

08202009, 02:58 AM

#1

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Promash grain bill % seems off.


I love using Promash but one thing that bugs me is that I cant simply input percentages of each grain then set the SG and have the program figure out how many pounds of each grain to use. I end up calculating this out by hand using the method in Ray Daniels Designing Great Beers. Ex. SG 1.060 total gravity points for a 6 gallon batch would be 360 (6 x 60), then use take your % you want say 80% base malt (360 x .80) = 288. Potential extraction of american 2 row in promash is 1.036 multiply by efficiency (36 x .75) = 27. Points needed from base malt/corrected extract efficiency (288/27)= 10.67 lbs of grain needed. When I follow this method for all my grains the percentages in promash are different than those I calculated. Any ideas on why this is?
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12022009, 02:26 PM

#2

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Hello Marshal,
The % column in promash is the percentage of weight.
The Ray Daniels Formula in DGB calculates the percentage of extract.
if you were to use the DGB formula and kept the potential extract of each grain the same for all grains (say 1.037) then it would relay correctly to promash
give it a try and let me know how you go
Does this make sense or help?
Rob.
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12082009, 04:43 AM

#3

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Hey Guys,
My above comments only work when using grains, when you add sugar (eg something with higher pppg (say 1.045) it throws it out.
Does anyone have a formula for calculating out the percentage of weight?
Rob.



12092009, 02:08 PM

#4

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Yes, provided you can solve a set of linear equations. Let's say you are doing a recipe with crystal 60 and 2row and want the final gravity to be 1.050, and want 2row to be 15 percent of the grain bill. 2row gives 36 ppg, and crystal 60 gives 34 ppg. Let x1 be the pounds per gallon of 2row and x2 be the pounds per gallon of crystal 60. The equations are:
x2/(x1+x2) = 0.15 or 0.85*x2  0.15*x1 = 0 (this is the equation for 15% c60)
36*x1 + 34*x2 = 50 (the equation for og points)
Now, since we have two variables (x1,x2) and two linearly independent equations, there is a unique solution (which you can get by solving for one variable in one eq. and plugging it into the other, or by matrix algebra), and it is:
x1 = 1.19048 pounds per gallon of 2row
x2 = 0.21008 pounds per gallon of c60
Then, of course, you multiply these numbers by however many gallons you want to make.



12162009, 10:31 AM

#5

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Rocketman768,
first of all you are a gentleman and a scholar for taking your time to explain this too us
I understand everything up to "36*x1 + 34*x2 = 50 (the equation for og points)" but don't understand enough algebra to solve the 2 variables (x1 and x2) for the 2 linear equations and how you got the x1 and x2 values.
The last part (converting to gallons) is easy.
If you don't want to explain the mathematics, please feel free to link to a web page that does.
Cheers
Rob.



12162009, 03:27 PM

#6

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Piggybacking on rocketman, if you're looking for an O.G. of 1.050 and you want 85% base (pppg 36) and 15% crystal 60 (pppg 34) you can look at like this.
O.G. if 50 points per gallon. Crystal will be 15% of the 50 which is 7.5 points. 7.5 divided by the 34 pppg that crystal offers per pound yields .22 pounds per gallon.
The base malt is 85% of the 50 which is 42.5 points. Base malt offers 36 points per pound so 42.5 divided by 36 will yield 1.18 pounds per gallon.
I truncated some of the decimals and used 100% efficiency for simplicity.
If you do want to account for efficiency just divide your pounds of grain by your efficiency. Example 1.18 pounds divided by 75% means you'll actually need 1.57 pounds of grain.
Hopefully I didn't overlook anything.
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12162009, 04:53 PM

#7

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Quote:
Originally Posted by randyrob
Rocketman768,
first of all you are a gentleman and a scholar for taking your time to explain this too us
I understand everything up to "36*x1 + 34*x2 = 50 (the equation for og points)" but don't understand enough algebra to solve the 2 variables (x1 and x2) for the 2 linear equations and how you got the x1 and x2 values.
The last part (converting to gallons) is easy.
If you don't want to explain the mathematics, please feel free to link to a web page that does.
Cheers
Rob.

No problem. Usually, Gaussian elimination is used to solve systems of linear equations. http://en.wikipedia.org/wiki/Gaussian_elimination
This page has an example in both equation and matrix form. Go through it and then go through my problem and see if you get the same answer as me. I think you'll find Gaussian elimination comes up A LOT in daily life (even in brewing beer).



12172009, 10:47 PM

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Let me give you another example of the power of linear equations and formulating your recipe. Let's take my example above. Now, since I have 2 variables, I must have exactly 2 equations to get a unique solution. If I'm willing to drop the equation specifying the percentage of C60, I can replace it with an equation so that I'll hit a target SRM. For example, if I want the SRM to be 12, this means that I need 20 MCUs. Since 2row is about 3L and c60 is 60L, replace the first equation with:
3*x1 + 60*x2 = 20
Now you're hitting both a target color and a target OG. The price you had to pay is that you can't control the exact amount of C60 you're using (which of course makes practical sense). Of course more variables (more types of grain) means more equations and more flexibility.



12192009, 05:37 AM

#9

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I've been trying to follow your method for a simple 3 ingredient
recipe as follows:
Pale Ale Malt (X) 38pppg 85%
Cane Sugar (Y) 46pppg 10%
Black Patent Malt (Z) 25pppg 5%
OG 60pppg
Now, applying your first method we get:
X/(X+Y+Z) = 0.85
Y/(X+Y+Z) = 0.10
Z/(X+Y+Z) = 0.05
We can convert these to:
0.15X  0.85Y  0.85Z =0
0.10X + 0.90Y  0.10Z =0
0.05X  0.05Y + 0.95Z =0
Applying your 2nd method, we get:
38X + 46Y+25Z = 60 (based on extracts)
Now this is where I get stuck. My basic understanding of Gaussian
Elimination tells me I need 3 equations to solve for 3 variables. Is
this right?
In practice I only have 2:
0.15X  0.85Y  0.85Z =0
38X + 46Y+25Z = 60 (based on extracts)
Which in matrix form look like:
[+0.15 0.85 0.85  0]
[38 46 25  60]
If I run a Gausssian Elimination on this, I get:
[ 1 0.0 0.4553566 1.3010205]
[ 0 1 0.9196429 0.22959186]
Which doesn't give me a value for X, Y and Z.
Am I missing something?
Cheers
Rob.



12192009, 02:13 PM

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Yup. You are missing something. You actually have 2 linearly independent equations for grain percentage, not just 1. What linearly independent means is that you can't describe one equation as a linear combination of the others. An intuitive way to explain this is: suppose I tell you I have 3 grains and I tell you the first one is 85% of the bill. Can you uniquely determine the percentages of the other 2? No. I need to tell you that the second one is 10% or that the third one is 5%. So, this means you can use any 2 of the 3 percentage equations you wrote. In general, if you have N types of grain, you can specify up to N1 equations for percentages. Now you have 3 independent equations and you can find the solution. I find that the solution is:
X = 1.34
Y = 0.157
Z = 0.0786
Let me expound a minute on the result you just obtained with the 2x3 matrix. You got
[ 1 0.0 0.4553566 1.3010205]
[ 0 1 0.9196429 0.22959186]
To put this back in equation form:
X = 0.455*Z + 1.30
Y = 0.919*Z + 0.230.
In these cases (underdetermined systems), you can still get a solution, but it's not unique. Notice if we just pick Z, we'll have a solution. Z is what we'd call a "free" variable in the solution. However many free variables you have is how many more equations you need in order to get a single unique solution.





