# Ethanol Water Contraction and Dilution

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Hi there,

We use a mathematical formula which approximates the amount ethanol and water contract when mixed for diluting our spirit pre bottling.

This assists us to bottle spirit in an efficient manner and without recourse for spending money on software to do the same.  However, our method is not quite right as at times we need to adjust our spirit prior to bottling to ensure the ABV is in the right tolerance range.

This can be time consuming so if anyone knows a fool proof method we would be very grateful !

Cheers

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PeteB    45

Download TTB tables, they are free, then a bit of high-school math and you will have the correct answer.

The actual formula is a monster and I don't have it, except in the background of Alcodens program

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30 minutes ago, PeteB said:

Download TTB tables, they are free, then a bit of high-school math and you will have the correct answer.

The actual formula is a monster and I don't have it, except in the background of Alcodens program

Will the ttb tables actually account for the shrinkage of liquid when you combine alcohol and water?  Iv never seen this listed on their tables.

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PeteB    45

TTB tables do account for shrinkage, but there is not a table that shows if you add a certain amount of water to a certain proof, there is your answer.

That is where the maths comes in.

I have only used TTB tables for mental stimulation, and it has been some time. (I am Aussie so I don't use them)

I suggest you post a theoretical blend that you are trying to achieve and someone will post the math of how it is done. If no-one posts then I will re-learn and post the method for you

Pete

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Ok so here is one theoretical blend.

You have 100 gallons of 160 proof ethanol and you add 100 gallons of water.  What is your final proof and what is your total gallons.  Assuming everything is at 60 degrees.

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meerkat    13

Disclaimer: I am the author of the AlcoDens blending app mentioned below, so I am probably biased.

This question of how to do blending calculations comes up fairly often, so I wrote this article to compare 3 of the methods.

I have not seen any really comprehensive guide to performing calculations using the TTB Tables, but I am aware of two distillers who are in the process of preparing books that will cover this.  Hopefully early next year (2018) things will be better.

The theoretical blend proposed by whiskeytango is unfortunately not in the form for which the TTB Tables were structured. The tables are designed to easily answer the question of how much water to add to dilute the 100 gallons of 160 proof down to 80 proof. But it can be done.  I will show my solution but perhaps someone who actually uses the TTB tables can show an easier way.

From Table 6, 160 proof spirit contains 80 parts of alcohol and 22.87 parts of water. BTW, the fact that these add up to 102.87 shows how the tables do include the effect of contraction.

If we now add 100 gallons of water to 100 gallons of 160 proof spirit we still have 80 parts (gallons) of alcohol but we now have 122.87 parts of water. The ratio of parts of alcohol to parts of water is 80/122.87 = 0.6511. Now we have to scan through Table 6 to find what proof corresponds to this ratio. As I said, the tables are not structured to make this easy.

At 81 proof the ratio is 40.5/62.95 = 0.6434
At 82 proof the ratio is 41.0/62.47 = 0.6563

By interpolation we see that a ratio of 0.6511 corresponds to a strength of 81.6 proof.

This diluted spirit obviously contains 81.6/2 = 40.8 parts of alcohol. This came from the original 80 gallons of alcohol in the 160 proof spirit. If 80 gallons is 40.8 parts then the total parts (i.e. 100) must be 80x(100/40.8)= 196.08 gallons.

Naturally, I checked this with AlcoDens to make sure I had the correct answers. Because I do not do these calculations using the TTB Tables very often I did make a few mistakes along the way, but the values above compare well with the AlcoDens answer shown below.

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9 hours ago, whiskeytango said:

Ok so here is one theoretical blend.

You have 100 gallons of 160 proof ethanol and you add 100 gallons of water.  What is your final proof and what is your total gallons.  Assuming everything is at 60 degrees.

Do it by weight, and do it with TTB table 4. https://www.ttb.gov/foia/Gauging_Manual_Tables/Table_4.pdf

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meerkat    13

Thanks Tom, using Table 4 is a bit easier because it provides data for every 0.1 proof and it is probably easier to understand.

For comparison with my earlier calculation here is the Table 4 method.

