By Tony Heath, Project Engineer

Oh, how do you measure a tree? If you’re feeling poetic, you might count the hours spent reclining in its shade or ask how many birds call its branches home. An urban planner might ask how the tree improves neighborhood outcomes, while a engineer might ask how much water it soaks up.

Of the many ways to measure a tree, one way is to ask how much carbon it captures and stores in its biomass and soils. This is known as carbon sequestration and a topic Carl Carman introduced in his blog post last week. Determining the carbon stored in a tree is an imprecise science, but one way to get a reliable estimate is to use allometry, the relationship between an organism’s body size and other characteristics. If we know what percentage of a tree is made up of carbon, then we can calculate the total carbon based on the tree’s biomass. Thus, Carl asked me to measure RORG’s trees for his analysis.

So, how do we measure a tree? We can’t put it on a scale and, even if we could, between 20-30% of a tree’s biomass is below ground. For help, we again turn to allometric relationships. While we can’t measure the biomass of a tree directly, we can estimate it as a function of the tree’s height and circumference. For help with those measurements, I turned to the American Forests “Champion Trees Measuring Guidelines Handbook.”

**Circumference**

The circumference (or girth) of a tree is the simplest measurement to take, especially for the Red Oak Rain Garden’s trees which are both upright and on level ground. The circumference is measured by taking a measuring tape and wrapping it around the trunk at approximately 4.5′ above mid-slope of the tree’s base or about chest height. If the tree has any large knotty growths, burls, or limb extensions measure at the smallest circumference between 4.5′ and the ground. One person usually can do this measurement, but another person is helpful for large trees like the 100 year old RORG “sisters”. Rebecca Martin, recent MUP/ACE graduate and my partner, graciously agreed to help. To get a precise fit, we used a piece of string wrapped around the trunk of the tree at chest height and then measured the length of the string. **Based on these measurements, the red oak has a circumference of 152″ and the sycamore has a circumference of 165″.**

**Height**

Measuring the height of a tree is a little more complicated and requires a little math. But, stay with us; we’ll walk you through it. The height of a tree is measured as the vertical separation between two planes, one of which passes through the very tip-topmost leaf and the other which passes through the mid-point of the base. The simplest way to measure this separation would be to climb to the top of the tree and drop a string down to the bottom, however, that’s usually not very practical. When that’s the case, the American Forest guidelines use a simple trick of trigonometry known as similar triangles.

*Image Courtesy of the American Forests Champion Tree Measuring Guidelines*

Two triangles are similar if their internal angles are congruent and their sides are in proportion. In the image above, triangle abc is similar to triangle ABC. This means that the ratio of a/A equals the ratio of b/B. So, even though the height itself can’t be measured we can use these other values to generate a reasonable estimate of the tree’s height.

To take these measurements Rebecca and I took a ruler and walked a little over 100′ away from the base of each tree. We then took the ruler (b) and letting it dangle vertically we moved it back and forth in front of our face until the top and bottom of the ruler were aligned with the top and bottom of the tree. We then measured the distance from our eye to the base of the ruler (a) and the distance from our eye to the base of the tree (A). Then, we could estimate the tree height such that B = b*(A/a). While American Forests recommend a more precise method for their Champion Trees using laser range-finders, this method gives us an accurate enough measurement for our purposes. **Using this method we estimated that the red oak is approximately 70′ tall and the sycamore is approximately 88′ tall. **

Tony standing 100′ away from the red oak. Photo by Rebecca Martin.

So it seems there are lots of ways to measure a tree, from the poetic to the practical. I enjoyed my brief dive into Forestry as part of our quest to estimate the carbon captured by the Red Oak Rain Garden. If you found this post interesting, you can learn more and read the American Forest guidelines yourself here.

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