,. ~-.uw—.~-..w~~q‘-. A SIMULATION MODEL FOR LOG YIELD STUDY Thesis for the Degree of Ph. D. MECHIGAN STATE UNEVERSITYV JORDAN ALEXANDER TSDLAKIDES 1968 1.5555 LIBRAR Y Michigan :tabt: ~\ Umvcmty This is to certify that the thesis entitled A SIMULATION MODEL FOR LOG YIELD STUDY presented by Jordan Alexander Tsolakides has been accepted towards fulfillment of the requirements for Ph. D. degree in WOOd TeChnOIOQY // ~. ,I ”" 4/5”“? é //// 54/ Nféjor profeéén Date May 6: I968 0-169 ABSTRACT A SIMULATION MODEL FOR LOG YIELD STUDY by Jordan Alexander Tsolakides A digital computer analytical technique has been develOped as a means of studying the effect of alternative sawing methods on the grade and volume yield of the same log. Real activities are simulated through the use of the computer. The work is methodological in nature. Its primary purpose is the develOpment of a model which can be used to increase production effi- ciency. In addition, the study has the objectives of developing a cir- cumference and defect reading method and of demonstrating the feasibility of the use of the model in a pilot project. This model, develOped in order to accumulate data for analysis purposes, should prove to be superior to methods available in the past. Step by step procedures are provided for experimental applications . The input data for the simulated processes are derived from a sample of six logs sliced into disks. A measuring method, develOped along with the main model, is used to record circumference points and the location of defects on the disks. The six 1093 are used to illustrate the simulated Operations and are sewn, via simulation, 164 times. Jordan Alexander Tsolakides The model consists of the main program and three supplementary sub- programs; one for sawing lumber, one for rotating the log into a new posi- tion, and one for cant production. Allowance has been made for one—eighth and one-fourth of an inch kerf sizes , which can simulate band sawing, gang sawing, and circular sawing. The size, board feet, and defects are given for each board produced. The model, written in FORTRAN language, has been executed on a CDC 3600 computer. It takes approximately three minutes to "saw" a log 16 times , in four different positions , and to measure the resulting boards. Several sawing methods have been utilized to test the workability of the model. This model, a simulation analysis of log yield (SALY), shows the feasibility of a new approach to solving the vital question of how best to saw a log. A SIMULATION MODEL FOR LOG YIELD STUDY BY Jordan Alexander Tsolakides A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Forest Products 1968 9/ /_ .'_-_ / (F L / ./ /; ‘99:. \ n r n! ACKNOWLEDGMENTS My deep appreciation is expressed to the members of my doctoral committee: to my chairman, Professor Aubrey E. Wylie, for overseeing my program and for enriching my understanding of the many aspects of wood production problems with his suggestions for the completion of this study; to Professor Otto Suchsland for direction in planning this project and for many suggestions concerning the final form of the results; to Professor Richard F. Gonzalez with whom the approach to this study was discussed. Last, but not least, my special thanks to Professor David N. Milstein, who helped to clarify certain aspects of the technique used in this study and who gave generously of his time whenever it was needed. Special recognition and appreciation is given to Professor Richard D. Duke, Director of the Urban-Regional Research Institute at Michigan State University, for the generous use of his computer facilities during the trial period of this model. Gratitude is also expressed to my parents , who encouraged me in my early academic steps. I am deeply grateful to my wife, Connie, for her help during the ex- periment, and for recording and proofreading a great part of the data. Her assistance and encouragement were a source of motivation for the successful completion of my studies. Iordan Alexander Tsolakide 8 iii TABLE OF CONTENTS ACKNOWLEDGMENTS . . . . . . . . . . . . ............ iii LISTOFILLUSTRATIONS vi LIST OF APPENDICES ..................... . . . vii I.lNTRODUCTION......................... 1 The Log Yield Problem .................. . . 1 Objectives of the Study .................... 2 II. LITERATURE REVIEW AND PROBLEM ANALYSIS . .6 ....... 4 The Hardwood Grade Lumber Yield Problem ...... . . . 4 The End Use Consideration. . .. . . . ....... . . 4 Grades of Hardwood Lumber . . . .. ., . . . . . . . . 6 Distribution of Defects in Logs . . . . . . . ., . .. . 8 Hardwood Log Grades . . . .. ............. 9 LogGradesanineld................. 10 Industry Practice . ................... , . . 12 Sawing Practices . ................. . . 12 TheRoleoftheSawyer................ 13 Research on Yield Improvement . . . . . . . . ....... 16 Past Treatment of the Problem ........ . . ., . 16 Other Possible Solutions . . . . . . . . .. . . . . . . 20 Computer Simulation ................. 21 III. METHODS AND PROCEDURES . . . . ............. 26 The Source chata ...... . . . . . . . . .. ..... 26 The Raw Material. . . . . . . . ....... .. . . .. 26 Log Preparation. . . ............. . . . . 27 Circumference and Defect Recording Method ...... 31 Recording Procedures. . . . . . . ...... . . .. 34 iv Computer Simulation ................... Preparation of the Input Data . . . . .......... SawingMethods ...... Sawing Program .................... Operating Characteristics of the Model ....... Lumber Grading .................... Yield Evaluation ................... Analysis of Variance ................. IV. RESULTS AND DISCUSSION .................. Evaluation of the Model. . . . . . . . . . ........ Model Characteristics .. ............... rThe Experimental Model ............... Pilot Project ........................ Experimental Runs . ................. Comparisons of Results ............... Implications ........................ Library of Log Defects ................ Laboratory Testing Technique ............ Data Recording Equipment .............. Future Refinements and On-Line Control ....... Application to Other Materials ............ V. SUMMARY AND CONCLUSIONS ................ LITERATURE CITED ........ . ................. APPENDICES 36 36 37 4O 46 47 49 50 51 51 51 52 59 59 63 67 67 68 70 71 72 73 77 79 LIST OF ILLUSTRATIONS Figure Page 1. Projections of the Small End Log Circumferences ...... 28 2. Log Marking Before Breakdown into Disks ......... 30 3. X—Y Coordinate Grid System for Defect and Circumference Measurements .............. 32 4. The Three Sawing Methods Used on the Same Log ..... 38 5. The Four Sawing Faces of the Logs Used in this Study, and the Starting Point for Each Face ....... 41 6. Simulation of Log Turning by Turning the X—Y Coordinates . g ...................... 48 7. Flow Chart of the Simulated Log Breakdown ........ 53 8. A Sample of the Simulation Output ............. 