1、O302.1-15/O302.2-15Scaling roundwood/Measurement of wood chips, tree residues, and by-productsLegal Notice for StandardsCanadian Standards Association (operating as “CSA Group”) develops standards through a consensus standards development process approved by the Standards Council of Canada. This pro
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15、sLOADTHISDOCUMENTONTOACOMPUTERFORTHESOLEPURPOSEOFREVIEWINGITsSEARCHANDBROWSETHISDOCUMENTANDsPRINTTHISDOCUMENTIFITISIN0$ rather, it is uniform for all the scaling methods (solid or stacked volume, mass, count, etc.).(e) Consequently, in accordance with the aims of the user, and the quality and value
16、of the product to be scaled, scaling methods more or less precise and expensive may be chosen, but the accuracy related to the sampling, or the accuracy related to the estimation of the means, should stay the same.(f) A large sampling error added to the errors identified in Item (b) produces almost
17、unusable estimates of volume or mass of wood. However, a greater accuracy requires a very large sample when the populations are characterized by a high variance.x(Replaces p. 32, March 2015)32 2015 CSA Group Scaling roundwoodOctober 2015wheresvvrnvvmmvmvm22222212=( )+( )( )() ( )= estimated sample u
18、nit volume= mean sample unit volume= mean sample unit massThe coefficient of variation, CV, forV may be calculated as follows:CV VsVvMs rrMsrrCV r()()( )=1001001002222222 Thus, the relative variation inV is identical to r becauseV and r differ only by a known constant, M.10.5.2 Confidence limitThe c
19、onfidence limit shall be calculated as follows:VtsV 2wheret = Students t for a specified probability level with (n 1) degrees of freedom (for a 95% confidence interval t = 2, approximately)10.5.3 Sample sizeThe width of the confidence interval (see Clause 10.5.2) is generally referred to as sampling
20、 error. When minimum sample sizes are estimated, confidence is expressed in terms of sampling error, E. In the case of ratio estimation, E shall be expressed as follows:EtsV2Substituting the alternative equation for sV2from Clause 10.5.1 into this equations yields the following:EtMnNsvvn221 If E is
21、expressed as a percentage ofV or r, CV may be substituted into the second equation in this Clause, as follows:EtnNCVnp1 srnNvvn21 =s2vvm37(Replaces p. 37, March 2015)O302.1-15 2015 CSA GroupOctober 2015Solving this equation for n yields the minimum sample size equation, as follows:nNt CVNE t CVp+ 2=
22、( )( ) ( )( )()( ) ( )2222whereEp= acceptable error, expressed as a percentage of or rCV = coefficient of variation, expressed as a percentage of or r (see Clause 10.5.1)10.6 Conversion of mass to solid volume by water displacementNote: For an alternative method see Annex F.10.6.1 Volume measurement
23、The volume of the sample shall be determined using the water displacement method.10.6.2 Sample measurements and calculations10.6.2.1 Sample unitThe sample unit shall be piece(s) or log(s) randomly selected from the load(s).10.6.2.2 Weighing the sampleThe sample unit shall be weighed to determine mas
24、s, inclusive of bark.10.6.2.3 Volume determinationThe sample unit shall be fully immersed in a water displacement tank. The gross volume of the sample shall equal the displacement of water, in cubic metres, minus any known displacement associated with equipment (i.e., grapple assembly).10.6.2.4 RotF
25、ollowing the water displacement procedure, volumetric deductions for rot in the sample unit shall be determined in accordance with Clause 6. Only rot that displaces water shall be measured.10.6.2.5 BarkA volumetric deduction for bark shall be made, based on a predetermined full coverage bark ratio,
26、by species or species group. The sample unit bark ratio shall be reduced proportionately for the percentage of bark missing on the sample piece(s) or log(s), as determined by the scaler.10.6.2.6 Calculation of ratioThe net ratio, r, shall be calculated in terms of net volume as follows:r =net volume
27、 of woodmass of wood with barkgross volume of wood deductions for bark and rotmass of wood with bark10.7 Conversion of mass to stacked volumeNote: It is standard practice to convert mass to solid volume. This Clause is provided for situations when conversion to stacked volume is desired instead.VV(R
28、eplaces p. 38, March 2015)38 2015 CSA Group Scaling roundwoodOctober 2015For example, if CV = 10%, thenn =( ) ( )( )=2103400944 445222.samplesThe finite population adjusted sample size isna=+=451452504511838 139.samplesFor simple random sampling, 39 truckloads are then selected using a table of rand
29、om numbers or randomly sorting the list using a computer program.* For systematic sampling, approximately 1 of 250/39 = 6 loads need to be sampled. One of the first six loads is randomly selected and every sixth load after that sampled (e.g., if load 4 is randomly selected, then loads 10, 16, 22, et
30、c. are sampled).*For example, MicrosoftOffice Excel.If CV is unknown and cannot be estimated from existing data, a small preliminary sample should be taken and CV estimated. In the following example, the first ten loads were scaled and used as a preliminary sample to estimate CV:Sample numberVolume,
31、 m3xixi210Total1 34.9 1 218.012 35.9 1 288.813 34.8 1 211.044 38.9 1 513.215 38.0 1 444.006 34.9 1 218.017 34.9 1 218.018 38.9 1 513.219 34.0 1 156.0034.0 1 156.00359.2 12 936.3071(Replaces p. 71, March 2015)O302.1-15 2015 CSA GroupOctober 2015The sample mean isxxn=359 21035 92.The sample standard d
