Calculating potential alcohol on Chocolate Raspberry Port

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bakervinyard

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I’m at a loss! I need help calculating the alcohol percentage on my Chocolate Raspberry Port.
int. Sg was 1.020
chaptalization at sg of 1.017
after chaptalization sg of 1.028
final sg was 1.007
can anyone chime in ?
Thanks in advance, Bakervinyard
 

bakervinyard

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Paul initial sg was 1.120
fermented down to 1.017
after I added the chaptalization pack, sg was 1.028
final sg was 1.007
I posted the wrong initial sg at 1.020

sorry for the confusion, Bakervinyard
 

sour_grapes

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Okay, that makes more sense.

The bad news is that we don't yet have enough info to get you an exact number. The good news is that we can get you close.

The WRONG way to do this calculation is to just add all the delta-SG values, and multiply by 131. To wit: [(1.120-1.017)-(1.028-1.007)]*131= (0.103+0.021)*131=0.124*131=16.2%. However, that ignores the increase in the volume due to the chaptalization. Therefore, it is an overestimate of the ABV.

To do better, you need to figure out the ounces (say) of ethanol after the first fermentation, and figure out the increase in volume due to chpatalizing. Next figure out how many additional ounces (say) of ethanol are produced in the second fermentation. Then add that to the initial ounces of ethanol, and divide by the final volume to get a better estimate of the ABV. However, I do not know how you chaptalized. I don't know what the characteristics of the chaptalization pack.

In previous exercises, I have found that chaptalizing with dry table sugar should result in an ABV about 0.5% less than the crude estimate outlined in the calculation above. If you use simple syrup, it is about 1% less.

We canot say more until we know more about the chaptalization pack. However, I would hazard a guess of about 15% for you final ABV.

EDIT: Obviously, there was a small typo.
Instead of [(1.120-1.017)-(1.028-1.007)]*131= (0.103+0.021)*131=0.124*131=16.2%,
I meant [(1.120-1.017)+(1.028-1.007)]*131= (0.103+0.021)*131=0.124*131=16.2%.
 
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BernardSmith

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Okay, that makes more sense.

The bad news is that we don't yet have enough info to get you an exact number. The good news is that we can get you close.

The WRONG way to do this calculation is to just add all the delta-SG values, and multiply by 131. To wit: [(1.120-1.017)-(1.028-1.007)]*131= (0.103+0.021)*131=0.124*131=16.2%. However, that ignores the increase in the volume due to the chaptalization. Therefore, it is an overestimate of the ABV.

To do better, you need to figure out the ounces (say) of ethanol after the first fermentation, and figure out the increase in volume due to chpatalizing. Next figure out how many additional ounces (say) of ethanol are produced in the second fermentation. Then add that to the initial ounces of ethanol, and divide by the final volume to get a better estimate of the ABV. However, I do not know how you chaptalized. I don't know what the characteristics of the chaptalization pack.

In previous exercises, I have found that chaptalizing with dry table sugar should result in an ABV about 0.5% less than the crude estimate outlined in the calculation above. If you use simple syrup, it is about 1% less.

We canot say more until we know more about the chaptalization pack. However, I would hazard a guess of about 15% for you final ABV.
Of course, I may be mistaken, but why would the calculation be so complicated? Why would any change in nominal volume be critical? (not a rhetorical question) no matter the added volume , we are measuring the gravity, not calculating it: this measurement does not depend on us KNOWING the amount of sugars added or the increase in volume. If after the first fermentation the SG was 1.017 and then the sugar pack was added and the gravity rose to 1.028 then that change is 11 points.
So...
SG 1.120 - 1.017 (interim FG) = 1.103 +1.011 (actual chaptalization) = 1.114 - 1.007 (actual FG) = 1.107 * 131 = 14% ABV. No?
 

sour_grapes

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No. It doesn't work that way. (As an aside, it is very difficult to interpret thought processes when you use an = sign when you don't REALLY mean that the left and right sides are, in fact, equal to each other. So it is possible I am misunderstanding your procedure.)

Here is an example that may help you see where your process leads to the wrong answer.

