Earlier this week, there was a post on the rate of ice thickness growth, but it seems like server problems might have resulted in the entry and discussion being deleted as part of a restore….
Anyways, this peaked my interest… An online google book (textbook) on cold climate engineering provided a few different equations, the simplest of which is called Stephan’s equation and describes the ice growth without a snow cover insulating the ice and slowing the process.
X = 0.983 * sqrt(time * dT) where
X is in inches of thickness
time is days
dT is temperature difference in degrees Fahrenheit from exposed surface of ice to water.
The following table shows examples of this simple case where 1 degree F where one does not have snow cover AND one is starting from the condition of having no ice thickness at the start of the process. So, if air is at 31F and water has already cooled to 32F from prior conditions, there exists 1 degree F difference from air to water and in the first hour, one would have 0.2″ of ice covering the surface. At the end of 24 hours, the ice has grown to 1″ thickness. It then takes 3 additional days to grow to a thickness of 2″ due to the insulating characteristic of the ice layer. At colder temperatures, obviously the rate of ice thickness growth is going to be faster.
Several members suggested 1″ per day, which happens to roughly describe the growth rate in the early winter when temperature drops to around 20F, ice forms and ice thickness reaches about 3″ where the folks begin to discuss going onto the ice. At that time of the year, the rate is about 1 inch per day for a 10 deg F differential which is where that figure of merit likely comes from….