32、eviation issxxnn=()=222112936 3359 21010 112936 3129024 6109.(.).=33 8369194. The coefficient of variation isCVsx=10010019435 954.%The minimum sample size isn =()(. )()()( . ).2539342916912 9613222(Replaces p. 72, March 2015)72 2015 CSA Group Scaling roundwoodOctober 2015The estimated ratio will ber
33、VM=359 2367 550 977.At this point, there is a sample of both mass and volume. The sample is not necessarily a representative sample of the entire population because the first ten loads were selected. Therefore, the best estimate of CV will be based on ()v vcircumflexnosp, as follows:svvn22142 499994
34、 7222()=()=.vvvvn=359 21035 92.CV =1004 722235 92605.%SamplenumberVolume, m3Mass, tonnes1 34.9 38.15 37.28 5.68022 35.9 35.01 34.21 2.84043 34.8 32.68 31.94 8.19354 38.9 40.85 39.92 1.04445 38.0 39.54 38.64 0.41186 34.9 38.74 37.86 8.76107 34.9 37.21 36.36 2.14528 38.9 36.52 35.69 10.30199 34.0 33.2
35、0 32.45 2.415710 34.0 35.65 34.84 0.7058Total 359.2 367.55 42.4999 v()vvcircumflexnosp275(Replaces p. 75, March 2015)O302.1-15 2015 CSA GroupOctober 2015The estimated minimum sample size is thennNt CVNE t CVp=+=()()( )()( ) ()( )( )()(. )()(2222222250 2 6 05250 3)()(.).22 2260536599 322250 146 39731
36、5 316+=+=Thus, 16 samples should be selected for piece scaling from the estimated 250 loads. Sample selection should use one of the sampling schemes specified in Clause 9.D.4.3 Estimation of totalsBased on the results in Clause D.4.2.3, 16 loads are randomly sampled from the population, with the res
37、ulting data as follows:N = 253 loadsM = 9361 tonnes (total weigh scale)n = number of loads selected for piece scalingm= 588.8 tonnes (sum of sample weigh scale)v= 577.6 m3(sum of sample piece scale)2= 65.6 (sum of squared differences between observed volume and ratio estimated volume)The estimated r
38、atio isrvm=577 6588 80 981.and the estimated total volume is. VrM=0 981 93619183The estimated variance ofV issVNnNnvrmn222211253 1()=1162531665 616 116389 34=.()v vcircumflexnosp(Replaces p. 76, March 2015)76 2015 CSA Group Scaling roundwoodOctober 2015The 95% confidence interval isVtsV2which gives9
39、183 2 16389 34 .9183 2568927, 9439The percentage sampling error isEtsVVp=10010025691832782.circumflexnospcircumflexnosp77(Replaces p. 77, March 2015)O302.1-15 2015 CSA GroupOctober 2015Annex E (informative)Alternative method for determining moisture contentNote: This informative Annex has been writt
40、en in mandatory language to facilitate adoption by anyone wishing to do so.E.1 ProcedureTo speed drying, the moisture content may be obtained from one or more sawdust samples instead of wood disks. Sawdust shall be collected in a plastic bag attached to a chainsaw by sawing through the whole log, or
41、 at least to the centre of the sample logs or tree lengths. The weight of each sawdust sample should be approximately 1 kg. After being collected, the sample(s) shall be sealed and weighed as soon as possible, with a precision of 0.1 g. The sample(s) shall be weighed again after being dried in an ov
42、en at 103 2 C until no further loss of mass is noticeable. The difference in mass is the moisture content, which shall be expressed as a percentage of the total mass of the sawdust, with a precision of 0.01%.E.2 CalculationThe moisture percentage shall be calculated as specified in Clause 10.8.1.2.3
43、.E.3 Moisture content variationIf a fast chainsaw is used to collect sawdust samples, the moisture content determined by the sawdust method and the disk method can differ slightly. These differences, typically in the range of 0.2 to 0.9%, are always negative and can result in overestimation of the o
44、ven-dry mass when the sawdust method is used. If the sawdust method is used, the moisture percentage may be adequately adjusted by occasional parallel testing of disks and sawdust from the same cut.(Replaces p. 78, March 2015)78 2015 CSA Group Measurement of wood chips, tree residues, and by-product
45、sOctober 20157.4.2.2 SampleThe sample shall be representative of the population and drawn randomly. The minimum mass of the sample shall be 250 g. If necessary, the sample shall be reduced by the cone-and-quartering method to the desired size for oven drying. The sample shall be stored and handled w
46、ith the precautions necessary to prevent changing its characteristics. To ensure that there is no moisture loss or gain between the time of sampling and weighing, each sample shall be placed in an airtight container, e.g., a polyethylene bag, and tightly sealed.7.4.2.3 ProcedureThe following procedu
47、re shall be performed without interruption:(a) The mass of the sample plus the container in which it was stored, M1, shall be determined to the nearest gram.(b) The mass of the empty, clean, and dry container, M2, shall be subtracted from M1 to give M3, the mass of the sample before drying.(c) The s
48、ample shall be transferred to a drying tray and placed in an oven operating at 103 2 C.(d) The sample shall be dried until it reaches a constant mass, then removed from the oven and weighed with its drying tray, to give M4. Under normal conditions, drying time of about 20 h is sufficient to reach an oven-dry state. If there is doubt that an oven-dry state has been achieved after 20 h, the sample shall be retu
