1. Volume Determination

2. 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

3. Board Foot
How many board feet in a cubic foot?

4. 1 MBF equals 1000 board feet 83.33 cubic feet of solid wood
Approximately 2 cords of wood

5. Board Foot Anomaly 1 board foot equals 144 in3
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

6. Kerf – wood lost as sawdust
Why 12 board foot of lumber isn’t actually what a cubic foot of wood yields

7. Bored Feet

8. Cubic Feet

9. Cord
Assume 80 cubic feet of solid wood due to air space

10. Roughly Half a Cord of Firewood

11. Variations on Cords
Face cord – since firewood is often cut into roughly 16 inch pieces, a 4 by 8 single stack is often called a face cord. It would take 3 face cords to equal a full cord
4’ X 8’ X 16”
Long cord – a pile of wood that 160 cubic feet
4’ X 4’ X 10’

12. Stem Form

13. 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: 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’

14. Girard Form Class
Diameter inside bark 17.3 feet Divided by Diameter Breast Height (DBH) (outside 4.5 feet) times 100
DIBtop
X 100 = FC
DBH

15. Extrapolate Top Diameter
Given a Bark thickness, DBH and FC, you can calculate Diameter Outside feet.
FC/100 = DIB/DBH
DIB + 2XBark = DOB
If bark = .5”, DBH = 20”, and FC = 80
DOBtop = 17

16. Common Local Form Classes

17. Historic Local Form Classes
Appalachian
Central States
Softwoods:
White Pine FC=79 Hemlock FC=78 Spruces FC=82 Cypress FC=78
Hardwoods:
White Oak FC=78 Red oaks FC=78 Yellow Poplar FC=78 Cherry FC=82 Basswood FC=80 Walnut FC=78 Beech FC=84 Maples FC=79 Birches FC=78 Upland ashes FC=82 Red & black gum FC=78 Hickories FC=78 Cottonwood & willow FC=78 Other hardwoods FC=78
Softwoods:
White Pine FC=80 Hemlock FC=78 Spruces FC=78
Hardwoods:
White Oak FC=78 Red oaks FC=78 Yellow Poplar FC=78 Cherry FC=82 Basswood FC=78 Walnut FC=78 Beech FC=82 Maples FC=79 Birches FC=78 Upland ashes FC=82 Red & black gum FC=80 Hickories FC=78 Cottonwood & willow FC=78 Other hardwoods FC=78

18. Factors affecting tree volume

19. Geometric forms of portions of tree
Newton’s Formula: V = h/6(Ab + 4Am + Au)

20. Standing Tree Volume Formulas

21. Tree Volume Tables – Doyle (FC=78)
Dbh (inches)
Number of 16-Foot Logs
1/2 1
1-1/2 2
2-1/2 3
3-1/2 4
Board Feet 12 20 30 40 50 60 14 70 80 90
100 16
120
160
180
190 18
130
200
220
260
300
320
360 22
170
230
280
340
380
420
460 24
290
430
490
540
600 26
440
520
590
660
740 28
620
710
800
880
510
630
840
940
1,040 32
270
730
860
990
1,120
1,220 34
680
850
1,000
1,140
1,300
1,440 36
350
580
780
970
1,310
1,480
1,640 38
390
1,100
1,290
1,680
1,860
1,230
1,450
1,660
1,880
2,080
Basically used by everyone except the US Government

22. Tree Volume Tables – International (FC=78)
Dbh (inches)
Number of 16-Foot Logs
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
110
140
160
180 16
150
210
250
280
310 18 70
190
240
320
360
400 20 90
170
300
350
450
500 22
290
430
490
560
610 24
130
510
590
660
740 26
410
600
700
790
880 28
480
810
920
1,020
220
550
690
930
1,060
1,180 32
260
470
640
940
1,080
1,220
1,360 34
530
730
900
1,380
1,540 36
330
820
1,010
1,200
1,560
1,740 38
370
670
910
1,130
1,340
1,940
420
1,250
1,480
1,700
1,920
2,160

23. Change the form class a little…
Rule of Thumb: Change of one form class = ~3% volume change

24. Derivation of Merchantable tree volume
See how form class defines the volume estimates for upper logs
 Refer to previous slide

25. Tree Volume Tables - Scribner
Dbh (inches)
Number of 16-Foot Logs
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
292
325
355 20 90
156
212
262
317
366
415
450 22
111
194
328
392
510
560 24
137
236
319
400
470
550
620
690 26
165
281
381
480
565
650
740
820
195
331
670
760
860
960 30
227
383
520
770
890
1,000
1,110 32
260
440
600
1,020
1,150
1,280 34
294
500
680
840
1,010
1,160
1,300
1,460 36
330
1,140
1,310
1,480
1,650 38
365
630
1,070
1,270
1,470
1,660
1,840
405
700
950
1,180
1,400
1,630
1,850
2,050

26. Contrasting Tree Scaling Rules

27. Weight Scaling of Timber

28. Scaling Timber by Weight
Sometimes trees are sold by weight (tons) instead of volume. Certain species, uses, and regions specifically (pulp, chips, low value logs, small diameter logs). Faster and cheaper than stick scaling.
Published tables of weight factors exist but since wood weights are influenced by multiple factors (species, time since cut, season, climatic conditions, growth conditions, age, live/dead, etc.) establishing local weight factors are recommended.
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.

29. Development of Weight to Volume 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.
USFS requires at least 10 observations with < 15% sampling error at the 95% confidence level.

30. Traditional Log Scaling
If you have data from traditional log scaling (species, gross cubic volume, and net load weight) you can develop weight to volume ratios that can be applied to loads of unscaled stems
Weight Factor = Net weight/Gross Volume

31. Xylodensimeter
Measures wood density in a similar fashion to the way a hydrometer works.
To estimate log weights, the density is multiplied by the gross cubic volume.
Mass = Volume X Density
The mean of at least 3 heartwood cores are taken at DBH, must be analyzed before losing moisture

32. Chunk Scaling
<8’ pieces volume calculated with Smalian’s formula and weight recorded to develop factor, chunks summed for each tree Weight Factor = Sum of Chunk Weights/Sum of Chunk Volumes

33. Smalian’s Formula

34. Large Chuck Scaling
1st piece is stump to DBH, other are 8’ pieces, entire merchantable bole volume and weight used for factor