Forest Mensuration. Brack and Wood

Assume that:

• the tree is truly vertical (i.e. point A is directly above point B),
• the operator's eye (point O) is above the level of the base of the tree,
• the distance to the tree (OC) is the horizontal distance from the operator to the geometric centre of the tree at the appropriate position on the trunk.

• Case A: Observer stands at any distance from the tree convenient for observation of both the tip and base, i.e. the distance OC is a variable.
  • Measure distance OC.
  • Measure angles AOC and COB.
  • Determine the lengths of AC and CB by calculator or reference to trigonometric tables.
  • Add AC and CB for total height AB, i.e.
    AB = (OC x TAN(AOC)) + (OC x TAN(COB)) or
    AB = OC x (TAN(AOC) + TAN(COB)).
• Case B: The observer stands at a specific distance (or multiple or fraction of it) from the tree, i.e. the distance OC is fixed as, say 20 m. The instrument is calibrated in terms of this specific distance and successive angles of elevation and depression, so that AC and CB can be read directly from the instrument (e.g. Haga, Blume Leiss and Relaskop).

In the situation represented in the adjacent diagram, calculate the horizontal distance OC (from slope distance OB and angle BOC) and subtract the length BC from AC.

   AB = AC - BC
      = OC x (TAN(AOC) - TAN(BOC))


where
   OC = OB x COS(BOC) 

Tables can be derived for various combinations of angles AOC and BOC, and slope distance OB, from which values of AB can be read.

http://online.anu.edu.au/Forestry/mensuration/HEIGHT2.HTM
Cris.Brack@anu.edu.au
Mon, 6 Jan. 1997