-·---
-J
\.IIV
I
VIV.;:)L
W'
. vv6
Service for official use
I
/.
Long Logs. or· Short Logs. with The Scribner Scale By GEORGE R. STAEBLER
Pacific Northwest Forest & ·Range Experiment St tion
AbOUt
T h'IS f1/
This F'1/ .
e Wa s
e. ,
cr eate
d bY sc
anning
ns iden
t
he An.
ti
fied by
nted P
howev
t h e so
U b/icat·l
e r' sorn
f
t
w
a
r
o n.
.
e have
e mist
'be
en
akes rn
c orrec
ay rem
tecl;) ain.
·
IV?'
. lssca
.
Reprinted from
.
An International Lumber Journal
PORTLAND, OREGON
Vol. LIV, No. 10
August, 1953
·
r
Although such a price schedule has the effect of paying the producer a price based on lumber recovery, it seldom re­
flects the difference in scale accurately. A preferable system would be' to use a· log scale that would always give the same volume to a tree regardless of the length of logs cut from it. One price could then be quoted per unit of vol­
ume. Buyer and seller would talk in the same terms and neither would need to ·
convert the scale or price to determine
I .
fr
'
74%
CI/BIC VOLIIME OF
IYOOO ,01/T$/OE
...
SC ALED. CYLINDE/IS,..,
C/18/C VOLI/ME OF
WOOD INSIDE
*
87%
SCALED CYLINDE/1$
·BIGGER LOG SCALE is secured by cutting four short logs from a 16-inch tree with mer­
chantable height of 64 feet to 8-inch top, rather than cutting two long logs. Chart shows
volume of wood inside and outside scaled cylinder in both methods of cutting.
Long Logs or Short Logs with The Scribner Scale .
H
.
By GEORGE R. STAEBLER
Pacific Northwest Forest & Range Experiment Station
OW MANY board feet are in
the logs of a tree by the Scrib­
.
ner log rule? This question can­
not be answered unless it is also speci­
fied what length logs are to be cut from
the tree. The Scribner log rule, com­
monly used in the Pacific Northwest,
makes no allowance for taper unless the
scaled log is 42 feet long or longer. The
part of the log that lies outside the
scaled cylinder, taper, is a greater pro­
portion of the total, volume in long logs
·than iri short . logs. Hence, ·the scaled
·.volume of a tree may be increased by
cutting shorter logs from it.
· Some of the wood that lies outside the
scaled cylinder may actually be used.
Scribner, .in ·making his rule; assumed
that only the cylinder could be ma,de in­
to. usable lumber, Undoubtedly, when
the rule was made this was largely true;
but today, taper.sawing, the use of gang
saws, the making of veneer, the increas
ed market for short lengths, and other
improved utilization and marketing
practices make more and more of. the
taper wood actually usable.
The difference between the log scale
and the board feet actually recovered is
termed' overrun {or under run in those
•
·
·
rare cases where sawed volume is less
than log scale). Overrun is partly due to
utilization of taper and partly to. better,
or. different sawing practice than is as­
sumed by the log rule. That part of
overrun due to utilization of taper is
greater for longer logs and· logs of
smaller diameter, as is shown by Table
1, which compares the Scribner rule
with the International rule. The Inter­
national rule assumes one inch of taper
in each eight feet of length and scales
the log in 4-foot sections. It also . as­
sumes somewhat better sawing practices.
The difference between the Scribner and
the International rule approximates the
overrun for the more efficient sawmills.
With today' s increased values, all the
way from trees to boar_ds, a means of
scaling tree volume independent of log:
length is desirable. Log prices must be
based on the amount of materia1 recov­
erable in the fina:l prodl!ct_:__log scale
plus overrun. Hence, under the Scribner
rule, long logs are worth more than
short logs, and log prices are, in fact,
often fixed to reflect this difference in
value. Usually prices are quoted for
long logs (24 feet or longer), with
some fixed deduction for shorter logs.
the most advantageous log length.
Such a scale would be especially de­
sirable for young growth trees. As long
as the woods provide large, high grade
logs from virgin . stands the scaling in­
consistencies are of. less consequence.
Rate of taper in old growth trees is uni:
form and occurs mostly in the unmer­
chantable part of the trees. Logs· from
young growth trees, oil the other hand,
have highly variable rates of taper. Such
trees· are utilized well up into the tops
where taper is large. Furthermore, taper'
varies grea ly from stand to stand, de­
pending on tree height. For these rea­
sons, a long-log scale usually does not .
represent fairly the volume actually in
young growth trees. Long-lo·g scale may
also contribute to poor utilization in
such st nds. For example, an 8-inch, 32­
foot log has so little scale (70 board
feet Dec. C) that the temptation may be
to leave it in the unused top of the tree.
