Volume Determination
Definitions
 Log = 8 or more feet long (usually 16 feet)
 Bolt or Stick = less than 8 feet long
 Scaling = the process of estimating or measuring wood
volume
Board Foot
How many board feet in a cubic foot?
1 board foot equals 144 in2
 1 cubic foot equals 12 board feet
 However, if timber is scaled in cubic feet –
12 board foot per cubic foot isn’t realized in
lumber
 This is due to…

Kerf
 Slabs
 Trim waste

Kerf – wood lost as sawdust
Why 12 board
foot of lumber
isn’t actually what
a cubic foot of
wood yields
Bored Feet
Cubic Feet
Cord
Assume 80 cubic feet of solid wood due to air space
Roughly Half a Cord of Firewood
Stem Form
Girard Form Class

Ratio of the inside-bark diameter at the top of the first 16 ft. log
to dbh. Defines the rate of taper in a tree.

Stump height (1 ft.) and a trim allowance (0.3 ft.) are factored
in, making the upper measurement at 17.3 ft. above ground.


Example: diameter inside bark at 17.3 feet: 14.3 inches
dbh: 17.8 inches
Girard Form Class: (14.3 / 17.8) = 0.803, or 80 percent

drawback: getting the inside-bark diameter at 17.3 feet.

 Can measure bark thickness, double it and subtract from DOB at
17.3’
Girard Form Class
Diameter inside bark (DIB) @ 17.3 feet
Divided by Diameter Breast Height (DBH)
(outside bark @ 4.5 feet) times 100
DIBtop
------- X 100 = FC
DBH
Extrapolate Top Diameter

Given a Bark thickness, DBH and FC,
you can calculate Diameter Outside
Bark @17.3 feet.
FC/100 = DIB/DBH
 DIB + 2XBark = DOB

If bark = .5”, DBH = 20”, and FC = 80
 DOBtop = 17

Common Local Form Classes
Historic Local Form Classes
Appalachian
Central States
Softwoods:
Softwoods:

White Pine
Hemlock
Spruces
Cypress
FC=79
FC=78
FC=82
FC=78
Hardwoods:

White Oak
Red oaks
Yellow Poplar
Cherry
Basswood
Walnut
Beech
Maples
Birches
Upland ashes
Red & black gum
Hickories
Cottonwood & willow
Other hardwoods

White Pine
Hemlock
Spruces
FC=80
FC=78
FC=78
Hardwoods:
FC=78
FC=78
FC=78
FC=82
FC=80
FC=78
FC=84
FC=79
FC=78
FC=82
FC=78
FC=78
FC=78
FC=78

White Oak
Red oaks
Yellow Poplar
Cherry
Basswood
Walnut
Beech
Maples
Birches
Upland ashes
Red & black gum
Hickories
Cottonwood & willow
Other hardwoods
FC=78
FC=78
FC=78
FC=82
FC=78
FC=78
FC=82
FC=79
FC=78
FC=82
FC=80
FC=78
FC=78
FC=78
Factors affecting tree volume
Geometric forms of portions of tree
Newton’s Formula: V = h/6(Ab + 4Am + Au)
Standing Tree Volume Formulas
Tree Volume Tables – Doyle (FC=78)
Number of 16-Foot Logs
Dbh
(inches)
1/2
1
1-1/2
2
2-1/2
3
3-1/2
4
Board Feet
12
20
30
40
50
60
14
30
50
70
80
90
100
16
40
70
100
120
40
160
180
190
18
60
100
130
160
200
220
40
160
20
80
130
180
220
260
300
320
360
22
100
170
230
280
340
380
420
460
24
130
220
290
360
430
490
540
600
26
160
260
360
440
520
590
660
740
28
190
320
430
520
620
710
800
880
30
230
380
510
630
740
840
940
1,040
32
270
440
590
730
860
990
1,120
1,220
34
300
510
680
850
1,000
1,140
1,300
1,440
36
350
580
780
970
1,140
1,310
1,480
1,640
38
390
660
880
1,100
1,290
1,480
1,680
1,860
40
430
740
990
1,230
1,450
1,660
1,880
2,080
Basically used by everyone except the US Government
Tree Volume Tables – International (FC=78)
Number of 16-Foot Logs
Dbh
(inches)
1/2
1
1-1/2
2
2-1/2
3
3-1/2
4
Board Feet
12
30
60
80
100
120
14
40
80
110
140
160
180
16
60
100
150
180
210
250
280
310
18
70
140
190
240
280
320
360
400
20
90
170
240
300
350
400
450
500
22
110
210
290
360
430
490
560
610
24
130
250
350
430
510
590
660
740
26
160
300
410
510
600
700
790
880
28
190
350
480
600
700
810
920
1,020
30
220
410
550
690
810
930
1,060
1,180
32
260
470
640
790
940
1,080
1,220
1,360
34
290
530
730
900
1,060
1,220
1,380
1,540
36
330
600
820
1,010
1,200
1,380
1,560
1,740
38
370
670
910
1,130
1,340
1,540
1,740
1,940
40
420
740
1,010
1,250
1,480
1,700
1,920
2,160
Change the form class a little…
Rule of Thumb: Change of one form class = ~3% volume change
Derivation of Merchantable tree volume
See how form class
defines the volume
estimates for upper
logs
 Refer to previous slide
Tree Volume Tables - Scribner
Number of 16-Foot Logs
Dbh
(inches)
1/2
1
1-1/2
2
2-1/2
3
3-1/2
4
Board Feet
12
28
48
66
78
89
100
108
14
40
70
96
116
141
160
170
178
16
54
93
129
158
191
224
248
263
18
72
122
168
207
248
292
325
355
20
90
156
212
262
317
366
415
450
22
111
194
262
328
392
450
510
560
24
137
236
319
400
470
550
620
690
26
165
281
381
480
565
650
740
820
28
195
331
450
560
670
760
860
960
30
227
383
520
650
770
890
1,000
1,110
32
260
440
600
740
890
1,020
1,150
1,280
34
294
500
680
840
1,010
1,160
1,300
1,460
36
330
565
770
960
1,140
1,310
1,480
1,650
38
365
630
860
1,070
1,270
1,470
1,660
1,840
40
405
700
950
1,180
1,400
1,630
1,850
2,050
Contrasting Tree Scaling Rules
Scaling Timber by Weight
 Sometimes trees are sold by weight instead of
volume. Certain species, uses, and regions
specifically.
 Weights are subject to influence by multiple
factors. Some of these include species,
logging practices (how long it stays in the field
after felling), season, climatic conditions,
growth conditions, age, live/dead, etc.
 Example – salvage cuts, ‘fire break’ cuts, clear
cuts, where all trees are to be removed
regardless. Saves time/money – don’t have
to scale trees before cut.
Development of Weight Factors
 When selling by weight, a weight to gross
cubic volume factor must be determined.
 Weight factors must be specific to species
or species groups.
 At least 10 observations with < 15%
sampling error at the 95% confidence
level.
Traditional Log Scaling
 Historical information (species
and product of load, gross cubic
volumes, net load weights) from
traditionally scaled logs
Xylodensimeter
the mean of at least 3 heartwood
cores are taken at DBH, must be
analyzed before losing moisture
Chunk Scaling
<8’ pieces volume calculated with
Smalian’s formula and weight
recorded to develop factor, chunks
summed for each tree
Large Chunk Scaling – 1st piece is
stump to DBH, other are 8’ pieces,
whole tree volume and weight
used for factor