Tree height is the vertical distance between the base of the tree and the tip of the highest branch on the tree, and is difficult to measure accurately. It is not the same as the length of the trunk. If a tree is leaning, the trunk length may be greater than the height of the tree. The base of the tree is where the projection of the pith (center) of the tree intersects the existing supporting surface upon which the tree is growing or where the seed sprouted.Frank, Edward Forrest. September 19, 2005. Base of Tree. If the tree is growing on the side of a cliff, the base of the tree is at the point where the pith would intersect the cliff side. Roots extending down from that point would not add to the height of the tree. On a slope this base point is considered as halfway between the ground level at the upper and lower sides of the tree. Tree height can be measured in a number of ways with varying degrees of accuracy.
Maximum heights The tallest tree in the world is a coast redwood (Sequoia sempervirens) growing in Northern California that has been named Hyperion. In September 2012, it was measured at tall. There are 7 other coastal redwoods known to be over in height, and 222 specimens over . There are only five species known to grow over in height worldwide.
There are historical accounts of extremely tall and large trees. In the northeastern United States, for example, there are frequent stories published in newspapers and magazines dating from the 1800s telling of extremely tall white pines (Pinus strobus). One extraordinary account in the Weekly Transcript, North Adams, Mass., Thursday, July 12, 1849, headlined "A Large Tree", reads:
In 1995 Robert Leverett and Will Blozan measured the Boogerman Pine, a white pine in Great Smoky Mountains National Park, at a height of 207 feet in 1995 using ground-based cross triangulation methods. This the highest accurate measurement obtained for any tree in the eastern United States within modern times. The top of the tree was lost in Hurricane Opal in 1995 and it currently stands at just under in height. It is possible that some white pines in the past reached heights of well over given the much larger area of primary forest prior to the timber boom in the 1800s, however, based on what grows today, it is highly unlikely they ever reached the heights in some of these historical accounts. These reported heights are likely just a mixture of personal and commercial bravado by the lumbermen of the time.
Approximate tree heights Of the various methods of approximating tree heights, the best options, requiring only a minimal amount of equipment, are the stick method and the tape and clinometer (tangent) method. To get accurate measurements with either method, care must be taken. First try to view the tree from several different angles to see where the actual top of the tree is located. Use that point for the measurements. This will eliminate the greatest potential for error.
Stick method The stick method requires a measuring tape and a stick or ruler and uses the principle of similar triangles to estimate tree heights. There are three primary variations of the stick method.<Walker, M.D. Root and Branch Reform: Teaching City Kids about Urban Trees.https://www.academia.edu/31387250/Root_and_Branch_Reform_Teaching_City_Kids_about_Urban_Trees
Standard Find a straight stick or ruler; Hold the stick vertically at arm's length, making sure that the length of the stick above your hand equals the distance from your hand to your eye. Walk backward away from the tree. Stop when the stick above your hand exactly masks the tree. Measure the straight-line distance from your eye to the base of the tree. Record that measurement as the tree's height to the closest foot.
If the top is not vertically over the base, this method will generate an error.
Stick-rotation Stick-rotation method or pencil method for trees on level ground and with top vertically over the base: grasp the end of a stick and hold it at arm's length with the free end pointed straight up; move back and forth toward or away from the tree to be measured until the base of the tree aligns visually with the top of the hand at the base of the stick and the top of the tree is aligned with the top of the stick; without moving the arm up or down rotate the stick until it is parallel to the ground. The base of the stick should still be aligned with the base of the tree. if you have an assistant, have them walk away from the base of the tree at a right angle to your position until they reach the spot on the ground that aligns with the top of the stick. If alone pick a distinctive point on the ground to mark this point. The distance from the base of the tree to this point is equal to the height of the tree.
Again, this method assumes that the top of the tree is vertically over the base.
Advanced
This stick method uses the same procedure outlined above with the addition of a few measurements and some basic multiplication. This method does not require that the length of the measuring stick be the same as the distance from your bottom hand to your eye, so it can be used in more varied settings to get a height measurement:
holding the stick as outlined above, align both the base of the tree with the top of your hand holding the stick and the top of the tree with the top of the stick. You can do this by moving toward or away from the tree, adjusting the stick length, and by moving your arm up and down; once aligned, measure the distance from the top of your hand grasping the base of the stick to your eye; measure the distance from the top of your hand to the top of the stick; measure the distance from your eye to the base of the tree.
