Whole grape port

sour_grapes · Apr 1, 2014

Interesting -- your source is quite linear, whereas the one I (randomly) cited has non-linearities in it.

I got your script running. (Nice work, clever approach.) I had a question about that factor of 0.05 (or 1/20). What is the basic root of it? Is it empirical, or is it based on molecular masses, etc.?

I was thinking of trying to identify the equations, and linearize them around the likely ending place (say, 20% ABV and 75 g/l sugar). Haven't taken pencil to paper yet, but I think that may work.

I also am wondering if the exact solution will turn out to be an eigenvalue problem, where we take your system of equations, express as a matrix, and set the determinant equal to zero....

vacuumpumpman · Apr 1, 2014

seth8530 said:
Yup, but the issue with that is that you add brandy and then you change your sugar level because of the brandy you added in the wine. Pretty much what the script does is tell you at which gravity do you need to add spirit and how much spirit to reach a certain ABV and sugar level.
.

Seth -
If I am using white brandy (everclear with oak added) will that still raise the sugar level ?

sour_grapes · Apr 1, 2014

vacuumpumpman said:
Seth -
If I am using white brandy (everclear with oak added) will that still raise the sugar level ?

No, he didn't say it would raise the sugar level. He said it would change the sugar level. It reduces the g/l of sugar because it adds to the denominator (i.e., increases the volume). Seth is assuming (in his script) that the spirit has no sugar at all.

seth8530 · Apr 1, 2014

sour_grapes said:
Interesting -- your source is quite linear, whereas the one I (randomly) cited has non-linearities in it.

I got your script running. (Nice work, clever approach.) I had a question about that factor of 0.05 (or 1/20). What is the basic root of it? Is it empirical, or is it based on molecular masses, etc.?

I was thinking of trying to identify the equations, and linearize them around the likely ending place (say, 20% ABV and 75 g/l sugar). Haven't taken pencil to paper yet, but I think that may work.

I also am wondering if the exact solution will turn out to be an eigenvalue problem, where we take your system of equations, express as a matrix, and set the determinant equal to zero....

Umm, I was having trouble getting a good system of Independent equations to make a system of equations work out.. Atleast I think that was the issue I was having. If you can make this work with an analytical solution then I shall tip my hat off to you.

What I did to come up with the factor of .05 was take

ABV=131*(FG-SG) Then I set that equal to K*(gLiterFinal-gLiterInitial)=ABV. I then set the equations equal to each other in an excel sheet and solved for K at a whole bunch of values. In each case it came up to around .0496 something.. So I just took the average and rounded up. I am attaching the excel sheet I used to come up with that if you are curios.

BTW, very cool work on getting my script running. What did you compile it with? I am currently in the final stages of getting a .exe version of my script ready for release that was rewritten in C++ which actually prompts the user for information to input.. But I am having a bit of trouble with my libraries at the moment.

BTW, very interesting thing to note... just like you said, our tables are not quite the same are they? Pretty close though

vacuumpumpman said:
Seth -
If I am using white brandy (everclear with oak added) will that still raise the sugar level ?

Nope only lower it just like grapeman said.

View attachment PortCalcStuff.zip

sour_grapes · Apr 2, 2014

seth8530 said:
If you can make this work with an analytical solution then I shall tip my hat off to you.

Umm, get ready to tip. I hate to tell you, though, I didn't have to pull out any big guns; it only required algebra. For a minute, I thought it was going to turn into a quadratic equation, but it didn't even do that.

I built off the excellent foundation you laid.
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.

I did check that this gives the same result as your MatLab script. (I didn't compile it, I just ran it on MatLab.)

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.

HTH, John et alii

sour_grapes · Apr 2, 2014

One more thought/question/complication. If you take 1 l of pure alcohol, and 1 liter of pure water, and you mix them, then you do not get 2 l of mixture. The volume is a bit less than 2 l. I don't think we need to worry about this in this case, because we are already dealing with ethanol/water solutions. However, I cannot be sure. I am quite confident, however, that the effect will be small in the present problem, smaller than the errors associated with measuring SG and volumes.

JohnT · Apr 2, 2014

sjo said:
" I made a small side batch of wine just for use in port" Quote from JohnT so I am going to call this the JohnT method.

I started to make what I thought was a port using 8 gallons of frontenac grapes. I fermented grapes and added sugar until yeast died out. somewhere around 18%. There is a little residual sugar (sg1.08) I then used the johnT method and brought to 24% alc calculated. Added oak and is now aging.

My question is why stop fermentation by fortifying instead of letting it finish the ferment and backsweeten later.
Scott

SJO,

My goal was to not add any sugar. I wanted the natural sugars of the grape only. With this in mind, letting the wine ferment dry is not an option.

A number of years ago, I used both methods, taking half a batch and stopping the fermentation, and allowing the other half to ferment dry and be back-sweetened and fortified.

I found that I preferred the "stopped fermentation" much, much more. It is, however, just a matter of taste.

