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Contents:
Brix and SG ("A.J deLange")
Berliner Weisse ("T. Rohner")
RE: Brix to Specific Gravity ("Mike Patient")
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Date: Tue, 8 Jun 2010 01:17:16 -0400
From: "A.J deLange" <ajdel at cox.net>
Subject: Brix and SG
For Jim: Apparently you are seeking the relationship between the
concentration of a wort and its specific gravity. In modern brewing
this is modeled based on the work of the Normal-Eichungskomission of
1900 under the leadership of Leo Plato. He measured the true specific
gravity (density at 20 C normalized by the density of water at 4 C)
of pure sucrose solutions (as did Brix and Balling before him) and so
when we do these interconversions we assume that wort is pure sucrose
which, of course it isn't, but other sugars behave nearly identically
to sucrose and so it is a good model not to mention that sucrose is
easy to purify and is not hygroscopic so it can be accurately weighed
out. The ASBC and EBC have taken the approach of taking apparent
specific gravities (20 C/20 C) ranging from 1.00000 to 1.08300 in
steps of 0.00005, converting these to true (in vacuo) values entering
these into the Plato tables and taking out the percent sugar by weight
for each specific gravity. Interpolation between adjacent Plato table
entries was done as required. ASBC and EBC publish the result in
tables found in the ASBC MOA's and in Analytica and these are the
"official" basis for all concentration/SG calculations. Because these
tables are based on Plato's work the units of concentrations (grams of
sucrose per 100 grams of solution) are referred to as "degrees Plato"
or just P. One enters the table with specific gravity and takes out
degrees P.
To replace the tables with a formula requires a curve fit. As you
noted the relationship between P and SG is almost, but not quite
linear. Curve fitting is a bit of an art and there are several options
available to the analyst. The ASBC publishes (in the MOAs) a third
order polynomial fit to the data in the table: P =(((135.997*S -
630.272)*S + 1111.14)*S - 616.868). This polynomial provides rms
agreement with the table of 0.00061P with a maximum error of 0.0038P
at SG = 1 (i.e. it doesn't go through 0 at SG 1.00000) but, as we
seldom deal with worts weaker than 1 P it is a very good
representation of what is in the table. It is, of course, possible to
make higher order fits which are forced to go through 0 or others
which emphasize a particular region (say 7 - 15 P) and one is, of
course, free to do that but the ASBC polynomial represents the
industry standard and should, therefore, always be used.
But you want to go the other way; from Plato to SG. The only "correct"
way to do this is by finding the value of SG which causes the ASBC
polynomial to evaluate to the desired value of P. There are a couple
of ways to do this. The ASBC polynomial is third order and so closed
form formulas for the roots can be written and the correct one chosen.
It takes a fair amount of algebra to get to the root to the point that
it is actually easier to code an iterative root finder and this is
what ProMash does. The reason it does it that way is so that if you
feed ProMash a specific gravity of 1.040 is will use the ASBC
polynomial to calculate 9.99353 P and if you feed it 9.99353 P it
will return exactly (to machine precision) 1.040.
You can, of course, fit the ASBC table to come up with a polynomial
for SG as a function of Plato. S = (((6.34964E-8*P + 1.27447E-5)*P +
0.00386777)*P + 1.0000131) is such a polynomial and it is quite good.
For example S(6) - root(6) = 2.19009e-06 where root( ) is a function
that iteratively inverts the ASBC polynomial. Thus we would expect S
and the ASBC polynomial to close pretty tightly e.g. S(P(1.040))
=1.04000198755817 where P( ) is a function that converts whatever
specific gravity is in the parentheses to Plato by the ASBC polynomial
and S_G( ) is a function that converts whatever is in the parentheses
to specific gravity using the inversion polynomial. Note that in
ProMash, root(P(1.040)) = 1.04000000031739 when the root bisector is
set for a tolerance of 1E-9.
