BC Firmwood and Northwest Log Rules Cubic. Neal Hart Jendro & Hart, LLC Sunriver, Oregon

Transcription

1 BC Firmwood and Northwest Log Rules Cubic Neal Hart Jendro & Hart, LLC Sunriver, Oregon Timber Measurement Society Annual Meeting, April 2013

2 Today I ll discuss: 1 How Smalian s formula tends to overstate cubic volume where butt dia. is > 30% larger than top 2 How NWLR s 0.7 inch diameter correction factor overstates Scribner diameter bias in today s harvest 3 How Scribner s truncation of fractional diameters causes significant variability in NWLR Cubic volumes 4 That improving accuracy of NWLR Cubic requires adoption of unbiased diameter measurement

3 If BC Firmwood and Northwest Log Rules Cubic scales gave the same results The conversion between them would be the ratio of their measurement units, or cf/m 3 : 1 meter = feet feet cubed = cf

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5 If BC Firmwood and Northwest Log Rules Cubic scales gave the same results BC Firmwood exceeds NWLR Cubic BC Firmwood is less than NWLR Cubic Ave -2.0% Dual-Scale defect free logs SED

6 What causes variance in the ratio between BC Firmwood and Northwest Log Rules Cubic Scales? BC Firmwood Formulas Smalian s C x L x (d1 2 + d2 2 )/2 NW Log Rules Two-End Conic C x L x (d1 2 + d2 2 + (d1 x d2))/3 Diameter Nearest 2 cm Scribner in. Length Nearest dm Scribner + 1 ft * Deducts Unsound Only Unsound Gross & Solid Merch * Logs 17 +, Scribner for logs <17

7 What causes variance in the ratio between BC Firmwood and Northwest Log Rules Cubic Scales? BC Firmwood Formulas Smalian s C x L x (d1 2 + d2 2 )/2 NW Log Rules Two-End Conic C x L x (d1 2 + d2 2 + (d1 x d2))/3 Diameter Nearest 2 cm Scribner in. Length Nearest dm Scribner + 1 ft * Deducts Unsound Only Unsound Gross & Solid Merch * Logs 17 +, Scribner for logs <17

8 The difference between Smalian s and the Two-End Conic formula derives from their estimates of average diameter and is independent of log length (L): Smalian s C x L x (d1 2 + d2 2 )/2 Two-End Conic C x L x (d1 2 + d2 2 + (d1 x d2))/3 Position of average diameter is in the center

9 Smalian exceeds Two-End Conic with decreasing log diameter and increasing difference between top and butt diameter If Top & Butt Dia. Difference is: 2 inches: Ave Cross Section Area (sq. inches) % Diff. in Top Butt Top & Ave 1-3 Ave Ave 1-2 Ave Cross-Section Dia Dia Butt Top Conic (d1) Butt (d2) in 2 d1 x d2 Dia. 2-End Conic Log india 2 Smalian Dia. Log Dia in Area % % in % % % Top Butt Ave Two-End Ave. Smalian Ave. % Diff % % % 0.7 in % % % % % % % % % %

10 Smalian exceeds Two-End Conic with decreasing log diameter and increasing difference between top and butt diameter If Top & Butt Dia. Difference is: 4 inches: Ave Cross Section Area (sq. inches) % Diff. in Top Butt Top & Ave 1-3 Ave Ave 1-2 Ave Cross-Section Dia Dia Butt Top Conic (d1) Butt (d2) in 2 d1 x d2 Dia. 2-End Conic Log india 2 Smalian Dia. Log Dia in Area % % in % % % Top Butt Ave Two-End Ave. Smalian Ave. % Diff % % % 2.7 in % % % % % % % % % %

11 Smalian exceeds Two-End Conic with decreasing log diameter and increasing difference between top and butt diameter If Top & Butt Dia. Difference is: 6 inches: Ave Cross Section Area (sq. inches) % Diff. in Top Butt Top & Ave 1-3 Ave Ave 1-2 Ave Cross-Section Dia Dia Butt Top Conic (d1) Butt (d2) in 2 d1 x d2 Dia. 2-End Conic Log india 2 Smalian Dia. Log Dia in Area % % in % % % Top Butt Ave Two-End Ave. Smalian Ave. % Diff % % % 6.0 in % % % % % % % % % %

12 The amount Smalian exceeds Two-End Conic increases with the difference between top and butt diameter and with decreasing top diameter

13 Adjusting for formula difference increases variance between BC Firmwood & Northwest Log Rules Cubic: Ave -2.7% Dual-Scale defect free logs SED

14 What causes variance in the ratio between BC Firmwood and Northwest Log Rules Cubic Scales? BC Firmwood Formulas Smalian s C x L x (d1 2 + d2 2 )/2 NW Log Rules Two-End Conic C x L x (d1 2 + d2 2 + (d1 x d2))/3 Diameter Nearest 2 cm Scribner in. Length Nearest dm Scribner + 1 ft * Deducts Unsound Only Unsound Gross & Solid Merch * Logs 17 +, Scribner for logs <17

