I have mentioned before the idea of Percent Cylinder Occupation. he percent cylinder occupation listing is a measure of what percentage the measured volume of the tree represents compared to a cylinder equal to the circumference breast height (CBH) of the tree times the height of the tree. Trees with a fat base or a trunk that quickly tapers scores low on the list, trees that taper more slowly have higher values. Those trees with broken tops will have anomalously high values. The table is not complete as it only lists a few of the largest species of western tree. The Sugar Pine and Western Hemlock are smaller than a number of other species, but were included as they are comparable to Eastern White Pine and Eastern Hemlock.
Looking at your numbers, the cylinder would be 4.8 meters in girth x 56.2 meters tall
radius = 0.764 m
cross section area = 1.833 meters2
cylinder volume = 103.4 meters3
The average for the hemlocks, comparable is size is 40.9%, ignoring the anomalously low values for the other species for the other species, you have a percentage of 39.6% for 7 species.
So my best estimate, for volume would be 40% x 103.4 m3 = 41.36 m3
This is somewhere between the volume of a cone (33.3%) and a paraboloid at (50%).
So this would make the tree somewhat smaller in volume that your estimates. If you just look at the 5 largest volume hemlocks, their average is 44.84% which would be a volume of 46.36 m3.
None of these calculations are including the material in the basal buttress where it is wider than cylinder radius of 0.764 m nor fro any of the branches.
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