Seth's ABV Equation Need Testers!

[seth8530]

Hey all, remember this thread?

http://www.winemakingtalk.com/forum/f6/calling-all-would-scientest-38884/

Well, pretty much my previous thread on coming up with an alternative ABV equation fizziled out when we encountered that ABV is a function of an unknown ABV correction. Pretty much what I have done is built on the previous work that we discussed on this forum but came up with an empirical correction for the previous equation that makes it solvable.

Also, in the attached PDF I went through the whole derivation in math format so it is all nice and pretty. If you do not want to deal with all the math the last page has an example and the final equation(s) depending on whether or not you want to iterate the solution until it converges.

What would be extremely helpful would be if some of you guys could use the equation in your ferments and report back the results, that way we can see how they compare to other equations that are out there. I have done some comparisons myself and it seems to be pretty good.

BTW, thank you all to helped contribute to the previous discussion!

View attachment ABV equation write up.pdf

 

[DoctorCAD]

All that math to find out that the current formulas are within 1.2%

And there aren't 3 people on this planet that could tell the difference between a 13.9% vs. 14.0% wine.

Interesting exercise, but not really worth the time.

 

[sour_grapes]

Seth,

Unlike the naysayers on these two threads, I think your efforts to model this are worthwhile and interesting.

However, I don't know what you are asking for in this post? How can we "report results" unless we have an independent means of measuring the alcohol? I'd be happy to help, but what help did you have in mind?

 

[seth8530]

Sour, I appreciate it. Something to keep in mind is that I did not really do this with the plan of accomplishing something. Ie, I understand the weaknesses of the equation developed and how in reality this equation is likely not any more accurate than any of the existing equations.. But is it not just kind of cool to think.. Wow, I came up with this and it is in the ballpark!

What would be great would be either you using the equation and seeing what kind of numbers you get compared to other equations or even possibly finding some literature that shows changes in gravity of bricks and displays the ABV as determined by experiment. Ie, something to validate the equation against. This could be useful for tuning the equation up.

One of the things I am not terribly sure is the empirical ABV approximation that I am using. Perhaps I should be using .59*(DeltaBrix) instead of .59*(BrixI) to better compensate for people with ferments that do not go dry.. Or perhaps it is possible the solution converges to a pretty good value after a few iterations. no matter what the empirical ABV part is so long as it is reasonable.

 

[seth8530]

BTW, I just found out something rather cool. If you take the second form of the equation

ABV = (.6473*.FG)*(BrixI-(-BrixF+.3159*ABV+.729))

it does not really matter what you guess your ABV to be inside of the equation. I have found that for guesses of 2 and 34 I end up getting 14.02455339% ABV and 14.01751522% ABV. Values from br squared page indicate values of

http://www.brsquared.org/wine/CalcInfo/HydSugAl.htm

13.8 14.3 14.6 13.3 14.1
% ABV based on 24.7 Brix. I started with 25 Brix. So in short, it appears the solution converges on a good solution pretty much no matter how bad of a guesser I am of my ABV.



ABV = (.6473*.992)*(25-(-2+.3159*2+.729));

ABV = 16.46348413
ABV = (.6473*.992)*(25-(-2+.3159*16.46348413+.729));
print(`output redirected...`); # input placeholder
ABV = 13.52962114
ABV = (.6473*.992)*(25-(-2+.3159*13.52962114+.729));

ABV = 14.12474413
ABV = (.6473*.992)*(25-(-2+.3159*14.12474413+.729));

ABV = 14.00402569
ABV = (.6473*.992)*(25-(-2+.3159*14.00402569+.729));

ABV = 14.02851297
ABV = (.6473*.992)*(25-(-2+.3159*14.02851297+.729));

ABV = 14.02354582
ABV = (.6473*.992)*(25-(-2+.3159*14.02354582+.729));

ABV = 14.02455339
ABV = (.6473*.992)*(25-(-2+.3159*34.02354582+.729));

ABV = 9.967629119
ABV = (.6473*.992)*(25-(-2+.3159*9.967629119+.729));

