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# Ciphering Fruit Beers

In recent years, fruit beers have seen an increase in popularity among both craft beer drinkers and homebrewers. They no longer are (if they ever really were) the beer that “non-beer drinkers” sip at the brewpub while their significant others wax poetic about the more “serious” styles.

One of the challenges associated with brewing fruit beers is determining the impact fruit additions — generally added to primary or secondary fermenters — have on the base beers’ gravities and alcohol levels. This is partly because there’s no way to directly measure the effective combined original gravity (OG) of a beer after fermentation has begun (or perhaps finished) and fruit has been added. All too often, the answer to the question “How much will ‘X’ weight of fruit increase my beer’s ABV?” is answered with the incomplete, “It depends on the fruit.” A better answer is that it depends on both the fruit and the beer, and it’s all about the volumes and concentrations.

There are fruit addition calculators available online, but the ones I have experienced have all been lacking in significant ways. In most cases, they ignore the fact that fruit contributes both fermentable and non-fermentable components (especially water) and therefore overestimate the effective original gravities and the alcohol by volume (ABV) of the final beers.

In 2019, a popular Midwest brewery known for its “slushy” beers found itself in the public spotlight after grossly overstating the ABV on its beer can labels. Lesson learned: Don’t treat fruit as if it’s just a sugar addition and call it a day! I did manage to find one calculator that purported to take water into consideration, but it did so in a way that always resulted in an estimated ABV increase, without asking the user anything about the base beer. In fact, many fruit additions can actually decrease a beer’s ABV, depending on the original beer and the type of fruit.

The goal of this article is to present a new model for predicting the impact of fruit additions, including the effective combined OG, final gravity (FG), and ABV for beer/fruit combinations, using a reasonable amount of input data that is readily available. With just a handful of characteristics, some of which we’ll need to calculate first, we can estimate the impact of any fruit addition to any beer. We’ll need the following characteristics:

Volume, OG, and FG (expected or measured) of the base beer

Volume, OG, and expected FG of the fruit addition

Readers will already be familiar with where to get their base beer numbers. Let’s assume the following for our base beer:

5 gallons (19 L)

OG = 1.060

FG = 1.012

ABV = 6.3%.

This article will focus on obtaining and calculating the fruit information, and then on how to combine it with the base beer’s information.

#### Basic Fruit Information

To estimate original and final gravity numbers for any particular fruit, we will need:

Nutritional data, i.e. serving size, total carbs per serving, and sugar per serving

Water content as a percentage of weight (and thus water per serving)

Percent of non-fermentable carbohydrates that are soluble

For most fruits, water content as a percentage of weight is an easy Google search. Similarly, searching for “nutrition” for a fruit will provide serving size, total carbs per serving, and sugar per serving.

For the percent of non-fermentable carbs that are soluble (and therefore contribute to gravity) we can use an estimate of 35%. (See the model assumptions sidebar near the end of this article for more details.)

Based on a Google search, for our example of boysenberries we’ll use 87% water, a serving size of 284 grams, total carbs of 35 grams per serving, and 20 grams of sugar per serving. Note that 87% water x 284 grams per serving = 247 grams water per serving, and that 35 grams total carbs – 20 grams sugar = 15 grams non-fermentable carbs.

#### Calculating the Fruit Characteristics

Continuing on, we need to calculate the estimated volume, OG, and expected FG for the fruit addition. We already have all the data we need; it’s just a matter of applying a little math. We’ll start with the OG.

Fruit Original Gravity

If you already have the fruit you plan to use, and can spare enough to obtain enough juice, you can measure its gravity directly. This is where a refractometer comes in handy as you can measure the gravity with just a few drops of juice. Otherwise, we can compute an estimate.

