Forest Mensuration. Brack and Wood

1. Plumb tip to ground to find point C. Plumb from two directions at right angles to each other, preferably in the plane of lean and at right angles to this plane.
2. Measure distance from operator to plumb point (C) - not from the operator to the base of the tree,
   i.e. find the distance O1 to C or O2 to C not O1 or O2 to B.
3. Measure height of the vertical component (AC) using the method described for vertical trees and the above horizontal distance (O1 or O2 to C instead of O1 or O2 to B).
4. Apply steps 2 and 3 for each of two suitable positions about the tree. The measured heights should agree within the limits of instrumental error (about +/- 2.5% for many hypsometers).
5. If worthwhile, calculate the linear or slope height (AB) from the vertical height (AC):

      AB = SQRT(AC^2 + CB^2)
   where SQRT denotes taking the square root.
   

Errors

With lean towards observer (from point O1), error is A1A2 (positive).

With lean away from observer (from point O2), error is A1A3 (negative).

The extent of these errors for various angles of lean and angles of observation is such that:

• the smaller the angle of observation (i.e. the further the operator is from the tree), the smaller the error.
• for a particular angle of observation, the greater the lean ABC, the greater the error.
• for a particular angle of lean, the negative error AWAY is greater than the positive error TOWARDS.
  The error away > error towards by 2 x A1E.

Note: In most cases, vertical height approximates linear height, i.e. CB is much less AC and the correction by 'Pythagoras' is unnecessary. The length of CB relative to AC will indicate immediately whether correction in step 5 is necessary.

The error involved in accepting the VERTICAL COMPONENT as an approximation to true height, i.e. AB vs AC in the above diagram:

• for leans to 8 degrees, error < 1%;
• for leans to 11 degrees, error < 2%;
• and for leans to 18 degrees, error < 5%.

A lean of 10 on a tree looks severe. Most leans are less than this. Therefore, for most purposes, height of AC, the vertical component, is a satisfactory approximation of true height. But do not be confused - the error in accepting the vertical component instead of the linear component is much smaller than the error introduced by using the incorrect horizontal distance (O1 or O2 to B instead of O1 or O2 to C)!

Measuring the height of leaning trees on sloping terrain presents real difficulties. If it is practical to use height sticks, do so - they eliminate all the difficulties of indirect measurement of height.

Experience has shown that when indirect methods are used to measure height (as against the direct methods - climbing, height sticks), measurement from two independent positions is essential. The readings from the two positions should agree within the limits of instrumental error - this is an absolute check on instrument and operator error (sighted to correct tip, etc.). Thus, differences of up to 1 m in readings for a 40 m tree are acceptable - precision of instruments under forest conditions is no better than this.

http://online.anu.edu.au/Forestry/mensuration/HEIGHT3.HTM
Cris.Brack@anu.edu.au
Mon, 6 Jan. 1997