WWII i } WMHHIH l I nll‘ |\ 1: | l 3% MW A STUDY OF TiME-VALUE RELAT EONSHIFS {N A SOUTHERN Micz‘flGAN 3AM?) MEL}. ‘Jhasis ‘Far flu; Degree 3% M. S. MICHIGAN S‘F’ATE CGLLEGE Maivin i). 3:62am 39519. TH ESIS This is to certifg that the thesis entitled ,4 571/0/ 0/: 7/Mé'-l/A’AUE £51.47/0/t/5fi/m05 /A/ x4 500774/5/61/ M/Cfl/G/l/L/ 5/74/19 M/AL presented l‘HJ M54 (///t/ .D, 580 W/l/ has been accepted towards fulfillment of the requirements for [74:76” of: {elfflcfdeqree MW? 4. ,./ r944 (/Major [DI‘OlCSM u‘ Date €‘/ ' (/7 0169 A STUDY OF TIME-VALUE REM‘I'I ONSHIPS IF A SOUTHERN MICHIGAN BAND MILL by Melvin D. Bram A THESIS Submitted to the School of Graduate Studies of Michigan State College of Agriculture and Applied Science in partial fulfillment of the requirements for the degree or MASTER OF SCIENCE Department of Forestry 1949 ’THFQ'C CONTENTS INTRmUCTION e e e e e e e e e e e e e e e e e e e e m PROBIIEM e e e e e e e e e e e‘ e e e e e e e e e abj.°t1vos . C O O O O O O O O O O O O O O O 0 Procedures . . . . . . . . . Equipment Used(Description of the Johnson Mill). Explanation of Abbreviations Used in the Manu- script 0 C O O O O O O O O O O O O O O C O FACTORS AFFECTING EUMEER'VALUES . . . . . . . . . . Prices . . . . . . . . . . . . . . . . . . SizeofLogs.......... ....... Effect of Thickness of Stock on Quality of Mber O O O O 0 O O O O O O O O O O Relationshi Between Rate of Lumber Cut and QualitofLumber............ m MARG INAL Lm O O O O O I O O O O O O O O O O O O m w AIIING R UIIE S O O O O O O O O O O O O O O O O O Lm GRmE S O O O O O O O O O O O O O 0 O O O O O O 0 Prediction of Log Values . . . . . . . . . Use of Log Grades in Scaling Logs . . . . . . . CONCLUSIONS 0 O O 0 O O O O O O O O O O O O O O O 0 APPENDIX I(Derivation of a Mill Tally Formula) . . . Curved Mill Tally Table For All Logs . . . . . APPENDIX II(Brief Outline of Hardwood Log Grades U89d1H.Th133tudY)eeeeeeeeeeeeeo APPENDIX III(Summary of Basic Data) . . . . . . . . Percent Distribution of the Number of Logs and Mill Scale Volume by Species . . . . Percent Distribution of Diameters by One-inch 0133898‘“mmg8eeeeeeeeeeee Distribution of Lengths by Species--All Logs. . Miscellaneous Data on Mill Operating Time . . . Current Prices Used in This Study . . . . . Estimation of Value Per Operating Minute For Each Species . . . . . . Actual Percent Grade Yield by Diameter Class ForAllSchloa...o...ooos.. xx 17““ ,2? l l. . ) c meg om (D Q 0101!?) CONTENTS Page Percentage Distribution of lumber Grades by Species and by Log Grades . . . . . . . . 57 Percent Grade Yield For #1.Iogs of All Species by Two-inch Diameter Classes . . . . 58 Percent Grade Yield For #2 Logs of All Species by Two-inch.Diameter Classes . . . . 59 Percent Grade Yield For #5 Logs of All Species by Two-inch.Diameter Classes . . . . . . . 6O INTRODUCTION The findings, discussed in this paper, deal primarily with band-sewn Michigan hardwoods. It is important to keep in mind the great variability in the quality and size of logs, within the same species, as well as between the species. Furthermore, mills are as variable as the logs that are cut in them. Each mill owner is confronted by problems that are peculiar to his own economic sphere and each mill has definite character- istics which influence the quality and the rate of manu- facture of lumber. The results of this study provide evidence that it should be of vital interest to both the producer of timber and manufacturer of lumber to follow good for- e.stry practices in utilizing the timber crap. It is heped that this study will aid in promoting more efficient timber utilization. THEKPROBLEM Objectives The main objective of this study is to bring to the attention of mill.0perators the correlation that exists between log quality and the time required to manu- facture logs into salable lumber. In order to achieve the above objective, the following points were considered: 1. The effect of log size on quality of the lumber that can be cut from the log. 2. The feasibility of using log grades as a basis of purchasing logs. 3. The relationship of time of manufacture to the size of legs. 4. The relationship of lumber value to the various scaling rules used in measuring logs. 5. The determination of the smallest log that can be cut into lumber at a profit. 6. The relationship of lumber prices to the grade of lumber cut from the log. use. Procedures The data for this study were collected at the L. L. Johnson Lumber Company of Charlotte, Michigan in levember and December of 1948, and in January of 1949. Logs were scaled and graded in groups. of eight or ten on the log-deck. Then, the mill tally and lumber grade of the actual lumber sawed from the log were determined at the trimmer. The tine of manufacture to the nearest one- quarter minute was recorded for each leg. The period of time spent on one leg is considered to be from the time the last board is cut on the previous log, until the last board is sawed from the log being timed. All delays due to break-downs and. saw changes were recorded separately. 3mm DATA CARD Log Ho. /15 Speciest. MAPLE Date 134/319! . / 4.1.1:. /2 Length IZGrade I Sawing time: ’7": to //~za-¢/5 Doyle Scale 45’ Defects '— from H. 2.2 _ ,5 sucarasu smcnmstmsnenram' Totals 3 / 4 .3 if / 41 4 ' * 715991546 Sit-Surface Measure 5 ’ ‘f 6 4 24 6 GR-Grade 3 / 5 lo 4 3 3 IL TH-micfizfigain BI-Board 5 l 6‘ 5 Measure 6 F’ 5 8 6 3 ‘f 6‘ E 3 ‘f 6 Figure A The lumber was graded according to the National Hardwood Lumber Association rules. For ease in grading, and because lumber is often sold that way, the select grade was ccmbined with the #1 common grade. Prices used are-those of air-dried lumber, f.o.b. mill, as published by the ”Hardwood Market Report" for January 29, 1949.1 A11 lumber values are on a thousand board feet basis measured immediately after sawing with.an allowance of ten percent for shrinkage and degrade due to air drying. All log diameters were measured at the small end of the log to the nearest inch. Lengths were drap- ped to the nearest foot, allowing about three inches for trim. Lumber thicknesses were recorded in quarter-inches except in the case of five-eighths inch stock. Scale for five-eighths lumber was adjusted to one inch thickness to make possible mill tally on the boardefoot basis. A total of 372 logs were graded and scaled. The average leg was approximately 15' in diameter at the small end, and slightly longer than 12 feet. Hard maple and American elm comprised 60 percent of the logs cut. The red and white oak groups, beech, basswood, soft maple, and white ash made up the bulk of the other 40 percent. The log grading rules used in this study are explained in Appendix II. Also, the method used in