57 vi Appendix LIST OF APPENDICES OOOOOOOOOOOOOOOOOOOOOOOOOOOOO Table 3. Table 4. Table 5. Table 6. Table 7 . Table 8. Table 9 . Table 10. Table 11. Table 12. Lumber Grade Yields by Method Circular Saw, Log Grade No. Lumber Grade Yields by Method Circular Saw, Log Grade No. Lumber Grade Yields by Method Circular Saw, Log Grade No. Lumber Grade Yields by Method Gang Saw, Log Grade No. 1 . Lumber Grade Yields by Method Gang Saw, Log Grade No. 2 . Lumber Grade Yields by Method Gang Saw, Log Grade No. 3 . Lumber Grade Yields by Method Log Grade No. 1 ....... Lumber Grade Yields by Method Log Grade No. 2 ....... Lumber Grade Yields by Method Log Grade No. 3 ....... Lumber Grade Yields by Method 1 and O I U G O O 1 and OOOOOO 1 and O O 0000 2. C; 000000 2. CCCCCC 2, OOOOOO 3, Log Grades No. 1, 2, and 3. . . Gross Lumber Yield Values Per MBF Log Scale, by Methods and Grades of Logs . Net Lumber Yield Values Per MBP Log Scale, by Methods and Grades of Logs (After Subtracting the Cost of Logs) . . . ............................. OOOOOOOOOOOOOOOOOOOOOOO vii 81 82 83 84 85 86 87 88 89 9O 91 92 93 I. INTRODUCTION The Log Yield Problem In the past several years , the sawmill industry has made significant improvements in mechanization. Prom headsaws to lumber sorting, the flow of materials is being automated to greater degrees. Push-button op— erations with memory-control systems are becoming increasingly a part of the sawmill operation. Improved equipment and new types of handling and controls are reducing production cost and improving the quality of the products. Still, there remain unanswered questions relating to log char- acteristics and the appropriate sawing method for maximum return. The nature of the logs presents the greatest problem since no two logs are alike. Studies conducted by various investigators applying a variety of sawing methods, have improved considerably the knowledge about the problem of Optimum log yield. Statistically designed experi— ments as well as linear programming and computer (mathematical) models, are some of the techniques which have been employed in order to find the most profitable way of sawing the log. However, the subject of more efficient conversion of logs into lumber needs further investigation as to the effect of log characteristics on yields of factory grades of lumber. More adequate information is needed as a basis for selection of the sawing procedures best suited to maximize the value of lumber produced from given qualities of log. 1 The effect of visible external defect orientation to the sawing faces of the log has been and is still being studied. Nevertheless, the effect of the same defects , when several available sawing methods are tested on the same log, needs further study in order to evaluate the log quality and variations in the grade of lumber as influenced by the sawing methods. What is needed is an analytical technique which will allow several sawing methods to be tried on the same log. The two main sources of variation in the yield, namely log characteristics and sawing methods, should be examined for their impact upon the yields obtainable. It is within this framework that this study will attempt to develop a methodology for the investigation of this problem. Objectives of the Study The general objective of this study is to develOp and test a model of log breakdown Operation wherein sawing activities can be simulated to the maximum extent possible. Such a technique will allow several sawing methods to be tested on the same log. Variations in the total yield from a particular hardwood log can be explored as a function of log character- istics and sawing methods. Such an investigation can produce informa- tion to be used for the develOpment of more efficient sawing practices. The specific objectives of the study are: 1. To develop a method of analysis for the investigation of the effect of sawing method on yield. With the use of a com- puter simulation, comparisons of the effect of the changing relationship between log characteristics and sawing methods on the final output can be studied, avoiding laborious phys- ical experiments. To demonstrate the feasibility of the use of such a model with a pilot project. II. LITERATURE REVIEW AND PROBLEM ANALYSIS The Hardwood Grade Lumber Yield Problem The End Use Consideration Hardwood lumber is used mainly in manufacturing industries. Of the total hardwood lumber used for all purposes (6) in 1960, about 92 percent. was consumed in manufacturing industries , with oak comprising one-third of the volume. Of the approximately 5. 6 billion board feet consumed by- the manufacturing industries, about 3. 1 billion or 55 percent was used by industries classified (SIC) as Lumber and Wood Products. The largest item in this group, about 1. 1 billion board feet, was consumed by the Dimension and Flooring Industries. The other large industrial group was the Furniture and Fixture Industry with a consumption of 1. 6 billion board feet or about 28 percent of the total. The largest amount in this group, about 1.3 billion board feet, was consumed by the Household Furniture Industry. Hardwood lumber, when used in manufacturing is converted and uti— lized in random lengths and widths of relatively clear dimensions according to the special requirements of each industry's Operations. The furniture industry, which is the biggest hardwood lumber user, requires clear or practically clear dimensions for its products. Since most hardwood lum- ber eventually is cut up into various sizes of clear dimensions, the value of rough boards depends simply on the amount of usable material they contain. What the end user (manufacturing industry) is interested in, is the percent of clear area each grade of lumber will finally yield when con- verted into specific size dimensions. This end use calls for a variety of sizes according to the particular needs and types of end products. For example, different sizes are needed for solid parts of case goods. or core materials for plywood and still other sizes for chairs and tables. Unlike other commodities , the rough lumber used by the manufacturer varies in quality and is seldom free of defects, resulting in waste when manufactured. The utility, therefore, of rough lumber varies and is a function of the grade of lumber used for the conversion of rough boards into blank dimension sizes. Utility is defined as the ratio of the volume of finished blank sizes of wood parts to the volume of rough lumber from which it was sawn (4). The percent utility, or yield, from the lumber of a given grade can be used as an estimating factor of the obtainable clear material. This percentage yield can be measured either as final machine size or final rough mill sizes. It varies with the species and the thick— ness of the board, decreasing as the board thickness increases (8). The degree to which the hardwood lumber can be worked into relatively clear cuttings becomes the key factor in satisfying the manufacturing needs for rough lumber. This end use criterion establishes a pattern of demand for the production of lumber which when remanufactured will produce larger percentages of clear cuttings. A price scale is the natural outcome of this demand, where lumber of higher quality commands higher prices. It becomes obvious then that lumber yielding higher percentages of clear cuttings and securing higher prices creates an incentive for the sawmill operators to seek and produce this type of lumber. A lumber grading system is applied as a yardstick to help the pur- chaser to buy the grade which best suits his manufacturing purposes, while allowing the vendor to secure higher prices for his better products. This system based on the ultimate use of lumber can also be used as a criterion to measure the effectiveness of mill operation reflected by the total output of the lumber both in value per unit and volume. Grades of Hardwood Lumber Hardwood factory lumber is graded on a yield basis , measured on the amount of clear or sound material that can be obtained from boards , in specified number of cuttings of minimum width and length (13). In each grade a minimum percent of yield in clear cuttings must be obtained in the number of clear-face or sound cuttings