So long as the yardstick is held straight up and down and the top of the tree is vertically over the base, the various measurements are still proportional and then you can calculate the height of the tree using a simple formula:
Using this formula the height of the tree can be calculated no matter what angle you are holding your arm, and no matter what the length of the yardstick that extends above your hand. This has a big advantage if you are measuring a tree on uneven ground or if you can only measure the tree from a single angle. One problem that also often occurs is in order to see the top of the tree; the surveyor must be farther away from the tree than possible using a yardstick length of (average arm to eye length). Using the simple formula above a smaller length of stick can be used allowing the surveyor to actually see the top of the tree. As with A. and B. above, this method assumes that the top of the tree is vertically over the base. If this assumption is violated, the triangles will not be similar and the ratio and proportion relationship of the sides of similar triangles will not apply.
Tree ruler Take a pencil, or a ruler, or any stick (straightedge) and a marker, such as a Sharpie Ultra-fine. Go to your local playground, and pace out a convenient distance from the basketball hoop, roughly distance about equal to the height of any tree you'd want to measure, 10 or 30 or 100 paces. Hold the straightedge vertically at arm's length. Align the tip of the straightedge with the hoop; slide your thumbnail until it's aligned with the base of the pole. Mark this on the straightedge; that's 10'. Make more marks to indicate 15, 30, etc., as desired. Now you have a "Tree Ruler" that can be used, on approximately level ground, to estimate tree heights.
Clinometer and tape method The clinometer and tape method, or the tangent method, is commonly used in the forestry industry to measure log length.Walker, M.D. Root and Branch Reform: Teaching City Kids about Urban Trees. https://www.academia.edu/31387250/Root_and_Branch_Reform_Teaching_City_Kids_about_Urban_Trees Some clinometers are hand held devices used to measure angles of slopes. The user can sight to the top of a tree using such a clinometer and read the angle to the top using a scale in the instrument. Topographic Abney levels are calibrated so when read at a distance of from the tree, the height to the tree above eye level can be directly read on the scale. Many clinometers and Abney levels have a percent-grade scale that gives 100 times the tangent of the angle. This scale gives the tree height in feet directly when measured at a distance of from the tree.
In general, the clinometer is used to measure the angle Θ from the eye to the top of the tree, and then the horizontal distance to the tree at eye level is measured using a tape. The height above eye level is then calculated by using the tangent function:
The same process is used to measure the height of the base of the tree above or below eye level. If the base of the tree is below eye level, then the height of the tree below eye level is added to the height above eye level. If the base of the tree is above eye level, then the height of the base of the tree above eye level is subtracted from the height of the treetop above eye level. It may be difficult to directly measure the horizontal distance at eye level if that distance is high off the ground or if the base of the tree is above eye level. In these cases the distance to the base of the tree can be measured using the tape along the slope from eye level to the base of the tree and noting the slope angle Θ. In this case the height of the base of the tree above or below eye level is equal to the (sin Θ x slope distance) and the horizontal distance to the tree is (cos Θ x slope distance).
Errors associated with the stick method and the clinometer and tape method: Aside from the obvious errors associated with bad measurements of distances or misreading the angles with the clinometer, there are several less apparent sources of error that can compromise the accuracy of the tree height calculations. With the stick method if the stick is not held vertically, the similar triangle will be malformed. This potential error can be offset by fastening a string with a small, suspended weight to the top of the stick so that the stick can be aligned with the weighted string to assure it is being held vertically. A more pernicious error occurs in both methods where 1) the treetop is offset from the base of the tree, or 2) where the top of the tree has been misidentified. Except for young, plantation-grown conifers, the top of the tree is rarely directly over the base; therefore a right triangle used as the basis for the height calculation isn't truly being formed. An analysis of data collected by the Native Tree Society (NTS), of over 1800 mature trees found, on average, the top of the tree was offset from the perspective of the surveyor by a distance of , and therefore was offset from the base of the tree by around . Conifers tended to have offsets less than that average and large, broad canopied hardwoods tended to have higher offsets. The top of the tree therefore has a different baseline length than the bottom of the tree resulting in height errors:
The error almost always incorrectly adds to the height of the tree. For example, if measuring a tree at an angle of 64 degrees, given an average offset of in the direction of the measurer, the height of the tree would be overestimated by . This type of error will be present in all of the readings using the tangent method, except in the cases where the highest point of the tree actually is located directly above the base of the tree, and except in this unusual case, the result is not repeatable as a different height reading would be obtained depending on the direction and position from which the measurement was taken.