tl:dr - Use the max temp the beer has been (after fermentation completion) in the priming calculator.
The Beersmith calculator as mentioned above says it is calculating using the current temperature.
The Brewer's Friend Calculator* says the following, which is contrary to what you're saying also.
I highly doubt the people who programmed these specific calculators used a formula different than the instructions they're giving you to use them correctly. What I mean is why would they have programmed them for use at a specified temperature and tell you to plug in a different temperature than it is made for. How can you say they are "inaccurate" I have had no issues using them per the instructions.
I personally do what jspain3 does and split the difference and have awesome results in carbing.
* Temperature of Beer used for computing dissolved CO2:
The beer you are about to package already contains some CO2 since it is a naturally occurring byproduct of fermentation. The amount is temperature dependent. The temperature to enter is usually the fermentation temperature of the beer, but might also be the current temperature of the beer. If the fermentation temperature and the current beer temperature are the same life is simple.
However, if the beer was cold crashed, or put through a diacetyl rest, or the temperature changed for some other reason... you will need to use your judgment to decide which temperature is most representative. During cold crashing, some of the CO2 in the head space will go back into the beer. If you cold crashed for a very long time this may represent a significant increase in dissolved CO2. There is a lot of online debate about this and the internet is thin on concrete answers backed by research. We are open to improving the calculator so please let us know of any sources that clarify this point.
The equation this calculator uses to compute the amount of dissolved CO2:
CO2 In Beer = 3.0378 - (0.050062 * temp) + (0.00026555 * temp^2)
Update 7/2013 - The calculator now displays the volumes of dissolved CO2 in the beer prior to adding priming sugar. As the beer was fermenting it naturally retained some CO2. The amount of dissolved CO2 is temperature dependent.
As soon as you rack to secondary / dry hop / disturb the head space volume to take a gravity reading, you throw the "CO2 reabsorption from head space" assumption out the window.
Even if the beer did reabsorb all of the CO2 in the head space, reducing the amount of priming sugar by 1/2 doesn't pass the sanity check. Based on my experience, I'm comfortable making this claim without a detailed mathematical proof.
I'll attempt to go thru the math below.
Even before you ever open the lid there is dissolved CO2 in the liquid and there is also CO2 in the headspace of the fermenter, and this amount of dissolved CO2 in the beer is based off of the temperature. Opening the lid may change the amount of CO2 in the headspace but it doesn't affect the amount of CO2 dissolved in the liquid, the temperature does.
The CO2 absorption doesn't just un-do itself when you open the lid or move the beer it is a constant dependent on the temperature of the liquid. It absorbs over time as it sits it doesn't happen instantly.
In addition, CO2 is more dense even if you open the lid you aren't losing all of the CO2 in the headspace as it is heavier. Ever notice how you can leave a chest freezer open for hours that you've been fermenting in and stick your head back in and there is still CO2 in the bottom?
http://www.draft-beer-made-easy.com/carbonation.html
Actually, carbonation is a function of not just temperature, but also CO2
partial pressure. Reduce the CO2 partial pressure at constant temperature, and the beer will off gas CO2 until carbonation and partial pressure are again in equilibrium. Increase the CO2 partial pressure at constant temperature, and the beer will absorb CO2 until carbonation and partial pressure are again in equilibrium. A couple of equations that approximate the carb level, temperature and pressure relationship are:
Vol = P * (0.0181 + 0.090115 * exp((32 - T) / 43.11)) - 0.00334
[ref]
P = -2.0049 - 0.0101059 * T+0.00116512 * T ^2+0.173354 * T * Vol +4.24267 * Vol - 0.0684226 * Vol ^2 [
ref]
Where:
P = Partial Pressure of CO2 in psi
T = Temperature in °F
Vol = Volumes of CO2 in solution
I removed the 'fudge factor' for gauge pressure vs. partial pressure from the above equations. Partial pressure of CO2 is gauge pressure plus 14.695 psi (atmospheric pressure) when the headspace contains pure CO2. If the headspace is not pure CO2, then the CO2 partial pressure is the fraction of CO2 in the mix times (gauge pressure + 14.695).
I know what you mean about carbonation escaping when beer goes flat, but there is actually still dissolved CO2 still in the beer that you aren't noticing and this amount is relevant to the temperature of it.
It is like any other liquid like water in a lake for instance that has CO2 in it that you aren't observing, but it is there it just isn't a noticeable amount. Neither is the CO2 in "uncarbonated" beer.
