#### Winter 2013

# Adventures in Tree Measurement

BY AMERICAN FORESTS BIG TREE PROGRAM COORDINATOR SHERI SHANNON

How do you measure the height of a tree when the view of the canopy is obstructed? This is something I immediately had to learn during a Native Tree Society (NTS) advanced tree measuring workshop at Cook Forest State Park in Pennsylvania with Laser Technology Inc. and NTS measuring masters Bob Leverett and Dale Luthringer.

Trees don’t always grow vertically in the middle of an open, flat area where you can easily choose a spot to take measurements. But with the proper equipment, NTS is able to calculate the height of a tree even when the tree’s base and top are not aligned — a problem that has caused inaccurate measurements with some other methods. So, how does it work?

Let’s first define tree height. Tree height is the vertical distance between the base of the tree and the highest point of the crown. NTS uses two key pieces of equipment to accurately measure height: a clinometer, which is a mechanical device that measures the vertical component of the angle between your eye and a targeted object, and a laser rangefinder, which sends a laser pulse in a narrow beam towards the object and measures the time it takes for the pulse to be reflected off the target and returned to the sender.

On my first attempt at measuring a tree with this advanced method, I immediately look up into the crown of a pine and think, “With a push of a button — in seconds — I’ll have the number I’m looking for on the screen of my laser rangefinder.” Well, there were some numbers, but they definitely weren’t what I was looking for. I had to move around for about 10 minutes to find an open area to get the best view of the crown. That’s when I realized that even with the best equipment, it takes time to measure a tree.

Before I know it, I’m standing in the presence of the tallest tree north of the Great Smoky Mountains: Longfellow Pine. It’s my turn to take the challenge and measure the height of this champion, but how am I supposed to go about doing that when the pine sits on a steep slope? Everyone disperses in different directions while I just focus on not falling and twisting an ankle as I climb over fallen branches and rocks to find the best view of the crown. I hear Bob and Dale shouting out various degrees of angles and calculations from their vantage points. A chorus of voices from 25, 50 and almost 100 feet away are echoing their observations, and I’m thinking, “Let’s just give this a shot.”

I start at the base and follow the trunk of the tree through the lens until I think I see the topmost branch peering through the sunlight. I’m not sure if it belongs to Longfellow Pine or its neighbor, so I point and shoot, make note of my measurements and move to another location. After 20 minutes of hits and misses, my best result is 178 feet. It’s not the same as NTS’ most accurate measurement of 183 feet, but at least it’s in the ballpark. By the end of the workshop, I am attached to the rangefinder and want to take it home with me.

NTS uses sine-based calculations as opposed to the more conventional tangent-based calculations to measure tree height. The slope distances from the eye to the top of the tree (L1) and eye to the base of the tree (L2), shown below, are measured with the infrared laser rangefinder and the corresponding angles (a1, a2) are measured with the clinometer or a tilt sensor. From these measurements, the height can be calculated as follows:

**H****1 **(the height to the top of the tree) = **L****1 **sin(**a****1**)

**H****2 **(the height to the base of the tree) = **L****2 **sin(**a****2**)

If top is above and base is below eye level:

**Total Height **= **H****1 **(height to top) + **H****2 **(height to base)

If both the top and the base are above or below eye level, such as when measuring a tree in a gully below you or on a cliff above:

**Total Height **= **H****1 **(height to top) – **H****2 **(height to base)

The latter calculation assumes the angles are entered in as positive values. If they are entered in as sine values, the formula above works in all cases.

I’m still learning the basics of how to measure trees, but for a more complete explanation, visit www.nativetreesociety.org. If you want to try measuring tall trees, but don’t have the equipment necessary, visit www.americanforests.org/bigtree to learn how to estimate tree height using only a common ruler and measuring tape.

Sheri, nice article on your adventure. I am glad you included the latter equation. To further elaborate, if the angle is less than zero, then the sine of the angle is negative, and the height (H2) below eye level is negative. If you use the latter equation then Total Height = (H1) – (H2). For example if the top of the tree is 100 feet above eye level and the base is 10 feet below eye level, then Total Height = 100-(-10) = 100+10 = 110. Example 2,if the top of the tree is 120 feet above eye level, and the base is 10 feet above eye level, the same equation can be used. Total Height = 120 – 10 = 110 feet.