Fortification calculation

[RiderEh]

Hi All,

I thought I'd post how I calculate how much brandy to add to port to boost the alchohol:

P=Port at start (what you made)
a=alchohol percentage of port you made (SG-FG)*131
b=alchohol percentage of brandy you are adding
A=final percentage alchohol you wish to have
B=brandy to add (what we are solving for)

P*a+B*b=(P+B)*A
P*a+B*b=P*A+B*A
B*b-B*A=P*A-P*a
B*(b-A)=P*(A-a)
B=P*(A-a)/(b-A)

Example:
P=12L, a=16%, b=40%, A=20%

B=12*(0.2-0.16)/(0.4-0.2) = 2.4L brandy to add.

 

[sour_grapes]

Nice.

Or you can use a Pearson Square: https://winemakermag.com/article/the-pearson-square


There are also times that one would like to make a port as they do in Porto (or Oporto), that is, by adding the fortifying alcohol during an active fermentation, so that the increased ABV stops the fermentation and leaves the desired amount of residual sugar (and the desired ABV). I worked out the math for that (quoted below) here: https://www.winemakingtalk.com/threads/whole-grape-port.44373/page-3#post-503223

I also wrote up a spreadsheet that will make this calculation for you:

Well, I put this into an Excel sheet, which you are welcome to (if I can figure out how to attach it). There are two sheets: one you input the sugar in g/l, the other you input the SG of the must instead. In both sheets, you input parameters in the yellow boxes, and the answers come out in the blue boxes.

View attachment 14828

Here is the calculation in all of its, ummm, glory:

Parameters:
volume_wine (in liters)
rho_i_wine (initial g/l sugar)
rho_port (desired g/l in port)
ABV_port (desired ABV of port)
ABV_brandy (I am using "brandy" as my spirit!)
(derived quantity: ABV_wine=(rho_i_wine - rho_f_wine)/20, as per Seth)

Unknowns
volume_brandy
rho_f_wine (final g/l sugar in wine)

2 independent equations

(1, the sugar equation) rho_port = rho_f_wine*volume_wine/(volume_wine + volume_brandy)

(2, the alcohol equation)
ABV_port= (volume_wine*ABV_wine + volume_brandy*ABV_brandy) / (volume_wine + volume_brandy)

I solved Eqn 1 for rho_f_wine to find:
rho_f_wine = rho_port*(volume_wine + volume_brandy)/volume_wine ,

then I shoved that into Eqn. 2 (after substituting your derived quantity for ABV_wine). You can easily, i.e., algebraically solve for volume_brandy.

The result is:


volume_brandy = {ABV_port - (rho_i_wine - rho_port)/20} / (ABV_brandy - ABV_port - rho_port/20)


This is the desired volume of brandy in liters.

You then substitute that value into Eqn. 1 to find rho_f_wine.

The result is:


rho_f_wine = (ABV_brandy - rho_i_wine/20) / (ABV_brandy - ABV_port - rho_port/20)


Remember, this is the residual sugar that you want (in g/l) at the time you should fortify to stop fermentation.

You can either use ABV as a number between 0 and 100 and use rho in g/l, or you can use ABV as a fraction (number between 0 and 1) and use rho (in g/l)/100; this comes from the fermentation conversion of rho/20, which provides the ABV as a percentage, so you have to divide by another 100 to get ABV to a fraction instead of percentage. I think most people would be best served to use ABV as a number from 0 to 100, and sugar in g/l.

For all you people who would prefer to use SG rather than g/l of sugar, the conversion is close to:

SG = 1 + rho/2644 where rho is in g/l,

Or, of course, rho = (SG-1)*2644.

 

[RiderEh]

The Pearson Square seems to go off the same type of formula's as mine (i checked and the math works out the same with both), but what I don't like is you have to know what your final quantity will be, whereas my calculation tells you the quantity to add just to boost the ABV of the batch. For some reason it confuses me as I'm better with algebra than drawing lines to perform calculations lol.

 

[bitterbad]

Math major here, I'm making some fortified wine and needed a calculation so I made one myself. Looked up this thread to add my input to it. Here it is:

Where F is the ABV of the fortified wine, w is the ABV of the wine you want to fortify, V_w is the volume of wine, s is the ABV of the spirit you want to add, and V_s is the volume of the spirit that you will add. Simply make variable whatever you value is unknown to you and make the rest constant, then do algebra, and you will arrive at your answer. Its just a weighted average. Alternatively you can plot it on a graph. This graph shows how much 95% everclear I would need to fortify 3 gallons of 11% wine to 18%.