Beer open to the atmosphere will go essentially completely flat, since CO2 is only 0.04% or 0.0004 fraction of the atmosphere. The partial pressure of CO2 in the atmosphere is 0.0004 * 14.7 = 0.006 psi.
Now on with the analysis of cold crashing's effect on priming sugar requirements.
When you ferment beer, there is a lot of CO2 generated, which pushes almost all of the air out of the fermenter, so the CO2 partial pressure in the fermenter is very close to 14.7 psi. So, we can use the equations above to determine how many volumes of CO2 are in the beer based on the temperature. If we raise the temperature post fermentation, then the CO2 partial pressure will stay at 14.7 psi (because of the air lock), and the beer will off gas CO2 due to the higher temperature.
Now if we cold crash, we will suck air back into the fermenter, the amount of CO2 in the headspace plus the beer will remain constant, but the CO2 partial pressure will drop. A small part of the drop will be due just to the temperature change, and a larger part will be due to more CO2 absorption due to the lower temperature.
1 volume of CO2 is equal to the density of CO2 at 0°C and 1 atmosphere pressure (14.695 psia), which is 1.9768 g/L of CO2 according to NIST [
ref].
The total amount of CO2 in the headspace is given by:
Headspace_CO2 [g]= Headspace_Vol [L] * 1.9768 g/L * (Partial_Pressure [psia] / 14.695 psi) * 273.15°K / (273.15°K + T [°C])
The last two terms in the equation adjust the CO2 density for partial pressure and temperature.
The total amount of CO2 in the beer is given by:
Beer_CO2 [g] = Beer_Vol [L] * Carb_Level [Volumes] * 1.9768 g/L
With the carb level volumes determined by one of the equations above.
The total CO2 in the fermenter is then:
Total_CO2 [g] = Headspace_CO2 [g] + Beer_CO2 [g]
At the peak temperature, the headspace is 100% CO2 (because no air is sucked in when raising the temp), so the CO2 partial pressure is 14.695 psi, and this is what the carbonation calculators use to calculate the starting volumes of CO2 in the beer. If you tell the calculator the cold crash temperature, then it still assumes the headspace is 100% CO2, but it is not (since air was sucked in), which leads to overestimating the starting carb level of the beer.
Let's do an example:
Assume we have 20 L (about 5.25 gal) of beer in a fermenter, with 4 L (a little over 1 gal) of headspace which is 100% CO2, at a temperature of 20°C (68°F.) The amounts of CO2 are then:
Beer CO2 = 29.689 g (0.751 volumes)
Headspace CO2 = 7.368 g
Total CO2 = 37.057 g
So, if we told the calculator we wanted 2.5 volumes, it would tell us to add enough sugar to create:
2.5 - 0.751 = 1.749 volumes
If we cold crashed and told our carbonation calculator that our starting temp was 0°C (32°F), it would incorrectly assume the headspace was still 100% CO2, in which case the CO2 amounts would be:
Beer CO2 = 64.668 g (1.636 volumes)
Headspace CO2 = 7.907 g
Total CO2 = 72.575 g
In this case the calculator would tell us to add only enough sugar to create:
2.5 - 1.636 = 0.864 volumes
And our total carbonation would only end up at:
0.751 + 0.864 = 1.615 volumes - whoa, way under carbed
The above assumes no CO2 got absorbed from the headspace during cold crashing. But, what if the cold crash was long enough for the headspace pressure and carb level to come back into equilibrium? Well it is possible to use "goal seek" in a spreadsheet to solve for the CO2 headspace partial pressure and beer carb level that keeps the total CO2 in the system constant. If we do that we get the following:
Beer CO2 = 33.262 g (0.841 volumes)
Headspace CO2 = 3.795 g
Total CO2 = 37.057 g
In which case we would want to add enough sugar to create:
2.5 - 0.841 = 1.659 volumes
So, worst case of using our max temperature to calculate carbonation sugar after a long cold crash is:
0.841 volumes + 1.749 volumes = 2.59 volumes
So, the worst case for using the max post ferm temp is over carbing by 0.09 volumes vs. the worst case for using the cold crash temp which is under carbing by 0.885 volumes (2.5 - 1.615). A 10x difference in the carb level error.
Conclusion: Use the max temp the beer has seen in the priming calculator.
Whew!
Brew on
) but my favorite explanation is simple: Those 'calculators' suck.
