### scaling of a N/Z type nomogram

Posted:

**Tue Dec 30, 2014 9:45 am**I got interested in nomograms because of its simplicity to do calculations while not having a pc etc at hand. It appears to be useful for my beer brewing hobby.

When brewing beer one starts with a sugary solution with a certain Original Gravity (OG). Yeast ferments the sugars leading to a decrease in gravity and at the end the gravity is FG (Final Gravity). The degree of fermentation (ADF) at the end of fermentation is calculated from the OG and FG by:

ADF=(OG-FG)/(OG-1).

Gravity is normally measured using a hydrometer yielding specific gravities. However nowadays it is more common to measure the starting and final gravities using a Brix meter.

All the equations are there and I converted it to a determinant. It yields a Z-type of nomogram. The problem however is the small scale for the B0 and B1 line compared to the ADF scale which makes it impossible to do a reading.

The longer version with equations:

OG=259/(259-B0)

FG=a+b*B0+c*B0^2+d*B0^3 + e*B1+f*B1^2+g*B1^3 ..(a…g are constants)

ADF=(OG-FG)/(OG-1) ..(OG>1 and FG>=1 and OG>FG) ADF varies from 0 to 1 but ADF is typically 0,5 to 0,9

B0 and B1 typically vary between 0 and say 20 where B0>=B1

I used the following functions to construct the determinant:

FG(B0,B1)=g(v)+f(w)

g(v)= a+b*B0+c*B0^2+d*B0^3

f(w)= e*B1+f*B1^2+g*B1^3

f(v)=OG= 259/(259-B1)

f(u)=ADF

f(u)=(f(v)-(g(v)+f(w))/(f(v)-1)

Determinant:

x ------------------------- y ----------------------

________________________________________________

f(u) -----------------------1 --------------------- 1 = ADF

(f(v)-g(v))/f(v) --------- (f(v)-1)/f(v) --------- 1 = Function of B0

f(w) ---------------------- 0---------------------- 1 =Function of B1

Below the constructed chart of B0, B1 and ADF demonstrating the problem: one wants to draw a line through B1 and B0 reading the final ADG. However the difference in scale make it impossible to use (yet ) The chart is plotted for realistic values of B0, B1 and ADF

In a later stage I also would like to add also the OG and FG lines since often these are used in combination with B0 and B1 and of course incorporate this in PyNomo-software.

I just installed the PyNomo-software and it works. When having a lead to an answer to my question I will see if it easy to learn the python language and make a nice nomogram.

But first things first.... scaling

Thanks in advance for having a look at my challenge.

William

**In short**:When brewing beer one starts with a sugary solution with a certain Original Gravity (OG). Yeast ferments the sugars leading to a decrease in gravity and at the end the gravity is FG (Final Gravity). The degree of fermentation (ADF) at the end of fermentation is calculated from the OG and FG by:

ADF=(OG-FG)/(OG-1).

Gravity is normally measured using a hydrometer yielding specific gravities. However nowadays it is more common to measure the starting and final gravities using a Brix meter.

**Goal**: Therefor I want to derive a nomogram to construct the ADF from the staring Brix (B0) and final Brix (B1).All the equations are there and I converted it to a determinant. It yields a Z-type of nomogram. The problem however is the small scale for the B0 and B1 line compared to the ADF scale which makes it impossible to do a reading.

**Question**: How do I apply a scaling to get the B0 and B1 lines on a similar scale compared to the ADF line?The longer version with equations:

OG=259/(259-B0)

FG=a+b*B0+c*B0^2+d*B0^3 + e*B1+f*B1^2+g*B1^3 ..(a…g are constants)

ADF=(OG-FG)/(OG-1) ..(OG>1 and FG>=1 and OG>FG) ADF varies from 0 to 1 but ADF is typically 0,5 to 0,9

B0 and B1 typically vary between 0 and say 20 where B0>=B1

I used the following functions to construct the determinant:

FG(B0,B1)=g(v)+f(w)

g(v)= a+b*B0+c*B0^2+d*B0^3

f(w)= e*B1+f*B1^2+g*B1^3

f(v)=OG= 259/(259-B1)

f(u)=ADF

f(u)=(f(v)-(g(v)+f(w))/(f(v)-1)

Determinant:

x ------------------------- y ----------------------

________________________________________________

f(u) -----------------------1 --------------------- 1 = ADF

(f(v)-g(v))/f(v) --------- (f(v)-1)/f(v) --------- 1 = Function of B0

f(w) ---------------------- 0---------------------- 1 =Function of B1

Below the constructed chart of B0, B1 and ADF demonstrating the problem: one wants to draw a line through B1 and B0 reading the final ADG. However the difference in scale make it impossible to use (yet ) The chart is plotted for realistic values of B0, B1 and ADF

In a later stage I also would like to add also the OG and FG lines since often these are used in combination with B0 and B1 and of course incorporate this in PyNomo-software.

I just installed the PyNomo-software and it works. When having a lead to an answer to my question I will see if it easy to learn the python language and make a nice nomogram.

But first things first.... scaling

Thanks in advance for having a look at my challenge.

William