Alcohol dilution when making Liqueurs

[fabio_abreu]

Hi everyone,


Probably the answer to this question is around the site somewhere but I can't find it.

I need help figuring out the equations for the screenshot I provide (calculators from the 'La Distillation Amateur' website). These are in french but I breakdown below.

1st calculator:
I want to dilute a 750ml bottle of 66%abv to 40%abv with a sugar content of 165g/L.
It calculates that I need to add 487ml of syrup made with 359ml of water and 204g of sugar.
How do I get to those numbers by myself?

2nd calculator:
I want to make a 750ml bottle of liqueur with 22%abv using 75%abv alcohol with a final sugar content of 150g/L.
It calculates that I need 220ml of alcohol and 530ml of syrup (made by blending 459ml of water with 112,5g of sugar).
What's the equation for this?

If you can provide me the formulas with the examples mentioned, I would really appreaciate it.

[Hügelwilli]

If it uses a simple formula then it is not accurate. This calculator looks very old fashioned. Probably it uses a simple formula.

There is contraction between alcohol and water and between sugar and water. This means that 1lt alcohol and 1lt water doesn't result in 2lt mixture but less. Same problem with sugar and water. But this would be calculable precisely enough with complicated polynomes. But I doubt that your calculator does this.

But then there is also expansion between alcohol and sugar. And this has been never studied. It means if you add a certain amount of sugar to water so that the volume rises by 100ml, then if you add the same amount of sugar to an alcohol-water-mixture, the sugar will raise it by more than 100ml. Me and a member of my forum have measured this many times, have built a detailed table and built a tool with it: https://hobbybrennen.ch/Rechner/en/Liqu ... lator.html
It's not exactly what you are asking for, but perhaps you like it.

Or if you post the link to your calculators, perhaps I can find out the formulas they use. Normally the code of such online calculators is visible for users and understandable.


Edit:
But you can do this even without much calculation. At least if you don't need the exact water amount. Simply by topping up with water. The calculated water amount of your calculator probably is wrong. But that doesn't matter in practice:

1.
750ml 66% are 750 x 66 / 40 = 1.2375lt 40%.
So you need 1.2375 x 165 = 204.2g sugar.
Dissolve the sugar with a bit water, mix it to the alcohol and then top up with water to 1.2375lt. Wait with the last bit of water until everything has mixed well.
As long you don't need to know the water amount, this is mathematically 100% exact.

2.
750ml 22% need 750 x 22% = 165ml alcohol.
So you need 165 / 75% = 220ml alcohol with 75%.
And you need 0.75lt x 150 = 112.5g sugar.
Also here dissolve the sugar with a bit water, mix it to the alcohol and then top up with water to 0.75lt. Wait with the last bit of water until everything has mixed well.
As long you don't need to know the water amount, this is also mathematically 100% exact.

[Kareltje]

I made a simple calculator in Excel, but that does not take the contraction into account. If you want to do that, you should use the link Hügelwilli gave.

OuzoEngels.xls

(39 KiB) Downloaded 9 times

[fabio_abreu]

If it uses a simple formula then it is not accurate. This calculator looks very old fashioned. Probably it uses a simple formula.

There is contraction between alcohol and water and between sugar and water. This means that 1lt alcohol and 1lt water doesn't result in 2lt mixture but less. Same problem with sugar and water. But this would be calculable precisely enough with complicated polynomes. But I doubt that your calculator does this.

But then there is also expansion between alcohol and sugar. And this has been never studied. It means if you add a certain amount of sugar to water so that the volume rises by 100ml, then if you add the same amount of sugar to an alcohol-water-mixture, the sugar will raise it by more than 100ml. Me and a member of my forum have measured this many times, have built a detailed table and built a tool with it: https://hobbybrennen.ch/Rechner/en/Liqu ... lator.html
It's not exactly what you are asking for, but perhaps you like it.

Or if you post the link to your calculators, perhaps I can find out the formulas they use. Normally the code of such online calculators is visible for users and understandable.