Yet, scaled as two 16-foot l9gs it could
contain more than 100 board feet (figur­
ing 3 inches taper in the top 16 feet).
.
New Scale on Taper Length
·
As long as the Scribner rule is used,
the only way to get a more nearly ac­
curate scale is to cut short logs so that a
higher proportion of the taper is s'caled.
This raises another question: "Just how
much increase in scale rnay be expected
by cutting short logs rather than long
ones?'.' The i crease may qe determined
by scaling a run of logs as both long
and short logs but this would have to be
done for each stand-perhaps each set­
ting. A more generally useful· scheme
. would be to determine theoretical scale
based on as umed rates of taper . and
logs of given length.
Such a log rule may be easily built up
from the formula ver ion of the Scrib-.
ner rule. This formula, fitted to the
published scale of 16-foot logs, is
V = .79D2 - 2D
4, where V is volume in board feet and D is diameter of the log in inches. The formula ap­
proximates the published volumes very closely and has the advantage of even, logical increases in volume from diam­
eter to diameter and length to length of log. One-sixteenth the -volume given by the formula may be taken as the con, tents of a 1-foot section and the volume C?f logs of any length may be computed ·
·
-
Table 1 .-Difference Between Scribner and International Rules
As An Illustration of Overrun.
16-foot logs
Log
Diameter
ln.
Scrlbner1/
b.f.
8
9 ................................... :.... . .. ... ... .... ..
10 ....... ... .. ..
\.... ..... ...... .. .... . ... . . .. ..... . ..
31
42
55
""'"''''"''''''"'''''"''"''''''"''' '"'''''"''''''"'
...
.
..
.
.
.
.. .
.
.
.
32-foot logs
Dlfl.
pet.
Intern.
b.l.
ScribnerY
b.f.
Intern.
b.f.
Dill.
pet.
39
51
65
26
21
18
61
84
110
103
131
162
69
56 47
14
13
139
172
207
246
288
196
233
273
316
363
41
35
32
28 26
24
22
11
20 18
11 ......,,_,,,,,. .. .. .... ..... . .. . . .... ... . . ... ......
12
13
....... ... .
14 . ................ .... .............. ,,,_,__,__,,,..
15 ... .. ....... . ...... ..... ,,,_,,,, ... ...... ..... .. .
86
104
123
144
80
97
115
136
157
16 .. .. ,,,,,_,..,,.. . .. .. ... . . . .. .... .. .
17 ............................................................
18 .. . . . ... . .. . .. ... .. ... . . . . .. . . .. .. ......
19 . ... . . ......... ....... . . . . ..... .. .. . . ........ ... .... .
20
166
190
216
243
272
181
205
232
260
290
9
8
332
381
432
486
544
413
466
522
581
644
21 ...... .... . .. .... ...... .... .. ............ ... . ..... ...
22 .. . .. .... ... .... .... . ....... .. .... .... . ..... .. . . .. .. 23 .............................................................. 24 . ..... ....... ..... . . .. .. .. . . . .. ...... .......... .. 25 ....... .... . ... . .. . . .... . ... .... .... .. ..... .....
\
302
334
368
403
440
321
354
388
424
462
6
6
5
5
5
605
669
710 779
851
926
1004
.
...
.
.......................
..
.
.
..........................................
..
.
······ . ...
. .
..
70 .
···········-························ .
.
.
.
..... .
. . ..
. .
.
.
.
.
. . ... .
.
.
.
.
. . . ..
.
................................
.
..
. ..
..
....
. .
.
.
.
. . .
.
. ..
..
..
..
..
..
.
.
..
. .
.
.
.
.
..
·-··"''"'''''"'"'""' .. ..
.
.
.
.
.
..
.
. . . ..
.
..
..
...
'Scribner volume py the formula, V =
L = length.
(.7.902
•
40
11
11
9
7
7
7
4).0625L
•
by multiplying this figure by the length
of log. If a rate of taper is assumed,
another equation may be written giving
the volume of a log of any length as
though the log were cut in two and the
two logs scaled separately. Having this
equation, the pefcentage difference be­
tween short-log and long-log scale may
be computed. For example, a . 32-foot
log 12 inches in diameter that tapers
1 inch in 8 feet, scales 209 board feet
if it is bucked and scaled as two logs.
Conventional scale would be 172 board
feet, so the short-log scale is 21.5%
greater than the long.-log scale.
