r
=========
====.====�
RESEARCH NOTES
/ssued
o/tM
PACIF'IC NORTHWEST FOREST AND RANGE
EX PERJMENT STATION
By
George R. Staebler Pacific Northwest Forest and Range Experiment Puget Sound Research Center The Scribner D ecimal C is the accepted log rule in the Pacific
Northwest. Usually volume, growth and yield tables are expressed by
this rule to give them practical meaning, Yet in the research required
for such studies , the rule is unsatisfactory because of rounded values
and irregular jumps in volume from diameter to diameter and length to
length.
As long ago as 1925, Donald Bruce publishe p mathematical formula
,79 D2 - 2D - 4,
fitted to the Scribner volumes for 16-foot logs : V
in which V is the volume in board feet and D is the diameter, inside
bark, in inches at the small end of the log, For scientific purposes,
volumes calculated from this form ula are superior to either the Decimal
C rule or the original values from which the Decimal C was taken,
Volume of a one -foot section of a log may then be taken as 1/16
the volume of a 16-foot log:
or
,0625(79 D2 - 2D - 4),
.049375 D2 - ,125D - ,25
Volumes computed from this formula are given in table 1 for logs from 6
to 40 inc_hes in diameter by 1/�0-inch classes.
Bruce, Donaldo
A'formula for the/Scribner rule.
Journal Forestry
2 3:432-433.
1925.
-·-·
· --- ---- - ­
Since the Scribner rule makes no taper allowance for logs up to
40 feet long, the volume of an log ma be determined b multipl ing the
volume of the one-foot section b the length of the log in feet. Table 2
gives the volumes so computed for logs from. 8 to 40 feet long b one­
inch diameter classes.
These tables are particularl useful for volume table construction
but also have wider application. A unique use for table 1 is in deter­
mination of the diameter of the average log when the length and volume
are known. Such information is often wanted in lumber grade recover
studies, cost of logging studies, and other studies in which those two
ve.riables are known. It is onl necessar to divide the volume of the
average log by its length to get its per-foot volume; then b comparing
this volume with tabular values in the table, its diameter may be read
directly. This is much simpler than interpolation for length and dia­
meter in a conventional table. Research workers will.find many more
uses for the tables •
•
-2-
Volumes for
Dia.
In.
Volume
Ed �_t_!.
Dia
lE;o
Table l0==Formula Scribner log rule
l foot section by tenth··inch diameter classesY
Dia.
In.
Volume
�_ft
.•
Volume'
Dia.;
lE;o
·
Volume
Ed. ft.
Dia.
2.62W+
10 .0
·
Volume
Bd.fto
-
6· ·10 inch diameter
-----('--
6 .0
ol
.2
o 7775
.8247
o3
oL
c5
.6
•7
.9222
. 9724
.s
.
9
.8730
1.0236
1.0758
1.1289
1 . 1 831
1.2382
'
7 .o.
.1
02
.;3
.;4
5
.;6
•7
.;8
.9
1.2944
1 . 3515
1.L 096
8.;0
ol
1.4687
1 . 5288
.;4
.;5
.;6 .;7 .;8
.9
1.5898
1.6519
1. 7149
1.7790
1.8440
.,1
.,2
o3
o4
o5
.6
.7
o8
o9
4.3494
4.4460
4 o 5436
4 o 6422
4. 7418
4.8423
L . 9 439
5.0464
5o15 00
5 o 2545
12 .; 0
,;1
o2
o3
.;4
.>5
.;6
.;7
o8
o9
5 . 3600
5 .4
6$
5 .5740
5.;6824
5 0 7919
5 o9023
6
c,0138
6 o 1262
6 .2396
6.354 0
16.0
.1
.2
.3
.h
.5
.6
.7
.;8
o9
10.3900
l0o5360
10.6830
10.8309
10.9799
1101298
11.2808
11.h327
11.5856
ll. 7395
17,;0
.;1
.2
.;3
n.8944
1200502
12.;2071
1 2 36Lt9
1205238
.h
.;5 12.6836
.;6 1208444.
