New way to calculate FG, what do you think?

[ScottM]

For the last few days I've been pondering over the FG calculation. I've mentioned this a few times over the last few days and not had very much interest but I guess that's because people, for the most part, just want to make some good brew :thumb:

However, I'm never happy doing something without knowing exactly what's going on so as soon as I started using calculators etc I wanted to see how they worked, feel free to use this info, comment on it or just plain ignore it... it's here now

I wasn't happy that most calculators just assume that 75% of a recipe is going to be converted to sugar regardless of what was in it, based on 75% attenuation of course. So I started trying to figure out the best way to get a more reasonable calculation based on the actual sugars in a recipe. Here is what I found with a working example....

Volume - 23L
Solids - 3kg
Yield of Solids - 95%
Fermentables in the solids - 80%
Attenuation of yeast - 75%

To work out the OG:

OG = 1 + the yield of the solids / by the volume * 0.36

The reason for this is that a 10g of sugar in 100ml of water makes a 36 point increase.

So...

OG = 1 + (((95% of 3kg)/23L) * 0.36)
OG = 1 + (((2.85)/23) * 0.36)
OG = 1 + (0.1239 * 0.36)
OG = 1 + 0.04461
OG = 1.045



Original calculation to estimate FG

FG = ((OG-1) - ((Attenuation/0.814) * (OG-1))) + 1

=((1.045-1) - ((75%/0.814) * (1.045-1))) + 1
=(0.045 - (0.9214 * 0.045)) + 1
=(0.045 - 0.0415) + 1
=1.004



The above calculation assumes that everything in the OG based calculation is fermentable and assumes that the yeast will consume exactly its attenuation figure regardless of how much sugar is actually available so I have now worked out a different method of calculating the FG that does take account of this...

ml of Sugar = (solids * % of solids that are sugars) * 0.645
ml of Sugar = (3000 * 80%) * 0.645
ml of Sugar = 2400 * 0.645
ml of Sugar = 1548ml

%vol of Sugar = (100/total volume) * ml of Sugar
%vol of Sugar = (100/23000) * 1548
%vol of Sugar = 0.00435 * 1548
%vol of Sugar = 6.73% sugar

Attenuation of yeast = 75%



FG = OG + 0.624 - SQRT(((%Sugar * 0.814 * (attenuation * 1.33))) / 100.3) - (OG - (125.65 / 200.6)) ^ 2 +(125.65 ^ 2 / (2 * (100.3) ^ 2)) + OG ^ 2 - ((OG * 125.65) / 100.3))

FG = 1.045 + 0.624 - SQRT(((5.464 * (0.75 * 1.33)) / 100.3) - (1.045 - 0.624))^2 + (15787.923/20120.18) + 1.045^2 - ((1.045 * 125.65)/100.3))

FG = 1.669 - SQRT((5.464/100.3) - (0.421)^2 + 0.785 + 1.092 - (131.304/100.3))
FG = 1.669 - SQRT(0.0545 - 0.177 + 0.785 + 1.092 - 1.3091)
FG = 1.669 - SQRT(0.445)
FG = 1.669 - 0.667
FG = 1.002


The reason for this is that the attenuation based calculation assumes that 75% of all solids are fermentable. In this example there are actually 80% of the solids fermentable. If we use this correction on the original equation you will see...


FG = ((OG-1) - ((Attenuation/0.814) * (OG-1))) + 1

=((1.045-1) - ((80%/0.814) * (1.045-1))) + 1
=(0.045 - (0.982 * 0.045)) + 1
=(0.045 - 0.0442) + 1
=1.001

The slight difference between both of the answers is down to the fact that the new calculation only uses the actual sugar to calculate the FG rather than the entire solids. The attenuation still becomes a part of the new equation as obviously a higher attenuative yeast will consume more of the complex sugars. The new FG calculation is based on the type of sugar that a 75% attenuation yeast would eat, but it still adjusts for any changes in the yeast used "(attentuation * 1.33)" takes care of this part of things.

Just to add, this info is only really of any use to people using kits, sugars and extracts. It's not really much use for AG brewing as that's where the 75% attenuation guess actually comes from. The actual amount of fermentable sugar in an AG kit will probably vary far too much to nail down accurately. I'll no doubt stick my head into that at some point in the future though.

Cheers :)

 

[Baz Chaz]

.... It's not really much use for AG brewing as that's where the 75% attenuation guess actually comes from.

I wish you'd said that at the start Scott, (I only brew AG) my 'ead was starting to hurt reading through those figures :wha:

Think I'll stick with BrewMate, not much of a headache using that :?