736
806
880
17
16
16
15
14
where D = Diameter small end of· log and
Here, then, is a convenient expression
of the increase to be expected from cut­
ting short logs. Percentage differences
computed in this manner for four rates
of taper are presented in Table 2.
This table may be used to estimate the
difference between long- and short-log
scale for a run of l<;>gs, or even to esti­
mate the difference to be expected in
standing timber. For these uses, the di­
mensibns of the average log and the av­
erage taper must be known or estimated.
For example, suppose 100 long logs
have been scaled; total scale is 12,200
board feet. Hence, the average log has
122 board feet. The scale sheet shows
that the average length. of log is 32 feet
Interpolation into tables giving log vol­
umes by Scribner formtila, as in Table
1, shows that such a log must have a
diameter. of 10.4 inches. Taper is esti­
mated to be 1 inch in 8 feet. Table 2
shows that a log 32 feet long and 10.4
inches in diameter, and having a taper
of 1 inch in 8 feet, would scale 27%
. more as two 16.-foot logs than as one
32-foot log. Hence, the short-log scale
of the 100 logs may be estimated at.
12,200 X 1.27 or 15,494 board feet. A
short-log scale so computed is less than
International so that a mill overrun is
still usually possible. The overrun will,·
however, be closer to that expected for
16-foot logs than for 32-foot logs.
The table shows that small changes in
average diameter, length, or taper cause
substantial changes . in per cent differ­
ence. If the log dimensions are not
known exactly, it is well to allow three
or four percentage points tolerance in
the tabular differences for small diam­
eter logs, and one or two ·percentage
points for large diameter logs.
Taper, especially, is likely . to be dif­
ficult to estimate, but may be determin­
ed accurately from careful measure­
ments on sample logs. In measuring
logs, only the small end and middle
diameters would be measured if the log
were actually bucked and scaled as two
logs; hence these two measurements are
the important ones. Mid-diameters,
however, are difficult to measure on un­
bucked logs because bark thickness must
somehow be determined to get diameters
inside bark. Taper for the ell\ire log, as
the difference between large and small
end diameters, may be used without
Table 2.-lncrease in Scaled Volume When Long Logs Are Bucked and Scaled As Two Short Logs.
Taper
I"
Taper
In 71
I"
In 8'
Taper
I"
Taper
In 9'
I"
in 10'
Length of log before bucking
36.
32
28
Piameter
8 _,,.. ... ... .. ....... ........ . .. .. . ... ..... .... ... ... .. . .....
9 ....................................................................... 10 ....................................................................... 42
34
28
11 ........ . ........ . .. .. ...... ... ...... .... ... . ... ... ...... . ... . .
12 .. .. ............... ..... . .. . .. . ... .. .... ... .... ...... ... 13 .....................................................................
14 .......................................... . ..... ..... .. 15 ................................................................... :.... . 28
32
24
22
19
18
16
27
24
22
20
19
18
17
15
14
12
22 19
17 15
14
24
22
19
18
16
16
15
13
12
11
19
17
15
14
12.
22
1 9.
17
16
15
13
12
11
11
10
15
14
13
12
11
17
16
15
14
13
11
11
10
9
9
13
12
11
11
10
15
14
13
12
11
10
10
9
8
8
12
11
10
10
9
13
12
12
11
10
10
9
8
8
8
11
10
10
9
9
12
12
8
8
8
7
7
10
9
9
8
8
11
10
10
9
9
8
7
7
6
6
9
8
8
7
7
10
9
9
8
8
32
28
25
23
21
21
19
17
15
14
16 ......................................................................... 17 ........................................................................ 18 ....................................................................... 19 ....................................................................... 20 ................................................................... 15
14
13
12
12
18
16
15
14
13
20
18
17
16
15
21
22
23 .......... :... ... ..... ... . .... ... ... . ..... .. ... .. . . .
24 .......................................................................
25 .........................................................................
11
10
10
9
9
13
12
11
11
10
14
13
13
12
12
..
. ...
.
... ..
.
.
. .
.
.
- .
.
.
..
..
::::::::::::::::::::::::·::::::::::::::::::::::::::::::::::::::::
..
...
..
.. .
...
.
. ...
48
39
"\
38
31
29
25
23
20
19
. .
.
.
36
31
26
22
25
22
19
18
16
. .
..
32
28
28
23
20
37
.
36
39
34
27
33
.
32
,34
29
24
41
33
28
..
I
28
Percent
32 26
22
36
29
25
.
I
36
45
52
45
..
I
11
10
10
35
30
25
·
I
Table 3 .-Average
Taper and Average Diameter of Log That May Be Expected When Cutting Trees
.
·
of Given Average Diameter Breast High and Mercha table Height.