To calculate the estimated OG for the fruit itself, we’ll need to first compute soluble carbs per serving, which equals the sugar per serving, plus the portion of non-fermentable carbs per serving that are soluble. Here’s the general formula that I have come up with:

Ss + (Cnfs × Ps) = Grams Soluble Carbs per Serving

Where:
Ss = Sugar (in grams) per serving
Cnfs = Non-fermentable carbs (in grams) per serving
Ps = Percent non-fermentable carbs that are soluble

For our boysenberries the equation looks like this:

20 + (15 × 35%) = 25.25

Knowing that we have 25.25 grams total soluble carbs per serving, we use that along with the 247 grams water per serving to compute OG. The 25.25 g of soluble carbs are, by weight, 9.3 percent of the total of soluble carbs and water together (272.25 g), so the concentration is 9.3 degrees Plato (°P). A general formula for converting °P to Specific Gravity (or OG) is:

259 / (259 – °P) = OG

For our boysenberries:

259 / (259 – 9.3°P) = 1.037 OG

For anyone getting a little nervous about all of the math, don’t worry. I have created and made available a free calculator, loaded with lots of dropdown selectable fruits, that removes the drudgery. (Details are at the end of the article.)

Fruit Final Gravity

Now that we have measured or estimated the fruit’s OG, we will need to estimate its apparent attenuation so that we can use it along with the OG to estimate the fruit’s final gravity. We can estimate the apparent attenuation by computing a weighted average apparent attenuation for all of the fruit’s soluble carbs (including sugars and soluble non-fermentable carbs).

The general formula, made simpler by a 0% attenuation for soluble non-fermentable carbs, looks like:

(Ss × As) / Css = Fruit Apparent Attenuation

Where:
Ss = Sugar (in grams) per serving
As = Apparent attenuation of sugar
Css = Soluble carbs (in grams) per serving

For our boysenberries, we use the 20 grams sugar and 25.25 grams total soluble carbs per serving:

(20 × 122%) / 25.25 = 96.6%

The formula above makes the assumption that the sugars from fruit are 100% fermentable (100% real attenuation), with an apparent attenuation of 122% (see attenuation sidebar near the end of this article). This leaves the non-fermentable soluble carbs with 0% apparent attenuation.

With the fruit’s OG and apparent attenuation, we can easily compute the fruit’s estimated FG. In general:

OGf – [(OGf −1) × Af] = Fruit Final Gravity

Where:
OGf = Original gravity of fruit
Af = Apparent attenuation of fruit

For our boysenberries:

1.037 – [(1.037 − 1) × 96.6%] = 1.001 Fruit Final Gravity

#### Fruit Volume

So far, we haven’t been concerned with how much fruit is in the addition. But to go further, we need to know its volume, i.e. the volume contributed by the water and soluble carbs in the fruit. We do not want to count any of the other fruit components, such as cellulose, because they won’t be participating in the liquid mix along with the beer. In other words, we only want the “effective” volume.

Suppose we’ll be adding 5 lbs. (2.3 kg) of boysenberries to our beer. We need to estimate the liquid volume they will contribute. To do that, we’ll first compute an “Effective Weight per Total Weight (EWpTW),” i.e. the percentage of the fruit’s total weight that will participate in mixing with the beer, namely the portion of its weight that is water and soluble carbs. The general formula is:

(Ws + Css) / SVs = Effective Weight per Total Weight

Where:
Ws = Water (in grams) per serving
Css = Soluble carbs (in grams) per serving
SVs = Serving size (in grams)

For our boysenberries:

(247 + 25.25) / 284 = 95.9%

This means that for every 1 lb. (0.45 kg) of boysenberries, approximately 0.96 lb. (0.44 kg) will homogenize with the beer, and the rest will be solids left behind.

Next, we need to determine the “Gallons per Effective Pound (GpEP)” of the fruit. Again, we’re only interested in the volume of water and soluble carbs that will participate in the mix with the beer, and not other fruit components. The general formula is:

0.1199 gallons per pound / Fruit OG = GpEP

The formula above uses a constant 0.1199 gallons per pound of water and the previously determined OG of the fruit to compute gallons per effective pound. Here it is applied to our boysenberries:

0.1199 gallons per pound / 1.037 = 0.116

This tells us that for each effective pound of boysenberries we can expect ~0.116 gallons of effective volume.

Now that we have Effective Weight per Total Weight (EWpTW) and Gallons per Effective Pound (GpEP), we can compute the effective volume contributed by the fruit. Here’s the general formula:

Total Fruit lbs. × EWpTW × GpEP = Gallons Fruit Volume

For our 5 lbs. (2.3 kg) of boysenberries:

5 × 95.9% × 0.116 = 0.556

Again, this is not the total physical volume occupied by the fruit, but rather the volume contributed by the stuff that will intermix with the beer, i.e. the “effective” volume.