<.7 13.0062
8 13.1690
.9 13.3327
2.,2548
2.3268
2.3997
2.4736
2.7012
2.7791
;,L
.;5
2.,9378
3.0186
3.1004
3.1832
3.2670
.;6
•7
.;8
2.5485
o9
2.8579
3.3517 3.4375
3.5242
,;1
.2
o3
3c6120
.;7
3.9728
4o0654
4.1591
.4
.5
.,6 8
.9
3.7007
3.7904
3.8811
4.2537
inch diameter
4
.;5 •6
67 .8
o9
I
6.4694
6.5857 6o 7031
6.8214
6.9408
7 00611
7.1824
7.3047
7 "LJ280
7o5522
14,;0
7.8037
,;3
8 0592
.;2
c>4
.;5
06
c7
.;8
o9
'
7.6775
,;1
7.9310
8o1884
8.3186
8.L 98
8.5819
8.7151
8 Bh92
15,;0
;,1
o2
o3
8.9844
9 ..
1205
9o2576
9o3957
9.5348
oL
.5
9.6748 ;,6 9.8159
9.9579 o7
.8 10 . 1010
o9 10.2h50
inch diameter
18.;0
.;1
,;2
•3
•L
.;5
;,6
n
.;8
c9
13.4975
13.6632
13.8300
13.9977
IL .; 1664
14.o3361
lLJ-05068
14.6784
ll..J.c8511
15.0247
}/'D iameter
-
.;1
.,2
.3
2.1839
13 .; 0
.;1
.;2
o3
16· 20
9.0
2. OLJ50
2ol139
,;2
.3
11"'15
ll00 lo9100
1.9770
.......
19o0
.;1
.2
3
.;h
.;5
.;6
n
8
9
&
15o199l..J.
15.3750
15 o5516
15.7292
15 0 9078
16o0873
16.2679
16.;449h
1606320
16o8155
20.0
.;1
,;2
.;3
17o0000
17.1855
17o3720
17.5 594
.;}..j. 17 0 7479
.;5 17.9373
.6 18.1278
.;7 18.3192
.8 18.5116
o9 180 7050
is diameter inside bark at the small end of the log0 Volume for
any length ma.y be computed by multiplying the length of log in feet by
the l=foot volumeo
=3=
Table 1,--(Continued)
Ino
Volmne
Bd.ft.
Dia.;
In.
Volmne
Bd0ft.
Dia.;
In.
Volume
Bd.ft.,
In�>
21=25 inch· diameter·
21.0
.1
.,2
.3
•4
o5
.6
.7
.8
o9
.
18o8994
19.0947
19.2911
19.4884
19.6868
19.8861
20.0864
20.2877
20.4900
20.,6932
22.;0
.;1
.2
3
.4
o5
.6
.;7
.;8
o9
20;8975
21.,1027
2L3090
21.5162
21.7244
21.,9336
22 1438
22;,3549
2205671
22.7802
23.;0
1
.;2
.;3
.;4
5
.;6
;,7
.;8
.9
22.9944
23.2095
23.4256
23.6427
23.8608
24.0798
24.2999
24.5209
24.,7430
24.9660
Volume
Bd,ft.
Dia.;
·
·
·
In,
Volume
Bd.ft,
25.;0
.1
.2
.;3
.4
.. 5
.6
.;7
o8
.9
27.4844
27.7192
27.9551
28.1919
28.4298
28.6686
28.9084
29.1492
29.3910
29.6337
37.6494
37.9237
38.1991
38.;4754
38.7528
39.0311
39.3104
39.5907
39;,8720
40.1542
30.;0
.1
.;2
.;3
.;4
.;5
;,6
;,7
.·8
.
