Yt 
(US. FOREST: SERVICE, 
RESEARCH NOTE WS-se ) 
LAKE SmAnkk=S) EOREST (EXPERIMEN STATION U.S. DEPARTMENT OF AGRICULTURE 
l ‘ | | ini U.S, DEFT. OF ASRICULTURE 
HATIONAL £O"GELTURAL LIBRARY 
- 
Red and jack pine poles are important 
products from the forests of northern Minne. 
sota. Considerable flexibility of thinning prac- 
tices is made possible by the wide range of 
pole sizes presently used; these vary from 4 
to 9 inches in top diameter and 10 to 45 feet 
in length. This range in sizes is troublesome. 
however, when numbers of poles must be con- 
verted to a single unit of measure as is some- 
times necessary in cruising, appraising, and 
scaling timber. The cubic-foot volume table 
presented here provides a common unit of 
measure for a wide range of pole sizes. 
To develop this table, the diameters of 
190 red pine and 149 jack pine poles were 
measured at the butt end, at 10-foot intervals 
along the stem, and at the top. They were 
measured in the mill yard of the Wheeler 
Lumber Bridge and Supply Co. in Cass Lake, 
Minn., on five separate occasions, thus per- 
mitting a sample of poles cut by different op- 
erators and from a wide geographic area of 
northern Minnesota. The cubic-foot volume 
including bark was computed for each pole by 
Smalian’s formula. A scatter diagram of cubic- 
foot volume plotted over the product of top 
diameter in inches (D) times total length (L) 
in feet (hereafter called DL) showed volumes 
curving upward with increasing values of DL. 
Also, variation increased in the larger sizes. 
Plotting the data on logarithmic paper result- 
ed in a straight line with uniform variation 
for all values of DL. Therefore, the data were 
transformed to logarithms for the regression 
analysis. 
cea 
DE 2¥ 1954 
Cubic-Foot Volume Table for Unpeeled Pine Poles Fy pEcORDS, 
Gu 
A separate analysis for each species show- 
ed the two regression coefficients were not 
significantly different. Although the means 
of these two regressions were significantly 
different (at the 5-percent confidence level) 
the magnitude was less than 0.2 of a cubic 
foot. This difference scarcely justified separ- 
ate volume tables for the two species. There- 
fore, they were combined to obtain the vol- 
ume equation: 
logarithm V=1.4719 (logarithm DL) -2.2964 
where V equals volume and DL equals the 
product of top diameter outside bark in inches 
times the length in feet. The standard error 
of estimate for the logarithm of volume is 
+ 0.05066, which is ¢ 12.4 percent in terms 
of cubic-foot volume.! Ninety-seven percent 
of the variation in volume among the poles 
sampled is accounted for by the formula. 
Because of the nature of logarithms, the 
formula tends to under-estimate volumes, the 
magnitude depending on the standard error 
of the estimate.” The correction for this re- 
gression was computed to be 0.68 percent and 
has been added to the volumes in table 1. 
Product specifications used in this study 
(table 2) could undoubtedly be modified 
somewhat without seriously affecting the vol- 
1 This procedure underestimates the lower limits 
of error slightly. A more accurate value can be 
obtained by dividing the volume by 1.124 (the 
antilog of 0.05066). 
@ Spurr, Stephen H. Forest inventory. 476 pp. Ron- 
ald Press Co., New York. 1952. 
MAINTAINED AT ST. PAUL Ay MINNESOFA, IN COOPERATION WITH THE UNIVERSITY OF MINNESOTA 