15 BC Firmwood NW Log Rules Lengths: Unbiased accurate to nearest 1 dm (~3.9 in) Diameters: Unbiased accurate to nearest 2 cm (~0.79 in) Scribner length + trim minimal bias 1.0 ft for logs ft for logs <17 Scribner (biased) truncated fractional diameters plus 0.7 in

16 Basis for 0.7 inch bias correction factor: Scribner s truncation of diameter fractions for logs with zero or even-inch ovality: 0.5 in. Butt Top Log with zero Dia. 12 Dia. 8 ovality Butt & Top

17 Basis for 0.7 inch bias correction factor: Scribner s truncation of diameter fractions for logs with zero or even-inch ovality: 0.5 in. Butt Top Log with even-inch Dia. Ave Dia. Ave ovality Butt & Top

18 Basis for 0.7 inch bias correction factor: An additional 0.5 diameter truncation occurs for logs with odd-inch ovality e.g., 1, 3, etc. Butt Top Log with 1 ovality Ave X Ave. 8.5 X Butt & Top

19 Basis for 0.7 inch bias correction factor: Scribner s truncation of diameter fractions for logs with zero or even-inch ovality: 0.5 in. Scribner s additional 0.5 diameter truncation for logs with odd-inch ovality: 0.2 in. 0.7 in. Additional 0.2 inch bias correction assumes odd-inch ovality occurs almost half the time at boththe Top and Butt

20 Scribner diameter truncation for round logs and logs with ovality

21 Scribner diameter truncation for round logs and logs with ovality

22 Scribner diameter truncation for round logs and logs with ovality

23 Scribner diameter truncation for round logs and logs with ovality

24 Scribner diameter truncation for round logs and logs with ovality in increments of 1/16 in Average Ovality (in) Truncation Zero & even-inch / / / / / / / / / / / / / / / & odd-inch All Ave Assuming an equal probability of logs in each class, average truncation is 0.72 in. and 50% have odd-inch ovality at bothtop and Butt

25 Given Scribner diameter truncation just discussed What s the impact of Scribner diameter bias on the difference between BC Firmwood and Northwest Log Rules Cubic?

26 Range of Scribner diameter bias relative to BC Firmwood scale: Where Scribner Diameter (Inches) is: Metric Diameter in centimeters is: For Round Logs: For Logs With Ovality of 1": Narrow Wide Metric Dia. Metric Rads Measure Measure Metric Dia. Metric Rads MinScribner Max Max Min MaxBC MinFirmwood Max Max Min Max cm cm

27 Variance in cubic volume caused by Scribner diameter bias: Scribner Diameter ' Log w/1" in 10' Taper BC Firm. Minimum NWLR BC Firm. Maximum % 22% % 17% % 12% % 5% % 7% % 6%

28 Variance in cubic volume caused by Scribner diameter bias: Scribner Diameter ' 20' Log w/1" in 10' Taper BC BC Firm. Minimum NWLR BC BC Firm. Maximum % -11% 22% 21% % -15% 17% 22% % -18% 12% 17% % -5% 5% 6% % -6% 7% % -3% 6% 5%

29 Variance in cubic volume caused by Scribner diameter bias: 40% 15%

30 Variance in cubic volume caused by Scribner diameter bias: Dia. Bias Top 0.67 in. Butt 0.26 in. Ave -2.7%

31 Variance in cubic volume caused by Scribner diameter bias: Dia. Bias Top 0.50 in. Butt 0.47 in. Ave -4.1% Dia. Bias Top 0.67 in. Butt 0.26 in. Ave -2.7%

32 Ave. Scribner diameter bias by diameter class ~500,000 logs exported from BC to US in 2000 NWLR Assumed dia. bias Ave

33 Variance in cubic volume using 0.55 instead of 0.7 correction for Scribner diameter bias: Dia. Bias Top 0.50 in. Butt 0.47 in. Ave -0.1% Dia. Bias Top 0.67 in. Butt 0.26 in. Ave -1.3%

34 To sum things up: 1 Smalian s formula tends to overstate cubic volume where butt dia. is > 30% larger than top 2 NWLR s 0.7 inch bias correction factor overstates Scribner diameter bias for today s harvest 3 Scribner diameter truncation causes significant variability in NWLR Cubic volumes 4 Improving accuracy of NWLR Cubic requires adoption of unbiased measurement protocol

35 Some recommendations: BC Firmwood: Adopt Two-End Conic formula NW Log Rules Cubic: Adopt unbiased diameter measurement protocol Adopt more representative correction factor for Scribner diameter bias

36 Neal Hart Jendro & Hart, LLC Sunriver, Oregon

37 Neal Hart Jendro & Hart, LLC Sunriver, Oregon