This was slightly problematic because I didn’t have a good feeling for how much of the beer was really left in the keg, and consequently how much priming sugar I should use to re-carbonate the beer. I whipped out the trusty volume of a cylinder equation (V = π × r ² × h) and estimated the volume of beer left in the keg by pulling the keg out of the fridge and measuring the height of the area where condensation had formed.

I took some initial measurements to find the volume of the entire keg. Since I know these kegs can hold 5 gallons I wanted to get a rough idea how close my pen and paper estimates were.

Keg measurements:

r = 4.125 in
h1 = 20 in

Unit conversion:

1 gal per 231 in3

Keg volume estimate:

⇒ V1 =  π × r2 × h
     = (π) × (4.125)2 × (20) ≈ 1069.12 in3
     = (1069.12 in3) × (1 gal ⁄ 231 in3) = 4.62 gal

⇒ What the frack = 5 – 4.62 = 0.38 gal

Somewhere in the measurements I potentially have an unaccounted 0.38 gallons. I’ll just add this on to the beer volume calculation later on…

Beer in keg measurements:

h2 = 10 in

Beer in keg volume estimate:

⇒ V2 = (π) × (4.125)2 × (10) ≈ 534.56 in3
     = (534.56 in3) × (1 gal ⁄ 231 in3) = 2.31 gal
     = 2.31 + (0.38 what the frack gal) = 2.69 gal

Alright, so looks like I’ve got ~ 2.69 gallons of beer. Fannnnnntastic. To figure out how much priming sugar I need I am using an equation I found on the Home Brew Digest mailing list. You can find the email, written by Bill Pierce, in digest #5471.

Definitions:

Vbeer      ≡ Volume of beer in US gallons
VCO2       ≡ Desired carbonation level in volumes of CO2
Tferm      ≡ Fermentation temperature of beer in °F
PS        ≡ Priming sugar weight in grams

Variables:

Vbeer     = 2.69 gal
VCO2      = 2.6 volumes of CO2
Tferm     = 58 °F

Priming sugar estimate:

⇒ PS = 15.195 × Vbeer × (VCO2 - 3.0378 + (0.050062 × Tferm) - (0.00026555 × (Tferm)2))
      = 15.195 × 2.69 × (2.6 - 3.0378 + (0.050062 × 58) - (0.00026555 × (58)2))
      ≈ 65 g

Well there you have it; 65 grams of corn sugar.  My volume estimate only ended up being off by about 11 ounces of what was actually left in the keg.   One last thing worth mentioning;  Mark Hibberd’s “A Primer on Priming“ was helpful in determining what volumes of  CO₂ is typical in different styles of beer.   Here is his table:

-------------------------------------------
Beer style                      Volumes CO2
-------------------------------------------
 British-style ales              1.5 - 2.0
 Porter, stout                   1.7 - 2.3
 Belgian ales                    1.9 - 2.4
 European lagers                 2.2 - 2.7
 American ales & lagers          2.2 - 2.7
 Lambic                          2.4 - 2.8
 Fruit lambic                    3.0 - 4.5
 German wheat beer               3.3 - 4.5
-------------------------------------------
Typical CO2 levels in bottled beers

Stir plate in action

This how-to describes all the steps I took to build my stir plate.  This idea isn’t my own; my buddy recently built one a few months ago and there are some other Do-It-Yourself articles scattered around the Internet.  Using a stir plate is one of the best methods for increasing the yeast count in your starter.  There is a great article on Yeast Propagation and Maintenance by MB Raines that discusses the advantages of culturing yeast using a stir plate.

The cost to build it was near $40 dollars.  The most expensive component was the enclosure; you could use Tupperware or craft one out of wood if you wanted to knock off additional cost.  Also, I wanted to use an LED, and an On-Off switch; they are cool but not required.  If you decide not to use those components you could do away with the circuit board as well.  This probably goes without mentioning, but you’ll need some basic tools like a drill and a soldering iron to put everything together.

Parts List:

1. $15.50 - Enclosure; Serpac A42-Series
2. $03.50 - Copper Clad Breadboard; Surplus store
3. $06.00 - Potentiometer; NTE 500 ohm single-turn / linear
4. $07.00 - DC Fan; Link Depot 2,500 RPM 12VDC 2.4W
5. $03.00 - AC to DC Power Adapter; SS-101, 300mA 12V
6. $01.50 - DC Power Jack; 2.1mm Philmore
7. $01.75 - Toggle Switch; GC Electronics On - On miniature bat handle toggle
8. $00.16 - Resistor; NTE 1/2W, 560 Ohm
9. $00.26 - LED; Linrose 20mA, 3V
10. $00.13 - LED Mounting Clip; Linrose
11. $00.00 - Rare Earth Magnet; (taken from an old hard drive)

Total: $38.80

I used Dia to draw out the circuit diagram (anyone know of good, free, circuit design software?).  Dia has a mixed bag of pre-drawn circuit components, so the electronic buffs out there will probably notice I am using both US and European style components.  In any case, here is my simple stir plate circuit:

Magnet harvest

Constructing this was really pretty simple so I’ll keep this brief.

If you’re going to harvest a rare earth magnet from your hard drive you’ll almost certainly need a special set of screw driver bits to open it up; or you know, a hammer and something to act as a wedge — that will do the trick too.  The magnets are located at the base of the arm.

