Top-down Brew: Recipe technical information

An old legal saying is that the devil is in the details. If details are important to you, the following technical information explains some of the inner workings and assumptions that the recipe calculators are based upon.

For the mash, the calculator begins by determining the total number of gravity points that are needed for a particular batch. (If gravity points are unfamiliar to you please check out this explanation from Brad Smith, the creator of BeerSmith software.) The next step is to use the percentage of each malt type from the user input to determine the gravity points that are needed for each grain type. The final step for each grain is to determine the weight that will be needed to achieve the desired gravity points.

Here is an example to illustrate how it works. Let's say that we want to produce 5 gallons of wort at a specific gravity of 1.050. The total gravity points for this beer will be 5 (gallons) * 50 (gravity points; from 1.050) for 250 total gravity points.

The next step is to determine the percentages that compose the wort. The simple recipe for this example will be for a wort that is 5% medium crystal malt and the rest (95%) will be two-row base malt. For 5% of the wort, we will need to get 12.5 gravity points of crystal malt (250 gravity points * .05 percent as a decimal = 12.5 gravity points of crystal malt). This is the first part of the formula that will go in the numerator.

To determine the corresponding crystal malt weight it will be necessary to know our mash efficiency and the theoretical gravity points from our grains. For this example we will use a mash efficiency of 75%, which is a good estimate for mashes that use batch sparging, and a value of 1.034 for the specific gravity of crystal malt. Multiplying the possible gravity points (34) by efficiency (.75) gives us 25.5. In other words, we can get 25.5 gravity points from each pound of crystal malt in our system. This part forms the denominator of our overall formula.

To complete the calculation, we need to divide the crystal malt gravity points that we need (12.5) by the amount that we can get from a pound of malt (25.5). Doing this step yields 12.5/25.5 = .490 lbs. Rounded off, we will need 1/2 lb of crystal malt for our recipe.

In summary:

[5 (gallons) * 50 (gravity points) * .05 (crystal malt percentage)] / [ 34 (crystal malt gravity points) * .75 (mash efficiency)] = approximately .5 lb crystal malt

Let's do the base malt now:

[5 (gallons) * 50 (gravity points) * .95 (base malt percentage)] / [ 37 (base malt gravity points) * .75 (mash efficiency)] = approximately 8.5 lbs of two-row malt

The calculator is careful to distinguish between the differences in efficiency for malts vs. sugars or malt extracts. The calculator adjusts the theoretical gravity points for each grain by the mash efficiency, as shown in the above example. For sugars and malt extracts, the efficiency is calculated at 100%.

An important part of the mash assumptions is that the percentages that the user enters are the percentages of the gravity points in the final wort composition. This is reasonable because from a top-down viewpoint what we really care about the most is the percentages in the final wort, not the weights of the ingredients going into the wort. This raises a cautionary note. Calculating the percentages for the wort may not be the same as calculating malt percentages by weight. The reason for this is that some malts vary significantly in regard to their extract potential. For example, the potential yield from two-row malt is 1.037 but the yield from roasted barley is only about 1.025. Some stout recipes call for 10% roasted barley by weight. If we factor in the lower yield of roasted barley, a 10% by weight corresponds to about 6% of the gravity points in the final wort. The practical implication is that entering 10% (percent by weight) into the present calculator (which uses percent by gravity points) might result in excessive amounts of roasted barley. Please be careful to not use percent by weight and percent of gravity points interchangably, because these are not quite the same due to the gravity differences between malts.

A similar approach is used to determine the hop weights that are needed for the late hop additions. The calculations begin with the user entering the overall target of IBUs for the recipe. If desired, the later aroma or flavor hop additions can be declared as a percentage of total IBUs. For example, a pale ale recipe might call for 30% of the IBUs to come from a late hop addition to the boil. The percentage of IBUs needed for the late hops is used to calculate the weights needed for the late hop additions. The remaining IBUs for the bittering hop additions are then calculated to determine the main hop addition. This approach, which is calculating the late IBUs first and the bittering IBUs last, is recommended by Ray Daniels in Designing Great Beers.

There are a number of assumptions that influence the calculation of IBU utilization. The boiling gravity change during the time course of the boil is somewhat crudely estimated by subtracting 1.001 from the target specific gravity for each 10 minutes of the boil. The IBU calculations for the bittering and flavor hop additions are based upon the Tinseth formula for hop utilization. A limitation of the Tinseth formula is that it does not calculate utilization for aroma hop additions added at zero minutes. This fails to model the abundant evidence suggests that hop bitterness is extracted as long as the wort temperature stays above 170F. To address this problem, the hop utilization of aroma hops (defined as <5 minutes of boil time) is conservatively estimated to be 5%. This 5% value for utilization of aroma hops is based upon a recent study of bitterness from aroma and steeped hops, which found that the utilization of steeped hops was consistently about 4% to 5% under a variety of conditions.

The yeast pitching rates are based upon the pitching formula of million cells * milliliters of wort * degrees Plato of the wort (White and Zainasheff, 2010, p. 122). The pitching rate is then translated into approximate amounts of commonly used homebrew yeast sources. The estimates of yeast cells in a gram of dry yeast varies widely, ranging from 5 billion to 20 billion. The estimate of 10 billion cells per gram of dry yeast is used in this calculator, which is the same as the calculator from brewersfriend.com. The number of cells in a White Labs tube or Wyeast smack pack is estimated to be 100 billion, but the actual number of yeast cells may be less due to aging that occurs after packaging. The number of tubes needed is rounded up, but not down, because it is not practical to use less than a full tube or smack pack. Estimating yeast cell numbers from a yeast starter is complicated. The simple formula used here estimates that one tube/pack in a two liter starter will produce about 200 billion cells (see White and Zainasheff, 2010, p. 143). The two liter starter represents an optimal trade-off for getting significant yeast cell growth yet not having a starter that creates a large volume. For more complex estimates of yeast starter cell growth please try using the excellent calculators provided by Mr. Malty or Brewer's Friend. In sum, the yeast pitching estimates are a ball-park figure that will point you in the right direction, but it is difficult to exactly project the number of yeast cells from homebrew yeast sources.

The default values for the malt specific gravities and the hop alpha acids are mostly from the BYO.com resources pages, such as the grains and adjuncts chart page and the hops chart page. If the resource guide gives a range of values, such as 5 to 6% alpha acids, the default value is an average of the high and low values (5.5%). In a few cases, values have been obtained from homebrewing books, like Beer Captured, or from other web sites.

Some checks have been built into the software. For example, if the specialty grains are over 100% it will produce an error message. Although a few checks are present, the software relies to a large degree on your own expertise and good judgment. Putting extreme values into the calculations might yield some odd recipes. There is no computer solution for inputs that are misguided.

It is important to acknowledge the limitations of the present calculator. The program has been deliberately kept simple in some regards. In part, this is due to the limitations of a web-based computation. An infinite number of choices for grains and hops is simply not feasible. Likewise, complex late hopping schedules may be beyond the capability of this software.


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