Till Birnam Wood Remove to Dunsinane

Until their recent switch to heat pumps, my parents heated their house primarily with a wood stove. For my whole life, my mother Sally has been responsible for splitting the logs they bought to a suitable size. Even at 71 years old, she continues to perform this task for the occasional fire they still enjoy. In preparation for installing more solar cells, they recently had part of the woods around the house cleared, and Sally has been splitting it. During that process, she asked me: How much does split wood dry over time? How much difference does the surface area of the pieces make? (Pieces split from wider diameter vs smaller diameter)

Here's a picture she took showing some different splits:

We want all the pieces to have roughly the same mass, but depending on the diameter of the log, this will mean different thicknesses of wedges. Intuitively, a thicker wedge will take longer to dry, since the water has farther to travel through the wood. I wasn't sure how I could model this, since there are so many factors that come into it, like the surrounding air temperature and humidity, not to mention the spread of the water inside the logs. Luckily, the USDA came to my rescue with an extensive document on drying lumber!

They compared the moisture level in pieces of lumber, varying the location in the US, thickness, type of wood, and date of stacking. Unfortunately, the way they present the data does not help to answer Sally's question: They show separate plots for each thickness, but we want to see how a changing thickness affects the drying time. To replot the data in a way to answer that, we first need to get the actual values. Normally, I'd take a couple points by eye, but I wanted to get more samples than I would have patience to do manually. I figured someone out there must have developed a tool for reading data from plots, and indeed they had! Using that, I got the data for the samples taken in Worcester, MA for Northern Red Oak, then did some interpolation and rearranging to get a plot of the drying times for wood stacked around September:

Where is gets really interesting is when we look at how this curve changes depending on the stacking date:

Interestingly, if you stack during the Fall, the times are fairly linear in thickness, but if you were stacking it now, there's a sharp climb for larger thicknesses. It's amazing to have mom who both asks questions like this, and has the stamina and will to test my findings – Thank you, Sally, for all the years of keeping me warm and thinking, and here's to many more!