determining the mill tally curve formula and summary of 1"Hardwood Market Report”, published weekly at Hemphis, Tennessee. -4- basic data are contained in Appendix I and III respec- tively, at the end of this paper. Equipment UsedLDescription of the Johnson Mill)_ The L. L. Johnson Company has a steam powered band. mill, producing about 9,000 board-feet per nine hour day. In conjunction with the sawmill the company Operates three Standard dry-kilns, a drying yard, a dimen- sion and planing mill, and complete logging, and hauling equipment. Logs are purchased from the area around Char- lotto, Michigan. The finished lumber is sold wholesale to local wood users and to the furniture trade in the Grand Rapids area. The mill also does some custom sawing. A layout of the mill is shown in Figure B. The sawyer at the Johnson mill is considered to be better than average. Quality lumber is given the first consideration and quantity next. Lumber is not scaled or graded until it is kiln-dried or sold, except that there is some sorting Of the low and high grades before kiln-drying. Generally, low grades are only air- seasoned. _ The Operation of the Johnson mill is very much like that of other mills of its type, with the exception of the use of air-dogs on the carriage. The carriage- dogs were originally of the hand-Operated type. Air-dogs were mounted on the number one and number three knees and are Operated by the block-setter from his position. Use -5- ”flu—w, ,# ll llll ll llll. I l. Ill-ll- l lll .l- . It ..| l. .lI I‘ll-ll -.I. l.ll| ll .l-l l ll I l. \W 3 9S woe-X, ..Q Otbxgku. a: bat VQ \a-Oxwteaou « .\ \Kbkbu 3C5 \5- Q-vszdR . VAN-69V Sedetifi. 3Q “KICK-ma, *00v9 3» (UN V- 004 \md QIOQ OOVV use YQOK m» 00 V -I .S-VWO ea: \NWQQQQNxQ IVKKQNQV‘QU VV\§\- QETQ \\\K k0,“, Q-VQES V Q0 V >\\v\x\,Q dab vb E r.- of the air-dogs is limited by their position on the carriage: logs under twelve feet cannot be: held with both dogs and some logs are too large for effective use of the dogs. The principle advantages; of the air-Operated dogs are,- an increased rate of cut and easier work for the block- setter. Eglanation of Abbreviations Used}; the Manuscgpj; The National Hardwood Lumber Association Hard- wood Lunber Grades are abbreviated as follows: First and Seconds PAS #1 Common and Select {108:8 #2 Common #20 #3 Common #50 Other abbreviations commonly used throughout this paper are: Diameter inside bark, small end d.i.b. 1000 board feet 11 Board feet b.f. Air-dried. m FACTORS AFFECTING LUMBER VALUES Prices Lumber prices vary with.the seasons, years, and with business cycles. The relationship between prices for various grades remains fairly constant, ex- cept that difference in price between FAB lumber and the lower grades tends to increase in periods of business depressions and to decrease in periods of prosperity.1 Explanation Of the above is simple. In times Of prosperity, when demand is high, lumber buyers cannot Obtain all the best grades they may desire, so they come pets with.each.other in purchasing lower grades, causing the price of lower grades to rise. When business is at low ebb, and demand for lumber is low, buyers will buy only the best grades. Low grades are then difficult to sell at any price. Herrickz, in his study of grade yields and overrun for Indiana hardwood sawlogs, places the relative value of each grade as: FAS(First and Seconds) 100 % #lC&S(#l Common and Selects) '70 I#ZC(#2 Common) 50 '#3C(#3 Common) 50 lbrown, II. 0., 'Imnber', John Wiley a. Sons, New York, 1947 23errick, “5 "Grade Yields and Overrun from Indiana Hard- wood Sawlogs , Agriculture Experiment Station, Purdue University, Bullettn 516, 1946 -3- .sone seasoned: Jens-eh Judd-u .o.o.u amen-EB” a no.“ one nee-2m .eonnednen. .nannae: as Bun-ooh consume-a {neon-om nexus: coo-6.3m...» need .hpdnnnnsnp unease .nan nunoaasm .nnssnom unnsanonum Headed-pong aanwodpem coo-53 eds-35. no.5 genera use suds-«H scene.- ..4 .xOHHnomm mama .samam .oz phenom .sannonnnoz on» as noosaq ones: as. .noonm .nonam no onsnonusnsa on» no mosses» «as: can noose. .nneasnonsq nonsense cannon .m .pa {nee-3..” an no sofa 2.3 no essence ca commends-e n.“ 3us Home «O eouhn Oman. an on an em on on mm me an on em as one no on oe as an on as me an on oe nw one on on on as as on on no ns.on an an sense I- cos .- ooa II con man a u a a a an annex nanndoapeaem owuem 932333” on owdsm nanonoaueaem mead essence .nooanm nonsense. need-Inooanm nooanm nuns-Ineoosensm an ocean nanonom scans: nonsensm «no «sense n.an-nnom Hon ensue nonsense nuance unsung OMEN—”mam BEG mom amazonnaamm mOHM-mtflamc H "macs According to the U.S. Forest Products Labora- toryl, the following relationship exists between PAS and #1 Common grades: FAS 1.50 (or 100 s) 4#1 Common 1.00 (or 67 %) Prices in Table I refer to species cut in.this area. The prices from.the "Hardwood market Report” are adjusted to thicknesses cut in the L. L. JOhnson mill. It was found that the price relationships used by Herrick will apply to most situations and can, there- fore, be used to compare relative values Of logs of dif- ferent diameters or of different log grades. Size Of Logs Grade yield of lumber from logs is very vari- able. In general, the quality of lumber increases with an increase in diameter of the log. Figure 0 shows the grade distribution of 572 logs of all diameters, of all species cut at the mill. The freehand curves were plotted from.the means for each diameter class. The data in dia- meters above 18" d.i.b. were grouped and averaged so that all points were based on a minimum of seven samples. The standard error of estimate of;the means was 5.2 percent, which.means that the average logs of a given diameter will contain the percentage distribution of grades shown by Figure C within 5.2 percent of the curved value 68 percent Of the thme. 1U. 3. Forest Products Laboratory, "Hardwood Log Grades for Standard.lumber-PrOposals and Reeults”,‘Dl757, 1949 ~10. s PERCENT GRADE Y/ELD FOR ALL L065 BY 0.18 ‘ 7 it as”; .I./s r /4 l6 )6 20 22 24 26 26 30 d.i.b. in [nebes 0 Figure B shows. the average value per 1 of lum- ber expressed in percent of PE lumber for each diameter of log. The curve was plotted from the grade distributim in Figure 0. Actual percentages and adjusted values. per Inlay be found in W111. It is interesting to note that in Figure D, the most rapid increase: in the. value of labor is in diameters up to 18" d.i.b. This gives, a rough indication of the minimum cutting size of legs. as 18 inch log, measured .11- LUMBER VALUE [OE/r“ M //V pffiCf/VT OF F345 [DP/CF T T ' E Y E 70 ¥——-—-—-e* l some.” “1-w— _»_ - I I . I sI sh- . ”I l 0 l 8m LLLLL +-—-~—+ I .K I Q _ , (055 ——TE» ~~~~~ IE I . 50——~ I» . e « ‘L O i a a _ a . .