Bottom line: Swamp coolers provide much more stable temperature, even if you aren't looking to lower the fermentation temperature.
When using ice to lower the fermentation temperature the temperature will drop very quickly as the ice melts in the water bath. If this drop in temperature is more than a few degrees yeast will start to prepare for dormancy. Once the temperature rises they will start fermenting again, but this is at a cost of energy. Unwanted byproducts are produced as the cells shift back and forth between these phases.(1) For this reason it's best not to use more than one gallon of ice in 5 gallons of water.
The temperature of the water in the swamp cooler goes through two distinct phases. Cooling, when the ice is added, and warming, after all the ice has melted. The cooling phase can be modeled fairly simply. There are two important considerations during this phase: time and temperature. The time it takes for the ice to melt is proportional to the size of the block of ice. Ice cubes will melt in a mater of minutes. A 20oz bottle of water will take about 45 minutes, and a 1 gallon container of ice can take up to 2 hours. The resulting low temperature can be approximated by considering thermal mass. This is simply the conservation of energy, and can be expressed with an equilibrium equation.
(mass of water * temperature of water) + (mass of ice * temperature of ice) = resulting temperature of water * (mass of water + mass of ice)The plastic tot bin that I use to cool my primary fermentor has six gallons of water in it. If the starting water temperature is 70 degrees and one gallon of ice is added the resulting low temperature will be 64.6 degrees. experimentally it seems that this takes about 2 hours, however the low temperature is never truly achieved because some energy is lost to the air and to the container.The warm up phase is highly dependent on the type of container that is being used to hold the water. A cooler will hold temperature much better than a plastic bin, but either will work just as well if the thermal coefficient can be calculated. The rate at which the water warms up is proportional to the difference between the water temperature and the air temperature. This can be modeled with an exponential equation:
(initial temperature difference from air to water) * e^ (temperature coefficient * t) = resulting difference in temperature
The temperature coefficient can be found by knowing two points on the time line of the warming water. After the ice has melted this can be measured with two temperatures and the time between them. For example:
air temperature 70 degrees
first measured water temperature 60 degrees
elapsed time 12 hours
second measured water temperature 65 degrees
(70-60) *e^ (temperature coefficient * 12) = (70-65)
=> temperature coefficient = -0.0578
The plastic bin that I use has a temperature coefficient of -0.136
Putting it together is a little more difficult. One challenge is that the heating of the water occurs during the melting phase of the ice. So the low temperature calculated as the equilibrium point assuming conservation of energy is never achieved. This is because some of the energy is lost to the air as the water temperature drops below the air temperature. Either relatively complex integrals will be needed to calculate this, or experimentation can be done to make up for this difference.
The big question that still needs to be answered is: "How much ice should I add to achieve a specific temperature?" The calculations, experimentation, and measurements outlined here will provide that answer, but here are some general guidelines:
For large plastic bin filled with 6 gallons of water:
* each gallon of ice will lower the temperature about five degrees
* each 20 oz bottle of water will lower the temperature about one degree
* larger blocks of ice will maintain a more stable temperature.
* aim for a target low temperature twice what you need to account for the warm up period. (for example, if your air temperature is 70 degrees, and you want to ferment at 65 degrees, shoot for 60 degrees which would be two gallon blocks of ice)
* Once the initial water temperature has been achieved, maintain it by adding one 20 oz bottle of ice for every degree below air temperature every 12 hours.