# What Do You See? FOR 274: Forest Measurements and Inventory. Logs and Scaling: Definitions. Tree and Wood Volume Log Volumes Cords Weight Scaling

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1 What Do You See? FOR 274: Forest Measurements and Inventory Tree and Wood Volume Log Volumes Cords Weight Scaling Logs and Scaling: Definitions Logs: cut trees lengths of 8ft or more The process of measuring the length and diameter of individual logs to obtain a volume via a rule is called scaling The units of scaling measurements are: Cubic feet (12 x 12 x 12 inches) Cubic meter = 35.3 cu ft Board foot = 1in x 12in x 12in = 144 cu in 1

2 Logs and Scaling: Why? Measuring Products for Sale To double check the projections of inventories To measure how much work was done in order to pay people Log Volumes: Geometric Solids Logs are not perfect cylinders! Logs taper from one end to another Truncated sections of a tree can be approximated as geometric shapes: - Cone - Paraboloid - Neiloid Log Volumes: Geometric Solids Geometric tree shapes follow the equation Y = K X r, where r =0, 1, 2, 3, etc 2

3 Log Volumes: Geometric Solids Volume of any geometric soild = average cross-sectional area * Length Huber s Cu Volume = (B 1/2 )*L Smalian s Cu Volume = (B+b)/2 * L Newton s Cu Volume = (B+4B 1/2 +b)/6*l Logs and Scaling: Measuring B Cross Sectional Stem Area or Basal Area Assume tree at DBH is a circle Then area = π*r 2 = π*(d/2) 2 = π*(d 2 /4) If DBH is in inches and we want area in sq ft: Area = π*(d 2 /4) = π*d 2 /(4*144) = *D 2 As 1ft = 12in so as squared = 12x12 = 144 Log Volumes: Geometric Solids 3

4 Log Volumes: Which Formula? Huber s Cu Volume = (B 1/2 )*L Assumes average cross-section area is at midpoint, which is rarely true Even if true: NEED to measure area within bark thickness, and In piles it can be impractical to measure the midpoint diameter Huber s = Poor Method Huber s Volume: Example Small end diameter = 6 in Midpoint diameter = 8 in Large end diameter = 9 in Length = 16 ft Huber s Cu Volume = (B 1/2 )*L B 1/2 = * (8*8) = Volume = * 16 = cu feet Log Volumes: Which Formula? Smalian s Cu Volume = (B+b)/2 * L Requires measures at both ends of log Easiest to measure Cheap to implement Least accurate: especially for swollen butts or flared logs Error twice as large as Huber s formula Smalian s = The Compromise Method 4

5 Smalians s Volume: Example Small end diameter = 6 in Midpoint diameter = 8 in Large end diameter = 9 in Length = 16 ft Smalian s Cu Volume = (B+b)/2 * L b = * (6*6) = B = * (9*9) = Volume = ( )/2*16 = cu feet Log Volumes: Which Formula? Newton s Cu Volume = (B+4B 1/2 +b)/6*l Requires measures at both ends of log and at midpoint Most accurate method Very expensive and restricted to research In piles it can be impractical to measure the midpoint diameter Newton s = Used to check accuracy of other methods or to develop growth volume curves Newton s Volume: Example Small end diameter = 6 in Midpoint diameter = 8 in Large end diameter = 9 in Length = 16 ft Newton s Cu Volume = (B+4B 1/2 +b)/6*l b = * (6*6) = B = * (9*9) = B 1/2 = * (8*8) = Volume = (0.442+(4*0.349)+0.196)/6 * 16 = cu feet 5

6 Log Volumes: Which Formula? 2-End Conic Rule = ( *L)*[(d 2 +D 2 +d*d)/3] d = diameter at small end D = diameter at large end Common rule used by several timber companies Accounts for dropped fractions when converting diameters to areas (as in D) Log Volumes: Which Formula? Sub neiloid Rule = ( )*[(d+D)/2] d = diameter at small end D = diameter at large end Common rule used industry when the logs are shaped like the frustum of the neiloid Log Volumes: Which Formula? Bruce Butt Log Formula= ( )*[0.25D d 2 )(RL+T)] d = diameter at small end D = diameter at large end RL = length T = trim (0.5 per section) Used to calculate cubic volume of butt logs 6