JohnT · Apr 2, 2014

Seth, SG, VPM,

I can not tell you how much I admire those that rise to a challenge!

You guys are simply the best!

johnT.

seth8530 · Apr 2, 2014

sour_grapes said:
Umm, get ready to tip. I hate to tell you, though, I didn't have to pull out any big guns; it only required algebra. For a minute, I thought it was going to turn into a quadratic equation, but it didn't even do that.

I built off the excellent foundation you laid.
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.

I did check that this gives the same result as your MatLab script. (I didn't compile it, I just ran it on MatLab.)

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.

HTH, John et alii

Looks like you did good work, I was originally trying to do the same exact thing you ended up doing, but for some reason it was not working out. Thus, I gave up and moved on to the solver script.

BTW, great to here that the answers are coming out the same! That is always a good check.

JohnT · Apr 2, 2014

Now if we cold only find someone that can convert this into an app, we could then share it with all the forum members! :try

seth8530 · Apr 2, 2014

Yep yep, I am working on cleaning up Sour's take on my stuff. I am trying to get it into a single equation which can be easily used. I have an "app" written and I should be able to upload it as a .exe as soon as I can compile it.

sour_grapes · Apr 2, 2014

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 fortification.zip

seth8530 · Apr 2, 2014

Looks like that will also work, I will try and verify your excel sheet against my code, I will also try and come up with a single equation just to sate my damaged pride (; .

Over all, great work!

sour_grapes · Apr 2, 2014

seth8530 said:
Looks like that will also work, I will try and verify your excel sheet against my code, I will also try and come up with a single equation just to sate my damaged pride (; .

Over all, great work!

Sounds great, Seth. If it makes you feel any better and partially salves your wounded pride

, I likely wouldn't have been able to solve it if you hadn't set the problem up first. And you are correct, working in grams/liter simplifies the algebra significantly.

I am a bit confused what you mean by "try to come up with a single equation." I already came up with the minimum number of equations, viz., two, one for sugar in the must, the other for volume of brandy. Do you mean you will re-derive and verify my result, or do you have something else in mind?

seth8530 · Apr 2, 2014

Lol, it does make me feel a bit better. Pretty much what I plan on doing is smashing the two equations down into one via substitution. That way only one equation needs to be solved. I was pretty close to getting to work out this morning, but I needed to go to my lab meeting and I was getting negative numbers due to an algebra error.

Ie just to give you an idea of where I am going I plan on taking

ABV=X+Y
Y=X^2+35

Thus
ABV=X+X^2+35

of course with different numbers and variables and all, but you get the idea.

BTW, just curious, where did you develop your math and critical thinking skills from?

sour_grapes · Apr 2, 2014

Yeah, that is what I did, as described in the initial post. That is, take a system of two equations in two variables, solve one of the equations for one variable, substitute into the second equation to get an equation in one variable, then solve it. Then back-substitute that solution into the first equation to solve for the first variable. (I.e., the standard approach for solving a system of two equations.)

When you do this, you'll eventually see that this is formally no more complicated a problem than "If one train leaves Wichita traveling south at 35 mph at 6 pm, and another leaves Oklahoma City traveling north at 20 mph at 7 pm, when and where do they meet?" However, the fact that the unknown variables appear in the numerator and denominator makes it much more complicated to solve. That is why I thought it would turn into a quadratic equation (along with the fact that you said your numerical approach gave false solutions), but, as I say, it didn't.

BTW, just curious, where did you develop your math and critical thinking skills from?

Well, let's see, I suppose HS, college, grad school, and 25 years of being a scientist!

seth8530 · Apr 2, 2014

Yeah, well my pride still demands I solve it myself lol.

Yup, you sounded like a fellow sciency guy, I guess technically engineering students are not scientist... I dont know, maybe they are lol

sour_grapes · Apr 2, 2014

seth8530 said:
Yeah, well my pride still demands I solve it myself lol.

Can't sez I blames you!

Yup, you sounded like a fellow sciency guy, I guess technically engineering students are not scientist... I dont know, maybe they are lol

I make little distinction.

Once in a while, the small differences in the approaches of the two professions becomes evident, but not often.

seth8530 · Apr 2, 2014

Yep yep, well I got kind of busy, so it might be a few days before I can double check your work in detail ( quality assurance). However, I look forward towards giving it another go soon.

JohnT · Apr 3, 2014

*** General Notice ***

If any of you folks feel like this is over your head, do not feel bad.

I have bs degrees in mathematics, comp sci, and physics. When I ran out of tuition money and had to get a job (about 30 years ago), I opted for IT.

What can I say, at the time it paid.

Long story short, I have not needed to use any of the math I learned in over 30 years and these two fella are smoking me.

The method I used last year was to keep playing with the two equations until I had a port with the correct residual natural sugar and the correct abv. It took a lot of back and forth and about an hour of my time. An app would be incredible helpful.

Aside: Rather than call this the johnT method, we should call this the WMT method!

Whole grape port

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