NTS,

A tulip tree growing down hill from our back door is with a fine target for practicing measuring from our upstairs bedroom window. The base of the tulip has a horizontal distance of 100.5 feet. The base is 43.2 feet below eye level. The top is not less than 84.5 feet above eye level, but that determination is not easy to arrive at. First a look at the whole tree.

As can be seen, the tree is arrow-straight and its crown still exhibits a somewhat flattened spear-shaped top. Let's see the top from a closer perspective.

What point would you select as the highest point from this vantage point? Let's move closer.

Can you see what the orange arrow is pointing to? It isn't the highest looking top, but one slightly to the left. Let's take a final look.

Neither my eyes or the lens of my TruPulse 200X or Cannon XS260 HS has the depth of field to show that the target top is behind the higher looking branch. It took my Zeiss 10 x 40 binoculars to do that, and it was clear as a bell. The near branch has a horizontal distance of 87.9 feet. The true top has a horizontal distance of 98.8 feet. The tops of hardwoods are not easy to decode. Binoculars with a good depth of field are worth their weight in gold.

BTW, a plumb line dropped from the true top falls to the right of the base and slightly in front of it. Since this is still a relatively young tulip tree growing in competition with tall oaks surrounding it and with fairly good wind protection, it remains a good candidate for the Tangent Method. But which top would a tangent measurer select? The odds of the true top being selected are slim.

The angle difference between the highest appearing top and the true top is 0.2 degrees, amounting to 0.6 feet using a 100.5-foot baseline 100.5 x [tan(40.8)-tan(40.6)]. The difference would reduce the overall error of 2.2 feet to 1.6 feet. Either the tangent measurement to the false top or true top is pretty good because the tree is straight, the crown relatively narrow, the high points more toward the center, and the eye 43.2 vertical feet above the base. Had the tree been measured 100 feet from the trunk on level ground, the results from the Tangent Method would not have been so close.

Bob