permitted. Almost all hardwood lumber in the United States is graded and sold under the rules of the National Hardwood Lumber Association. There are outlined procedures and steps to be followed in grading lumber (13). A reference to these rules shows that these rules, allowing for mini- mum lengths and width for each lumber grade such as 6" x8' for F.A. S. 4" x6' for Selects and 3” x4' for all Common grades, provide the basis 7 for determining the yield that may be expected from each grade. This yield is determined by specifying the lengths and widths of cuttings re- quired, and the number of cuttings permitted in relation to the total area contained in the board. However, lumber grades generally reflect the yield which can be expected within the minimum sizes permitted. Some users recognize that there are variations in the types of boards within each grade not indicated by the grading rules (4). These various board types , although they do not affect the ultimate utility of the board, due to the location of defects , do influence the yield of the board when converted into the requirements of a specific industry. Dosker (4) clas- sifies the boards into three types: (a) Rip type, (b) Cross-cut, and (c) Neutral type, depending on the distribution of the defects along the board. The type of board will determine whether it will be ripped or cross—cut or both in order to obtain maximum yield. The factors which determine the prOper grade of lumber from which wood parts will be produced are the sizes which can be obtained, their quality, and the percent of total yield. Another factor is the processing cost which varies with the grade of the lumber input. Log characteristics can greatly influence the grade of the produced lumber and considerable variation may be expected in the type of board within the species and the log from which they were produced. The demand of the end-user for clear cuttings can better be satisfied if the raw material from which they are produced is examined for its con- ditions and variations. Sawlog characteristics such as size and location 8 of defects are the factors which determine the sawing practices for the production of grade lumber. The variations in log characteristics suggest variations in the sawing practices. Therefore, an examination of the ef- fect. of log characteristics on the grade lumber yield is considered neces— sary. Distribution of Defects in Logs Logs , unlike most other raw materials , due to their nature cannot be appraised adequately for their interior conditions in terms of defects. Thus it is very difficult to make precise predictions as to the value of the lumber to be produced from them. It is principally the existence of defects that determines the utility of logs for grade lumber production. Sawlogs are seldom clear of defects. Some defects appear on the outside) surface of the log and are easy to detect. Knots, scars, frost cracks, end checks, grub holes and bark distortions that clearly indicate an overgrown knot are some of the defects that appear on the outside of the log. Other defects such as mineral streaks, insect holes, overgrown knots and rot are usually hidden inside the log. In many cases, the ends _ of the log reveal some of. these interior defects , like shakes, core rots , and splits, thus giving an indication of their presence. In general, al- though some of the defects can be noticed on the surface of the log or de- tected from existing surface indicators, their extent inside the log cylinder is very difficult to predict. An estimate only of the pattern of the defect distribution and especially the existence and size of knots inside the log 9 can be obtained by examining the size of the tree from which a log has been produced. Larger trees usually have a thicker layer of knot-free wood than small trees. On the other hand, extremely large over-mature trees are usually more defective than young trees. As a rule, the defect frequency in a typical hardwood log increases from the outside toward the center of the log cylinder. From the above discussion it becomes apparent that the value of logs for grade lumber production varies widely for different logs due to size , location and distribution ofdthe defects. In fact these considerations are the ones that will determine in the subsequent work the choice of the best sawing method. A log grading system is used to segregate the logs into value classes according to their individual characteristics. A grading system provides a measure of log value that enables both the buyer and the seller to arrive at a reasonable price for logs. It also provides a basis for the processing method to be used in order to maximize the grade and volume of the pro- duced lumber. Hardwood Log Grades Logs vary according to their diameter, their defects , location in the tree and their length. Therefore, any grading system must first of all re- late those log characteristics to the product that is to be cut from them. The Forest ProduCts Laboratory (21) has develOped a grading system which provides a relationship between surface characteristics of logs and 10 the grade of lumber sawed from them. This grading system has been de— vised primarily to (a) separate from wood—run logs those that are suited for sawing into standard factory lumber, and (b) segregate such logs into high, medium and low value categories as determined by the lumber-grade yield pattern they will produce when sawed into lumber by a skilled sawyer. According to the Forest Service Standard Specifications , hardwood factory lumber logs are separated into three grades: F1 , F2 and F3. For all three grades , there are limitations as to the log diameter, length, number of clear cuttings on the grading face, sweep and crook allowance and scaling deductions. Detailed Specifications can be obtained from A Guide to Hardwood Log Grading published by the Forest Service (15). The advantages of this system (1) are that the value of a group of sawlogs can be estimated and the lumber volumes and grades can be pre- dicted correctly. The use of log grades allows for the assumption that the average log in any grade '. cut at one time, will be very nearly the same as a corresponding log cut at any other time. Despite their advan- tages, these log grading rules are too complex and include too many var- iations and exceptions to be handy and easy to apply. They are too elab-I orate to be used with convenience and without any variances. In addition, log grades include the element of uncertainty, because the assignment of grade depends upon judgment. Log Grades and Yield A study by the Forest Products Laboratory of approximately 11 , 000 logs 11 sawed at 28 mills, presents lumber yield tables by log grade and diameter of the logs separate for several species (21). As it is shown in these tables , the percent of the grade yield of lumber within a species varies greatly according to the log grade, and less within the diameter range. There are overlappings of course, but those must be expected since there are variations in log qualities even within the same grade. In general, these tables confirm the fact that the average lumber grade yield of the three log qualities comes very close to the anticipated when the output is grouped into No. 1 Common and better, and all other grades below this grade into a separate group. In that case and for red oak (upland), which is also the species used in this study, the tables show an average yield of 70 percent of No. 1 Common and better for log grade F1 with the biggest portion of F.A. S. , a 54 percent yield for log grade F2 with the biggest portion on No. 1 Common, and a 32 percent for log grade F3 with the biggest portion on No. 1 Common. In the latter case and considering the overall output, the No. 2 Common and 38 Com- mon seemed to be the predominant grades. The lumber grade mix produced from log groups separated by size varies within the same log grade when each log size is examined sep— arately. These variations may occur due to variations in the individual log, but also due to variations in the sawing method or the human judg- ment exercised in sawing. The influence of these sawing practices and the involvement of human judgment will be discussed in the following sections . 