scaling of a N/Z type nomogram

Mathematics about graphical computing
Glen
Posts: 67
Joined: Fri Jan 25, 2008 4:11 am
Location: Australia

Re: scaling of a N/Z type nomogram

Postby Glen » Tue Feb 03, 2015 6:30 am

With the image -- I don't understand why my image doesn't show up in my post then, since I think I did pretty much exactly that.

I've been playing with a determinant with B0,B1,OG,FG,ADF in it. I keep getting sort of close to something nice -- but it's tricky
Glen
Posts: 67
Joined: Fri Jan 25, 2008 4:11 am
Location: Australia

Re: scaling of a N/Z type nomogram

Postby Glen » Wed Feb 04, 2015 5:25 am

Hmm. I may have something.

It looks like it's possible to have a nomogram for ADF/OG/FG and ADF/B0/B1 with a common ADF scale, a shared scale (I think right down to the tick-mark labels, but I need to double check that) parallel to it for two of the variables, and then the remaining variables on two separate axes (one curved), but with an interesting relationship between them that might possibly be worth highlighting on the nomogram (or maybe doing that doesn't have any value).

I need to go through the details again to make sure I have it all correct, but I think it might work well enough.
kloekwil
Posts: 10
Joined: Mon Dec 29, 2014 8:00 pm

Re: scaling of a N/Z type nomogram

Postby kloekwil » Wed Feb 04, 2015 6:22 pm

You are really making me curious :roll: Already thanks in advance for putting the effort in this

Probably the B0 variable en the OG variable will be on the same axis parallel to the ADF axis whereas both the B1 and FG axis are curves of one of them is curved.

For your information the physical story behind this:
Brix and Gravity both depend on sugar concentration and alcohol concentration. During beer production sugar is converted to alcohol meaning that sugar concentration decreases and alcohol concentration increases. At time=0 there is no alcohol present and the sugar concentration is maximal so Brix=B0 and gravity=OG. Therefor at time=0 there is a simple relation between B0 and OG (making the scales coincide).

The conversion between sugar and alcohol is a simple linear relation: one part of sugar (in moles) is converted to two parts alcohol (in moles). In weight percentages there is a conversion factor between those two.

Brix value depends on both sugar concentration and alcohol concentration but has a difference sensitivity to both of them. There will a relation like Brix=a*sugarconcentration+b*alcoholconcentration.
Gravity also depends on both sugar concentration and alcohol concentration and has a difference sensitivity to both of them. There will a relation like Gravity=c*sugarconcentration+d*alcoholconcentration.
Therefor I expect the B1 and FG lines to be differently orientated (curved) but may be parallel to each other due to differenr constants a, b, c and d.

The nice thing is that when one knows OG or B0 and the ADF, the alcohol content is also known independent on using either the OG-FG-ADF nomogram or the B0-B1-ADF nomogram. The alcohol content should be some kind of connecting line.

The alcohol content by volume (ABV) is given by: (in terms of OG and FG): ABV = 486.8693 * (OG - FG) / (4749.804 - FG)
Glen
Posts: 67
Joined: Fri Jan 25, 2008 4:11 am
Location: Australia

Re: scaling of a N/Z type nomogram

Postby Glen » Mon Apr 06, 2015 4:42 am

Sorry about the long delay; I got encouraged into preparing for and then running to be moderator of a largish forum. ... and then once I was elected, I had to learn the ropes

Still learning, really.

Anyway, I hope to get myself back up to speed on your problem and hopefully show you something useful.

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