#### Bringing It All Together

As you’ll recall from the introduction, we needed the following information to estimate the impact of fruit on ABV:

Volume, OG, and FG (expected or measured) of the base beer

Volume, OG, and expected FG of the fruit addition

We now have all of that:

Base beer: 5 gallons, 1.060 OG, 1.012 FG (6.3% ABV)

Boysenberries: 0.556 gallons, 1.037 OG, 1.001 FG

We can now calculate a weighted average OG and a weighted average FG for the combined beer and fruit contributions. Here’s the general formula for weighted average gravities:

[(Gb × Vb) + (Gf × Vf)] / (Vb + Vf) = Combined Gravity

Where:
Gb = Gravity of beer
Vb = Volume of beer (in gallons)
Gf = Gravity of fruit
Vf = Volume of fruit (in gallons)

For our base beer plus boysenberries weighted average (combined) OG:

[(1.060 × 5) + (1.037 × 0.556)] / (5 + 0.556) = 1.0577

Similarly, we can calculate the weighted average (combined) FG:

[(1.012 × 5) + (1.001 × 0.556)] /  5 + 0.556 = 1.0109 Combined FG

All that’s left is to apply a standard ABV calculation to the combined OG  and FG. Here is a formula for ABV:

(OG − FG) × 131.25 = ABV %

Applying the general ABV formula to our example, we get:

(1.0577 − 1.0109) × 131.25 = 6.1% ABV

Note that the final predicted ABV is 6.1%, which is lower than base beer’s 6.3%. This decrease is not uncommon for beers with fruit additions. It’s also worth noting that if we had simply treated the boysenberries as a sugar addition, ignoring the volume contributed by the water and the soluble non-fermentable carbs, we would have predicted a final ABV of about 6.8%. Depending on the base beer and fruit involved, the differences in results can be even more extreme.

Of course, before packaging a fruit beer, we’d want to get an actual post fruit fermentation FG measurement, to use along with the estimated weighted average OG to calculate an estimated ABV. Commercial brewers should, of course, not rely on an estimated ABV where regulations require otherwise.

I mentioned a calculator that removes the math drudgery, as well as the need to research fruit characteristics. The calculator is an excel workbook called FruitCalc, and it’s a free download available at http://sonsofalchemy.org/library in the “Brewing Software” section. The same logic is also integrated into BrewCipher, which can be downloaded from the same site.

In summary, fruit additions add a level of complexity to our beers’ effective gravities and ABVs. Taking into account the fruits’ effective volumes as well as fermentable and non-fermentable carbohydrate contributions can lead to a more accurate estimate of their impacts.

#### Model Assumptions (sidebar)

Like most models, this fruit additions model makes some assumptions. Here are some of them, the reasoning behind them, and what you could do differently if you choose.

Fruit Fermentability
The model assumes that all of the sugars (but not other carbohydrates) in a fruit are fermentable, i.e. have 100% real attenuation. This is because for the most part sugars in fruits are simple sugars. Depending on the fruit, there may be small amounts of more complex, unfermentable sugars. However, detailed information on fruit sugar profiles is somewhat hard to find, and of those that can be found, many do not even identify sugars that are present in very small amounts. That said, if you would prefer to make an assumption of, say, 95% (real) attenuation instead of 100%, simply replace the 122% (apparent) attenuation number (As) in the fruit weighted average apparent attenuation formula (in the “Fruit Final Gravity” section) with 115.9% (i.e. 122% x 95%), for example.

Homogenization of the Beer and the Fruit
The model assumes that all the water, sugar, and soluble non-fermentable carbs in the fruit will interact with and homogenize with the base beer. If you believe some of the water/soluble carb content of the fruit will not be reached by the beer, a factor could be applied to the fruit’s volume (Vf) in the combined OG and combined FG calculations.