12 Industry Practice Sawing Practices* The end use demand of the industry for clear lumber and the variations in the quality of the input logs are the two principle factors which gen- erate the need for and forces the sawmill Operators to apply a variety of sawing. practices when grade sawing. The basic principle that governs these practices is that each board, before it is cut, is evaluated on its own merit for its potential yield. The potential grade of the four faces of the log are examined and the log is sawed on the face with the highest grade until the grade of this face drOps below that of the other faces. During the processing, the logs are manipulated on the carriage in such a way that as many boards as possible of the higher grades canbe extracted. However, the success of this processing method depends on the general quality of the log and its size. Creighton (3) reports that profit cannot be realized in sawing every log, as is the case with small defective logs. In that case the grade yield advantages of the above processing method may be offset when smaller and lower grade logs are sawed, by the increase in the machine and labor cost associated with logturning and handling and cutting individual boards as compared with a gang saw process. Malcolm (11) , gives a detailed description of how *In small sawmills where all cuts except edging and trimming are made with the headsaw. l3 logs of different qualities should be sawed for best results. He also out-l lines several procedures in selecting a sawing face, based on the surface defects of the log and their distribution. The application of these procedures requires a number of log turnings and handlings. The conformity of these procedures to the requirements of grade sawing makes such an Operation a very complex one. Not only skill, but knowledge as well as sound judgment is required by the sawyer who decides how to proceed, when a specific pattern of defects appears. Grade sawing know—how is of paramount importance in this operation. There are two main variable inputs which determine the final output of the mill: (a) logs of various grades, and (b) the sawyer's decision as to the way the lOg should be sawed for better grade yields. While the grade of a particular log cannot be altered as such, the sawyer's deci— sions when he manipulates the log on the carriage can cause variations in the grade output of this log. The effect of the sawyer's judgment will be examined in the following section. The Role of the Sawyer Several decisions are required‘in "grade sawing" in order to effec- tively convert the logs into grade lumber. The sawing method used is determined by a set of rules which the sawyer applies during the break- down process of the log. The implementation of these rules is not auto- matic, but depends on the sawyer's evaluation of the characteristics of each particular log. 14 The existence of the defects , the variation in their size, and espe- cially their distribution occuring on a board's face, requires the sawyer’s judgment in order to evaluate it for its potential grade. Following this evaluation _. a choice must be made between cutting this board or turning the log and cutting another face of higher potential grade. This kind of selective sawing procedure must pay off, if the quality of the log processed contains great percentages of high grade lumber which can be produced by this method, thus compensating for the time and effort required. In this case, the board-by—board decision made by the sawyer is a big advantage. On the other hand, logs of low quality will require too much attention and time which possibly will not be warranted by the small gain in grade that will result. These low quality logs may be processed in a simpler way determined by a single decision upon one view of the log. The problem of grade yield of each of the log grades has to be inves- tigated for the effect of the sawyer's board—by-board judgment. Such an investigation may reveal to what extent this judgment helps to increase the overall grade lumber. It may also reveal that with certain logs there is no need for such a judgment since the character of the log itself ex- cludes larger amounts of grade lumber or the time required to extract higher grades of lumber is very high, making this Operation too costly. The lack of precise knowledge as to what constitutes a maximum yield or the percent lumber grade mix of the individual log does not allow for a standardized sawing method to be used in order to compare the results 15 of such a method. An investigation which will produce results of alterna- tive sawing methods on the same log might indicate the possibility of the application of such a method and also to what extent and with what grade of logs this application will be more desirable. A procedure which will relate the characteristics of a log with various sawing methods can help the investigator to differentiate between the effect of log characteristics and sawing method on the total lumber grade yield. If the same lOg can be sawed several times with different sawing methods and the outcome of this practice is evaluated in terms of grade of the produced lumber, then this may point out the way to better understanding of the log value and the yield variations as they are influenced by the sawing method. Production data that are now available give yield and lumber grade distributions in averages from a certain number of logs. Variations in yield that may occur among the individual logs , or the causing factors of these variations are hard to detect. Factors which can cause variations can be the machine, the log, or the judgment of the sawyer. Excluding variations due to machine, the other two factors are hard to determine. As a result of this it is very difficult to determine exactly the impact of log grade on the yield without having the log variations associated with variations in the Operator's decision. Yield records thus established in most cases may not be considered as the best measures of the obtainable yields from logs if these logs Were processed in the most efficient manner. It is therefore desirable to eliminate other factors in the comparisons 16 of various sawing methods, using a standardized process, and to evaluate the resulting lumber grade of each method produced from the same log. Ultimately, what is required is a suitable basis for choosing among 1the alternatives and their results. A better understanding of the interaction between log characteristics and sawing method will aid greatly in achieving correct decisions . Research on Yield Improvement Past Treatment of the Problem Literature dealing with subjects similar to this study is rather rare. The following literature, however, can be cited as using techniques from the area of ”Operations Research" and also related to the subject matter of this study. The effect of defect placement and taper set out on lumber grade yields when sawing hardwood logs was studied by Malcolm (10). A sta- tistically designed experiment was used to study the grade yields of red oak species sawed by six sawing methods. The sawing methods tested utilized two different positions of sawing faces relative to location of major defects, and two degrees of taper setout. One of the six methods was used as a control method in which defect placement and adjustment for taper as such were ignored. Average lumber grade yields and monetary values from all log grades combined were compared with each sawing method. Yields and monetary values of each log grade were also compared for each sawing method. 