--- a +— . g ' - I l | ‘7. I I I _ - .. . .- ArammIm/yd of . I [umber Jo‘s/ed ' romia Loy - - - -4 _ - l inflfitkeni {Maggie}.-- . . f‘bé‘ea’pn A4] Spec/es? -. _-._ _. .. m. 4. . ._, , --L. E- - __ __ 4-7” . .. ‘ ‘ l I I . , , ‘ ‘ . I ”I i 8 IO M I4 [6 la .20 22 24 26 :6 30 d.i.b. in Inches l ._-____ —9—_—..._ _ Va/ue in & at the small end, with a length of 185 feet would be about 20 to 22 inches dbh if‘measured in the standing tree. _ The lumber from a 20 inch log will have approximately twice the value per I of the lumber sawed fru an 8 inch log of the same species. Of 372 logs sewed during this study, the grade distribution was; as followsdfrom Appendix. III) rm.......1e.2x' #50.......2s.e #10d8.....25.8 Timbers... .4.0 ”6......” -.I"C.'IO ‘4' an. ' | .O-uew'eeee Giving the above data- . value or as = 1001 3 {was flex: #2:: =50¢g #30 and Timbers =3o%; the follow- ing values are obtained: FAB 19.2 X 1.00 =3 19e2° flea-s 25.8 x .70 = 18.06 C 22e4 1 e50 = 11.20 #30 28.6 1 e30 = 8e60 Timbers 4.0 x .30 l 20 Totals 15.0 58.25 S Less 10% due to degrade and shrinkage=52.4 % This total indicates that min-rm lumber has approxim- ately 52.4 percent of the value of PAS lumber. Using actual prices for January, 1949 for the various species, the following relationships were found: rams II ACTUAL VALUES 0? HIE-RUN LUMBER Ieighted AD Aver e Value in Species Value/l! or Value 1 of PAS PAS Lumber 01' Lumber Imber Elm $112 $66.40 59% H. laple 184 89 .40 49 S. Maple 139 70.00 50 Beech 148 62.50 42 I. Ash 137 68.30 50 Basswood 164 95.60 5'? has on: 158 75.00 43 Average 142 71.75 50 .5 The actual‘percentage of 50.5 percent is less than the percentage found by using the average price re- lationships, because actual #50 values were about 25 per- cent or the PAS prices, whereas 50 percent was. used in -13- computing the average. Actual prices were for lumber ship- ped by car-load, f.o.b. mill. Low grades, sueh as #50, can often be sold at slightly higher prices locally or by cutting it into hardwood dimension. Table III shows the percentage of #1 Common and Better lumber by length, for all logs of all species. ' TABLE III PERCENTAGE OF #1 COMMON AND bETTER LUMBER BI LENGTH FOR ALL SPECIES Length Number Average % #lC&Btr. from.tetual.% % of or d.i.b. Figure B for #lC&Btr. Error Log Logs in Inches Average d.i.b. 8' 29 12.0 27 6.5 20.4 10' 72 14.6 42 44.9 2.9 12' f 138 15.4 44 47.1 3.1 14' 73 14.9 ' 45 46.8 3.8 16' 52 15.0 43 45.8 .8 Quality of lumber sawed from.logs does not vary greatly in legs 10 feet and over. Logs 8' long definitely have a lower output of the better grades. Figure B does not give a good estimate of the grade output of 8' legs but is very close in predicting the output for an aver- age diameter for lengths over 8'. gégect of Thickness of Stock on quality of lumbar The current market requirements determine the thicknesses into which.lumber is cut. The mill owner will attempt to have best grades sawed into thicknesses that will net the greatest profit. Production of the ~14- better grades in desired thicknesses is an indication of the skill of the sawyer. In the case of hard maple the best market for the better grades is in 5/4 stock for the furniture trade. Lower grades of maple are more salable as 4/4 stock or as planks. or timbers t0 the local trade. TABIE Iv DISTRIBUTION or THICKNESSES BY GRADES 1708* HARD mm T322]:- FAS WWW Totals 4/4 28 51 68 59 49.6 5/4 72 49 25 4 55 .5 6/4 -- -- 5 9 2.7 8/4 -- -- 4 28 7.5 Timbers -- -- - - 4.7 *Based on 11,981 board feet Average thickne s s 3 l . 318” TABIB v DISTRIBUTION or THICKNESSES BY GRADES FOR ELM“ Thick- Distribution Percent e ness PAS TIFF—Ecu—mfig Totals 4/4 8 26 42 78 58.7 5/4 16 15 10 5 11.1 6/4 10 20 18 9 15.8 8/4 57 52 25 7 28.5 10/4 9 7 7 1 5.6 Timbers - - - - 2.5 *‘Based on 20,590 board feet Ayerage thickness: 1.559" -16.. Relationship Between Rate of Lumber Cut and Quality of Lumber or great importance to the mill Operator is the time of manufacture of lumber from logs of various sizes. The board-foot rate of cut is affected by the following factors: 1. Skill of sawyer and block-setter. 2. Capacity and type of equipment. 3. Log size and.amount of defect. 4. Species of log. 5. Quality of lumber cut. 0f the above factors, skill of sawyer and block-setter, and capacity and type of equipment are concerned with.the efficiency of the mill and shall not be considered in this study. The last three factors are dependent on the quality and size of the logs. The quality of lumber to be out from the log varies inversely to the rate of out. If a sawyer is to cut for quality, he will sacrifice time to get higher grades. He will do this by turning the log more often, and more thoroughly utilizing the taper and by reducing waste. This closely correlated with.species. The saw~ yer will be more particular in sawing hard maple be- cause of its high market value. Elm will be sawed at a more rapid rate because of the lower value of the lumber. Logs of low grade of any species will be rushed rapidly through the sawing process, since, regardless of the skill of the sawyer, only. lumber of low grade can be -15- pr oduc 0d e Size of log is the most important factor in sawing rate. Rate of cut varies directly with length of log. _ TABLE'VI RATE OF LUMBER CUT AS AFFECTED BY LENGTH OF LOG Length Average b.f. per Mill Tally in Logs Average Minute of Each Length d.i.b. 8' 9.8 b.f./min. 1460 12.0 10' 18.0 " ” 7860 14.6 12' 18.4 ” " 20250 15.4 14' 20.1 " " 11570 14.9 16' 21.2 ” ” 9620 15.0 The above figures are based on all logs. The differences are not great, but there is evidence of a fast- er rate of cut for longer logs. Rate of cut varies with diameter. Figure B shows the rate of cut per minute of 372 logs of all spec- ies sawed in the mill. The form of the curve is para- bolic and has the general formula: Y=A+ 13x 4- 0x2 where Y is the rate of cut per minute and x is the dia- meter of the log in inches; A, B, and C are the unknown coefficients. The formula for the parabolic curve in Figure E is: Y=17.5 + 1.2451: - .052x2 Standard error of estimate of the means is 1.14 board feet per minute. -17- \SAW/NL; fflle 53490 /'[[7 9.9 AMA/L f‘: (DU/”PU?“ d/b. of 019a 7652‘“ I 0/2.: (i/fpt/f ---- 2“ 4 ? \_" L) x b C a m § 5 xz \n \ 9,. 7‘ j _ ,0 ‘ :5 ! E I i ~ \ ‘L l I ‘ gfir 1 t4. + 1 “.1111 i Q ' 1 3 ' FigureE J 3 + i Q fondord Error of € ! J tor/mare of Mean: 1: //4bf °§ M [a 13“” )6 _ 7137—170’M'2; -. 2425—113 30 ":32 _ J4 ‘— d/fb m Inc/205 (V) VAL (/5 OF ORE/24 T/,rt€~r’—/JUA’ /A/ FENCE/V T 0/“ [/45 A (Xi/BER may - -- Co 0 '0‘ o, L ‘a \ 0 4 8 K St -_ g. .-- . ,. i In" I -_+. .- I ! “A 15 ope/‘0’ .09 5f 7. of 545 (amber "* 5 .5“ 001) 0 his :ma/Arsf A757 fnof' Con/d be sowed I.