Malt extractable sugar (as percent)

[D_BLOCK]

I've been reading up on all-grain brewing and the amount of sugars you can expect to get out of your malts. I don't understand how to convert the percent yield (weight of extractable sugar / weight of malt) to specific gravity or points per pound per gallon. I have a table that does this, but I am trying to understand an equation to do this.

I tried to do this with sucrose, which has a 100% yield. I came up with: (3.8 kg water + 1/2.205 kg sugar) / 3.8 L water = 1.119 kg/L. Thus, one pound of sugar dissolved in one gallon of water should yield a solution with a specific gravity of 1.119, or 119 GU points per pound per gallon.

However, this is off by a factor of ~2.6, as we all know the correct answer is 46 points.

I get the same thing when I calculate using metric units (points per kg per liter): (1+1)/1 = 2. So 1000 points. It should be about 386 points. Again I am off by a factor of ~2.6.

There must be something I am not understanding or something wrong with my methodology. Does anyone know how the values in those % yield to GU point conversion tables are derived?

I guess this isn't necessary to understand for the brewing process, but i figured someone on here may be able to come up with an answer.

THANKS

 

[david_42]

You've got some confusion in the terminology and your conversion.

1 lb = 454 gm

454/3785 = 11.9% AKA 11.9 Brix, not points. Points are about 4xBrix.

 

[D_BLOCK]

Thanks David.

I did convert the pound of sugar to kilograms (1 lb/(2.205 lb/kg) = .454 kg), sorry if that wasn't clear in my formula above. I thought if I took the weight of water in a gallon plus the weight of dissolved sugar, and divided by the volume (one gallon), that would give me the specific gravity (well, density in kg/L which is the specific gravity minus the units). It seems like it should, right? Converting that to points is just a formality.

Obviously I'm doing something not quite right though, because when you simplify the formula I posted above, it turns into 1 + Brix (3.8/3.8 + mass sugar / 3.8). Or maybe the specific gravity of the sugar solution can only be determined empirically?

 

[D_BLOCK]

Allright, so I figured out what was wrong in my original equation. It turns out dissolved sugar displaces a significant amount of water. I’m sure you all know this, but I underestimated the impact of this phenomenon. I determined roughly how much water is displaced per kg of sugar using the following equation:
(3.8 kg – volume displaced by sugar L * 1 kg/L+ .454kg)/3.8L = 1.046kg/L.
Solving for the volume of water displaced by the .454 kg of sugar yields .28 L. Thus, one kg of water displaces .616 L of water.

When I plug this number into the points/kg/L equation, the result works out. (1kg – (.616 kg/L * 1L) + 1 kg)/1L = 1.384. Which is pretty close to the tabular value of points per kg per liter of sugar.

Fascinating. I guess this could be useful if you are interested in determining how adding sugars (from malt or other sources) to your wort will affect the volume. I guess otherwise it has no use