17 Results as reported by Malcolm, show that ignoring taper and the relative position of defects on sawing faces results in a loss of potential grade. The placement of defects at the cOrner of sawing faces results in higher quality lumber than when defects are placed in the center of the faces. Full taper setout had a greater potential for producing higher lum— ber grades than one—half taper setout. When taper was ignored, lumber grades comparable to that obtained from full taper could be obtained from similar logs having Opposite low and high quality faces if the low quality faces" were sawed first. Sawing the low quality face first automatically puts the high quality face parallel to the saw line, resulting in production of full length boards from the high quality face. Malcolm's study was based on present day sawing practices of log turning, testing sawing instructions as they are given by the FPL, against some of the variation, employed by the sawyers at the field, when grade sawing. Jackson and Smith'(9) studied the problem of sawing the log in the most profitable way consistent with the market requirements of various lumber sizes. A linear programming technique was used to determine the Optimum combination of lumber sizes to be produced from each log size. Sawing procedures were selected for each size that yielded the highest net profit on the basis of the total amount of lumber of each size that can be sold. Under this program all logs had been utilized by one process or another. However, the most profitable ways of converting the log were 18 not utilized, because some sales restrictions would have been exceeded, resulting in excessive amounts of product for which there would be no market. The above study was restricted to certain product sizes to dem— onstrate the use of linear programming as a technique to determine the Optimum production combination which will maximize profits. Linear programming technique was also used by Row, Fasick and Guttenberg (l9) , in order to study sawing problems of a high speed southern pine mill. The area of their study included four basic factors; (a) amount, quality and cost of timber; (b) possible sawing patterns and their yield; (c) machine time available on the mill equipment; and (d) sales requirements. Data on yield of logs sawn by several patterns , the time requirements of each pattern and log class , on each machine including restrictions on machine time, were analyzed by linear programming technique. Although the log and lumber grades of southern pine are different from those of hard- wood and specifically red oak, it is interesting to note their findings. The grade of C and better and No. l lumber yield declined as the log grade decreased, while No. 2 grade increased as log quality fell. The log grade No. 2 seemed to be the break—even point of this study. The influence of sawing pattern was significant only in conjunction with log grade and machine time. Their lumber yield findings by sawing patterns were associated with bandsaws , linebar resaws , horizontal re- saws and a sash gang saw. The mix of boards and dimensions cut was reported in relation to the particular patterns of these machines. 19 The authors arrived at best sawing patterns on the basis of the most profitable ones , according to sales policies , and the cost of raw material. As they point out, at any given price set the total recovery values will vary with the sawing pattern and also, patterns that give the greatest lumber yield return may not be the most profitable. In effect, the alter-:- native machine time cost may exceed the gain from Operations that in— crease the product value. An experimental approach to theoretical sawing of logs was reported by Peter and Bamping (16). The authors analyzed the application of a new technique for evaluating sawing methods. A log was actually sawed and j the defects were measured on the produced boards and plotted on an end section diagram of the log. By applying then a transparent overlay indi— cating theoretical sawlines, grade and value figures of the (theoretically) produced lumber were obtained. Lumber yields were based on a "right cylinder, " i.e. , in a cylinder determined by the diameter Of the small end of the log, and "clear diagram” faces were used as quarter sections of the log circumference in which no knot penetrated the ”right cylinder. " Data based on this technique were reported separately by effect of width, grade, and a combination of them, based on the number of clear diagram faces and lumber value per thousand board feet. A breakdown by sawing method on lumber values indicated that board width values between log quality groups did not indicate any trends despite 20 variations in the average diameter of the groups. The effect of grade indicated increasing average grade values as the log quality improved. When grade and width were combined, a value spread within groups and a value increase between groups was observed. Riikonen and Ryhainen (18) used a computer (mathematical) model in order to find the best sawing method among different sawing alternatives , which gives the most profitable economic results. Their basic approach was a mathematical expression of produced board sizes along cone shaped softwood logs, as the radius of the log changes at a'distance X from the large end. The effect of price and cost factors was used in order to im- prove the reliability of the results obtained. The quality variations of the raw material and product were considered by calculating parallelly the results given by a good quality and a poor quality log, and placing the results of individual logs between these extreme values. Other Possible Solutions Considering the nature of the raw material as well as its limitations , the investigation of Optimal grade yield can be approached in different ways. One way would be a statistical approach, using a large size sam- ple of each log grade used today. Thus, the difficulty of testing identi- cal logs for this type of analysis may be overcome. The sample logs can be processed in subgroups for various sawing methods, using one method per subgroup. The results can be evaluated in terms of grade and volume, averaging them for all logs of the same subgroup. The statistical approach 21 can help in such investigations, provided that machine and human judg~ ment variations are considered. The disadvantages of this approach are the cost and time required, and the fact that alternative sawing methods have to be used in different logs. Another testing approach can be the use of a theoretical log. Experi- menting with such a log, while it will fill the need for the use of the same log for the testing of several sawing methods, is weak from the point of view that it is not realistic. Any data derived from the experiment will correspond to the constructed theoretical log and not to the actual One. Also, defects have