“ " a prof/f if ffic /og5 were y/ ver/ 71) f/‘c, Operafor,‘ de/xvered ‘ Ave/“aye Vo/z/e/Ho. r m X of 513 Z (/0758 r (ha 2 ""of M. 29-25.; T"”‘T 4‘ 1 . ._.-. , n t l 4 ' ! . . : Figure}? ; 1 1 4. _¥ 4 i I 1 10 /Z /4 lb #9 4."- 28 84 26 25 30 (11:1) //7 4' 1': Ch (,‘5 -13- The Optimum cut of lumber, when expressed in board feet of lumber produced per one minute of operation, is for logs between 22" and 50" d.i.b. Logs larger than this have a slower rate of cut for the following reasons: 1. Presence of heartrot and other defects in larger legs. 2. Time required to turn.and handle very large logs with inadequate equipment. If we consider quality of the log and time of cut, the relationship takes the form.shown in Figure F. The curve in this chart was calculated by taking the average value by diameter from.Figure D and the volume from logs of each diameter that can be cut in one hour. (Delay time included) The actual percentage relation- ships of Figure F is shown in Table VII. The optimum size of log, considering time of cut and value of lumber, is about 28"‘d.i.b. That is, the average 28" log is most valuable to the mill Oper- ator. This is the average for all species and may vary either way, although it is definite that logs over 50" are too large for most efficient Operation. Figure F may be used as follows. If the average diameter of a group of logs is 14", the average value of an hour's Operation will be about 46.5 percent of the value of PAS lumber for the species concerned. If hard maple is valued .1: $180 per n for FAS, f.0.b. mill, AD, then the value of output for one hour will be -19.. about $84(for 14” logs). 950 board feet. Dividing $84 by .95 M b.f. gives the The rate of cut for one hour is value per M of lumber as about $88 for AD mill-run lumber. TABLE VII VALUE OF LUMBER CUT PER HOUR IN PERCENT OF FAB LUMBER FOR DIAMETER CLASS % of Rate of Cut % of 5 FAS‘Value/Hour d.i.b. FAS Per Hour FAS with Logging and Class Value, Delays Value Hauling Costs Per 11 Included Per Hour 516111664" 8 28.50 425 b.f. 12.00 6.50 10 55.50 625 22.20 14.10 12 45.60 800 54.80 24.40 14 49.00 950 46.50 54.20 16 52.80 1075 56.80 42.80 18 55.10 '1175 64.80 49.50 20 57.20 1250 71.50 55.20 22 58.70 1500 76.50 59.40 24 60.40 1525 80.00 62.80 26 62.50 1550 84.10 66.50 28 65.50 1525 84.20 67.00 “An arbitrary figure of $25 per M Doyle scale is used as the logging and.hauling costs. be placed on these costs because they vary with each Operation. diameter. No definite amount can Also, logging and hauling costs vary with In Table VII, an average overrun of 55 per- cent was used making the hauling and logging costs equal to $18.50 per M for actual mill tally. This is equal to about 13 percent of the average FAS price of lumber at the present time. THE MARGINAL LOG The cost of Operation of a mill includes labor, depreciation on equipment, insurance, taxes, selling and buying costs, supervisory and clerical help, interest on indebtedness and capital, miscellaneous mill expenses, and a normal profit. A decision as to the smallest log that can be sawed at a profit(the marginal log) can be reached by application of costs to the value of lumber sawed per hour. Total costs for this band mill are estimated to be about 60 cents per minute or 36 dollars per hour of Operation. This figure was arrived at in the following way for all logs cut during this study5* Total value of lumber cut................$3,696.99 Less amount paid for logs at log-deck.... 1,842.92 (Includes stumpage, logging, and hauling) Gross Operating margin...................$l,854.07 Grozso maactfira: in = Minutes '3 $0°593/ Minute, (including all delays) or approximately 60 cents per minute or 36 dollars per hour. This figure includes profit. The average weighted value of FAS lumber was $142 per M. Average rate of cut was 980 board feet per hour. Multiplying $142 by .98 M b.f., an average value of PAS lumber as $139 per hour of Operation is obtained. With.costs at $36 per hour, the relative cost of Operating *From Appendix III one hour 1";%§§t or 26 percent of the value of FAS lump ber. This means that the Operating costs at the time of this study were about 26 percent of the selling price of FAS lumber. By reference to Figure F, we find.that 26 percent exceeds the value of all logs under 11' d.i.b. Therefore, any log under 11' d.i.b. will not have an average value great enough to cover costs even if the logs were given to the Operator free, delivered at the mill. Logging and.hauling costs vary with each Oper- ation and no definite figure can be set. A Doyle scale price of $25 per l is not excessive to use as an average figure for this area» lith.an average overrun of 35 per- cent for all logs, this would.make logging and.hauling costs about $18.50 per I, when applied to actual.mill~ 5.11:. Dividing $18.50 by 5142(95. average price of ms lumber at this time) we find that logging and.hau1ing costs are about 13 percent of the average value of PAS lumber. Figure C shows the value per hour in percent of the FAslvalue of lumber for cash average diameter af- ter logging and.hauling costs have been paid. The break-even point is Just below aal3' 10g. This means that a log must be at least 13' before the mill owner can pay any stumpage price ihatsoever and still meet costs. Figure-G is slightly in error for some spec- ies because of: -22- 30 V \bt.\%.\h\\< wad .QQU « My @ Bu 74.x)?» :. 5.354 .871.» .\ \kthxg oh 0N em. tN NN cw mt Ex 3 mq c\ we 6 egg“ memoN \\ T Kok DfifikUhYV ..CKNK ”Yuk .to ck. WNV A 0 0/ fl w J O c s, 9H; /J Q\\\.\§< Wmukuxwx v T a O m _ .ruv w _ J _ a w. w m . 6b a _ Z w .1 on W m m t on W - , 3 W a a r O\ , (4.30th umwlmcu :35 Sue hulk k0 act SSSQENQ ask taste .3:- 1. Higher value of some species» 2. Variance in.rate of out between species. 