If an example grain spec has:
The mass of sugars M should be given by:
Into 1 gallon, the degrees plato (P) should be:
Now, given that 1 lb sugar in 1 gal yields 1.046, the SG should be:
Now... the PDF at http://www.ams.usda.gov/AMSv1.0/getfile?dDocName=STELPRDC5091778 has a conversion table between Brix and SG. The interesting rows:
It seems to me like, while the calculated numbers are close, the degrees plato are off from the lbs sugar per gallon.
Am I calculating °P wrong? It should be (sugar wt / total wt) and there are ~8.34 lbs per gallon water (8 lbs / gal gets closer, but is less correct).
For distilled water: http://www.engineeringtoolbox.com/water-density-specific-weight-d_595.html
%FG = 80% (Fine Grain Extract Yield)
%M = 4% (Moisture)
G = 1 lb (mass of grain)
V = 1 gal (vol of water)
E = 100% (Mash efficiency - to make calculations easier)
%M = 4% (Moisture)
G = 1 lb (mass of grain)
V = 1 gal (vol of water)
E = 100% (Mash efficiency - to make calculations easier)
The mass of sugars M should be given by:
M = G * (%FG - %FG * %M / 100) / 100 * E
M = 1lb * (80% - 80% * 4% / 100) / 100 * 1 = 0.768 lb
M = 1lb * (80% - 80% * 4% / 100) / 100 * 1 = 0.768 lb
Into 1 gallon, the degrees plato (P) should be:
P = M / (8.34 lb/gal * V + M)
P = 0.768 lb / (8.34 lb/gal * 1 gal + 0.768 lb) * 100 = 8.43°P
P = 0.768 lb / (8.34 lb/gal * 1 gal + 0.768 lb) * 100 = 8.43°P
Now, given that 1 lb sugar in 1 gal yields 1.046, the SG should be:
SG = (%FG - %Meff)/100 * G * 46 pt*gal/lb * V * E / 1000 + 1
SG = 0.768 * 1 lb * 46 pt/(lb*gal) * 1 gal * 1 / 1000 + 1 = 1.0353
SG = 0.768 * 1 lb * 46 pt/(lb*gal) * 1 gal * 1 / 1000 + 1 = 1.0353
Now... the PDF at http://www.ams.usda.gov/AMSv1.0/getfile?dDocName=STELPRDC5091778 has a conversion table between Brix and SG. The interesting rows:
Code:
°P / SG @ 20°C / lb dissolved solids per Gal
8.4 / 1.03344 / 0.722
8.5 / 1.03385 / 0.731
8.8 / 1.03508 / 0.758
8.9 / 1.03549 / 0.767
It seems to me like, while the calculated numbers are close, the degrees plato are off from the lbs sugar per gallon.
Am I calculating °P wrong? It should be (sugar wt / total wt) and there are ~8.34 lbs per gallon water (8 lbs / gal gets closer, but is less correct).
For distilled water: http://www.engineeringtoolbox.com/water-density-specific-weight-d_595.html