to be generated which then increases the complexity and the disadvantages of this approach. A third approach, which combines the advantages of the two previously mentioned testing methods , can be the simulation approach, with the use of real logs. It is this approach which has been developed in this study as a possible solution to the optimum grade yield problem. Computer Simulation Simulation—defined as systematic abstraction and partial duplication of real world phenomena, activities, or Operations—is used for the design of a system in terms of certain conditions, and the analysis of specific rules, policies and procedures (20). Further, simulation as a method for systematic abstraction suggests the construction of a model used as a key for the solution of the simulated activity. McMillan and Gonzalez (12) 22 refer to simulation as the process of conducting experiments on the model instead of with the real system. Although a simulation model is fallible, there are a number of applica- tions where it is preferred. In our‘case no other feasible experimental means exist which can utilize the same log for various sawing methods. Application of other techniques described above are not considered feasiw ble due to magnitude of computations involved and the disadvantages men- tioned. For more information about simulation, one can review the existing literature on this subject (7 ,14). At this point it is more desirable to discuss how this technique can be applied to logs and, consequently, to sawing methods. The replication of the sawing activities is prOposed to be done in two stages. In the first stage an assessment of the log exterior and interior characteristics will be made so that input data on the size, shape, and defect location can be gathered. For this purpose the real log will be cut into disks (elements) sufficiently small to reveal most of the interior de-a fects of the log. The disks are of discrete thickness, the same for all of them. The circumferences as well as the defects on the face of the disks, are measured and recorded. These measurements provide one set of input data. Thus the location of the defects appearing on a board cut from that log in any orientation relative to source reference plane of the defect along the log axis can be determined. 23 In the second stage the sawing methods, which become the parameters of this study, are selected. One of the sawing methods will be that which allows for the turning of the log. Other methods will be those that allow the use of the gang saw in one or two passes. In all these methods the position of the log in relation to the outside main characteristics will be considered. These sawing methods provide another set of input data. The computer program which was written for this study, utilizing the two sets of input data plus appropriate instructions , is used to simulate the sawing activity. A detailed description of both stages is presented in the next section. This technique allows the same log to be sawed several times and also the test of any alternative hypotheses desired on real logs, taken in small sample size. The approach becomes feasible in the event of com— puter use, which permits enormous saving in time and cost. The simulated log breakdown operation can be used to synthesize a basic sawing method, based on present day sawing practices, against which the results of alternative methods can be compared. The principles of other sawing machines, such as gang saws, can also be introduced by assigning their Operating characteristics as program parameters. The re— sults of the same log can be compared with those obtained from machines used at present. v Major advantages and disadvantages of a simulation model are cited below (17). Advantages: Disadvantages: 1. 24 Provides better understanding of the system by those who Operate it. Results in quicker acceptance of prOposed changes be- cause, once the Operators of the system understand and accept the description of the system given by the model, they can proceed with the evaluation of the assumptions contained in the input data and the implications of the output in future decisions. Can stimulate and produce ideas. When the model is completed and tested for reliability, new operating con~ cepts can be advanced. Promotes complete analysis. Analysis of the Operational factors can be expanded to great depths. The model does not depend on a mean or median value in order to describe a variable. The complete range of variables, as well as their relationships, can be intro- duced. 1. The modelling prOcess may invite excessively unreal— istic assumptions. The quality of these assumptions determines the value of the model. Obtaining accurate input data is a difficult problem, often underestimated or neglected. Model develOpers can easily become technique oriented rather than problem oriented. 25 4. Simulation models permit evaluation of ideas created by the human mind and therefore they are only as good as the ideas are. In the present study, due to the destructive nature of the technique used for the production of the input data , the log cannot be processed for lumber production. Therefore, there are no real standard results for com- parison. Also, certain necessary simplifications. are introduced in order to carry out the simulation. For example, the output of the simulated sawing is presented as printed pictures of boards. Due to printer limita— tions various errors in the size and shape of the appearing defects, to be discussed later, will be unavoidable. The output shows one face of the board only. (Note, however, that in this case both faces are alike and either choice would represent "poor face. ") III. METHODS AND PROCEDURES The Source of Data The Raw Material The simulation of the log breakdown Operation was accomplished with the use of information. obtained from red oak logs. There are several species included under this name , all belonging to the Erythrobalanus group. Because the wood of the species included in this group cannot be identified with certainty, any reference hereafter to the species will refer ' to this group. Red oak was selected because of its importance to the hardwood-using industries. The wood of this species, as in the white oak, is generally straight-grained, heavy, strong in bending and endwise compression, and high in shock resistance. Further, it machines well and finishes smooth. Due to these characteristics red oak lumber is widely used in flooring, where its hardness , high resistance to abrasion, and ability to finish smoothly makes it most desirable. It is also greatly used in the furniture and cabinet. industry and in general millwork. A total of six logs were used for this experiment, with two logs as- signed for each log grade. The selected logs were graded according to the U. S. Forest Service standard grading rules (15). After the grading each log was numbered with a grade, and a serial within the grade. Thus 26 27 the logs were numbered 1. 1 and 1. 2 for the tOp grade ,‘ 2.1 and 2. 2 for the medium grade, and 3. l and 3. 2 for the low grade. The diameter of the logs at their small end were: 13 inches for both 1.1 and 1. 2 logs, 11 inches for both 2.1 and 2. 2 logs, and 15 and 13 inches for logs 3.1 and 3. 2 respectively. The length of the logs varied from 10 to 12 feet. In this experiment they were arbitrarily set to an eight—foot length, with the sole purpose of reducing the time and effort required for the execution of the work. It is realized that most of these logs were not average logs for their respective grades. For example, the diameter of log 1. 