Honer’s
Volume Equations
Honer’s (1967) total volume
equation has been widely used throughout eastern
The original form of Honer’s total volume equation (Honer 1967) was:
_{}
where,
V_{Tot} = Total volume in ft^{3}
D = diameter outside bark (inches) measured at breast height (4.5 ft)
H = total height (ft)
b_{0} and b_{1} are species specific regression coefficients.
Honer’s equations, as originally developed, were based on the English measurement system. To make these equations appropriate for the metric system, Honer et al. (1983) developed a series of modifications to convert the cubic–foot volume based on English measurements to cubic–meter volume based on metric measurements.
The conversion process was as follows:
1. cubic feet to cubic meters conversion:
_{}
where
V_{Tot}_{(E)} = the total volume in ft^{3} as estimated from Honer’s original equation (see above) based on D_{4.5,int} (diameter measured in inches at 4.5 ft) and H_{ft} (height measured in feet).
2. height in feet to height in meters:
Since total height is measured identically in the English system and metric system, the conversion for height is straight forward:
_{}
and
_{}
3. dbh in cm (d_{1.3,cm}) to dbh in inches (D_{4.5,in}):
The diameter conversion is trickier since the measurement point differs in the two systems. DBH in the English system is measured at 4.5 ft (1.37 m), while dbh in the metric system is measured at 1.3 m. The conversion factor has to account for both the conversion from cm to inches as well as the taper in the tree stem (diameter at 1.3 is going to be larger than the diameter at 1.37 m). To address this issue, Honer et al. (1983) proposed a simple taper function:
_{}
where,
D_{1.37} = diameter at 1.37 m (4.5 ft) in centimeters
d_{1.3} = diameter at 1.3 m in centimeters (metric dbh)
c_{1} = species specific taper coefficient
Finally, D_{4.5,in} can be obtained using:
_{}
and the volume equation becomes:
_{}
So now we have an estimate of total volume in m^{3}
based on dbh in cm measured at 1.3 m and total height
in m that is compatible with the original English total volume estimates in ft^{3}. This compatibility was crucial since Honer’s (1967) English volume equations were so widely
applied and we needed compatible estimates of volume as
_{}
and
_{}
and
_{}
The volume equation then becomes:
_{}
Table 1 gives the original coefficients for Honer’s (1967) volume equation (b_{0} and b_{1}),
the taper coefficient (c_{1}) and the metric derived coefficients (a_{0},
a_{1}, and a_{2}) for the major species found in
Table 1. Original coefficients for estimating total volume (ft^{3}) based on Honer’s (1967) volume equation, the taper coefficient for conversion of dbh_{1.3} to DBH_{1.37} (Honer et al. 1983), and the metric derived coefficents for estimating total volume (m^{3}) by species.
Species 
Honer's (1967) coefficients 

Taper 

metric derived coefficients 


b_{1} 
b_{2} 

Coefficient 

a_{0} 
a_{1} 
a_{2} 
White Pine 
0.691 
363.676 

0.184 

0.691 
110.848 
0.004319 
Red Pine 
0.710 
355.623 

0.151 

0.710 
108.394 
0.004331 
Jack Pine 
0.897 
348.530 

0.151 

0.897 
106.232 
0.004331 
Black Spruce 
1.588 
333.364 

0.164 

1.588 
101.609 
0.004327 
Red Spruce 
1.226 
315.832 

0.169 

1.226 
96.266 
0.004325 
White Spruce 
1.440 
342.175 

0.176 

1.440 
104.295 
0.004322 
Balsam Fir 
2.139 
301.634 

0.152 

2.139 
91.938 
0.004331 
Cedar 
4.167 
244.906 

0.155 

4.167 
74.647 
0.004330 
Hemlock 
1.112 
350.092 

0.155 

1.112 
106.708 
0.004330 
Trembling 
0.312 
436.683 

0.127 

0.312 
133.101 
0.004341 
Balsam Poplar 
0.420 
394.644 

0.127 

0.420 
120.287 
0.004341 
White Birch 
2.222 
300.373 

0.176 

2.222 
91.554 
0.004322 
Yellow Birch 
1.449 
344.754 

0.181 

1.449 
105.081 
0.004320 
Maple 
1.046 
383.972 

0.145 

1.046 
117.035 
0.004334 
Basswood 
0.948 
401.456 

0.145 

0.948 
122.364 
0.004334 
Beech 
0.959 
334.829 

0.145 

0.959 
102.056 
0.004334 
Black Cherry 
0.033 
393.336 

0.145 

0.033 
119.889 
0.004334 
White Elm 
0.634 
440.496 

0.145 

0.634 
134.263 
0.004334 
Ironwood 
1.877 
332.585 

0.145 

1.877 
101.372 
0.004334 
Red Oak 
1.512 
336.509 

0.145 

1.512 
102.568 
0.004334 
References
Honer, T.G. 1967. Standard volume tables and
merchantable conversion factors for the commercial tree species of central and
eastern
Honer, T.G., Ker, M.F. and Alemdag,
I.S. 1983. Metric timber tables for the commercial tree species of
central and eastern
Shailer, S., Kershaw, J.A., and Zundel, P. 1998. Comparison of total
volume equations for use in southwestern