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

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

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

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’

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: 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

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) 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

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

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 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

Contrasting Tree Scaling Rules

Weight Scaling of Timber

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.

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.

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

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

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

Smalian’s Formula

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