7 Log Volumes: Which Formula? For perfect cylinders these eqns are identical In some cases a constant taper rate can be assumed: e.g. ½ in per 4ft increment Butt logs: Huber method underestimates by 5% and Smalian method overestimates by 10% Intermediate logs: Huber method and Smalian are very close to the Newton method Measuring Stacked Wood: The Cord One cord = 4 x 4 x 8 ft = 128 cu ft Measuring Stacked Wood: The Cord Cords include: wood, bark, and voids It is unlikely that: wood will be 4ft lengths ricks will be 32 sq ft For Feet Measures: Cords = (width x height x stick length)/128 7

8 Measuring Stacked Wood: The Cord How Many Cords is this? Measuring Stacked Wood: The Cord If sticks < 4feet: cord = short cord - Commonly used for firewood If sticks > 4 feet: cord = long cord - Long cords will contain more wood than a standard cord: typically: 8x4x5 ft Sound Cords: extra wood is added to account for wood lost due to defects In the U.S. pulpwood commonly is cut into log lengths of 5, 5.25, and 8.33 feet. Measuring Stacked Wood: The Cord How Much Actual Wood is Here? 8

9 Measuring Stacked Wood: The Cord The amount of actual wood available in the space occupied by a cord is dependent on: Species (bark thickness) Conifer bark ~10-30% of sticks Method of stacking loose piles = more air = less wood straightness of bolts smoothness of bolts (knots!) Diameter of sticks Length of sticks Measuring Stacked Wood: The Cunit A cunit = 100 cu ft of solid wood When using cords for pulpwood, typical specifications in the United States are (Avery and Burkhart, 5 th Ed): 1. Bolts must be minimum of 4 DIB at the small end 2. Bolts not to exceed 24 DOB at the large end 3. Wood must be sound and straight 4. End should be cut square and limbs trimmed flush 5. No burned or rotten wood 6. All nails and metal should be removed 7. Mixed pines are hardwoods are not acceptable DIB = diameter inside bark, DOB = diameter outside bark Calculating MBF Value: An Example Assume you have 100 pieces of lumber of sizes 3 by 6 by 16 selling at \$210 per MBF. Step 1. Calculate Cubic Feet: 100*(3/12)*(6/12)*16 = 200 cubic feet Step 2. Calculate MBF: (200*12) / 1000 = 2.4 MBF Step 3. Calculate the \$ Value: 2.4 * 210 = \$504 9

10 Weight Scaling: Typical Variations The main factors that affect weight for a given species are: volume, moisture content, and specific gravity Aspen %MC variations in the Cloquet Experimental Forest (Jensen and Davis, 1953) Weight Scaling: Pulpwood For pulpwood, weight scaling has been widely used since the mid 1950s. Advantages: 1. Enables fast delivery of freshly cut wood to mills 2. No special handling is needed 3. More accurate than manual scaling 4. Incentive for better piling of wood on trucks increases volume to mills Notes: Mainly mills prefer freshly cut material as it can be stored longer before it deteriorates Weight Scaling: Pulpwood Clearly, the weight of logs change over time. This change is dependent on: a) Wood volume b) Moisture content c) Specific gravity: density of sample /density of water in the wood So oven dry samples density decreases as you move up the stem as proportionally less heartwood Variations of volume within a cord are dependent on: a) Bolt diameter, length, and quality b) Bark thickness 10

11 Weight Scaling: Pulpwood Knowledge of the moisture content and specific gravity allows you to calculate weight (lb) per cubic foot as: Density = sp gravity x 62.4 (1+ %MC/100) Or in metric: Density = sp gravity x 1.00 (1+ %MC/100) Weight Scaling: Sawlogs What limitations would exist in applying weight scaling to sawlogs? 1. Weight is not the same as quality Price adjustments have to be made to account for variations in log grade, size, and shape. Weight Scaling: Sawlogs What limitations would exist in applying weight scaling to sawlogs? 2. Weight is not a measure of quantity Lots of small diameter logs (less lumber) can weigh the same as less large diameter logs 11

12 Weight Scaling: Sawlogs Weight scaling of saw logs is particular suited for plantations or other even-aged stands, especially where single species are harvested. Widely applied in southern pine logs as logs are fairly uniform in size and quality 12

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