So who here can help a guy with beer algebra?

[DSorenson]

I'm trying to get a handle on ibu calculations. The Palmer book has given me these solid estimation equations which consider many variables so I like them.

AAU= aa% * oz

IBU = (AAU * u * 75) / 5 (final volume in gallons)

u = f(g) * f(t) (where g is gravity and t is time)

f(g) = 1.65 * 0.000125^(g - 1)

f(t) = (1 - e^(-.04) * t) / 4.15

Now to do this right I need to know g (the gravity of the boil... I assume a the time of hop addition) and t. The t is easy... it's just the time the hop spends boiling.

The g is tough because it is a function of volume (which changes through out the boil for each hop addition). My boil volume can be estimated by f(t) = (7/240)t + 5. Assuming evaporation is linear. And I'd bet it Isn't.

Now if I used 12 lbs of grain and achieved about a 1.052 SG reading in 5 gallons...

What is my gravity at any point in the boil?

I came up with .438 points per lb/gal. But that can't be right because my sg at 6.75 gallons would be about 0.779 which is less dense than water. Let's assume that heat doesn't factor into it.

Thanks guys!

 

[DSorenson]

Correction, now that I'm thinking about it, my points per lb of grain to achieve a specific gravity of 1.052 would be about .004 gravity points. Am I correct in thinking that the volume of beer when doing a specific gravity reading does not enter into the equation?

 

[Nashbrewer]

For the sugar concentration volume does play a role, but I may be mis-understanding your question. If you have 5 Gallons at 1.052 you have(52*5=260) 260 gravity points. Now if you take that and dilute it to the pre-boil level. 260 / 6.75 = 1.0385 preboil gravity. You are loosing about 26% volume in the boil. If that is an hour boil that is pretty high as most recommend 10-15% per hour. If that was a 90 minute boil then that is better. Assuming it is linear that is either a .43% a minute or .28% a minute boil off rate that you can use to determine volume for any minute in the boil. (OV-(OV*(T*BR))) = Current Volume. Then 260/CV= Current Gravity.

I think that is right.

Edit: To clarify (OV-(OV*(T*BR))) = Current Volume26/

6.75 - (6.75* (30 minutes into boil * .43))

6.75 -(6.75*.129)=5.87 Current volume at 30 minutes into boil.

Also 260 / 12 grain = 21.66 repeating gravity points per lb. Which I think is about 60% brew house efficiency. 21.66/36(this second number varies by the malt).

 

[ajdelange]

Based on my measurements the Tinseth formula seems to give the most accurate predictions:

Utilization = 100*((1 - exp(-0.04*t))/4.15)*(1.65*0.000125^(SG-1)) %
where t is the time in minutes. Note that the parameter, 4.15 depends on your particular setup and procedure. 3.726 better fits my beers than 4.15. Also note that the SG factor does not have a profound effect on the result. For example

(1.65*0.000125^(1.050-1))/(1.65*0.000125^(1.040-1)) = 0.914048

which says that if you thought your OG was going to be 1.040 but it turned out to be 1.050 your utilization would drop by 9% (of the percentage IOW if your utilization was going to be 10% it would go down to 9%). You should be measuring your OG in the kettle so you will be able to adjust the formula before you add hops if the observed OG is much different than the planned.

 

[DSorenson]

... You are loosing about 26% volume in the boil. If that is an hour boil that is pretty high as most recommend 10-15% per hour.

Thanks for the input, Nashbrewer! I was doing my calculations incorrectly. Apparently I have trouble with unit analysis...

In answer to the above qoute, yes, that was an hour boil. I calculated that based on my first brew with a blichmann burner and 10 gallon brew kettle. Of course there was a 20 minute steep of specialty grains, as this was my last extract brew. I assumed the evaporation would be negligible on a 20 minute steep starting at 170 degrees F. Also, my loses include wort lost after siphoning off of the break material when siphoning into the fermenter. I ended up topping off with an additional 0.75 gallons in the fermenter. I started my boil with about 6 gallons of water.

But now that you mention it, I can't really call any loses not related to the boil loses due to evaporation. Of course I do not have good data for the second time with this set up, because it was my first all grain. I do know that I still came up about 0.25 gallons short in the fermenter the second time, assuming that I'd lose 0.1 gallons per pound of grain due to absorption (12 lbs grain) and 1.75 gallons during the process. Of course I didn't really drain the mash lauter tun completely either. (after 5 minutes of dribbling I called it.)

this is off topic, but could someone explain why there is such a thing as recommended boil off rates? Is there anyway with an uncalibrated blichmann propane regulator to even account for that kind of thing?

 

[cageybee]

holy crap.....mine doesn't go past: 1+1+1 = buzz. I have some serious learning to do.

 

[Nashbrewer]

From what I have read on the boil off it seems to be related to the speed at which the wort condenses increases the likelihood of caramelization and burning. Also I've read that it can increase melanoidins and possibly be detrimental to hop aroma or flavor is the wort is boiling too hard when those are added. Take that all with a grain of salt.

Your second volume and boil off rates make more sense. I'd say you were boiling off about 10 -12% and leaving a .25G behind for trub and probably starting out under 6 gallons(5.75-6). So increase your water by .25-.5 to adjust. I'd add it in the sparge water.

AJ seems to have answered your question about the SG part though. Essentially negligible, unless you want extreme accuracy.

 

[DSorenson]

Excellent, guys! Thanks for all the input. Yay for math.

 

[jmf143]

I do know that I still came up about 0.25 gallons short in the fermenter the second time, assuming that I'd lose 0.1 gallons per pound of grain due to absorption . . .

I think I recall absorption being closer to .13 gallons per pound of grain. Perhaps that accounts for the additional 1/4 gallon you lost.

 

[DSorenson]

Yeah, that could definitely be it!