5. Ihicknesses into ihich.various species are sawed. However, Figure G is fairly accurate in pre- diction of the marginal log and may be used as illustrated in the following example: ms The curve in Figure G is based on a- band mill sawing about 9800 board feet per nine hour day, or* 1100 board feet per hour. rho average log is.be- tween 14' and 15' d.i.b., and 12' in length. To find the marginal leg for a given species, the fol- lowing steps are:necessary: Assuming a price for FAB hard.maple lumber as $184 per I and milling costs as $56 per hour, then, 36:19.5 percent(Costs are 19 .5% of as price) In.Figure 0, find 19.5 cn.the leftéhand margin. Follow to the right, straight across to the curve. From.the point of intersection with the curve read straight down to the bottom margin. The reading is the diameter inside bark at the small end of the marginal log for hard.maple; it is very close to a 11' log. For elm.logs: ii :232%, or the marginal leg is about 14" d.i.b. To saw 10' elm.legs and break even, the costs of operation would.have to be 14 -24- percent of the value of Fas lumber or approximately $16 per hour of Operation. Figures H and I ere break-even charts for hard maple and elm respectively. Curves are based on actual prices and costs at the time of this study. Additional curves are included for a range of logging and hauling costs. The results check closely with those obtained by using the break-even chart for all species(Figure G). The optimum logs for hard maple and elm are lower than the 28" d.i.b. predicted from Figure G. This ia due to the slower rate of cut for large logs and the high amount of defect in large logs of both species. The break-even point orathe marginal log may be used interchangeably in expressing the diameter of the smallest log for which the mill Operator can afford to pay a stumpage price, and from which he may expect to realiae a normal profit. THE MARCIA/AL LOGaHARD MAPLE : 1 I lance: are f5r 245 900 % 1_Lumber,fo b m/// o) 1‘ | ‘ January, /949 g a \\.w 1 l f 8 ! r—L- Opf/mum ZaJ .c l L . ‘m * l "\*\ Cross Value of / § ? , ' //0 m of O/OeI‘J/IOO O/oa ‘ § E, r i Q ; : Cw ‘ 9 ; géd“ - A - - -- - ~ " ‘L’ " ~3o/., Qanye aflogymg 0k) .. -— —— f " “ " ‘ " - - Ties/w {flay/my Cosfs 4d ; QQ‘) / : * - j‘. M////n Coj‘fS 0* \b J 2 z E I ' l {36/ , ( Pilaf/7‘ [fit/.1 6 ,_ _ r l l . l i . V ' I i i l J ' I ‘ " Figure H 1 ' “(diary/”01103: // a/Ib L i L O V 1 a A312 20 22 24 l0 dz. .0. m Inches THE MARGl/VAL LOG- ELM {\ $— * I a; Pr/ces are For AD -l(/moer [0.16. M///, § A 1 _ Jar/7 z/ory, /.949 a i i g l QO/whw— . - ------ - ‘7 —-A- a r > v ‘ I _. 4L _ i : i ' I Sm 1 l a . if a L V 0' +2»; -1 . ~ 1 K Gross Ya/ue of AHoz/r I f ’0" 07 0g g 04 of 7L_019era_f/_o_n_ ! ’ __.... T t I -§’adf + —— — ————— ‘3 i K ' i 360 l * __. _+ __‘.‘__ __ _ _ 4 1L2 _ _~ -L ‘ \ Q V " logy/0y g“ ivy/mg 60.) 71> do x037!) ngn L - 4———J£- « “XL.--” —--———47—~—+- « Q“: r M/////)g' Cos/5 at JS/flow T D 2 _ -_,_ ' _ _ ____+ ______ {ID/‘Of// 1/7 } , p w b 1* . j ' 5 i , #Ma/‘Jma/ Log /4 “L 1 Figure]: 06 lb Id /4 /6 /6 . :0 24 24 26 28 do 0.0.1). If) 1. I) C h e 3 .86- LOG SCALING RUEEB The Doyle rule is used almost exclusively in this section of Hichigan as the basis for measurement in log purchases. There are two main.reasons for its cone tinned use, although the International‘}' rule is the official rule of Michigan: 1. The‘Doyle rule is a deeply rooted custom, and both buyer and seller are adverse to change. (The iDoyle rule price seems higher to sellers of logs the do not understand the difference in rules.) 2. The Doyle rule is very close to a value rule. The second statement needs further elaboration. The merits of the Doyle rule have long been a matter of contention between foresters and millmen. The rule was develOped by formula and great errors in actual board- fcot measurement are encountered, particularly in small logs. However, when logs are purchased, the buyer is interested in quality as well as in quantity. If a rule that measures quantity, such as the International rule, is used with a single rice, the amount paid for small logs(of low quality) will be more than that the logs are actually worth in tense of value of lumber that can be sawed from.them. likewise, large logs.that have high quality of lumber will be underpriced. Both the Doyle rule and the International in -27- rule have approximately the same board-foot scale for 12' logs of 28" d.i.b. Giving the 28" log a value of 100 percent and using the average values found in Figure». B, relative values of logs of each diameter can be com- puted.1(colmsn B,’Table VIII) For example, the average 10" log has 6.2 percent of the value of a 28" log. Col- umn G in Table VIII shows the relative value of logs of each two-inch diameter class in terms of a 28", 12." log with a volume of 432 board feet by either scale. For a 10" log the relative value was computed by taking 6.2 per- cent ef 432.(.062 x 4:52:27) The figures in Column 0 can be considered a M2 M. The correlation between the value scale in Column 0 and the Doyle rule in Column D is very close. The International %“ rule in Column E overscales the average values up to about 24" d.i.b. Above 24" d.i.b., both rules show little error. This correlation is cal- culated for second-growth Michigan hardwoods and may or may not be applicable to logs from other areas, or to softwoods. Figure J' shows the percentage overrun found for various diameters for all species sawed at the mill. Overrun varies with species, thickness of lumber cut, width of saw-kerf, andwith the efficiency of the mill oper ation . llill tally from Appendix I -28- Aonada am we acceded a.“ wonder owsaepda. woe row new we” oo.ww oww ow.ww on one wwe wwe ooe ow.ow one ow.ww ww on» wow wow ew sw.ww roe ow.ww ww oaw oow wow ww ow.ow wen oe.ow cw oww new new on or.wH www or.ww ww on woe owe «e owewa new ow.rw ow ope sea red «w ew.oa wwa oa.ww we owe woe woe ww ww.r wed ow.ww we cos we on w.ra ew.w woe oo.oe «a or we we w.HH we.» or ow.we we we sw rw w.w rw.a ew ow.ew oa ww we we a.» no. on ow.ww w eases woe weqeww mood weqeww qu .wa haaea an new .enenH assures “ma “Mum. an“? ”can“ m“. 2%» who u n o w 4 2.33% I wfiom .m flonaezwmazH 92 noon HHH> an. Hm Son ”noon 800% NH ho ”gab. EBSMM ho gunman—Soc -29- K>£i/?c7£ifiV'7' (DI/Z?fi?/Povur FROM 00 YLE ¢‘ [N nip/VA 770m; LOG SCALES I I I I I I /6 T _-_IOI/errun /3 for A? foo)“ l /0y5 from dye/7.199 m; '// 224/} for 7 // 5,066/05 /fid Ik-——— I —--—- r I ’50 Wed 0 2‘ f/fic: Job/Joan bofldFm/H . I I I . /4s —wI—~ I~——I«~~—+— wI-—-«I -[—T I Io———P——+ § 1’23» I . -.-~I>~ - —I r 4 - } . - - F+1~—--;J——L——j t I I I g) /00" — II - —~-—~umsoaa.«mooaua4m «coeds» weapoaaoc on» usage nose weapam ens AHHH Hacnennd floateceaw mod #23 new “—53.90 33% one made: he covegeaee as: d nasaoo be or on o.ne m.sm H.na H.eo on.an an om or om «.ms n.ne e.sa r.om om.ae «a ooa cod ooa m.aa . ooa om.ao an ImIGESHoo m 85500 G gaoo o ghfiaoo m nasaoo d 85500 season» ooH .aas com 0H scene won asoaaa> co «m.aoo a m.aoov meoanuuwon .e.r-rso a cg an. seen are ampere pesto noses» opera aoruaoao Haas or flatness no no osaa> no ooaam new mom aaom no owns and; epaueaem spam o>aueaom ovum o>HueHom .Ho R ad eras; Mama 8H we; 20mm 334% Egg mo mHDAd> Man—“Baum unH Ends -33- CURl/E'D REZAT/VE VALUES PE)? M OFAI/MBER BYLOG‘ 69/1055 //\/ PIECE/V7 0F FAS Ll/Mfifl‘? PR/CE 70L a / / e , , 3 1/ j,* K , A ’ I Q6 // agage’ 72 o) / AV, 2 025 Q. ’ / f,“ A (a / // I 0 5 / / / AL I N K ’3 oz: / M I 7 ,g X/ 4,, I A E / x/ * / f . I é, V // Q~ /,/7* ** gym/5% 4w \ F1 0 K § 5_ I I __ i /e 16 20 22 24' 25 26 30 205 /o /2 /4 did m [ac/ms increase in value of logs with an increase in diameter, was shown in Table VIII. Tables I, II, and III show the development of a value scale for each leg grade using the curved values. per ll of lumber from Figure I. The same method used in Table VIII was employed. Values: of each diameter class.