()9
40.4375
40.7217
41.0070
41.2932
41.5804
41.8686
42.1578
42.4479
42.7391
43.0312
52.5775
52.9012
53.2260
53.5517
53.8784
54.2061
54.5348
54.,8644
55.1951
55.5267
35.;0
.;1
.;2
.;3
.4
.5
.;6
o7
.8
.9
55.8594
56 1930
56.5276
56.8632
57.1998
57 /)373
57.8759 58.,2154
58.5560
58.8975
Dia.;
·
24.;0 25,1900
1 25.4150
.;2 25.6410
.;3 25.8679
.;4 26.,0959
5 26.3248
.;6 26.5548
;,7 26.7857
.;8 27.0176
.g.:.'Z7 .2505
\
26 30 inch diameter 26.,0
.1
;,2
.3
.,4
.5
.6
o7
29.8775
30.1222
30.3680
30.6147
30.8624
31.1111
31.3608
31;,6114
8 31.8631
o9 . 32.1157
27 0
.1
;,2
.;3
.;4
5
.;6
n
.;8
o9
32.3694
32 6240
32.8796
33 1362
33.3938
33.6523
33.;9119
34.1724
34.L 340
34.6965
28.;0
1
;,2
.;3
•4
5
.;6
7
.;8
.9
34.9600
35,2245
35.4900
35.7564
36.,0239
36o2923
36.5618
36.8322
37'.1036
37.3760
2910
1
.;2
.;3
4
.>5
.;6
n
.;8
o9
31 35 inch diameter
31.0
43.3244 43.6185
.2 43.• 9136
.. 3 Lt4';2097
.4 44.5068
o5 44.8048
.6 45 01039 .7 45.LJD39 .8 45.7050 --22_ 46.0070
.,1
32.;0 .;1
.;2
.;3
.4
.;5
.6 n
.;8
o9
46.;3100
46.6140
46.9190
47 .;2249
47.;5319
47.8398
48.1488
48.4587
48.7696
49o0815 33.;0
.;1
.;2
3
.;4
5
.;6
.;7
.;8
.9
49.3944
49.7082
50.0231
50.3389
50.$58
50.9736
51.2924
51.6122
51.9330
52.2547 34.;0
.;1
.;2
.;3
.L
.;5
;,6
•7
.;8
.9
36-40 inch diameter
36.0
.;1
.;2
.3
.4
.;5
.;6
•7
.;8
o9
59.2400
59.;5835
59.9280 60.2734
60.6199
60.9673
61;,3158
61,6652
62.0156
62.3670
37 .;0
.;1
.;2 .;3
.;4
.;5
.;6
.;7
.8
.9
62.7194
63.;0727
63.4271 63.7824
64.1388
64.4961
64.8544
65.;2137
$.5740
65.9352
38.;0
.;1
.;2
.;3
4
.15
.;6
.;7
.;8
(19
66.2975
66.6607
67 ;,0250 67.3902
67.7564
68.;1236
68.4918
68.8609
69.2311 69.6022
-4­
39.;0
.;1
2
.;3
.;4
.;5
.;6
.;7
.;8
(19
69.9744 _40.0
70.3475
70.7216 71.0967
71.4728
71.8498
72.2279
72.6069
72.9870 73.3680
73.7500
Table 2.--Formula Scribner log rule feet long by l inch diameter classes Volumes for logs 8- to
Top
diameter
of log
inside
bark
Inches
-
8
feet
-
10
feet'
Volume of lo
by l ngth
12
feet
16
feet
14
feet
- - - - - - - Board feet -
18
feet
-
20
feet
- - - -
-
22
feet
- - -
Top
diameter
of log
inside
bark
Inches
14
23
34
47 62
16
26
38
52
69
17
28
1.]2
58
76
6
7
8
9
10
70
86
104
123
1Wt
78
96
116
138 162
87
107
129
154
180
96 118
11.]2
169
198
11
12 13
14
15 145
167
189
213 238
166
190
216 243
272
187
214
243
274
306
208
238
270
304 340
229
262
297
334
374
16 17
18
19
20 227 251
276
302 330
265
293
322
353
385
302
334
368
403
Wto
340 376
414
453 495
378
418
460
501-t
550
! 16 460
506 554
605
21 22 23
24 25
299
324 350
376
404
359
388
1.]20
LJ-52
485
418
453
489
527
566
478
518
559
602
647
538
583
629
678
728 598
647
699
753
809
657
712
769
828
890
26
27 28 29
30 347 370
395
1.]21 Wt7
433
463 491-J.