Joe mixes up a 1-gallon batch of must with a SG of 1.100. He let's this ferment down to 1.010. [At this point, the ABV should be about (1.100-1.010)*131 = 11.8%.]

He then adds a 600 gallon vat of apple juice with SG = 1.050 to this gallon. After this chaptalization, the SG will now be about 1.0499. Joe lets this ferment down to 1.000.

By your procedure, as I understand it, we calculate that the that we have 1.100 - 1.010, or a change in SG of 0.090. Later, we had a change in SG of 1.0499 - 1.000, or a change of 0.0499. Se we conclude that our total change is 0.090 + 0.0499 = 0.1399, giving us a ABV of 0.1399*131 = 18.3%. So, somehow, we magically made the 600 gallon batch of cider, having a PA of about 6.5%, into a potent brew with 18.3%, just by adding it to a gallon of juice (that itself had a PA of 13%). I wish it were that easy!

If I have misunderstood your proposed procedure, please let me know how you would calculate it your way.
 

BernardSmith

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No. It doesn't work that way. (As an aside, it is very difficult to interpret thought processes when you use an = sign when you don't REALLY mean that the left and right sides are, in fact, equal to each other. So it is possible I am misunderstanding your procedure.)

Here is an example that may help you see where your process leads to the wrong answer.

Joe mixes up a 1-gallon batch of must with a SG of 1.100. He let's this ferment down to 1.010. [At this point, the ABV should be about (1.100-1.010)*131 = 11.8%.]

He then adds a 600 gallon vat of apple juice with SG = 1.050 to this gallon. After this chaptalization, the SG will now be about 1.0499. Joe lets this ferment down to 1.000.

By your procedure, as I understand it, we calculate that the that we have 1.100 - 1.010, or a change in SG of 0.090. Later, we had a change in SG of 1.0499 - 1.000, or a change of 0.0499. Se we conclude that our total change is 0.090 + 0.0499 = 0.1399, giving us a ABV of 0.1399*131 = 18.3%. So, somehow, we magically made the 600 gallon batch of cider, having a PA of about 6.5%, into a potent brew with 18.3%, just by adding it to a gallon of juice (that itself had a PA of 13%). I wish it were that easy!

If I have misunderstood your proposed procedure, please let me know how you would calculate it your way.
But my assumption is that a sugar pack is a nominal increase in volume. That was something I explicitly specified, and while bakervinyard made no mention of the volume, I assumed because there was no mention that the change in volume was statistically insignificant - 100 cc? in 4 L or 23 L ( a half cup more in 1 gallon or 5 gallons) ? and not 600 TIMES the original volume. If the volume is for all intents and purposes the same, then all we are doing is adding more sugar and not significantly changing the volume.. IF - IF the volume was significantly increased then your concern is absolutely correct.
 

sour_grapes

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But my assumption is that a sugar pack is a nominal increase in volume. That was something I explicitly specified, and while bakervinyard made no mention of the volume, I assumed because there was no mention that the change in volume was statistically insignificant - 100 cc? in 4 L or 23 L ( a half cup more in 1 gallon or 5 gallons) ? and not 600 TIMES the original volume. If the volume is for all intents and purposes the same, then all we are doing is adding more sugar and not significantly changing the volume.. IF - IF the volume was significantly increased then your concern is absolutely correct.

Okay, great. I am glad you understand these concepts. I pointed out in my first post that the errors from the simplified procedure are on the order of 1% ABV for additions of concentrated sugar solution. Whether or not that overestimate is "critical" is for the user to decide.

I am glad to have been mistaken, but I did not get the sense from your first post that you were aware that this was an approximation valid only for small changes in volume. You said "any change in nominal volume" in your first post, and "nominal increase in volume" in the second; these are very different things. And my impression was influenced by phrases like "no matter the added volume" and "does not depend on us KNOWING the amount of sugars added or the increase in volume" in your first post. IMHO, my inference from the first post (that you were under the impression that delta-SG alone was determinative) was a reasonable one. But I am glad to know my inference was incorrect.
 