Non-Fermentable Carbohydrates Solubility
This is the approximate portion on the non-fermentable carbohydrates that are soluble. The 35% value was derived by looking at nutritional data for many fruits and their corresponding commercial juices, and determining what percentage of the fruits’ non-fermentable carbs transfer to the juice. The average value was 35%, which can be used in the absence of juice data for a specific fruit. The rationale is that non-fermentable carbs that end up in juices are likely soluble, and

those left behind (cellulose, for example) are not soluble. I have measured the gravity of some commercial fruit juices, and the results were quite consistent with all of the juices’ listed carbs (or some equivalent amount of other soluble compounds) being dissolved in the juice. Because the soluble non-fermentable carbs are not fermentable, they are present in both the OG and FG. Varying this value won’t have a significant effect on the ABV answer, but in some cases may nudge it, due to the impact the carbs have on volumes. If you would prefer to use some other value for the percentage of non-fermentable carbs that are soluble, simply use it in place of the Ps value in the “Grams Soluble Carbs per Serving” calculation.

The Case of Non-fermented Fruit
The model assumes that the sugars in the fruit are allowed to ferment out. However, if the brewer will add fruit and then pasteurize the beer, or otherwise halt fermentation, ABV is only affected (reduced) by dilution. In this case, the combined ABV can be computed as a volume weighted average of the base beer’s ABV and 0% ABV for the fruit.

Simply use the weighted average OG (or FG) formula from the “Bringing It All Together” section of the article, substituting ABV values for the gravity values.

#### Real Attenuation and Apparent Attenuation (sidebar)

The fruit addition model assumes that the sugars (but not the other carbohydrates) in fruit are 100% fermentable, meaning 100% “real” attenuation.

When we measure gravity with a hydrometer, comparing final gravity (FG) to original gravity (OG), the attenuation we compute by the formula (OG – FG) / (OG – 1) is “apparent” attenuation rather than real attenuation. Apparent attenuation is always a larger number than real attenuation. The reason is that the alcohol in the beer is less dense than water. Therefore the FG is skewed downward by the alcohol, and is lower than would be expected simply from the loss of the fermentable sugars.

To compute apparent attenuation from real attenuation, we can multiply real attenuation by 1.22. Thus our 100% real attenuation is approximately 122% apparent attenuation, and that’s what we use in the model for the fruit sugars.

For a more thorough treatment of attenuation, check out http://braukaiser.com/wiki/index.php/Understanding_Attenuation.

## Fruit Recipes

#### Blood Orange Hefeweizen

(5 gallons/19 L, all-grain)
OG = 1.053  FG = 1.013
IBU = 9  SRM = 4   ABV = 5.2%

Blood orange is a perfect match for the banana and clove of a traditional hefeweizen. The OG and SRM are for the base beer. The FG and ABV include the fruit addition.

Ingredients
4.3 lbs. (1.95 kg) German Pilsner malt
6.4 lbs. (2.9 kg) pale wheat malt
2.1 AAU German Hallertau hops (55 min.) (0.55 oz./16 g at 3.8% alpha acids)
49 oz. (1.4 kg) blood orange purée
1⁄2 tsp. yeast nutrient (10 min.)
White Labs WLP300 (Hefeweizen Ale), Wyeast 3068 (Weihenstephan Weizen), or SafAle WB-06 yeast
7⁄8 cup corn sugar (if priming)

Step by Step
Mill the grains and dough-in, targeting a mash of around 1.5 quarts of water per pound of grain (3.1 L/kg) and a temperature of 154 °F (68 °C). Hold the mash at 154 °F (68 °C) for 60 minutes. Mash out or begin recirculation, then sparge with enough water to yield a total volume of 5 gallons (19 L) of post-boil wort.

Boil for 70 minutes, adding hops and yeast nutrient as indicated. Chill wort to 70 °F (21 °C) and transfer to a sanitized fermenter. Do not oxygenate beyond incidental splashing. Pitch yeast and ferment at 70 °F (21 °C), adding the orange purée at high kräusen.

When final gravity has stabilized, package and carbonate the beer to 2.8 volumes of CO2

Extract with grains option:
Replace the Pilsner and pale wheat malts with 5.9 lbs. (2.7 kg) Bavarian wheat dried malt extract. Bring 4.7 gallons (17.8 L) of water, plus the amount of water expected to boil off in 60 minutes, to a boil.

Remove the kettle from heat and stir in the dried malt extract. Return to a boil. Boil for 60 minutes. Follow the remainder of the all-grain recipe.