- of 12' logs were calculated in percent of the value of a 28" log. i value scale was then computed by multiplying a. board-foot scale of a 28" 103(452 mt.) by the percentage value of each diameter class. The value ‘0 ~34- H «assuage acne head» Haas: ooe new con moo baa om.ro one o>.mo on owe one one «we ooa oe.mn one on.mo mm or» or» no» no» no on.>m roe oo.>o on com can com «on ob o>.em «on oo.oo on one one new mom on oo.ma new on.oo we can cam «ea com me oo.na one oe.eo om cod osfl sea and on os.HH era oo.ne ma oma one mo” aaa em eo.m med oo.ao we on ooa or we om ee.o ace oo.oo ea as or me an ea me.e or oo.oo «H odor .odsm aw aneuwoggmm asae> won .ma adage conga mom co senoeH o .oon descends ease oases won .om no Haas u ea a you ea aemndaem aaepmH cahon e5ae> no R eodeb e.wa esas> oo>aso .n.«.c Q. Mn _ mud-Ho EEHQ Hm mac-H Hfi mo mad-w $33M”- x Hunda _ -35- H aeoeoooe acne heed» Haas: ooe eoe pee wee oae oe.ae one oo.eo on oee one ewe eov ooa oe.oe. new oo.se me can ob» non Hen om oe.ne see oe.em oe coo can con Hen es ee.eH eee oe.oo ee one cow owe «me on ee.ee owe on.oe ee ode ode eea see so no.ea one oe.ne oe one ope see one on oo.e owe o>.eo ea oeH one mod ode be oe.> ova oo.oe ea oo ooa me He ea ee.e eoe oo.ee «a co or, me on we be.» or oo.e« ea case case rm eeeumqq.ee oeae> moo .ea haeea ooeae wee eo noeoeH o .ooo Heeoeoee ease cause moo gee eo Haas use a mom a- gos-pane...“ uaouoH 3”th era-g me a e3” e> a.- ma end!- uopedo . p. a to mmdqo mam-«4H9 Hm M609 mi mo mum—HHS, ”BK—”Bag Hun Emma.- -33- H 38.84 sch 53 So... 8e e8 e8 e8 3H 8.8 one 8.5. 8 o3 8e 8.. e3 o8 8. ee. 2% 8.5 we o8 98 n8 . e8 8 8. 8 Se 8.3 oe 8 8.... 8 88 2. 8. 8 e8 8. 3 «e 8e 8e nee 8e 8 8...: 8e 8. me ee 8e 8e e8 e8 3 8.8 one 8.3. 8 o8 . o5 SA 88 8 88 see 8.? ea 8a 8a e8 8: ee oo.e e: 8.: 8 oo o8 es 8 ea 83 o8 3.8 3 8 2. we 8 2 em.e 2. 8. 8 ea 8 3 se 8 e E...- 8 8. 8 8 oe oe ea ea . v 8. 8 8.8 e 83- 83- ..w eneueogfie and.» e8 .ee his 32.- use ea 385 o 63 H33»!- edpm .78 e3 .8 as a: m 3 a are n.- .8328 3-35 .83 3d:- eo u use...» 13 and; 823 5.46 umdflo mHBMHQHnTHm nOQH 9%.m6 afifindb.fl>Hadflflm HHN Mnmdfi ~57- scale developed in this way gives each diameter of log a scale that is relative to the value of a 28" log. (The common log rules are approximately equal at this diameter.) By comparing the Doyle, International 1", and . .__.._..—.-_— the Scribner Decimal 0 rules in Tables x, x1, and, x11, it Mi is found that the Scribnur-rulg moge___nearly indicates the M value of the log than the other two rules. . The Internat- ional i" rule overscales the value and the Doyle rule un- derscales the value, when log grades are used. However, it is believed that the errors in the use of the Doyle rule when buying by log grades is not great when the mill Operator considers that small logs require more than the average sawing time per thousand board feet of lumber. Since the Johnson mill buys on the Doyle rule, the approximate prices this mill should pay for logs of each grade can be estimated. An average price paid for legs at the mill was used in this study. Lumber from #2 loge was actually 49.8 percent of the value of FAS lumber for all species(Table II). The lumber from the average mill-run log had a value of 52.4 percent of FAS lumber (See page 13). Lumber from #2 legs has a value very close to the mill-run value, so the average price paid at the mill for #2 loge should be approximately equal to the average price paid for all logs. Using the relative values from Table II, Column E, the price to pay for logs of grades land 5 can be es- timated from the following proportion: -33- Relative Value fl Logs_Relative Value isgor £1) Logs Average oyle rice " oy e price or 3 or 1 gs Wmsing above preportion) Average price paid for hard maple:$60/M Doyle. then, 75.2 __ 100 30 " X '75 .2 x = 6000 X = 380/! Doyle, the price to pay for #1 hard maple logs delivered at the log-deck. Table XIII shows the estimated Doyle price that should be paid for logs of each log grade for various average de- livered log prices. TABIE XIII ESTIMATE OP DELIVERED DOYIE PRICE FOR EACH La} GRADE IF AVERAGE PRICE IS KNOWN Average *10g #1 Log #2 Log #5 Log Price Price Price Price tee/n ’ see/n tee/n tsv/n 60 80 60 34 55 73 55 51 50 67 50 29 45 ‘ 6O 45 26 40 53 40 23 35 47 35 20 ‘Average prices used in this study can be found in Appendix III. -39- CONCLHSIONS §g§ll Logs Are Undesirable Logs under 13" d.i.b. cannot be sawed into lump ber at a profit in a mill of the size covered by this study, even if no stumpage is paid for them. The mill cp- erator cannot expect to cut all large logs, because some small logs must be taken from the taps. However, he should control his purchases to the extent of buying the least number of small logs'possible. To offset the losses from cutting small.logs it is necessary for mill Operators to make a greater profit on the larger logs. Greater profit to the mill owner and increased stumpage prices will result if the small trees are not cut. Igngrades Can.Be Used to Predict log Values Log grades, based on the amount of clear.sur- face and the location of defects in the log, provide an acceptable method of predicting log values. When both the time consumed in manufacture and the quality of each log grade is considered, there is a minimum of overlap- ping of values between log grades. There was no over- lapping of values in this study when at least five logs were present in each grade. The-major difference between the log grading rules used in this study and those preposed by the U.S. Forest Products Laboratory“ 13 in the amount of cull *Report Number D1757, ”Hardwood Log Grades for Standard Lumber-PrOposals and Results", March, 1949 allowed in #1 and #2 log grades. From.the results of this study, it is believed that cull should be allowed in large diameter logs where the amount of clear surface meets the requirements for the grade concerned. The prime requisites of a system of log grad- ing rules are the simplicity of use and the accuracy of estimation. The rules deve10ped by the U.S. Forest Pro- ducts Laboratory meet these qualifications. The Dgyle Rule is a Close Estimate of Value The Doyle rule is very close to a value rule and may be used as a measure of average quality of the log as the log diameters increase. The overrun gained by use of the Doyle rule decreases, as quality increases. The Doyle rule may be used with or without log grades with a single price. There is nothing in the use of the Doyle rule that should encourage the practice of