Lesson 1- How to Measure the Height of a Tree
On September 7, 2006 the San Francisco Chronicle reported that researchers had just discovered a 378 foot (113 meters) tree that is probably the world's tallest living tree. If you think you can find a tree that can break that record, or just want to measure that tree in your backyard, try these techniques. These methods can also give you a good approximation of the heights not only of trees, but also of telephone poles, buildings, magic beanstalksÂpretty much anything tall.
1)Shadow Method -Know your exact height in the shoes you will be wearing to perform this method.
2)Stand next to the tree or the object to be measured. For best results, do this method on a bright, sunny day. If the sky is overcast, it may be difficult to tell exactly where the shadow's tip is
3)Measure the length of your shadow. Use a tape measure or yardstick to measure your shadow from your feet to the tip of your shadow. If you don't have someone to assist you, you can mark the end of the shadow by tossing a rock onto it while you're standing. Or better yet, place the rock anywhere on the ground, and then position yourself so the tip of your shadow is at the rock; then measure from where you're standing to the rock
4)Measure the length of the tree's shadow. Use your measuring tape to determine the length of the tree's shadow from the base of the tree to the tip of the shadow. This works best if the ground all along the shadow is fairly level; if the tree is on a slope, for example, your measurement won't be very accurate. You want to do this as quickly as possible after measuring your shadow, since the sun's position in the sky (and hence the shadow length) is slowly but constantly changing. If you have an assistant you can hold one end of the measuring tape while he or she measures the tree's shadow, and then you can immediately measure your shadow.
5) Calculate the tree's height by using the proportion of your shadow's length to your height. Since you know the length of the tree's shadow, and you also know that a certain height (your height) produces a certain shadow length (the length of your shadow), you can determine the tree's height with a little math. Multiply the length of the tree's shadow by your height, and then divide the resulting number by the length of your shadow.
For example, if you are 5 feet tall, your shadow is 8 feet long, and the tree's shadow is 100 feet long, the height of the tree is (100 x 5) / 8 = 62.5 feet. Note that the order of your multiplication does not matter.
Fixed Angle of Elevation Method
1) Fold a square piece of paper in half so that it forms a triangle. The triangle will have one right (90 degree) angle and two 45 degree angles.
2) Hold the triangle near one eye so that the right angle faces away from you and one side is horizontal (parallel to the ground, assuming the ground is level).
3) Move back from the tree until you can sight the top of the tree at the top tip of the triangle. Close one eye to sight the tree's top. You want to find the point where your line of sight follows the hypotenuse of the triangle to the very top of the tree.
4) Mark this spot and measure the distance from it to the base of the tree. This distance is also the height of the tree. This works because the angle of elevation using your triangle is 45 degrees, and the tangent of 45 degrees = 1.