Looking at the numbers in your table 6.000P interpolates to 1.02369166
in the ASBC table. root(6) = 1.02369005432759 and S(6) =
1.0236922444224 so the inverse fit polynomial is closer to the table
than inversion of the ASBC polynomial (which isn't too surprising
since a simple fit to the table gives a polynomial slightly different
from the ASBC polynomial. But the inverse of the polynomial must be
considered the "correct" answer as it closes with the official
polynomial. Since ProMash uses the inverse it should return 1.02369
for 6 P input. For 9 P it should return 1.035899639 and for 12 it
should return 1.0483692. The fact that the values you obtained from
ProMash are different suggests that something is wrong. The 1.02277
corresponds to 5.771 P and 1.04644 corresponds to 11.54 P which are
way off - i.e. too far off even to be explained by the small
differences between the actual Brix scale and the Plato scale. I can't
believe ProMash has become "broken" to this extent. It checked when I
worked with Geoffrey on these algorithms but that has been years.
Could you check those ProMash numbers?
Bottom Line: S = (((6.34964E-8*P + 1.27447E-5)*P + 0.00386777)*P +
1.0000131) is an inverse fit to the ASBC table data and is good for
almost any purpose. To 5 decimal places it gives answers identical to
your number (3).
An exact inverse of the ASBC polynomial may
actually be less accurate (because the ASBC polynomial isn't the best
fit to the table) but is to be preferred because it has the imprimatur
of the ASBC upon it.
A.J.
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Date: Tue, 08 Jun 2010 11:30:42 +0200
From: "T. Rohner" <t.rohner at bluewin.ch>
Subject: Berliner Weisse
Hello all
i was reading the posts on "Berliner Weisse" with much interest. A
couple of months ago, i was looking for information on the subject.
It doesn't seem to be a very popular style among homebrewers. I can
imagine why...
After some internet research, i found a pretty easy way to let the
lactos do their work, while still using a bacterial-free fermentation
regime.
The "four No's" way seems a bit adventureous to me.(I didn't try it..)
The way i do it, is tweaked a bit from the original way i found on the
internet. The way i read about, is closer to the "four no" method.
Here the way i did it: (i use SI units...)
Malt: 4kg wheat, 3kg pilsner (Weyermann)
I mashed 90% of the grist at 63 C for 45 min
then 30 min at 71 C.
Then i cooled it down to 48 C and added the remaining 10% of the
grist.(for the lactos on the malt)
I let it sit for 14 hours for the lactos to do their work.
Then i heat it up to 63 C again for 30 min, then to 71 C for another 30
min and then to 77 C for mash-out.
After lautering, i boil it for 60 min and add a little hop for 30 min.
I fermented it with a mixture of American Ale and Wheat yeast.(Both dry
yeast from Fermentis) I did this, because i remember the beer in Berlin
as relatively clean tasting.(Not very wheaty...)
The smell of the sour mash in the morning was a bit strange at first,
but when we bottled the first batch, i was pretty confident, that it
turns out nice.
Now, after having brewed 3 batches(150litres), we are very happy with
the results. Even my SWMBO who doesn't drink "normal" beers, judged it
very positively.(Not only verbally, but she drank a imperial pint of it
with our woodruff sirup.)
In Berlin, many people drink it with "Schuss", which is a shot of
raspberry or woodruff sirup. It takes a little sourness out. After
having tried our product in the pure form, i went in the forest to
gather some woodruff to make sirup. The sirup turned out very nice and
with some green food colorant it looks like the commercially sold version...
If there is some interest in a more detailed recipe, i could post it, or
even send the Promash file.
Cheer Thomas
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Date: Tue, 8 Jun 2010 11:48:33 -0400
From: "Mike Patient" <mpatient at rta.biz>
Subject: RE: Brix to Specific Gravity
I have been making brewing software in my free time and have been looking at
various resources for formulas.
Wikipedia defines brix as 261.3 x (1-1/g)
Making g 1-(261.3/b)
This is also a linear formula, and my bet is that in reality it isn't.
However, the relationship might be pretty close to linear for the range
acceptable for brewing. I am not sure if it is the case.
If anyone has more info, I am quite interested as well.
Mike
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End of HOMEBREW Digest #5694, 06/08/10
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