Gravity/ABV calculation with late sugar addition

[beerisyummy]

Hello!

I just brewed up a Belgian Blond, following a recipe I found on BYO.

The article had some interesting advice regarding late addition of simple sugars (when fermentation is nearly done) which I have decided to follow.

So the OG of the maltose part of the brew is about 1.046. After a few days in the fermentor I'll boil up 1 lb. of table sugar in some water, cool, and add to the carboy.

So how do I figure out what the OG of the whole batch is?

Not that I care that much, as long as it tastes good and has alcohol
But, I'll feel like a slacker if I don't have numbers.

Any help from more sciency people than myself will be greatly appreciated.

 

[doug293cz]

Calculate points in the original wort:

Points_1 = 1000 * (Wort_SG - 1) * Wort Volume​

Calculate points in the sugar solution:

Points_2 = 1000 * (Solution_SG - 1) * Solution Volume​

Calculate effective OG:

SG = 1 + (Points_1 + Points_2) / (1000 * (Wort_Volume + Solution Volume)​

Note that the sugar solution volume will be greater than the volume of water used to make the solution, so measure the volume after the sugar is dissolved. Also, you can leave the factor of 1000 out of all the equations and get the same results.

If you really want to nerd out, you can use a rigorous mass balance approach:

Final °P = (Wort °P * Wort Weight + Solution °P * Solution Weight) / (Wort Weight + Solution Weight)​

Once you know your effective SG or °P, you can use the standard formulas to calculate ABV.

Edit: 5/31/18 7:20PM (PDT) Corrected errors in first two equations. They are correct now.

Brew on

 

[Kent88]

You can use software like BrewersFriend to see what the OG would be. You can plug in your recipe, or just plug in your pre- simple sugared volume, enough extract to give you your OG, and then adjust the volume and add the sugar.

Or you could take a gravity reading of the sugar-water solution you're adding, along with its volume, and use algebra... and it looks like doug beat me to explaining how that would work. Thanks, sir!

 

[beerisyummy]

Calculate points in the original wort:

Points_1 = 1000 * (Wort_SG - 1) / Wort Volume​

Calculate points in the sugar solution:

Points_2 = 1000 * (Solution_SG - 1) / Solution Volume​

Calculate effective OG:

SG = 1 + (Points_1 + Points_2) / (1000 * (Wort_Volume + Solution Volume)​

Note that the sugar solution volume will be greater than the volume of water used to make the solution, so measure the volume after the sugar is dissolved. Also, you can leave the factor of 1000 out of all the equations and get the same results.

If you really want to nerd out, you can use a rigorous mass balance approach:

Final °P = (Wort °P * Wort Weight + Solution °P * Solution Weight) / (Wort Weight + Solution Weight)​

Once you know your effective SG or °P, you can use the standard formulas to calculate ABV.

Brew on

Awesome, that is just what I was looking for.

 

[doug293cz]

Awesome, that is just what I was looking for.

I'm here to help (where I can.)

Brew on

 

[beerisyummy]

I'm here to help (where I can.)

Brew on

Hi, will you check my math please? (I'm a musician, not a scientist!)
The OG of the mash & boil as I said was 1.046.
I boiled up 1 lb. white sugar in 1 quart water and got OG 1.166.
So then I calculated as follows:

1. 1000x(1.046-1)/5 gal = 9.2

2. 1000x(1.166-1)/.25 gal. = 664

1 + 9.2+664/(1000x5.25)

= 1 + 673.2/5250

= 1 + 0.13

= 1.13


1.13 seems reeeealy high. Did I mess up?

 

[JimRausch]

Hi- either you messed up or maybe the equation is incorrect. It does seem overly complicated to me.
Here's a simpler method I use:
Original OG=1.046 in 5G. 46x5=240 gravity points. 1 lb. sugar will add about 40 points. 240+40=280.
280 divided by 5.25(new volume)=53.3333.
So the answer to your original Q is your new OG would be around 1.053.
I'm too lazy to try and figure out where you went off in the calculation. Besides, I'm a veterinarian, not a math geek. Simpler the better.

 

[doug293cz]

Hi, will you check my math please? (I'm a musician, not a scientist!)
The OG of the mash & boil as I said was 1.046.
I boiled up 1 lb. white sugar in 1 quart water and got OG 1.166.
So then I calculated as follows:

1. 1000x(1.046-1)/5 gal = 9.2

2. 1000x(1.166-1)/.25 gal. = 664

1 + 9.2+664/(1000x5.25)

= 1 + 673.2/5250

= 1 + 0.13

= 1.13


1.13 seems reeeealy high. Did I mess up?

Hi- either you messed up or maybe the equation is incorrect. It does seem overly complicated to me.
Here's a simpler method I use:
Original OG=1.046 in 5G. 46x5=240 gravity points. 1 lb. sugar will add about 40 points. 240+40=280.
280 divided by 5.25(new volume)=53.3333.
So the answer to your original Q is your new OG would be around 1.053.
I'm too lazy to try and figure out where you went off in the calculation. Besides, I'm a veterinarian, not a math geek. Simpler the better.

Damn, damn, damn, I hate when I make a mistake, especially if I get caught. All I can say is that it was late when I posted. The correct formulas are:
Calculate points in the original wort:

Points_1 = 1000 * (Wort_SG - 1) * Wort Volume​

Calculate points in the sugar solution:

Points_2 = 1000 * (Solution_SG - 1) * Solution Volume​

Calculate effective OG:

SG = 1 + (Points_1 + Points_2) / (1000 * (Wort_Volume + Solution Volume)
​

The Plato formulas are correct in the original post. I'll go back and edit the formulas in my first post.

So @beerisyummy 's numbers would look like this:

1. 1000x(1.046-1)x5 gal = 230

2. 1000x(1.166-1)x.25 gal. = 41.5

1 + (230 + 41.5) / (1000x5.25)

= 1 + 271.5/5250 = 1.0517

This is close, but you didn't account for the fact that the sugar solution has a volume greater than 1 qt (because the sugar adds volume). The volume of your sugar solution is:

(1 [lb] + 1 [qt] * 8.33 [lb/gal] / 4 [qt/gal] ) / (1.166 * 8.33 lb/gal) = 0.317 gal or 1.27 qt​

If we put that back in to eq 2.

1000 * (1.166 - 1) * 0.317 = 52.6​

The the final eq becomes

1 + (230 + 52.6) / (1000 * 5.317) = 1.0532
​

Not a huge difference, but I like to try to be accurate.

And, @JimRausch also made a small calculation error, but ended up with the correct answer anyway. I'll leave it as an exercise for the reader to find Jim's error.

Brew on

 

[beerisyummy]

Thanks to Jim & Doug.

I'm gonna say this is "close enough for jazz"

 

[JimRausch]

And, @JimRausch also made a small calculation error, but ended up with the correct answer anyway. I'll leave it as an exercise for the reader to find Jim's error.

Hah! Thank you Doug! Same excuse, plus I was switching between the Red Sox/Houston game plus the Softball tournament games, so was doubly distracted.