This week, I take a look at how to calculate the appropriate starter size for home brewing beer with liquid yeast. In part 1 of this in-depth series on yeast, I covered how you can calculate the required pitching rate (number of yeast cells needed) for a given batch of beer, understanding the viability of yeast over time, and also how to hydrate and use dry yeast. This week, I’ll finish the detailed calculations for liquid yeast as well as provide a summary on how to do the entire end-to-end calculation.
I ended part 1 on yeast starters explaining that all liquid starters are not created equally. The growth rate of the yeast (number of ending cells divided by the number of starting cells) varies depending on the pitching rate of the yeast. In fact if we pitch a typical liquid yeast package (vial or large smack pack) of 100 billion cells into starters of varying size we get the graph to the right. This is extracted from “Yeast, A Practical Guide” by Chris White and Jamil Zainasheff.
What this shows is that 100 billion cells pitched into a 2 liter starter will only grow to a bit over 200 billion cells (growth rate of 2.05), while the same 100 billion cells in a 20 liter (5+ gallon) starter will grow to about 600 billion cells (growth rate of 6.0). However, a 20 liter starter is essentially no starter at all if your batch of beer is only 20 liters.
In part 1, I covered how to calculate the ideal number of cells needed for an average batch of beer. A sample 5.25 gallon ale at 1.048 gravity needed about 177 billion yeast cells. So using the graph at the right, a 100 billion cell packet pitched into a starter of just over a liter would be sufficient for this beer. However, if we factor in viability (the aging of the yeast which was also covered in part 1), a larger starter of 2-3 liters is needed, since we won’t be starting with a fully viable 100 billion cell yeast package.
Since you don’t want your starter to be so huge it is a major fraction of your beer, the practical range most home brewers operate in is really on the left end of this graph – typically 1-4 liters for a five gallon batch. This means that in most cases, you will not achieve a growth rate above 3.0 for your starter unless you use a multi-stage starter.
The above graph is great if you always pitch a 100 billion cell starter and are always brewing a 5.25 gallon batch, but often this is not the case. To generalize the above graph, we need to use it with larger or smaller starters and batch sizes.
It turns out this is not hard to do – since yeast growth depends primarily on the starting population and amount of wort available. To calculate starter size for the generic case we need to introduce a new term called the “inoculation rate”.
The amount of yeast per unit volume you start with is called the “inoculation rate”. Inoculation rate is typically expressed as millions of cells per milliliter of wort. For example, a 100 billion cell yeast pack in 2 liters of wort would work out to 50 mil/ml (50 million cells per milliliter). Inoculation rate is really easy to calculate, since you just take the starting number of cells and divide by the size of your starter. The math gets easy when you realize that 1 billion cells into a liter is the same as 1 million cells per milliliter.
So if we look at growth as a function of inoculation rate (see graph), we can see the same effect as described earlier – high growth only occurs in starters with relatively low inoculation rates. Since most homebrewers are using a 100 billion cell starter in 1-4 liters of wort (inoculation rates above 25 mil/ml) – we’re basically working on the left end of the graph at growth rates below 3.
In practice, very large starters are often not desirable for the homebrewer so often you need to start with more than one vial/pack of liquid yeast in a batch. Doing this limits the growth rate needed so you don’t end up with a starter that is almost as big as your beer batch itself.
For example, lets look at making the same 5 gallon batch from a single small size (not the large one) Wyeast smack pack. Assuming the package is new (100% viable with 18 billion cells), the 5 gallon batch which we calculated needed 177 billion cells would give us a growth rate of 177/18 = 9.83. No matter how large a single starter is we are not going to get a growth factor greater than 6.0.
The alternative is to use two small smack packs in the starter which gives us 177/(2*18) = 4.91 growth. However, this is still a huge starter – since looking up a 4.91 growth on the chart gives us a starter size of nearly 4 gallons (15 liters) to make a 5 gallon beer. Clearly this won’t work either.
