Of straight lines and carbon

At the heart of our understanding of the tree’s storage of carbon (beyond the physiological processes) is the discovery that the black walnut trunk from ground to tip grows as a very slender cone. How did we discover this? We take measurements annually of tree height (H) and diameter at breast height (DBH, a forester’s standard; for us 1.35m from the ground) of the 575 trees in Field 3. All trees grow at different rates, so what we were measuring was diameter (D) at 575 different distances from the tree’s tip (DFT) on our ‘average’ tree. When we plotted D against DFT on graph paper, we saw a straight line. Successive annual measurements of H and DBH, converted to D and DFT, of the same 575 trees gave us the same straight line. ‘Same’ in this regard means parallel to the lines for previous years, but with very small differences in lateral distance between lines. Using trigonometry, we can calculate the tip angle of our cone, which turns out to be very close to 1.5^o. In other words, the tree, every year, lays a new cone down on top of the previous one, of uniform thickness at all points along the length (actually height) of that cone.