 

[ScottM]

.... It's not really much use for AG brewing as that's where the 75% attenuation guess actually comes from.

I wish you'd said that at the start Scott, (I only brew AG) my 'ead was starting to hurt reading through those figures :wha:

Think I'll stick with BrewMate, not much of a headache using that :?

Sorry bud

It can easily be used for AG calculations but you would need to do some other calculations first. Basically you need to know how much fermentables are in your wort and you can then do a the above calculation to work out the FG.

For example..

Grain1 when extracted is 60% fermentable
Grain2 when extracted is 70% fermentable
Grain3 when extracted is 80% fermentable

G1 Fermentables = 0.6 * weight of grain1
G2 Fermentables = 0.7 * weight of grain2
G3 Fermentables = 0.8 * weight of grain3

Total fermentables = G1 + G2 + G3

From there you know the weight of the sugar you have so you can then use the calculation above for an accurate figure.

Obviously I'm just making up the %age figures as I assume they will be a lot lower than that but you get the idea :)

Easy peasy

 

[abeyptfc]

Did you have a George Malley moment from 'Phenomenon' and wake up in the middle of the night with that equation?!

 

[ScottM]

Did you have a George Malley moment from 'Phenomenon' and wake up in the middle of the night with that equation?!

I wish

Even though it doesn't look it it's actually the Alcohol% = (OG - FG) * (100.3 * (OG - FG) + 125.65) equation transposed.

 

[Baz Chaz]

Sorry bud

It can easily be used for AG calculations but you would need to do some other calculations first. Basically you need to know how much fermentables are in your wort and you can then do a the above calculation to work out the FG.

For example..

Grain1 when extracted is 60% fermentable
Grain2 when extracted is 70% fermentable
Grain3 when extracted is 80% fermentable

G1 Fermentables = 0.6 * weight of grain1
G2 Fermentables = 0.7 * weight of grain2
G3 Fermentables = 0.8 * weight of grain3

Total fermentables = G1 + G2 + G3

From there you know the weight of the sugar you have so you can then use the calculation above for an accurate figure.

Obviously I'm just making up the %age figures as I assume they will be a lot lower than that but you get the idea :)

Easy peasy

Oy buggerlugs ... you've just done it again :wha:

I enjoy my brewing and it's gone pretty well, I keep saying AG brewing isn't rocket science ........... and I'd rather keep it that way :lol:

I'm sure your calculations are of interest to others though :ugeek: :ugeek: :ugeek: so take no notice of Old Barking Baz, I'll happily keep plugging away in my own happy (hoppy) world of brewing :thumb:

I love the Aussie saying ...... KISS

keep it simple stupid :thumb: (think they had me in mind :whistle: )

 

[Aleman]

Nice lot of working in theory, but there are too many variables to be able to determine it with any accuracy. What is the difference in fermentability with a mash at 64C compared to 66C for example?

If I want to know the FG I simply do a fast fermentation test, normally get to know within 24Hours well before the main batch has finished.

 

[ScottM]

Nice lot of working in theory, but there are too many variables to be able to determine it with any accuracy. What is the difference in fermentability with a mash at 64C compared to 66C for example?

If I want to know the FG I simply do a fast fermentation test, normally get to know within 24Hours well before the main batch has finished.

This is where it comes down to the user, how far they wish to take it etc. For extract brewing it's ideal as you can find out exactly what is in all ingredients.

The calculation is used to predict what you will see more accurately than current calculations. I would rather know what sort of alcohol a certain recipe was going to make before I actually made it.

 

[jamesb]

If I want to know the FG I simply do a fast fermentation test, normally get to know within 24Hours well before the main batch has finished.

+1

There's just too many variables involved. Especially the first time you do a recipe.

 

[ScottM]

If I want to know the FG I simply do a fast fermentation test, normally get to know within 24Hours well before the main batch has finished.

+1

There's just too many variables involved. Especially the first time you do a recipe.

I take it you are also referring to AG? As I said in the initial post, this isn't really aimed at AG brewers (although I honestly can't think of why it can't be used, but I haven't done AG yet).

 

[ScottM]

Nice lot of working in theory, but there are too many variables to be able to determine it with any accuracy. What is the difference in fermentability with a mash at 64C compared to 66C for example?

If I want to know the FG I simply do a fast fermentation test, normally get to know within 24Hours well before the main batch has finished.

Just been re-thinking this.

Surely it's the yield that changes when the temperature changes rather than the %age of fermentables? Afterall, the yield is made up of fermentables and non-fermentables.... does the percentages of each change when the yield doesn't based on temp?