Number of 32-foot logs in average tree
Average
D.b.h.
sawlog
frees
in.
12
13
14
15
16
17
18
19
20
21
22
23
24
Dla. of
32-ft.
logs
in.
Vol. in
32-fl.
logs
b. f.
74
89
105
118
136
155
172
192
214
238
258
283
310
1
·
I
I
IV.
I
1%
I
I·
1%
I
2
2V•
I
2'h
I
2%
I
3
I
3%
I
3%
feet per Inch of taper
10.0
6.7
8.6
9.2
9.8
10.3
10.9.
11.5
12.0
12.6
13.2
13.8
14.3
14.9
15.5
erious error for all except butt logs.
Taper is usually abnormally large in the
first 6 feet of a tree, and if large and
small end diameters are measured on
long butt logs, the result will be an
overestimate of rate of taper. On these
logs the mid-diameter inside bark must
somehow be measured and taper in the
top half «f the log computed.
For standing timber, Table 3 may be
used as. a guide to average taper and
size of log. Here the average diameter
breast high of trees to be utilized for
logs and the average number of logs per
tree must be known or estimated. In
making this table, it was assumed that
the 16-foot form class of the trees aver­
ages 80 and that utilization is to an 8­
inch 'top for trees under 20 inches diam­
eter. breast high. For trees over 20
inches,. minimum top is one-half the
_scaling diameter of the butt 16-foot
log.1 Taper and size of average log read
.from this table may be used to read the
expected difference between long- and
.
short-log scale from Table 2.
.
.
The Puget Sound Research Center has
checked both the differences between
,long-log and short-log scales and the
tables presented in this ar.tif=le on the
'These limits of utilization are the same as used in
"Board·foot Volume Tables for 16-Foot Logs," by
James W. Girard at d Donald Bruce.
.
.2
'
10.0
7.5
6.0
10.0
8.0
6.7
'
10.0
8.3
7.1
6.2
10.0
8.6
7.5
6.7
10.0
8.8
10.0
8.9
8.0
7.6
7.8
7.0
6.7
6.4
7.3
7.0
6;7
McCleary Experimental Forest at Mc­
Cleary, Wash., a co-operative experi­
mental forest owned by the Simpson
Logging Co. The 55-year-old trees on
this forest are being thinned by a small
operat_or under the supervision of the
Research Center. In one sale, 273,000
board feet were marked and harvested,
to be paid for on the basis of short-lo
scale, although long -logs 'were cut and
scaled. The average diameter breast
high of the marked trees' was 15.8
inches. Such a tree in this stand will
contain two 32-foot logs. Table. 3 in­
dic;ttes hat .the average 32-foot log C].lt
would be 10.8 inches in diameter and
.
the average taper would be 1 inch in
10 feet. Table 2 shows that short-log
scale would exceed long-log scale by
20%. As a check, a sample of 149 long­
logs from the operation were scaled as
long-logs and again scaled after they
were bqcked into short-logs at the mill
site. Actual difference between the two
scales in this sample was l9.7%.
10.0
9.5
9.1
8.7
8.3
10.5.
10.0
9.6
9.2
10.4
10.0
The Scribner log rule makes no al­
lowance for taper, hence the scale vol­
ume of a long-log may be increased by
cutting it into two or more short-logs.
For small logs with relatively fast taper,
the difference in scale is surprisingly
great. Young growth stands, which
yield logs with these very characteristics,
;1re usually severely penalized in volume
if made into long-logs and scaled as
g
In another check an 27 fd'led and
bucked trees in 40- to 45-year-old, more
open timber on the same forest, an ac­
tual overrun difference of 24%· was
.
found. Average dimensions of the trees
.
measured were 15. 5 iQ.ches diameter
breast high and 1% 32-foot logs. Using
the tables as before shows that the expected scale difference would be 23%.
10.0
9.0
8.6
8.2
7.8
7.5
SjlCh.
A log rule may be constructed that
shows the volume of long-logs as
though they were cut and scaled as two
logs. Such a rule depends on rate of
taper, as well as conventional measures
f diameter and length. Using this rule,
a percentage difference table was co.n­
structed to show how .much short-log
scale exceeds long-log scale. This article
presents a table of these differences for
each of four different rates of taper. ·
These tables may be used to predict in­
crease in scale from long to short logs
when the log of average dimensions is
known. This may be done either for
harvested logs or standing trees. If for
standing trees, another table is given to
show overage taper and size of log
based on average tree cut.
The tables presented have been check­
ed in actual practice on. the McCleary
Experimental Forest and have been
found to work well.
·
·
·