Abstract
Coniferous tree which grows on the slope of the snowy region of Japan suffer a heavy pressure on the basal part of a trunk, and consequently there are so many “Butt-sweeps” in this region.
It may have been considered to be a difficult problem and almost no study has ever been done on this problem in spite of a considerable amount of commercial loss caused by this sort of demage.
On the present paper, the authors studied how to estimate the volume of the curved part of the trunk and also how accurate this method was.
Xylometer was used for determining the correct volume of the samples used.
The results obtained are:
1) Sectional figure of the curved part is elliptical having the longer diameter along the slope. Relation of the longer and shorter diameter to the height grade of a tree is represented by the parabolical formula,
y=a+bx+cx2
2) Both the inner curve of the Butt-sweep (the curve of the upper part of a trunk) and that of the opposite side are:
y=(a+bx)x
3) The first fomula for estimating the volume of a Butt-sweep was obtained:
V=l/90{32(G1/4+G3/4)+12G1/2+7(Gon+Gn)}……Hada (I) G0……area of the basal end.
G1/4…… area of the section, 1/4 from the base.
G2/4……area of the section 1/2 from the base.
G3/4……area of the section 3/4 from the base.
Gn…… area of the top end of the sample.
4) The second formula was obtained for estimating the volume of the curved part, V=G. R. α……Hada (II) G…… area of the elliptical section of the middle part at right angle to the stem axis.
R…… The radiaus of the arccrossing the center of gravity of the given ellipse.
α…… Center angle (radian)
5) HADA's formula (I) is as accurate as Sectional Measurement. Accuracy of the formulas introduced by the present and previous authors can be ordered as follows:
1. HADA's formula (I).
2. SMALIAN's sectional measurement.
3. BREYMANN'S.
4. RIECKE'S.
5. SIMONY'S.
6. SCHIFFEL'S.
7. HOSSFELD'S.
8. HADA's (II).
9. HUBER'S.
10. ‘Suekuchi-Jijo-Ho’ method.
11. SMALIAN'S.