 

[graysalchemy]

In all grain brewing ajusting the temp of the mash will effect how the starch is broken down into fermentable and unfermentable sugars because of the enzyme pathways.

Now malt extract will vary from batch to batch as most malt extract is a blend of many different malt extracts bought in like so many food stuffs so consistency is never going to be the same. Obviously different yeasts and temps will also play their part in all this.

 

[ScottM]

In all grain brewing ajusting the temp of the mash will effect how the starch is broken down into fermentable and unfermentable sugars because of the enzyme pathways.

Now malt extract will vary from batch to batch as most malt extract is a blend of many different malt extracts bought in like so many food stuffs so consistency is never going to be the same. Obviously different yeasts and temps will also play their part in all this.

So what you are saying is no-one ever cares what their FG is going to be before they actually make a recipe? And they don't even bother to use a calculator to give an approximation of the alcohol or FG they are looking to achieve? They just chuck in ingredients and hope for the best, checking in a few days with a fast fermentation test to see what they are working with?

This seems highly unlikely to me. I haven't made a recipe yet where I haven't worked out the approximate FG and Alcohol that the recipe should attain.

Maybe I'm just different then but I always want to know how much alcohol I will be seeing in a recipe.

 

[graysalchemy]

I usually make my beers to 1055 and using the same yeast nottingham I know they will usually drop to 1014/15 so I get a beer of about 5.3% that is all I need to know.

Beer Engine gives an estimation of what it should attenuate too, but I think this is based on attenuation rates and efficiency figures that you put in which is gained through trial and error really and also the OG of the beer.

 

[rich27500]

Impressive maths mate, you may want to check out the calculator on the BIAB forum. They are ridiculously technical over there. That's one of the reasons I like this forum, people worry less about figures. I still like to do a bit of working out but not too much because it spoils the art for me.

 

[ScottM]

I usually make my beers to 1055 and using the same yeast nottingham I know they will usually drop to 1014/15 so I get a beer of about 5.3% that is all I need to know.

Beer Engine gives an estimation of what it should attenuate too, but I think this is based on attenuation rates and efficiency figures that you put in which is gained through trial and error really and also the OG of the beer.

All the calculators I have looked at use the first calculation I put up. I don't know if I've looked at beer engine though.

I think it's obvious that if you are making the same beers, from the same ingredients, with the same yeasts, with the same staring OG it'll be fair to say that the FG will be pretty much a given. That's not really my point though is it?

I'm making various different beers with different yeasts and ingredients constantly, not to mention wines and ciders, so I am constantly working out new recipes and what they will attain.

If I use Honey it will obviously have an impact on the FG as opposed to using sugar. It'll also have an impact on the OG but not to the same degree.

As I say, it's not really for the AG guys... and I'm beginning to notice for more reasons than one. I remember telling my Gran one day that the flavouring goes into the super noodles before taking them out of the pot rather than after. I got a similar response then.

 

[oldstout]

For the last few days I've been pondering over the FG calculation. I've mentioned this a few times over the last few days and not had very much interest but I guess that's because people, for the most part, just want to make some good brew :thumb:

However, I'm never happy doing something without knowing exactly what's going on so as soon as I started using calculators etc I wanted to see how they worked, feel free to use this info, comment on it or just plain ignore it... it's here now

I wasn't happy that most calculators just assume that 75% of a recipe is going to be converted to sugar regardless of what was in it, based on 75% attenuation of course. So I started trying to figure out the best way to get a more reasonable calculation based on the actual sugars in a recipe. Here is what I found with a working example....

Volume - 23L
Solids - 3kg
Yield of Solids - 95%
Fermentables in the solids - 80%
Attenuation of yeast - 75%

To work out the OG:

OG = 1 + the yield of the solids / by the volume * 0.36

The reason for this is that a 10g of sugar in 100ml of water makes a 36 point increase.

So...

OG = 1 + (((95% of 3kg)/23L) * 0.36)
OG = 1 + (((2.85)/23) * 0.36)
OG = 1 + (0.1239 * 0.36)
OG = 1 + 0.04461
OG = 1.045



Original calculation to estimate FG

FG = ((OG-1) - ((Attenuation/0.814) * (OG-1))) + 1

=((1.045-1) - ((75%/0.814) * (1.045-1))) + 1
=(0.045 - (0.9214 * 0.045)) + 1
=(0.045 - 0.0415) + 1
=1.004



The above calculation assumes that everything in the OG based calculation is fermentable and assumes that the yeast will consume exactly its attenuation figure regardless of how much sugar is actually available so I have now worked out a different method of calculating the FG that does take account of this...

