Wort Shrinkage

When figuring out the necessary runoff volume for a target batch size, I know that we have to account for shrinkage, due to the temperature difference between the pre-boil wort and the 68F mash water, sparge water, or chilled wort in the fermenter.

But why do we use 4%? Isn't that the shrinkage expected when cooling from boiling (212F) to 68F? Pre-boil runoff is what I measure in the pot... before boiling it. It's closer to 150F at this point.

Please help me see what I'm missing.

I'm sorry... your post title amused me... i skim read titles and all I noticed was shrinkage.

Me too and I never even saw that show.

Yes, the volume of water decreases by about 4% in cooling from near boiling to room temperature but there is also a loss from evaporation in the kettle. This obviously depends on your equipment, how you use it and how long you boil. Many brewers ROM evaporation at 10%/hr.

"But why do we use 4%? Isn't that the shrinkage expected when cooling from boiling (212F) to 68F?"

Say I end up with 5.25 gallons in the kettle immediately after the boil when it is essentially at boiling temp. I take a sample, cool the wort, take a gravity reading and figure I really need to dilute it to hit the desired OG. But how much water to add?

That 4% contraction means I will be able to ferment a maximum of 5 gallons. I calc the makeup volume needed above 5 gallons to hit the target OG. Now is the time to add unsterile make-up water and boil it for a few minutes.

The 4% figure is used because you are ultimately calculating your volume into the fermenter at pitching temp. Most people that really use this figure the most are those doing full boil volumes and AG brewing with no desire to top off.

Recipes that are calculated according to a needed top off take the shrinkage into account already knowing that top off water will be used such as partial boil recipes and extract brewing

If your process works well you should be hitting your expected OG with no need to top off regardless of shrinkage.

I'm doing full boils, all grain. In order for me to predict my volume and gravity at pitching, I need to have the correct pre-boil volume and pre-boil gravity.

My problem is that everything I read quotes a shrinkage compensation that assumes a change from 212 to 68 degrees. But that is not what happens. I measure pre-boil volume and gravity after filling the boil kettle from the MLT. I'm at mash temperature, not 212. So why would I use 4% shrinkage? Am I supposed to boil, and then measure volume? Doesn't seem right.

Wort density changes in about the same ratios as water density so if you want to know the change in volume going from any arbitrary temperature to any other arbitrary temperature just look up the volume change of water between those two temperatures and apply the ratio to the wort.

Good plan. Anyone know if the relationship between volume and temperature is linear?

No. It isn't. The density in grams/cc (the volume in cc/gram is 1/density) for centigrade temperature T is. As you can see this is 8th order but is accurate to almost 6 decimal places:

density = 0.99984+T*(6.7715e-05-T*(+9.0735e-06-T*(1.015e-07-T*(+1.3356e-09-T*(1.4421e-11-T*(+1.0896e-13-T*(4.9038e-16-9.7531e-19*T)))))))

ajdelange said:

density = 0.99984+T*(6.7715e-05-T*(+9.0735e-06-T*(1.015e-07-T*(+1.3356e-09-T*(1.4421e-11-T*(+1.0896e-13-T*(4.9038e-16-9.7531e-19*T)))))))

Click to expand...

AJ, I think you're cat must have crawled across your keyboard (as can be seen in the quote above)

I was hoping for something more technical and mathematical. But I can work with this anecdote. Thanks!

I assume you are kidding but in case you aren't that was copied and pasted from a piece of code that computes the density of water. You should be able to copy it (everything to the right of and including the equals sign) from your browser, paste it into an Excel spreadsheet and replace each instance of T with the address of a cell that contains the temperature. The cell containing the formula will display the density.

It would probably be more readable if spaced out better and the e's capitalized:

0.99984 + T*(6.7715E-05 - T*(+9.0735E-06 -T*( etc.

SWMBO keeps telling me to work on my sense of humor. I was kidding. Thanks so much for the details. My spreadsheet has a space reserved for your formula!

For the record, when I am moving water from one vessel to another in increments I need to control (and be conscious of), the water is always around 150-170 degrees; therefore, the shrinkage I calculate is 3% (vs. the standard 4%). My thinking is that the water is going to grow by about a percent during boil, but because we aren't concerned with the volume of water during boil, keeping track of the 1% growth, and its subsequent shrinkage is unnecessary, as I will always be left with a net loss of around 3% after cooling.

Don't forget evaporation loss. It can be as much as 10%/hr