cutting small logs. The fact that the Doyle rule gives such 'low values for small logs should tend to discourage cut- ting of trees of small diameter. The International i” rule overscales the value of small logs. With a single price for a group of logs, it would overvalue the small logs. 0n the other hand, if the price were lowered be- cause of these small logs, the large logs would be under- valued. Log Quality Varies with Length.and Diameter The length into which logs are cut makes little difference in the quality of lumber, if the logs are 10' or over. ‘Logs under 10' tend to have a greater percentage of lower grades. Quality of lumber increases directly with.diameter of the log. A log smaller than 12" d.i.b. has very little clear lumber. The value of a log in- creases rapidly up to 18” d.i.b., and then increases at a slower rate above this diameter. Logs above 25" d.i.b. tend to have a larger amount of defect and more cull. Quality of each.diameter-size of log varies with.species. Twelve inch maple logs averaged 40 percent of the volume in #1 Common and better lumber. Twelve inch elm logs averaged 24 percent of the volume in #1 Common and better lumber. Rate of Cut Increases Directly_With.Diameter The rate of cut increases with diameter up to about 28' d.i.b. Above this diameter, the handling and turning time causes the rate of cut to decrease. Logs between 22" and 28” d.i.b. are the Optimum.size for the Johnson Mill. The rate of cut for larger legs is affected by the log-turning equipment. Prices of Each.Immber Grade Have a Definite Relationship Immber prices are relative. That is, the value of each grade remains approximately preportional to the value of the FAS market price. The value ratio is also approximately equal to the minimum clear lumber require- ments for each grade. Number 1 Common 1umber* requires 67 percent in clear cuttings, while the value of Number 1 *National Hardwood lumber Association Grading Rules Common averages close to 70 percent of the value of FAS lumber. Number 2 Common lumber requires 50 percent of the area in clear cuttings and the average value of Number 2 Common lumber is about 50 percent of the value of ms lumber. Number 3A and :53 Common require 33 1/3 and 25 percent of the area of the board in clear cuttings: the average value of Number 5 Common lumber is approx- imately 30 percent of the PAS value. ‘ggices for Each Log_Grade Can be Estimated if the Average Pgige is Knogg Millerun lumber will have a value approximately 50 percent of the value of FAS lumber. Number 2‘logs will produce lumber approximately equal in value to mill-run lumber. Therefore, if the value of mill-run lumber is known, prices that can be paid for logs of grades 1 and 3 can be estimated. APPENDIX I DERIVATION OF A MILL TALIX FORMULA Mill tally is the actual board-foot volume that is cut from a log at the sawmill. In determining a curve for mill tally, three variables are involved: length LIA, diameter inside the bark at the small end of the log ‘21, and the actual board-foot volume sawed from the log 3.).- Length and diameter are measured values and become the in- dependent variables, while volume becomes the dependent variable(dependent on L and 2) . ' If a log is considered as a cylinder the board- feet volume would be:_ vhfirfi) 1:21., or v=.oes4s D21. (1) where 2 is in inches and I. is in feet, and no allowance is made for saw kerf or waste. However, in a log, 1 does not increase as to the square of 2 or directly as to 33.. Usable taper will cause 1 to increase at an increasing rate. Therefore, _V_ will increase at some power of L. The preportion lost in slabs, edgings, and kerf will decrease‘asdiameter is in- creased. Ihis will cause 2 to have an exponent greater thantwo. The constant( .0555) will be reduced because a certain proportion of every log is lost in saw kerf, edgings, and slabs. The reduced constant shall be desig- nated g. We now have the correct formula for _V_ as: v=n>bL° (2) where b and g are the unknown exponents and K_ is the l‘. unknown constant. Changing the above formula (2) to logarithms we have: log V = b(log D) t c(log L) + log K (3) The exponents, b and 2, can now be determined by the method of least squares by use of the following normal equations: E(x)2-gggf_]b @xzbgzngizz] . =Emn-gzxnzn] [am (txlgiz)]b+E(Z)2-3§%z 2c] fin!)- (935222](5 = number of samples and c = unknown exponents of D and L ,3, and z = the logarithms of. L V and 2 the sum of IMINIo'lu‘ then, losxsm-bIBE'E-ci‘o'é‘t' (a) To test the linearity of'the logarithmic vol- ume equation, the logarithms of 1 and Q, and of 1 and _L_, were plotted. Results of the plotting of averages for hard maple logs are shown in Figures a and b. From Figures a and b, it is evident that the relationship of the logarithms of board-foot volume to the logarithms of diameter inside bark, and the relationship of the. logarithms of board-foot volume to logarithms of length, is linear. Calculation of a formula(and curve) by the least squares method eliminates all errors due to free-hand curve fitting. Curves derived by this method e Bar over term indicates the average for all samples. -45- ORA PH/C 7‘55 T F0}? L/NEA/i/TY K- 4/ ' /Z I Hard MJ/o/t /_ 0g 5 ”‘5 r———'----r———--r~ w——-~-~ — --~— - ‘ o C ! \ : - \26 ' ‘ ‘ ‘ "1/ § ; I , , ' D , r r a” 7: K24}- - - r) § - J _..-/ ’1’ \ . 2 .V - I 1 ,4 a = ' . . o‘ ' {/5 2G 1 ’ ‘ 9 Q its . . . . . . . '\ 5 743 Figure a g)... _ . 7 . ._ . w . \J v n I ‘ '49§'_/56"73;' _/./0 [/51 A20. “/25 730 I 1.55 h /4( A 1. 090m rhm of d/ b. m [/7 Ch 8 s 24 " ha“ Hard Ado/(#6 [095‘ ‘Q i ., -__. I So! ‘ x I §u ‘ ‘ ’3 3/ + If 'QZO ‘ / s j .\ , E ' i" , 5 *1? . , . O F was s C Figure b O V /.5J a --i.___._i_____.--i.-___-e-_-__- _-_ a.