Size up the components and determine placement.  Make all the necessary holes and modifications to mount everything.  I drilled holes in the panels of the enclosure for the power switch, potentiometer, and the LED.  The enclosure’s rivet holes made the fan sit awkwardly, so drilled some holes in the circuit board, and then mounted the fan to circuit board, which was screwed into the rivet holes.

Modified enclosure

Remove any labeling on the center of the fan, and glue the magnet in the center of the fan; I used Gorilla Glue.  When I first did this I glued 2 magnets side by side.  You don’t want to do this (at least not how I had them aligned).  Using 2 magnets side-by-side made the stirbar dance around wildly.  It wasn’t effective at all.

The fan you buy will most likely have 2, 3, or 4 wires.  You’ll only need two (power and ground) for this setup so the least number of wires the better.  I went with a very simple approach — I am using potentiometer to behave as a rheostat to vary the resistance.  The potentiometer will increase or decrease the speed of the fan depending on the direction turned.  As a side note, it occurred to me that Pulse Width Modulation (PWM) using 555 timer is probably a better approach if I ever wanted to build some kind of super stir plate used during primary fermentation, but for yeast starters it doesn’t really matter.

One magnet worked better than two

If you went to the trouble of using a circuit board, you’ll probably want to solder pin headers to circuit board that attach to the LED, switch, power, and potentiometer using wires.  On the reverse side of the board you can then use a wire wrap tool, or soldering iron to wire the circuit together.

That’s pretty much it!  Here is the stir plate in action:

Below is a number of photos a took when I made it. 

If you take a look at Norm Pyle’s Hops FAQ he lays how to calculate Jackie Rager’s method for estimating IBUs.  One of steps in this method is to calculate the hop utilization, which is a function of how long the hops are boiled.  Here is the table of data points provided:

Boiling Time (minutes) %Utilization
-----------------------------------
 0 -  5                       5.0
 6 - 10                       6.0
11 - 15                       8.0
16 - 20                      10.1
21 - 25                      12.1
26 - 30                      15.3
31 - 35                      18.8
36 - 40                      22.8
41 - 45                      26.9

As an alternative to the table a function was given to approximate the hop utilization.  Note that x is the number of minutes the hops are exposed to a boiling wort.

I wasn’t able to find the original article (”Calculating Hop Bitterness in Beer”, Zymurgy Special 1990) by Rager, so I’m not entirely sure where the function came from or if the data points referenced are exactly as I have them here.  In any case, I graphed the function above against the plotted points to see how well they matched up.   I found that the curve deviates from the data as much as 10%.  I wanted to find a curve with a more accurate representation of the data points.  Specifically a curve that actually hit each point in the data set.

There are a few different methods of finding a best-fit line.  The first method I tried was polynomial interpolation.  The result wasn’t horrible but the function shot off wildly when x went beyond the scope of what was defined by Rager’s data set.  The piecewise method of interpolation, cubic spline, ended up giving me the nicest looking curve.  The graph below tracks 4 pieces of information; (1) Rager’s data points, (2) Rager’s data points on 5 minute intervals, (3) Rager’s utilization function, and finally (4) the cubic spline interpolation of Rager’s data points.

The nice thing about the interpolation is the utilization percentage at a specific boiling time is extremely close to the actual data set.  You don’t get that with Rager’s utilization function.  Unfortunately the function defining the cubic spline interpolation is definitely not as easy on the eyes as its curve is!  I mentioned earlier the cubic spline method of finding a best-fit line is done piecewise, so there is a polynomial defined between each interval in the data set.   As you’ll see in the function below I am using Rager’s function when x > 45; this is because I don’t have data for hop utilization beyond 45 minutes.  It’s not clear what the function is suppose to look like after x > 45, so it seemed reasonable enough to just do exactly what Rager’s utilization function did.

I’m not entirely sure interpolation is any how “better” than Rager’s utilization function, or even just using the table directly.  The 10% deviation I mentioned is probably not very noticable. Until the day I have a chemist’s lab in my house and am able to measure IBUs I’ll be stuck with the art of estimation.  I’ve heard it’s best to stick with one particular method, and regardless of actual IBUs you’ll at least be able to consistently hop the beer.  Makes sense to me!  For those interested here is the PDF of my Maple Worksheet: Interpolation of Rager’s Data Points.  Cheers!

• 10.5 lbs. 2-row
• 1.5 lb. 60L Crystal
• 1 oz. Amarillo hops (60 min. boil)
• 0.5 oz. Amarillo hops (15 min. boil)
• 05. oz Amarillo hops (5 min. boil)
• 2 oz Amarillo hops (dry hop)

Our mash temperature started around 154ºF and settled around 150ºF by the time we started the vorlauf and lautering process.  We ended up with ~4 gallons with an original gravity of 1.060.  We started with about 6 gallons prior to the boil.  So we lost 2 gallons to evaporation!  I didn’t expect quite that much to boil off.  I think its partly due to all the time I’ve spent doing extract brews…  The amount of water required is different.  Most extract beers come with a fair amount of LME, so I’m sure that offsets a portion of the liquid lost to evaporation.  In any case next time we’ll have to aim for a better wort volume.

So today I checked to see how the fermentation was doing, and sadly there was no activity.  I made a yeast starter with packaged yeast and priming sugar.  Dude, Brian you took my DME! Haha.. Anyway, I just pitched the starter after waiting about 32 hours from the time I pitched the first batch of yeast.  So I’m thinking from here on out I am going to make a yeast starter for all of my beers.  I would hate to have 4 hours of brewing wasted by stubborn yeast.