In practice, you need to limit the growth of the starter generally to less than a factor of 3.0 so you don’t make a starter that is almost as large as your finished beer. You can do this by upping the number of packets each time your required growth goes over 3.0. So in the above example, moving to three small smack packs gives us a required growth of 177/(3*18) = 3.2 growth and four small smack packs gives 177/(4*18) = 2.45 growth. So four small packets would be needed with (from the chart) a starter of approximately 3.5 liters.
Knowing this now, its usually best to calculate the number of packets first, adjusting the growth rate needed, and then calculating the actual starter size.
Here’s a summary of the entire yeast starter calculation from end to end as a step-by-step process:
Calculate the total number of yeast cells needed for your batch based on the starting gravity and volume of your batch. It is typically expressed in billions of cells – and recommended you pitch 0.75 million cells per milliliter per degree plato for ales, 1.5 mil/ml-P for lagers and 1.0 mil/ml-P for hybrids. If you are not used to working in plato and milliliters, the english equivalents would be (approximately): 0.71 billion cells per gallon per point of specific gravity for an ale, 1.42 bil/gal-point for a lager and 0.948 bil/gal-point for a hybrid. A sample 1.050 gravity, beer would have 50 gravity points and for a 5 gallon batch need -> 1.42 x 50 x 5= 355 billion cells.Calculate the Viability of Your Yeast Packs – As covered in part 1, Wyeast and White labs large tubes/packs have a little over 100 billion cells when new, and the small Wyeast pack has about 18-20 billion cells. However, these packages lose about 20% of their cells per month of aging. So a 100 billion pack/vial would only have about half of its cells (51 billion) viable after three months.Calculate the Growth Rate Needed – Divide the total number of yeast cells needed by the number of viable cells in your yeast pack. So if you are brewing the lager mentioned above which needs 355 billion cells from a single pack of yeast that is one month old (which has about 80 billion cells), the growth rate needed is 355/80 which is 4.4.Decide if You Need More Packs or a Multi-Step Starter – If you need to achieve a growth rate above 3.0, it is probably time to look at adding more yeast packs to your starter or creating a multi-step starter. The reason is that beyond a growth rate of 3.0, the starter sizes start to get very large relative to the size of your batch of beer. In the example we just mentioned (growth rate of 4.4) you would need to have a starter of well over 10 liters (almost 3 gallons) to get that growth level in our 5 gallon batch. Buying a second yeast pack would cut the growth rate needed down to a more manageable level of 2.2.Look Up the Innoculation Rate – Now that we know the growth rate needed, and have adjusted it down a bit (to less than 3.0) if needed, we can determine what our initial inoculation rate should be. The easy way to do this is by looking at the graph above and work backwards. Find your desired growth rate on the Y axis, and then look up the needed inoculation rate on the X axis. For example if we need a growth rate of 2.2, the inoculation rate is approximately 50 mil/ml.Find the Starter Size – Since we know how many total yeast cells we are using for our starter based on the viability and number of yeast packs, and we have the inoculation rate, we can just divide the two to get the starter size. Divide the number of viable cells in your yeast pack by the inoculation rate to get the starter size. For the example we’ve been tracking, we decided in step 4 to use two starter yeast packs, each with 80 million viable cells for a total of 160 million cells. We found our inoculation rate from step 5 would be 50 mil/ml (which is also 50 billion cells/liter). Dividing the two we get 160/50 which is 3.2 liters – so a 3.2 liter starter is ideal here.Create the Starter – Once you have the size, you need only create the starter itself. An ideal starting gravity for your yeast starter is 1.036 (9 plato). To create the starter, just open BeerSmith (or your favorite tool), create a blank recipe with the starter size, and add enough dry malt extract to reach a starting gravity of 1.036 for your starter. If you don’t have the tool handy, a good rule of thumb is about 0.2 lb of dry malt extract per quart of starter (or 90 grams/liter).The whole process is a bit complex, which is why I’ve added a separate calculator to the upcoming version of BeerSmith to make it much easier. Thank you for joining me on the BeerSmith Home Brewing Blog – I hope you will subscribe for more great articles, and have a great week!
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