Tips For Success:
If controlling mash chemistry, target a pH of about 5.3.

Add rice hulls to the mash, or have some on hand, in case of a stuck lauter.

If kegging, consider backsweetening in the keg with 12 fl. oz. (350 mL) of frozen orange juice concentrate.

#### Boysenberry Crème Blonde Ale

(5 gallons/19 L, all-grain)
OG = 1.065  FG = 1.024
IBU = 15  SRM = 5   ABV = 5%

This fruit beer straddles the line between decadent and quaffable. The OG and SRM are for the base beer. The FG and ABV include the impact of the fruit addition.

Ingredients
4.9 lbs. (2.2 kg) Golden Promise pale ale malt
4 lbs. (1.8 kg) 2-row brewer’s malt
0.5 lb. (0.23 kg) light Munich malt (6 °L)
0.5 lb. (0.23 kg) pale wheat malt
2 lbs. (0.9 kg) lactose (30 min.)
4.3 AAU Cascade hops (60 min.) (0.6 oz./17 g at 7.2% alpha acids)
5 lbs. (2.3 kg) frozen boysenberries
1⁄2 tsp. yeast nutrient (10 min.)
White Labs WLP002 (English Ale), Wyeast 1968 (London ESB Ale), or LalBrew London ESB Ale yeast
3⁄4 cup corn sugar (if priming)

Step by Step
Mill the grains and dough-in, targeting a mash of ~1.5 quarts of water per pound of grain (3.1 L/kg) and a temperature of 150 °F (66 °C). Hold the mash at 150 °F (66 °C) for 60 minutes. Mash out or begin recirculation, then sparge with enough water to yield a total volume of 5 gallons (19 L) of post-boil wort.

Boil for 60 minutes, adding hops, lactose, and yeast nutrient at indicated times remaining. Chill the wort to 66 °F (19 °C) and transfer to a sanitized fermenter. Oxygenate thoroughly.

Pitch yeast and ferment at 66 °F (19 °C) until gravity has stabilized, or nearly so. Thaw and crush the boysenberries. Split and chop the vanilla bean. Rack beer into a secondary fermenter, on top of the boysenberries and vanilla bean. Alternatively, add the boysenberries and chopped vanilla bean to the primary fermenter, avoiding splashing.

Ferment for about a week at 70 °F (21 °C), or until the sugars in the fruit are fermented out.

Package and carbonate the beer to 2.5 volumes of CO2.

#### Boysenberry Crème Blonde Ale

(5 gallons/19 L, partial mash)
OG = 1.065  FG = 1.024
IBU = 15  SRM = 5   ABV = 5%

Ingredients
4.8 lbs. (2.2 kg) extra light dried malt extract
0.5 lb. (0.23 kg) light Munich malt (6 °L)
0.5 lb. (0.23 kg) pale wheat malt
2 lbs. (0.9 kg) lactose (30 min.)
4.3 AAU Cascade hops (60 min.) (0.6 oz./17 g at 7.2% alpha acids)
5 lbs. (2.3 kg) frozen boysenberries
1⁄2 tsp. yeast nutrient (10 min.)
White Labs WLP002 (English Ale), Wyeast 1968 (London ESB Ale), or LalBrew London ESB Ale yeast
3⁄4 cup corn sugar (if priming)

Step by Step
Mill the grains and conduct a partial mash with about 2 quarts (1.9 L) of water and a mash temperature of 150 °F (66 °C). Hold the mash at 150 °F (66 °C) for 60 minutes. Wash the grains with 2 qts. (2 L) of hot water, then add enough water to yield a total volume of 5 gallons (19 L) of post-boil wort.

Raise to a boil, remove the kettle from the heat, and stir in the dried malt extract. Return to a boil. Boil for 60 minutes. Follow the remainder of the all-grain recipe.

Tips For Success:
If boysenberries are not available, raspberries are a good substitute.

If controlling mash chemistry, target a pH of about 5.4.

Because of the large amount of lactose, expect the specific gravity to be near 1.027 when it’s time to add the boysenberries and vanilla.

Spritz the vanilla bean with Star San solution before splitting and chopping.

Issue: May-June 2021