[tommymorris]

I have a spread sheet I use to calculate brew parameters and log information.

One of the math models I use in my spreadsheet estimates gravity points (GP) post boil from GP preboil and pre and post boil volumes. The same model is used by Beersmith and many other beer recipe software tools.

GP(post boil) = GP(preboil)*Volume(preboil)/Volume(post boil)

In my experience, this model always over estimates post boil GP by 2-4 points.

One factor that can impact my results is volume measurement accuracy. I measure volumes with a dip stick with 0.1G graduation marks. I believe my dip stick is reasonably accurate. I will leave reasonable undefined.

Another factor that can contribute to inaccuracies from the GP formula is wort temperature when measuring volume. To avoid this problem, I correct all volumes to relative volumes at 75F before using the GP formula.  I assume 4% expansion between 75F and 212F and assume this expansion is linear across that temperature range.

I attribute the missing gravity points to hot and cold break, hops absorbing some sugar, and to hop additions affecting the measure post boil volume.

Preboil the hot and cold break are suspended in the liquid and affect the specific gravity. Post boil the hot and cold break have dropped out of suspension causing them to no longer contribute to specific gravity of the liquid while still contributing to volume. I don't know how to estimate the contribution of the hot and cold break to the missing gravity points.

For the hops, if the hops do absorb some sugar, then that sugar is no longer in suspension to affect the specific gravity of the wort. This will decrease the measured gravity. I do not know how to estimate the GP formula error due to hops absorbing sugar.

Hops additions during the boil also add volume.  The added volume from hop mass will contribute to some difference in measured versus predicted gravity. One ounce of hops pellets has approximately 2 ounces volume. In a 6 gallon batch, adding 1 ounce of hop pellets should increase the volume by 0.0156 gallons and decrease the GP prediction by 0.1 points for a 40 point wort and 0.2 points for an 80 point brew.  At these levels hops volume can have a significant impact on the error. For a 6G 50 point wort with 5 ounces of hops the predicted GP is decreased 0.64 GP. However, this moves the predicted GP closer to the measured GP, ie. decreases error.

A few questions:

1. Does my experience match other brewer's experience?
2. Has anyone ever mathematically modeled these effects?

My brain hurts from writing this.

[HoosierBrew]

I use the GP x preboil volume / post boil calculation as well, and compare it to my actual post boil reading as well. Yeah, I think at best it's a crapshoot to try to hit it perfectly. As you say, there is the supposed 4% expansion, as well as possible (likely) inaccuracies in our volumes. I tried very hard to calibrate my measurements on my measuring stick accurately, but let's say each calibration mark is only an oz or two off - it's possible that by the time i got to my 5.5 gallon postboil mark that I was off by + or - a pint or more. That could easily throw gravity readings off by a couple points.
I've always wondered how linear the 4% expansion is as well.

[tommymorris]

You're right. All my error could be from bad volume measurements. Since I use the same dipstick every time this could explain the consistent error also.

I wonder how much hot and cold break contribute. Is it negligible or significant?

I think about this in the context of explaining why my preboil and post boil efficiencies are always different.

I know I am over analyzing the problem, but, it's fun.

[HoosierBrew]

Yep, it's fun to figure out ways to try to be more precise. I've gotten to where I collect exactly 7 gallons preboil each time (with the mash tun drained dry) because I boil off right at 1.5 gallons/hour. So I'm always left with the 5.5 post boil that I want. My preboil OG,if not spot on, is within a point or so (occasionally two), as is my post boil OG. I feel like the discrepancies are probably within the margin of error of volume measurements on the measuring stick, as well as the fact that malts from different maltsters can have different extraction rates IMO. All in all, I'm good with it.

EDIT  -  In terms of the hot and cold break question, I have no idea there. I would think negligible, but I don't know that for sure.

[a10t2]

I wonder how much hot and cold break contribute. Is it negligible or significant?

It's not just negligible, it's zero. The hot and cold break proteins are suspended in the wort, not dissolved. Same for the hops - they don't increase the volume of the wort, they just displace it. There are some hop components that are dissolving, but I don't think that would be measurable. Alpha acids are the major one, and even that's at the ppm level.

Are you accounting for the fact that "gravity points" aren't linear? 7.0 gal of 1.0500 wort would boil down to 5.5 gal at 1.0645, not 1.0636, for example.

What are the error bars on your measurements? If you're measuring gravity to ±0.0005 SG and volume to ±0.05 gal, then in the example above, the error in post-boil gravity is ±0.0017 SG. Relative errors for multiplication and division are additive.

