Gravity/volume calculations

[FatsSchindee]

I posted this in the cider forum, but got no responses... The general math applies to beer, too, so maybe one of you can chime in... Thanks!

Did a quick search, but either nothing specific came up, or too specific (math I am too tired to try to comprehend right now). So my question is this: how do you adjust gravity when combining volumes of different gravity?







Here's my example:

I am making one gallon batches of cider (upstate mikes Carmel apple, in this case, with some adjustments). I took a reading of the Kirkland (Costco) juice I used;
Was 1.047 (at 79 degrees - but so were the rest of my readings, so shouldn't have to convert based on temp, right?). I poured half of the gallon into my 1gal glass jug, and added 1/2 cup dextrose to the remaining 1/2 gal in the plastic jug. After shaking/mixing it in, my reading was 1.062. (I also did a second batch using 1 cup dextrose - for comparison - and got 1.079 in the 1/2 gal of that one.)

I know that to convert to gravity points, you multiply volume by gravity. So I'd have 0.5 gal X 62 = 31 gravity points (or 0.5 X 79 = 39.5 grav pts for the second batch), and have 0.5 gal X 47 = 23.5 for the plain juice. So do I just add the two together (because they are equal volumes added together) to get the gravity of the combined one gal mixture? Thus... 31 + 23.5 = 54.5, or 1.055 (rounded up) for the first batch, and 39.5 + 23.5 = 63, or 1.063 for the second?

It seems intuitively correct (setting aside the fact that the sugar dissolved in the juice may increase the volume above 0.5 gal a bit... But should be negligible, no?), but just not sure if I'm doing the math correctly. I just want to make sure I'm then calculating the abv correctly (am factoring temp diffs/corrections to readings here, of course).

Thanks for any input!

(FG was 1.003 for first and 1.000 for second (corrected to 60*), after 12 days, having pitched onto a Nottingham yeast cake from two previous one gal batches (which is why I didn't take the OG reading from the mixed gallon after, I guess? Didn't want to lose the volume of the sample, or risk oxidation by putting it back into the jug with the yeast... I guess? I don't honestly remember!) Anyway, should give me an abv of around 7.2% for the first and 8.6% for the second, if my math is correct...)

 

[woozy]

1/2 gallon at 1.062 = 62 gravity points x .5 gallon = 31 gravity points-gallon
1/2 gallon at 1.047 = 47 x .5 = 23.5 gravity points-gallon.

A gravity point is a proportion. A gravity point-gallon is a specific quantitative amount.

Add 'em and you get 1 gallon that has 54.5 gravity points-gallon, a *specific* amount. Divide by the volume, 1 gallon, to get 54.5 gravity points (now a proportion) or 1.055.

*OR* simply say: since the original volumes are equal I'll get the average of the gravities. (1.047 + 1.062)/2 = 1.055.

In both cases the math is absolutely correct *and* absolutely the same.

A gravity point-gallon is kind of an abstraction. Technically it is 1/46 of a lb. (Because 1 lb of sugar into a gallon of water yields 46 gravity points). But it's true purpose is merely to convert gravity points as a proportion measure into measurable quantities for specific volume.

(setting aside the fact that the sugar dissolved in the juice may increase the volume above 0.5 gal a bit... But should be negligible, no?)

In theory, the sugar is completely soluable and does not effect the volume at all. ... in theory. That's actually the entire basis of the math.

 

[FatsSchindee]

Thanks for the response... That does clear it up.