Edit:
But you can do this even without much calculation. At least if you don't need the exact water amount. Simply by topping up with water. The calculated water amount of your calculator probably is wrong. But that doesn't matter in practice:

1.
750ml 66% are 750 x 66 / 40 = 1.2375lt 40%.
So you need 1.2375 x 165 = 204.2g sugar.
Dissolve the sugar with a bit water, mix it to the alcohol and then top up with water to 1.2375lt. Wait with the last bit of water until everything has mixed well.
As long you don't need to know the water amount, this is mathematically 100% exact.

2.
750ml 22% need 750 x 22% = 165ml alcohol.
So you need 165 / 75% = 220ml alcohol with 75%.
And you need 0.75lt x 150 = 112.5g sugar.
Also here dissolve the sugar with a bit water, mix it to the alcohol and then top up with water to 0.75lt. Wait with the last bit of water until everything has mixed well.
As long you don't need to know the water amount, this is also mathematically 100% exact.

That was really helpful and simple, I think it breaks down exactly what I was looking for. I was going crazy for not getting the readings that the calculator applies with water and sugar mixture it needs to get the exact abv and sugar % I needed. But still, if there is a way, I would love to know the formulas (taking contraction into account as best as possible).
This is just so I understand these better (out of curiosity).


Another thing:
That "bit of water" that you wrote goes into the final measurement of water needed, correct?
Do these measurements make exactly a 750ml bottle with 22%abv and 15% sugar content?

Here is the link:
https://fairesagnole.eu/page4/page28/diluer.html

I really like your calculator. Saved

[fabio_abreu]

I made a simple calculator in Excel, but that does not take the contraction into account. If you want to do that, you should use the link Hügelwilli gave.

OuzoEngels.xls

I saw this in another thread when searching for answers and I thank you for taking your time for providing me it.
It was in another language that I don't understand.

[Hügelwilli]

Another thing:
That "bit of water" that you wrote goes into the final measurement of water needed, correct?
Do these measurements make exactly a 750ml bottle with 22%abv and 15% sugar content?

That bit of water is to make sure you use the right amount water so that you end with the right total amount.
When you mix alcohol and water, little bubbles appear and the mixture heats up a bit. Those bubbles have to go away and the mixture should come to 20°C again before you fine-tune the water addition.
Like I wrote, this calculation is mathematically correct. Not only precise. Only the exact amount of water you will not find out easily.
The definition for 40%abv is that 1lt at 20°C mixture contains 400ml alcohol. And the definition of 100g/lt sugar is that 1lt at 20°C mixture contains 100g sugar. Some things would be easier if the industry would use alcohol by weight. But then they would need to write on the bottle not the volume but the weight. And that would be very strange for drinks. Drinks have always a volume not a weight. The bottle Whisky has "700ml", not 650g perhaps.

Actually for me it this a great thread. I think I will code a similar calculator like this, but with more exact water amount calculation (and the first calculator strangely lacks of a calculation of the final volume although this is easy). I will PM you when it is published.

[fabio_abreu]

Thank you for your help and please let me know when it's ready.

[NZChris]

For small batches, I make up simple syrup with a known amount of sugar and weigh and measure the resulting syrup so that I can express it as g/l and g/kg. If g/100ml and g/100g is easier for you, use them. It keeps in the fridge for several weeks.

To make up a desired volume, I calculate how much of the spirit to use for the ABV and how much simple syrup to use for the sugar, then top up with water to the desired volume. If I was being fussy, I would put the product in a 20C incubator overnight and top up the water the next day, but I don't bother.

If you intend to make repeat batches of the same recipe, weigh the water before you use any, then again after you finish. The difference is how much water to use next time.

If you weigh and record every ingredient the first time you make a batch, subsequent batches are quick and easy and can be done on the scales in one vessel, or the bottle, with no measuring jugs to clean up afterwards.

[fabio_abreu]

Thank you for your contribution NZChris, that is exactly what I'm looking for, consistency...and convenience.

I realized that it does make a difference but it can be negligible in small batches, which I intend to do for now.

Trying to learn with the pros