1 and 1. 2 was the minimum diameter required for logs of this grade. The diameter of logs 2. 1 and 2. 2 was also the minimum diameter for that grade. In addition, the reduction of their lengths into eight feet, further contributed to the deviation of the aforementioned logs from an average log of their respec~ tive grade. Thelogs were chosen at random from a limited. supply, and therefore the choice was made between a few logs of each grade. All logs were purchased at a local sawmill, where they were also marked and disked in order to expose and measure their internal defects. * An end section diagram of the logs with projections of all outside defects, is given in Figure l. (Scaled illustrations ofall logs are given in Appendix B.) Log Preparation Before the logs were cut into disks for the measurement of the internal *A cut-off, De Walt, radial arm saw was used. The saw utilizes a 40—inch blade and is driven with a manual crank. 28 ..n .00 00 39:23:53: 3: EB :25 2: do «Steinem 3‘ .9: .00 OO 00 29 defects, and in order to be able to reconstruct their shape , they were marked along their long axis. Each lOg was balanced on one face, and a vertical line was drawn passing through the pith at each end. Then another line was drawn, perpendicular to the first and again passing through the pith. These axes, designated as X and Y on both ends of the log, were used as the ends of three marking lines cut with a portable electric circular saw, along the 109's long axis (Figure 2). After each log was marked, it was sliced into disks of one-inch nominal thickness. The actual thickness of the disks was one inch minus the kerf, or a net thickness of three-quarters of an inch._ In the present study, the disks are taken at their nominal one-inch thickness. _ All disks were numbered in a sequence as they were cut, starting from the small end of the logs. A total of 96 disks was produced from each logy. Slicing the log into disks, ratherthan. boards , greatly facilitates the precision and convenience of data recording. Disks are closer to a real- istic situation, where the shape of the circumference—not likely to be circular, or otherwise uniform—can better be traced as it varies along the long axis of the log. Disking also fits better with the develOped technique for circumference and defect recording. This technique, as it will be explained further below, enables one to handle the whole log rela- tively easily. If the logs instead were to have been sawn into boards, the inside defects similarly would have been revealed. Transformation of all defect 30 «:3 25 5833.5 236% 3:36! uoq .N§k 31 locations from board to disk format could be made. This method, however, cannot conveniently give the shape of the logs as is the case with disks. Crooked logs , for example , would be difficult to trace—particularly for slabs falling short of the full length of a log. Also, especially for lOng logs, the actual process of measuring defect locations on boards as against disks would be tremendously more cumbersome. The disks weremade one inch thick so measurements of the defects could'be taken according to their actual size andlocation inside the log in discrete, uniform data intervals. The transpositiOn of these defects to the resulting boards was thus performed by projecting one-inch units of defects on the boards' faces. This established a control procedure that permitted cross-checking the location of defects in the board and log by measuring the distance of the defect alongthe boards and matching it to the disk cut from the log at the distance. in inches indicated by the disk number. After the logs were cut into disks, the three lines marked along the logs appeared on the circumference of each disk. These three marks were used as the reference points for the placement of the disk on the measuring device . Circumference and Defect Recording Method An important aspect of this study“ was to develOp a method of recording directly the circumference, as well as the size and location of the internal defects of the logs. A coordinate system of X and Y axes was used for 32 325» 55 ”3 5.5 255233! 3:235:23 use Etna s8 E293 Ftp 23.563 xuk 66E l x o¢ 33 that purpose (Figure 3). A grid was drawn, on a transparent polyethylene sheet, consisting of 100 by 100 squares. These squares, a quarter of an inch each, were used as the measuring units for both the circumference and the defects of the disks. Circumference points were recorded by the coordinates of the unit, which included these points. Each defect was also given in units instead of its absolute size. Thus, the error that automatically was involved in this type of measurement was limited to the range of zero to one-quarter of an inch. Defects covering any part of a square were considered as covering the whole. The advantages of this approach are that the size Of the defect can be measured in discrete units whose position on the face of the disk can be recorded by standard X and Y coordinates. Each pair of coordinates gives both the size of the defect and its location. The disking procedure permitted measurement of the circumference of the log and the log defects to be taken in intervals of one inch. When the three circumferential marks on each disk were placed on the coordi- nate system grid, any variance from the hypothetical line. connecting the two end-centers of the log or any change in its diameter was immediately indicated and recorded—to the nearest inch for the former, and quarter of an inch for the latter. Since each disk in a given location represents the whole log in that particular distance, cutting the logs into one-inch thick disks satisfied the need for a three-dimensional reading. Also, defect readings were 34 facilitated under the assumption that any defect appearing on one face of the disk extends for one inch inward. Readings of the defects were taken on the front face of each disk, in the two dimensions, X and Y. The depth dimension, being one inch, wasintroduced automatically. In cases where face defects do not extend to the depth of one inch —i. e. , back clear—then there is an error in the reading of approximately a quarter of an inch to one inch. This error, however, is balanced by the assumption that face defects of consecutive disks are continuations of the previous disk's back defects. For example, a defect appearing on the face of disk No. 73 is considered to be also the back of the preceding disk, No. 72, even if disk No. 72 has a clear front face. Under this as— sumption, measurements were taken only on the front face of each disk. This had the effect of cutting the working time by 50 percent. For practi— cal applications of this experiment, this is a considerable reduction. Recording Procedures In order to obtain the coordinates of the circumference of the disks and the location of the defects, each disk was placed underneath the transparent grid. The two Opposite marking points were placed on the Y axis at X=50, and the third on the X axis at Y=50 (Figure 3). All four points of the circumference at X50 and Y50 were recorded, to the nearest quarter of an inch. Any other salient point was also recorded so that the actual shape of the log easily could be reproduced during the processing of data by the computer. Next, the defects on the face of the 35 disk were measured to the size of quarter of an inch square units. Defects larger than one squate inch were recorded in units of one square inch and were especially coded with the number one so that the final reading will appear again in quarter—inch units. Distinctions