[tommymorris]

I wonder how much hot and cold break contribute. Is it negligible or significant?

It's not just negligible, it's zero. The hot and cold break proteins are suspended in the wort, not dissolved. Same for the hops - they don't increase the volume of the wort, they just displace it. There are some hop components that are dissolving, but I don't think that would be measurable. Alpha acids are the major one, and even that's at the ppm level.

Are you accounting for the fact that "gravity points" aren't linear? 7.0 gal of 1.0500 wort would boil down to 5.5 gal at 1.0645, not 1.0636, for example.

What are the error bars on your measurements? If you're measuring gravity to ±0.0005 SG and volume to ±0.05 gal, then in the example above, the error in post-boil gravity is ±0.0017 SG. Errors for multiplication and division are additive.

Sean, I know that the contribution of the hot an cold break to Gravity is zero post boil because the break is particulate and particles do not contribute to the liquid's specific gravity. My question is how much does that same material affect the preboil gravity measurement when it is part of the liquid (before a chemical reaction causes it to drop out). If the preboil gravity is slightly higher due to this it will affect the predicted post boil gravity using the GP equation.

[tommymorris]

I wonder how much hot and cold break contribute. Is it negligible or significant?

Are you accounting for the fact that "gravity points" aren't linear? 7.0 gal of 1.0500 wort would boil down to 5.5 gal at 1.0645, not 1.0636, for example.

No. The equation I cited definitely has a linear relationship. Is there a better model?

[a10t2]

The protein molecules are never dissolved, just suspended in the wort. I would assume they form colloids since they have hydrophilic and hydrophobic regions, but protein structure is really complicated and variable and way over my head. The coagulation and settling of the denatured proteins to form the break material is a purely mechanical process.

No. The equation I cited definitely has a linear relationship. Is there a better model?

It isn't a model per se, it's just the nature of the units you're working in. The only solution as far as I know is to convert to a w/w unit (Brix, Plato, etc.).

[tommymorris]

I don't understand your comment about 7G boiling down to 5.5G. Why is the gravity 1.0645 not 1.0636? What am I missing?

[HoosierBrew]

It isn't a model per se, it's just the nature of the units you're working in. The only solution as far as I know is to convert to a w/w unit (Brix, Plato, etc.).

So I assume just sub in the Brix equivalent in the equation, Sean ?  In other words, if my preboil on 7 gallons is 10 Brix, then 10 X 7 = 70. Boiled down to my 5.5 gallon target, 70 / 5.5 = 12.72 Brix, ie., ~ 1.051ish. So this takes into account the 'non-linearity'  ?

[a10t2]

I don't understand your comment about 7G boiling down to 5.5G. Why is the gravity 1.0645 not 1.0636? What am I missing?

SG is essentially density - it's a w/v (mass over volume) unit. When you dissolve something, the mass stays constant (conservation of mass) but the volume doesn't. So a 10°Bx sucrose solution (10% by mass) has an SG of 1.040, but a 20°Bx solution has an SG of 1.083. You might assume that reducing the volume of the 1.040 SG solution by half would yield an SG of 1.080, but in this case you'd be off by almost 4%.

Going straight to Brix doesn't actually totally solve the problem (you still have a circular relationship between density and volume), but it's much closer. Halving the volume of a 10°Bx solution yields ~19.9°Bx. When I did the batch sparging calculator I took the easy way out and had it iterate through a loop three times to more or less eliminate that error.

[a10t2]

So I assume just sub in the Brix equivalent in the equation, Sean ?  In other words, if my preboil on 7 gallons is 10 Brix, then 10 X 7 = 70. Boiled down to my 5.5 gallon target, 70 / 5.5 = 12.72 Brix, ie., ~ 1.051ish. So this takes into account the 'non-linearity'  ?

It doesn't really take it into account, it just eliminates the need for the non-linear units. It still isn't exact (see above), but for normal gravities and boil off percentages, it's going to get you within your measurement error.

[HoosierBrew]

So I assume just sub in the Brix equivalent in the equation, Sean ?  In other words, if my preboil on 7 gallons is 10 Brix, then 10 X 7 = 70. Boiled down to my 5.5 gallon target, 70 / 5.5 = 12.72 Brix, ie., ~ 1.051ish. So this takes into account the 'non-linearity'  ?

It doesn't really take it into account, it just eliminates the need for the non-linear units. It still isn't exact (see above), but for normal gravities and boil off percentages, it's going to get you within your measurement error.

Cool, thanks Sean !

[tommymorris]

Thanks. I will have to try using Brix and see what happens to my error.