-. _ in .90 .ve LOO 105 /./0 /./5 120 [(35 T30. Logarl'fhm of‘ Lenyfh in FeefL -46~ are objective and comparisons between species or groups of logs of the same species are possible. Computation of Standard Error of Estimate The standard error of estimate for a group of data indicates the accuracy of the formula. Ono standard error of estimate means that about 68 percent of the cases will fall within one standard error of estimate of the predicted values, 95 percent will fall within two standard errors of estimate, and 99.73 percent of all cases will fall within three standard errors of estimate of the val- ues predicted by the curve. The simplest method of calculating the standard error of estimate is to take the square root of: the sum of Jactual values - Egedicted values)2 umber o samp. so or in the case of formula (2), vPl-rw m where V' is the value obtained from the formula or curve for any given value of Q and L. The standard error of estimate increases in direct prOportion to diameter. For example, in maple and elm the standard error of estimate averaged approximately 12 to 14 percent of the actual mill tally for all diameters. Hill 52ng for Hard m1. . The formula for mill tally of 104 sound hard maple logs was found to be: -47- In legs 12' d.i.b. and under, the.standard error of estimate was 9.8 board feet based on 46 logs, and 15.9 board feet for 82 logs over 12” d.i.b. The standard error of estimate for all logs(104) was 15.8 board feet. In other words, about 68 percent of the logs of a given diameter and 1ength.will have a boardpfoot vol- ume within 13.8 board feet of the value given by the forms ula. This standard error of estimate is not great considering that all diameter measurements were made to the nearest inch. The increase in board-foot volume due to a one inch.increase in diameter is about 15 board feet for a 12T-12' log and about 25 board feet for a 21'-12' log. Hill Tag. for Elm The mill tally formula for elm is quite dif- ferent from hard.maple. It was necessary to divide the curve into two parts: legs 15' and smaller, and logs lar- ger than 13'. The basis for this division is that elm.logs larger than 13" were cut in thicknesses averaging better than 1.5", while logs smaller than 14' were cut mostly in- to l” boards; that is, the two divisions were of different pepulations and were not comparable. The formula for elm legs 15” d.i.b. and under was: V = .00846 D2.6788 L’9777 (9) The standard error of estimate for the above formula, based on 40 logs, was 9.5 board feet. From. —-48- this, the following conclusions can be drawn: 1. Loss. due to kerf, slabs, and edgings is greater in elm than in maple, as evidenced by the low val- ue of g. 2. The exponent of Q is larger, indicating a more rapid rate of increase in volume with an increase in diameter. 3. Low utilization of taper and lack of us- able taper is indicated because the exponent of L is less than 1. Smaller diameter elm logs may have slight crook making impossible higher output from longer logs. The formula for elm logs over 15" d.i.b. was: V: .02846 92.0817 1.1.1252 (10) The.standard error of estimate for the above formula, based on 57 logs, was 25.4 board feet. From the formulas for elm and hard maple the following may be noted: 1. Hard maple has a higher constant (g). This indicates greater utilization of the log and more careful manufacture. 2. The exponent of 2 is larger in elm. This is attributable to greater average thicknesses and wider boards sawed from elm logs. 5. ‘Ihe exponent of L is larger in elm, indi- cating more taper in larger elm logs. Most butt logs of elm have a buttress base in which usable lumber is cut. This is not prevalent in maple. 4. Elm has a higher standard error of estimate (maple-13.8 b.f., e1m918.8 b.f.). This is due to a lar- ger average diameter for the elm.logs sawed. The standard error of estimate for maple was 12.9 percent of mill tally while the standard error of estimate for elm was 12.0 per- cent of the mill tally. That is,-the standard error of estimate increases with an increase in diameter. A general formula for logs cut at this mill, based on 318 sound logs, is as followss 2.1298 1.0939 v = .0261 D L (11) TABLE 1 CURVED MILL TALLY TABLE FOR ALL LOGS d.i.b. length of Lo in Poet Class 8' 10' 12' 14' 16' 9 -22 27 33 39 45 10 34 43 53 63 73 12 51 64 79 93 109 14 70 99 109 129 150 16 93 119 145 172 199 19 120 153 196 220 256 20 150 191 233 277 321 22 194 235 295 340 397 24 220 293 342 409 472 26 262 339 407 492 560 29 307 394 476 566 656 -50- .aeesu peep n no spasm necked ho cedddaouod ad.m0H uo cease eueeuoo Added» no cosh one pod» oesu.dese d0 needs one mwdaande aeoao .uuodx ue_noda .hHopsndmoe codeodadoe ocean e no dose duds wed one wdAdedUa hp thsdaap codddaepoe one neesm doapedboe HHdo hds don cascade ease- .opons us oceoadd .on we hoped node no «_aodda dd cesoaae dado .epone as mesons unloads p03 .woa on» no ode on» no noon madam dd uovdaedd one Ewan 3 .23 cheat uqooHo edoz Andaman ode .pdeedueandoo .uxeed .650. Jason undemdd .ueaod tenor .ouoe .omsduvapoeuen uneduodcoc Hana 893 no men oo .5 no 5. ..H .9 5 ..a capo-33¢ a62,...“ . .. use .8 n\m new .8 {my Agnoflvooae 93? 5 339 a a n « «adEANdavoosu hen senadz adoapeaduuoa 0d .m .m adddddfidvduwdoq Kneesu n umoo.dovmmdapodo suede .m .3 .3 Agassidowooq am sad sad addaadddvdepeaeaa smog nfi. smog mu. smog flu. aaouosm edema .HQDBm mHmB 2H QMmD mmnflmw uQH adoiam::/96Vdume P59 CENT 0/5 m/Bur/O/v OF DIAMf 75/93 a y ONE - INCH (IL/13.553 -/4[./. 1068 a? x 0 .L_1 '1 [ j . Fbrcenf of To fo/ 0. Figure d ! .c—‘Cj.-_.- r11] O 8 IO /4 14 J /6 I8 .30 .32 J4 J6 Log d/Lb. ('0 £2 24 26 28 in Inc/x33 -52- ' TABLE 3 DISTRIBUTION OF LENGTHS BY SPECIES--ALL LOGS Species %W¥figm Totals white Ash. 2 ll 8 5 3 1 30 Basswood 0 3 5 l 2 0 11 Bosch 1 7 20 12 5 l 46 Black Cherry* 0 0 l 0 0 0 1 Cottonwood 0 0 0 1 0 0 1 Elm 11 18 43 22 20 4 118 Hickory 3 1 2 0 l l 8 Hard Maple 4 22 44 25 15 0 110 30ft Maple 0 3 5 1 1 0 10 Red Oak 5 6 7 4 5 0 27 white Oak. 3 l 3 2 0 l 10 _Tntalé.. 29 72 #138 73 52 8 312 Percent 7.8 19.4 37.1 9.6 14.0 2.1 00.0 TABLE 4 HISGELLANEOUSHDATA.ON MILL OPERATING TIME Tatal Operating Time During Study. 0 e e e e e e3, 777 e0 Mine Total Saw-Changing Time . .210.2 Min. “-1 Other Delays. e e e e e e e .171e5 nine Total.Delays...............................381.5 Min. Net Operating Time.......................3l395.5 Inn. Average Time to Change Saw..................l3.1 Min. Percent Delay Timc..........................10.1 at Total Volume Sawed-dDoylo Scale.............45 I Estimated Total Mill Tally..................61 I Approximate Rate of Cut Per Nine Hour Day...9.8 I -53- 541313 5 CURRENT PRICES new IN THIS STUDY“ L’Average Weighted Lumber Prices Per 1! Species olivered Air-Dried f.o.b. Mill b. Grade Log Prices FAB #10898 EC $30 Doyle Scale ' whit. 550/11 $137.00 $96.00 $66.00 $32.50 Ash Basswoo4 50/11 . 164.00 119.50 75.00 35.00 Beech 45/14 146.00 104.50 69.50 33.00 Elm 45/11 112 .00 89 .50 65 .00 35 .00 Hard 60/M 194.00 122.50 74.00 40.00 maple Soft 45/11 139.00 102.00 69.00 33.00 maple Red 0.1: 45/11 , 156.00 119.00 69.00 35.00 Ilhite _ - . 45/14 157.00 119.00 66.00 35.00 0.1: Hickory 45/11 --- 70.00 40.00 30.00 Cotton- 45/11 --.. 90.00 50.00 30.00 wood Cherry 45/11 --- 125.00 76.00 35.00 *SCurce of prices is ”Hardwood Market Report", published weekly at Memphis, Tennessee. Prices are for AD, f.o.b. mill, Vausau, Wisconsin or from the Memphis, Tennessee area if the species is not listed on the Northern market. Prices for #3 Common are from a local wholesaler in most cases. Prices are weighted as to the thicknesses sawed in the Johnson mill. All lumber prices are for car-load lots. 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