Beer's Tree Volume equations
These tree volume equations have proven to be useful in many teaching situations here in Missouri. Published by Tom Beers in 1964 these equations can produce cord, cubic volume without bark, cubic with bark, and International 1/4" board foot volume.
$$ a = \frac{D^2(D+190)}{100,000}$$
$$ b = \frac{1}{100} \left[ \frac{H(168-H)}{64}+\frac{32}{H}\right]$$
$$ c = 475 + \frac{3H^2}{128}$$
Volume in cords \( = a * b \)
Volume in cubic without bark \( = 76 * a * b \)
Volume in cubic with bark \( = 92 * a * b \)
Volume in boardfeet \( = a * b * c \)
where D is the diameter at breast height in inches, Hi is the merchantable height in feet, and volumetype can be "cords", "cubic", "cubicbark", or "boardfeet".
Example
- Imperial Units
- D = 10 in inches
- L = 26 feet
- unittype = "cubicbark"
- Answer = 10.84 cubic feet
- D = 10 in inches
- L = 26 feet
- unittype = "boardfeet"
- Answer = 57.84 board feet
Board feet is a imperial units only system.
Code
This code is stored in my Github.com\larsendr site. These are direct links to the raw code.
Excel® Visual Basic Code
R Statistical Package Code
Python Code
Go Code
Javascript for Node Code
C Code
Reference
Beers, T. W. 1964 Composite Hardwood Volume Tables. Purdue University, Agricultural Experiment Station, Lafayette, IN. Research Bulletin 787. 12p.
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