ml of Sugar = (solids * % of solids that are sugars) * 0.645
ml of Sugar = (3000 * 80%) * 0.645
ml of Sugar = 2400 * 0.645
ml of Sugar = 1548ml

%vol of Sugar = (100/total volume) * ml of Sugar
%vol of Sugar = (100/23000) * 1548
%vol of Sugar = 0.00435 * 1548
%vol of Sugar = 6.73% sugar

Attenuation of yeast = 75%



FG = OG + 0.624 - SQRT(((%Sugar * 0.814 * (attenuation * 1.33))) / 100.3) - (OG - (125.65 / 200.6)) ^ 2 +(125.65 ^ 2 / (2 * (100.3) ^ 2)) + OG ^ 2 - ((OG * 125.65) / 100.3))

FG = 1.045 + 0.624 - SQRT(((5.464 * (0.75 * 1.33)) / 100.3) - (1.045 - 0.624))^2 + (15787.923/20120.18) + 1.045^2 - ((1.045 * 125.65)/100.3))

FG = 1.669 - SQRT((5.464/100.3) - (0.421)^2 + 0.785 + 1.092 - (131.304/100.3))
FG = 1.669 - SQRT(0.0545 - 0.177 + 0.785 + 1.092 - 1.3091)
FG = 1.669 - SQRT(0.445)
FG = 1.669 - 0.667
FG = 1.002


The reason for this is that the attenuation based calculation assumes that 75% of all solids are fermentable. In this example there are actually 80% of the solids fermentable. If we use this correction on the original equation you will see...


FG = ((OG-1) - ((Attenuation/0.814) * (OG-1))) + 1

=((1.045-1) - ((80%/0.814) * (1.045-1))) + 1
=(0.045 - (0.982 * 0.045)) + 1
=(0.045 - 0.0442) + 1
=1.001

The slight difference between both of the answers is down to the fact that the new calculation only uses the actual sugar to calculate the FG rather than the entire solids. The attenuation still becomes a part of the new equation as obviously a higher attenuative yeast will consume more of the complex sugars. The new FG calculation is based on the type of sugar that a 75% attenuation yeast would eat, but it still adjusts for any changes in the yeast used "(attentuation * 1.33)" takes care of this part of things.

Just to add, this info is only really of any use to people using kits, sugars and extracts. It's not really much use for AG brewing as that's where the 75% attenuation guess actually comes from. The actual amount of fermentable sugar in an AG kit will probably vary far too much to nail down accurately. I'll no doubt stick my head into that at some point in the future though.

Cheers :)

You got a lot of time on your hands Scott :whistle:

:lol: :lol: :lol: :lol: :lol:

I have a method of calculating my FG, and it's much less complicated :thumb: :thumb:



:whistle: :whistle: :whistle:


:hmm: :hmm: :hmm:



I see how many bottles I can drink :hmm: :hmm: :hmm: before I fall over making my way back into the bedroom :drunk: :drunk: :drunk: :drunk: :thumb:



Just drink it - forget the science :drink:

:

 

[ScottM]

Impressive maths mate, you may want to check out the calculator on the BIAB forum. They are ridiculously technical over there. That's one of the reasons I like this forum, people worry less about figures. I still like to do a bit of working out but not too much because it spoils the art for me.

It's really not as complicated as it looks, honest, it just looks like a lot to take in when its all laid out. In order to test out the working I just made up a simple excel sheet that asks for a few different values. It looks something like this..

Volume -
Solids -
%Yield -
% of solids that are fermentable -
Yeast Attenuation - Default 75%


I then have another column where the following is calculated using the above

OG
FG
% Alcohol

It's all automatic and any changes to the first 5 values are automatically re-calculated down below.

I just wanted to show my working in case anyone was interested and wanted to look into it. I definitely didn't expect the type of response I've gotten anyway. The same has happened with just about every thread I've started on here, from recipes to trying to help out. So I'm more and more tending to think that this forum just isn't for me at all.

 

[ScottM]

You got a lot of time on your hands Scott :whistle:

:lol: :lol: :lol: :lol: :lol:

I have a method of calculating my FG, and it's much less complicated :thumb: :thumb:



:whistle: :whistle: :whistle:


:hmm: :hmm: :hmm:



I see how many bottles I can drink :hmm: :hmm: :hmm: before I fall over making my way back into the bedroom :drunk: :drunk: :drunk: :drunk: :thumb:



Just drink it - forget the science :drink:

:

I like that philosophy but I also like to know that I won't have to physically swim in the stuff to feel a dunt

 

[oldstout]

Haha I like it :thumb:

Feeling the dunt :lol: :lol: :lol:



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