526 559
520
556
593
631
670
607
648
692 736
782
693
741
790
841
894
780
834
889
946
1005
866
926
'988
1052
1117
953
1019 1087
1157 1229
31 32
33 34 35 474
502
530
560
590
592
627 663
700
738
711
753
796 840 885
948
1004
1061
1120
1180
1066
1129 1193
1260 1328
1185
1254
1326
1399
1475
1303 1380
1459
1539
1622 36
37
38 39 40 6
7
8
9
10 6
10
15
21
28 8
13
19
26
34
9
16
23
31
41
11
18
27
37
48
11 12
13
14
15
35
43
52 61 72
43 54
65
77
90
52
64
78
92
108
61 75
91
107
126
16
17 18 19 20
83
95
108 122
136
104
119
135
152
170
125
143
162 182
204
21
22
23
24 25
151
167
184
202
220 189 209
230
252 \
275
26 27 28 29
30 239
259
280
301
324
31
32 33
34
35
36
37
38
39
40
829
878
928
980
1032
=5­
12 21 31
42
55 Table 2.--(Continued) I
ter "'''
di
24
0 f log feet
inside
bark
Inches
6
7
8
9
10
Volume of log by length
28
feet
26
fe.et
-
19
31 46
63
82
=
30
feet
--
34
feet
- - - Board feet -
22 36 53
73
96
20
34
50
68
89
32
feet
-
-
38
feet
36
feet
-
-
-
-
-
-
40
feet
-
-
Top diameter of log inside bark
Inches
23
39
57
79
103
25
41
61
84
llO
26
44 $5
89 l17
28
47 69
94 124
30
49
73
100
131
31
52
76
105 138
6
7
8
9
10
11
12
13 14
15 104
129
155
184
216
113
139
168
200
234
122
150
181
215
252
130
161
194
230
270
139 .
172
207
246
288
1l.1-8
182
220
261
305 157
193
233
276
323
165
204
246
292
341
174
214
259
307
359
11
12
13 14 15
16
17
18 19
20
21.1-9 285 324 365
408
270
309
351
395 442 291
333
378
426 476
312
357
405 456
510
332 381
432
486
544 353
404
459
517 578
374
428 486 547
612
395
452
513
578
646
416
476
540
608
680
16
17
18
19
20
21 22
23 24
25
454
502 552
605 660
491
5l.J.3
598
$55
715 529
585
644 705
770
567
627
690 756 825
605
669
736
806
880
643
711
782 856
934
680
752
828
907
989
718
794
874
957
1044
756
836
920
1008 1099
21
22 23
26
27 28
29
30 717 777
839
904
970
I
.24
25 777
842
909
979
1051
837
906
979
1054
1132
896
971
lOLJ.9
1129
1231
95 6
1036
1119
1205
1294
1016
l101
1189
1280
1375
1076
1165
1259
1355
1456
1135
1230
1328
1431
1537
1195
1295
1398
1506
1618
26
27 28 29 30 1213
1297
1383
1472
1564
1300
1389
1482
1577
1676
1386
1482
1581
1682
1788
1473
1575
1679
1788
1899
1560
1667
1778
1893
2011
1646
1760
1877
1998
2123
1733
1852
1976
2103
2234
31
32
33
·74
35
1$59
1756
1856
1959
2065
1777
1882
1989
2099
2212
1896
2007
2122
2239
2360
2014
2132
2254
2379
2508
2133
2258
2387
2519
2655
2251
238 3
2519
2659
2802
2370
2509
2652
2799
2950
36 37 38
39 40 31
32
33
34
35
lOl.J.O
1111
1185
1262
1341
1126
1204
1284
1367
1452
36
37
38
39
L-1-o
1422
1505
1591
1679
1770
1540
1631
1724
1819'
1918
I
-6­