Calculating Protein With The Pearson Square

When I read the comments on my "More Thoughts On Growing Animal Feeds" post, I realized that there are quite a few of you researching and pondering the same thing, and coming up with a similar conclusion, that it's a complicated and often discouraging topic. Methods and opinions often contradict one another, as does the research. For goats though, most agree that forage (grass, browse, hay) should be the mainstay of their diet, supplemented with grain as needed, free choice minerals tailored for one's particular location, and plenty of fresh water.

Here is something though, that is useful for those of us wanting to make our own grain mixes, whether homegrown or purchased. It's the Pearson Square, a tool that can be used to calculate the amounts of two components needed in a particular mix. It was originally developed to standardize the fat and protein contents in commercially produced milk. Since then, it has been used for wine making, juice mixing, cheese making, baking, and of course, feed formulation. I read about it awhile back but didn't undertand it until Karen sent me a couple of links, this one at Colorado State, and this one from the Virginia Cooperative Extension. The first article helped especially, and in an attempt to master it myself, I'm going to try to explain it to you!

It can be used for any animal and any nutrient, but since I've been pondering protein, that's what I'll use in my examples. I'll start with whole wheat and cowpeas, things I've grown successfully here.

Problem: Determine the amounts of whole wheat and cowpeas needed to mix a goat feed of 16% crude protein (CP).

1. Target amount goes in the middle of the square. 

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Example: I'm working on crude protein for goats, 16%

2. Values for the feed stuffs are placed at left hand corners

Rule: The number in the middle must be 

intermediary between the numbers at the corners

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Example: 16 is between 13 and 23

3. Find the differences across the diagonal

Rule: subtract the lower number from the higher. 
Number order doesn't matter, just the difference. 
Write these in the right hand corners across the diagonal

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Example:
16 - 13 = 3
23 - 16 = 7

4. Look across the horizontal legs of the square for the parts needed for the ration

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Example: Going from left to right, I would need 7 parts whole wheat
and 3 parts cowpeas to get a 16% crude protein ration

The parts are translated as weights, so for example, I could mix 70 pounds of whole wheat and 30 pounds of cowpeas to achieve a 100 pound dairy goat ration of 16%.

Obviously the Pearson Square is very useful if only two things are involved. But what if I have more? What if one year I harvested 100 pounds of wheat (13% CP), 50 pounds of grain sorghum (10% CP), 90 pounds of cowpeas (23% CP), and 45 pounds of black oil sunflower seeds (16% CP). How would I know what amounts to mix to get my 16%? This gets trickier. I would have to make two mixes first, figure out the crude protein in each mix, and then use the Pearson Square to calculate how much I'd need of each. Wheat and grain sorghum could be combined as my grain mix, while the cowpeas and BOSS would be my protein supplement. This means math!

Problem: Determine the amounts needed to make a 16% crude protein feed mix with more than two ingredients.

Step 1: Find the percentage of each component in the mix.

Using the grain mix as an example, I'd first need to find out what percent of wheat I have, and what percent of sorghum. The easiest way would be with an online percentage calculator like (click here) this one. In that case you can skip to Step 2. If you're having to do this out in the barn by hand, or just want to understand the process, the formula is

Formula to determine the percentage of the parts

Example: to find the percentage of each ingredient in my grain mix, I first need to know the total (whole) weight.

100 lb wheat + 50 lb sorghum = 150 lb total

100 lb of wheat is what % of 150 lb?

Plugged into the formula...

Calculating the percentage of wheat in my grain mix

100 divided by 150 is .6666666 parts of 100. Rounded up, it equals 67%. 100 lb of wheat would be 67% of my 150 pound grain mix.

For the grain sorghum, 50 lb of sorghum is what % of 150 lb?

Calculating the percentage of grain sorghum

50 divided by 150 is .3333333 parts of 100. Rounded down, it's 33%
50 lb of grain sorghum would be 33% of my mix.
CHECK: 67% wheat + 33% sorghum = 100% grain mix

Step 2: Find the protein in the grain mixture

The formula is:

So for my grain mix, I'd plug in the percentages I calculated, and the crude protein for each:

I would follow the same steps for my supplement of cow peas and BOSS. I'll spare you the calculations, but the answer would be a mix of 20% crude protein.

Step 3: Plug these numbers into my Pearson Square

Calculating the parts needed for a homegrown dairy goat grain mix

The equal number of parts in my final mix means I have a 50/50 blend of the two mixtures.

There is website to help you figure this out too, the online Pearson Square calculator at prechel.net. You need to know the percent of each mixture plus a target percentage, also the weights. The calculator will give you the weights of each component needed to achieve the goal. That goal could be any nutrient: protein, fat, calcium, etc.

When I researched crude protein in various grains and seeds, I discovered quite a variation in estimates. Soil condition plays a huge factor in this, the more deficient the soil, the lower the protein and other nutrients will be. For now, I thought it best to stick the lower percentages. As we improve soil fertility, I know the nutritive value of our grains, hay, vegetables, and forage will improve as well.

I don't know if that makes any sense to you dear readers, but writing it out like this has helped me tremendously. If it's still confusing please let me know. I had to work through my own examples to get a grasp on it and will have to refer back to this post when I actually start doing it. I'm just thankful to have another tool tucked under my homesteading belt.

For those of you interested in keeping a copy of this information handy, I've put it and more together in a little eBook entitled How To Mix Feed Rations With The Pearson Square: grains, protein, calcium, phosphorous, balance, & more. It includes the steps covered here plus information on commercial feed ingredients, choosing the right feeds for various farm animals, crude protein, nitrogen, phosphorous, feeding to prevent hypocalcemia, ketosis, and urinary calculi. Also contains charts of nitrogen, calcium, and phosphorous content of common feedstuffs. Click here for chapter listings and where to buy.

Calculating Protein With The Pearson Square © February 2012
by Leigh at http://www.5acresandadream.com/