160 pf spirit has 0.13903 WG/lb.  Table 4 only starts at 1 proof and from standard engineering tables the specific volume of water at 60 degrees F is 0.12008 WG/lb.

The weight of the spirit is therefore 100/0.13903 = 719.27 lbs and the weight of the water is 100/0.12008 = 832.78 lbs

The total weight is 719.27+832.78 = 1552.05 lbs.  This contains the same 160 PGs that were in the original spirit so we have 160/1552.05 = 0.10309 PG/lb

Table 4 shows (without interpolation) that this is 81.6 proof and the specific volume is 0.12633 WG/lb

Total volume is 1552.05 x 0.12633 = 196.07 gallons

This is definitely shorter and more direct than my earlier calculation.  But AlcoDens still wins, especially if the temperature is not 60 F and the calculated PG/lb requires interpolation.

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PeteB    45
18 hours ago, whiskeytango said:

You have 100 gallons of 160 proof ethanol and you add 100 gallons of water

The answer for this blend does clearly show shrinkage, but it is not the most common type of diluting done in a distillery.

More often the question would be: How much water do I need to add to bring the proof down to 80?

Meerkat could you show these calculations please.

As Tom said above use mass not volume for your measurements then you don't have to do temperature calculations.

I have done TTB calculations in the past and sometimes it is easier to understand and calculate if it it done in volume at 60f, but at the end convert back to mass for actual measurement.

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5 hours ago, PeteB said:

The answer for this blend does clearly show shrinkage, but it is not the most common type of diluting done in a distillery.

More often the question would be: How much water do I need to add to bring the proof down to 80?

Meerkat could you show these calculations please.

As Tom said above use mass not volume for your measurements then you don't have to do temperature calculations.

I have done TTB calculations in the past and sometimes it is easier to understand and calculate if it it done in volume at 60f, but at the end convert back to mass for actual measurement.

Yes very true,  your request is much more common.

What i would like is a formula that lets me take a density reading and determine that i have X proof alcohol.  Then i would like to add an exact amount of water then take a new density reading showing a lower proof because of the water i added.   Then i would love to be able to have something that says i have an unknown volume of X proof that i add a known volume of water to and also have a final proof.   So by using the change in proof and the known quality of water added determine my total volume of spirit at the final proof.

Does that make sense?

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meerkat    13

PeteB - The calculation for the quantity of water required to dilute to a target proof is illustrated in the article I referenced before.  The example is based on volumes, but it could easily be converted to weights using a similar method to what I showed above when using Tom's suggestion to use Table 4.

whiskeytango - The questions you are asking are exactly those AlcoDens was designed to answer.  The formulas are way too complex to use in manual calculations.  They are freely available from the OIML site if you want to see just how involved they are.

Quote

What i would like is a formula that lets me take a density reading and determine that i have X proof alcohol.

The AlcoDens calculator for doing this can convert back and forth between Mass (Weight) %, Density, Volume % (ABV), Proof and Molar %

Quote

Then i would like to add an exact amount of water then take a new density reading showing a lower proof because of the water i added.   Then i would love to be able to have something that says i have an unknown volume of X proof that i add a known volume of water to and also have a final proof.   So by using the change in proof and the known quality of water added determine my total volume of spirit at the final proof.

As an example assume there is an unknown quantity of 150 proof spirit to which we add 100 lbs of water.  After mixing the proof is 100 proof.  What was the unknown volume of 150 proof spirit and what volume of 100 proof spirit has been produced?

In the example shown below Source 2 is the pure water (Proof = 0).  I have set the Source 2 quantity to mass and given the weight as 100 lbs, but you could equally well give the quantity as volume.  In the bottom right panel you tell the program that the quantity of Source 2 is the known quantity.  Set the Source 1 and Final Blend quantities to Volume and it will calculate how much 150 proof spirit was used and how much 100 proof has been produced.

THis could be solved using Tom's Table 4 method provided all quantities are in weight terms by starting off with the classic "Let X be the mass of 150 proof spirit" and noting that the number of proof gallons does not change when you add pure water.  Once the answers have been calculated in weight terms they can easily be converted to volumes.