BernardSmith

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Totally understand, and apologies if my post/s were less than clear. My underlying assumption was that if we can dismiss any change in volume as negligible, then the approximation is , for all intents and purposes, good enough if Bakervinyard is simply looking for a handle on the ABV of their port after adding some sugar to the wine. But when volumes are concerned, I believe you need to use a version of a Pearson's Square to calculate the true ABV. Or would that work only if both volumes are wine?
 

bakervinyard

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Paul, Bernard, the amount of the chaptalization pack was 400 gr.. The package didn’t specify what actually it contained. To me it looked as though it contained “sugar” of some sort. Whether it was dextrose I don’t know. It also looked like there may have been some yeast nutrient. I’m guessing on the nutrient because the fermentation didn’t stall.
I made the “same” kit about 10 years ago and it was a headache to ferment. You added the chaptalization in 3 stages. It stalled at around 14% abv. I then fortified with 2 bottles of brandy.
hope this information helps? Bakervinyard
 

bakervinyard

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Paul, it’s a 3 gallon kit.
I was looking at the sg readings and I calculated the alcohol as 16.25%. This is what I did.
Initial sg was. 1.120. Fermented down to 1.017
1.120 minus 1.017 is o.103 times 131 is 13.49%
added chaptalization pack sg was 1.028 fermented to final sg of 1.007
1.028 minus 1.007 is 0.021 times 131 is 2.75%
I added 13.49% and 2.75% is 16.24%
Does that make any sense ? Or am I calculating it wrong ?
bakervinyard
 

sour_grapes

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Paul, it’s a 3 gallon kit.
I was looking at the sg readings and I calculated the alcohol as 16.25%. This is what I did.
Initial sg was. 1.120. Fermented down to 1.017
1.120 minus 1.017 is o.103 times 131 is 13.49%
added chaptalization pack sg was 1.028 fermented to final sg of 1.007
1.028 minus 1.007 is 0.021 times 131 is 2.75%
I added 13.49% and 2.75% is 16.24%
Does that make any sense ? Or am I calculating it wrong ?
bakervinyard

Okay, this is now enough information.

Firstly, your calculation is not technically correct, but it is close. This is the SAME calculation that I offered in post #4 as the "wrong calculation." Technically, it is not correct because it ignores the increase in volume upon chaptalization. But, as the back-and-forth with @BernardSmith pointed out, it is a close approximation.

But now you have given me enough info to back out a close approximation of the added volume! I will below perform the "correct" calculation, just for the record. It won't be much different from your estimate, I am sure. Leaning on Fermcalc...

First, how much alcohol did your first fermentation produce? You went from 1.120 to 1.017. As you say, our usual calculation gives us 13.49% ABV. [I will use this figure, but note that Fermcalc gives other values (depending on the calculation methods) ranging from 13.9 to 14.4. For simplicity's sake, I will use 13.49.] But how many ounces of ethanol is that? For 3 gallons (384 fl. oz.), it is 0.1349*384 fl. oz. = 51.8 fl oz of ethanol. We will need this later.

You added enough sugarwater to increase the SG from 1.017 to 1.028. Fermcalc tells me that if I add 340 g of sugar to 3 gallons, I get 3.0554 gallons of liquid with a SG of 1.028. But your pack weighed 400 g., so there must have been ~60 ml of water. To an excellent approximation, your volume after chaptalizing was 3.0554 gallons + 60 ml = 3.071 gallons = 393.12 fl. oz.

How much alcohol did your second fermentation produce? Your must went from 1.028 to 1.007, increasing the ABV by (1.028-1.007)*131=2.75% (as you calculated). This means that your post-chaptalization fermentation produced 0.0275*393.12 fl oz = 10.8 fl oz of additional ethanol.

So, all told, you have 51.8 + 10.8 = 62.6 fl. oz. of ethanol. This composes part of 393.1 fl oz total liquid volume, so the ABV is 62.6/393.1 = 15.9%

Again, as I said in post #4, the simple method yields a close approximation, but is a slight overestimate (by ~<0.5%). Note that the different methods of calculating ABV (Duncan, Berry & Acton, etc.) produce variations as large as this difference, so my mentioning this dilution effect was probably unnecessary. :)
 
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