ABV = 14.84728073
ABV = (.6473*.992)*(25-(-2+.3159*14.84728073+.729));

ABV = 13.85746188
ABV = (.6473*.992)*(25-(-2+.3159*13.85746188+.729));

ABV = 14.05824288
ABV = (.6473*.992)*(25-(-2+.3159*14.05824288+.729));

ABV = 14.01751522

 

[sour_grapes]

Seth, I don't understand why you are iterating that equation to find ABV. Why don't you just solve for ABV algebraically (just like Mr. Jenkins taught you in HS )? The answer is:

ABV= 0.6473*FG*(BrixI-BrixF-0.729)/(1+0.6473*FG*0.3159)

That would explain why the equation converges no matter how poor your guess. There is a unique solution, so no false minima.

 

[seth8530]

Nice find, the reason why I decided to go for an iterative solution was because I intended the ABV inside of the equation to be an empirically derived ABV. However, for this format of the equation, it does appear that when you set the empirical ABV and the non empirical ABV equal to each other and solve for it.. It appears that it does give the same answer within very close reason of the iterative solution.

Sometimes, it takes another set of eyes to find these things. Thanks!

Nice find!

 

[Rosa321]

Oh my gosh......I LOOOVE math!

But I need to read this when It's not past midnight and I didn't open a bottle of wine hehehehe

 

[JohnT]

Boy are you guys giving me a headache!!! LOL..

SG,

I came in rather late in this thread, in your formula...

ABV= 0.6473*FG*(BrixI-BrixF-0.729)/(1+0.6473*FG*0.3159)

What is FG, Finished SG?

Also, is the following correct?

BrixI = Initial Brix?
BrixF = Finished Brix?

 

[sour_grapes]

SG,

I came in rather late in this thread, in your formula...

It's not my formula. This is all Seth's work. In the first post, he gives a link to a nice pdf to explain it all.

What is FG, Finished SG?

Also, is the following correct?

BrixI = Initial Brix?
BrixF = Finished Brix?

Well, yes, but I would have said "Final Gravity" and "Final Brix."

 

[Rocky]

Wait a second, here. I thought if was "thirty days has Septober, April, June and no wonder, all the rest have peanut butter, except my Grandma, who has a little red tricycle."

 

[seth8530]

It's not my formula. This is all Seth's work. In the first post, he gives a link to a nice pdf to explain it all.



Well, yes, but I would have said "Final Gravity" and "Final Brix."

Sour is right on with a small correction.

Brixi is your initial brix

FG is your final gravity

But BrixF is your final Brix as measured by a hydrometer. BrixF is not your true final Brix, but their is a correction inside of the equation that takes BrixF and attempts to make it represent the true final Brix.

But as Sour said, that is all in the PDF as well.

 

[seth8530]

So it was brought to my attention by bzac on winepress that yeast are not 100% efficient and he even provided me a nice pdf that gives details into some of the uncertainties that go into making an exact ABV equation. Very useful information.

http://wineindustrynetwork.com/uploads/tips/gqRwa10bvFXsGDBIHfLKmE7A9yjiCt.pdf

According to the pdf, observed ethanol yields are 90-95 percent of what they theoretically should be. This factor can easily be added into the equation.

So, I thought this was kind of interesting. If I assume FG=.992 and Efficiency =.93

my leading coefficient of my equation ends up being equal to .597.

Then take a look at this link

http://www.brsquared.org/wine/CalcInfo/HydSugAl.htm

Looks like I am right on top of the PA number 3 approximation where PA=.59*Brixi

Just thought that was kind of cool.

 

[JohnT]

Wait a second, here. I thought if was "thirty days has Septober, April, June and no wonder, all the rest have peanut butter, except my Grandma, who has a little red tricycle."

.... But have they taken in account their current altitude above sea level, the current position of the moon, and the current position of earth on the elliptical orbit around the sun and the effect this might have on gravity??...

All kidding aside, coming up with a good equation for a more accurate ABV is pretty cool. You should write an app!