To deal with the variations in a real world non-uniform white pine trunk
taper would it be possible to pick a tree that we have volume data on,
(either a Smokies, Mohawk or Cooks tall white pine), use it as a model
case, apply its irregular form/taper to the values required for a Royal
Navy mast and see where the height falls so-to-speak? This would have a
fairly high margin of error since we know the form of a white pine top
so variable, might be able to get within 15-20 ft. which is better than
nothing. But... if this exercise was done across say 20 of the tallest
white pines in the east the margin of error might be reduced to
something usable.
Is there a way to come up with a value for average thickness of bark and
cambium/sapwood at the base of the trunk and at the upper end for a
mature white pine to factor in approximately what the top and bottom
diameter of the log section needed to be before it was shaped into a
mast sized log? Maybe it's too early in this thought process to start
trying to work on that variable.
Not being very mathematically inclined I can only suggest possibilities
but can't actually come up with the algorithms.
-AJ
Bob wrote:
Don, ENTS,
The following formula projects the remaining height of a tree
using a main log and an assumption about overall trunk form. I will
use computer symbols for the mathatical operators.
Let
R1 = radius of lower end of log
R2 = radius of upper end of log
L. = length of log
H. = height of remainder of tree
P = form factor
P = 0.5 for paraboloid
P = 1 for cone
P = 1.5 for neiloid
Then
H = [L * R1^(1/P)] / [R2^(1/P)- R1^(1/P)]
If you apply this formula, you quickly see than assuming a conical
form leads to a greater height than assuming a paraboloid form.
The actual trunk form may change several times, so that this
approach to projecting remaining height probably can't be reliably
used for many conifers - especially older ones. I'll give examples in
another email. Typing on this iPhone is a pain in the #%*.
Bob
Sent from my iPhone
