficiency * Max Extract Points)

Grain	Formula	Value (lbs)	Value (lbs And oz)
2-Row	143.6 / (0.7 * 37)	5.5 lbs.	5 lbs. 8 oz.
Munich	126.7 / (0.7 * 34)	5.3 lbs.	5 lbs. 5 oz.
Chocolate	59.2 / (0.7 * 34)	2.5 lbs.	2 lbs. 8 oz.
Crystal 60	42.25 / (0.7 * 34)	1.8 lbs.	1 lbs. 13 oz.
Roasted Barley	42.25 / (0.7 * 25)	2.4 lbs.	2 lbs. 6 oz.
Blackprinz	8.5 / (0.7 * 25)	0.5 lbs.	0 lbs. 8 oz.
TOTAL:		18 lbs.	18 lbs. 0 oz.

STEP 3: Calculate Remaining Water Amounts

We now continue where we left off calculating our water amounts. Our last calculation was for the pre-boil volume, so we start there:

• V_pre-boil = 6.5 gal.
• Transfer loss: ~0.25 gal.
• Grain Absorption: 18.0 lbs. * 0.2 gal./lb. = 3.6 gal.

• V_total = 10.35 gal. ≈ 10 gal. 1.5 qt.
  
  

STEP 4: Calculate Mash and Sparge Volumes

For my mash, I am going to use 1.3 quarts of water per pound of grain. Also, remember that I have a full 4 quarts of space under my false bottom in my mash tun, so that needs to be added to the mash water.

V_mash = 1.3 qt/lb * 18.0 lbs + 4 qt

V_mash = 27.4 qt ≈ 6.85 gal. = 6 gal. 3.5 qt.

The sparge volume is now just a matter of subtracting the mash volume from the total volume.

V_sparge = V_total – V_mash

V_sparge = 10.35 gal – 6.85 gal.

V_sparge = 3.5 gal. = 3 gal. 2 qt.

Since I doubt I am 100% correct, I will make sure I have probably 5.0 gallons of sparge water available. I will just need to make sure I hit the proper volume in my boil kettle while watching the gravity readings of my runnings.

Conclusion and Remaining Information Needed

So that is it for calculating our grains and water. Of course, there is some information missing in regards to brewing the recipe:

1. We really didn't do anything with the hops. We know the IBU we need to hit, and I mentioned that we are using the Tinseth method for IBU calculations. Through that, we can estimate our hop amounts (it also depends on the actual %AA of the hops you purchase). Maybe this will be my next post.
2. Based on the gravity and volume amounts, I believe the 3 packages of dry yeast will be sufficient for this big beer. One thing we did not cover is the fermentation schedule (times and temps). This will definitely be racked to a secondary fermentation where we will allow the beer to sit on bourbon-soaked oak cubes for probably 6 months. I am not 100% sure, but I will probably let this sit in primary for two weeks; with week one being at a cooler temperature of maybe 60 degrees or so, and the second week at around 68 degrees. The secondary will be 6 months, and that temperature will probably be the same 68 degrees (not a lot of options for my basement).
3. Speaking of bourbon-soaked oak cubes, how much bourbon and how many cubes? Since we only have 3 gallons, I am assuming one 1 ounce cube. As far as the bourbon, I am not sure yet (amount or brand). I used Makers Mark and oak chips for my last beer and was less than happy, so this time I am moving to cubes and some other bourbon brand.

So these are questions that still need to be answered, but we are well on our way to making a first attempt at our clone. If this recipe doesn't work out, we get to drink what will probably still be a great beer and then try again. If it does work, we make more. Truly a win-win.

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.