Taper Analysis  Bob Leverett

TOPIC: Taper Analysis

== 1 of 1 ==
Date: Fri, Nov 16 2007 6:50 am
From: dbhguru


Will and I are presently working with his Tsuga Search hemlock database. We're doing form analysis with respect to the trunks of the hemlocks in Will's database. Our efforts are primarily aimed at assessing how closely old growth hemlock trunks come to the paraboloid shape, the conoid shape, or some mix of.the two. The following formula is being employed:

x = [C/H] * [f1 * SQRT(H * (H-h)) + (1-f1) * ( H-h)]


x = circumference at height h feet above base as predicted by the aove equation
C = circumference at height 4.5 feet above base
h = chosen height above eye level (95.5 feet for the hemlock test)
H = full height of tree less 4.5 feet.
f1 = weight as a decimal value given to paraboloid form. This typically will be 1, 0.667, 0.5, or 0.333
c = circumference at height h feet above base as measured by the macroscope or by climbing
d0 = laser-measured distance to base of tree
a0 = angle to base
h0 = height of tree below eye level as determined by h0 = d0*sin(a0)
D = eye level distance to tree = d0*cos(a0)
h1 = h - h0 = height of selected point above eye level
a1 = arctan(h1/D) = computed angle to chosen spot
d1 = diameter of trunk at chosen spot = c/PI

Steps for locating spot on trunk and calculating x:

1. Using clinometer, locate point on trunk at angle a1 above eye level
2. Measure diameter with Macroscope at that point
3. Calculate c as c = PI * d1
4. Calculate x successively for f1 = 1, 0.667, 0.5, 0.333, 0
4. Calculate p = (x-c)/c*100 = measure of how far x is from c for each x based on the values of f1.


The closer p is to 0, the closer the fit for the value of f1
f1=1.0 represents a parabola; f1=0 represents a cone; other f1 values a forms intermediate to
paraboloid and cone.

Results of the analysis will be reported in a future e-mail.