between defect and cir- cumference recordings were shown by assigning the code number two to the latter type of data. Measurements of each unit defect were recorded, first for the X axis and then for the Y axis. Since the diameters Of the logs used were greater than 10 inches , the grid was divided from one to 100 units in both the X and Y directions. Thus, each measurement was represented by a pair of numbers, each containing from one to three digits. In the case of this experiment, all data occurred as two-digit numbers , except when units of one square inch were measured. In those special cases, the additional code number preceded the others. As an example, the reading of a defect indicated with the number 3964 means that this defect is located at X39 and Y64. A 13964 means that this same unit should be expanded to the right and down for four units (one square inch), thus including a total of 16 units. A number 23050 should be read as a point at the circumference, ‘ as indicated by the initial number 2, and that this point is located at X30 and Y50. Making it a practice to read first the X's and then the Y's , it becomes a routine process to measure and record any desired point (on the surface of the disk. The time required for this work varies with the quality of the 36 log and the number of defects appearing in its particular disk. I In any event, it takes between two and 15 minutes per disk, or 192 to 480 minutes for all 96 disks of a log. Later in this study a new technique will be de- scribed, involving a digitizer device , which cuts the time requirement to a very small portion of the above mentioned. Computer Simulation Preparation of the Input Data All the data derived from the measurements of the disks were punched on data processing cards. A very simple coding was used for this trans-- formation. It was mentioned previously that the number one in front of any pair of coordinate numbers indicated a square of 16 units, and that the number two was used for circumference points. Therefore, the maxi- mum number to be recorded for each measurement was a five-digit number, requiring five columns on the data processing card. (Where no special code designation was required, the first column was left blank.) On each card, out of the 80 columns available ,1 the first five were reserved for log and disk identification. Columns 6 to 55 were used for circumference readings, and the remaining columns for defect readings. When one card was not enough, the remaining data were punched on a new card, starting in column six. Some disks required as many as ten cards. » A computer program was written for the execution of all calculations required in this study. The final program, written in FORTRAN language, was executed on the CDC 3600. This program is given in Appendix B. 37 Sawing Methods Sawing methods can be divided basically into two categories: sawing through, or live sawing, and sawing around the log. Through sawing con— sists of parallel saw cuts through the log. It may require one turning of the log, or no turning at all if a gang saw is used. This kind of sawing can be used with both circular and gang saws. Sawing around the log re- quires turning of the log two, three or more times. Various sawline com- binations can be used in this type of sawing. This kind of sawing can be used in circular or band saw Operations. To make the applicability of the present study as broad as possible, a variety of presently used, basic sawing methods was chosen. The only requirement was that some of the methods be usable on both circular and gang saws. Since the effect of outside characteristics of the log on the grade yield would be, in studies of this kind, the main criterion in eval— uating the results of each method, four different positionings of the sawing faces of the log—relative to the main outside defects—were used (Figure 5). Altogether , three sawing methods were employed in the simulated log breakdown operation (Figure 4). They represent basic sawing methods from which other combinations can be derived. All the methods used one- half taper and were applied twice to each log: first, with a one-fourth of an inch kerf to simulate circular saw cutting, and second, with a one— eighth of an inch kerf to simulate gang or band saw cutting. 38 \ METHOD N... I I. Circular Saw 2. Sash Gang Saw METHOD No. 2 I. Sash Gang Saw 2. Circular Saw and Sash Gang Saw Cants: 4"and 6" METHOD No.3 I. Circular Saw (SYNTHISIZED) Fig. 4. The Three Sawing Methods Used on The Same Lag 39 From the three methods used, one—the grade sawing method—was designated as a control against which to compare the grade yields of the other methods. This method, described below as Method No. 3, is a synthesized method. That is, after the log was cut into boards by sawing through, the produced boards were used to develOp manually a sawing pattern based on present-day sawing practices. The procedures followed in this method are described in the following section. At this point it must be stated that although Method 3 is a simulated method, the com— plete simulation involves the results of the computer sawing, and the manual manipulation of the resulting boards , to achieve the pattern cor- responding to Method 3. Therefore any reference hereafter to Method 3, will imply both computer and manual simulation. The methods used in this study are the following: 1. All logs were sawn by through sawing, in four different posi- tions each 45 degrees apart. This method allowed for posi- tioning the sawing faces between defects , at the center of the defects, and parallel to them. 2. All logs were sawn in four different positions, as in Method 1. Cants of four and six inches were left to be sawn by a gang saw. 3. All logs were sawn by through sawing, in two positions: first, placing the sawing face between the major outside de-r fects and sawing through; second, by sawing perpendicular to the first cut. The boards produced by these two sawings were graded manually, and were used for the "synthesized" sawing pattern referred to above. In the simulation, each log was sawed 14 times; four for Method 1. eight for Method 2, and two times for Method 3. The use of two kerf sizes 40 increased the number of simulated sawings to 28. Multiplying the number of sawings per log by the total number of logs results in 164 sawings. This can be compared to the 164 logs, which would be needed to apply these sawing methods on a one-to-one (non-simulated) ratio. . Sawing Program The first requirement of the sawing process was to select the initial sawing face. In the previous section, in describing the sawing methods, it was stated that each log was sawn in four different positions , using Methods 1 and 2, and in two positions using Method 3. The best sawing face of each log was one of the four sawing faces, but not necessarily the first one sawn. The following is an explanation of how the logs were cut in this study. The same procedure can be used as a general guideline for any given log. The starting point for the sawing of all logs was the mark corresponding to Y=50 and X=30 in Figure 3. (Figure 3 in this case is considered as rep- resenting the end section diagrams of the logs shown in Figure 1.) This point is assigned to. a line forming a zero degree angle with respect to the X axis. For the sake of simplicity, and in order to illustrate the procedures followed, let us consider a circle representing the end section diagram of a log. The three marks previously explained are placed on the same cir- cumference locations as in the real logs (Figure 5). A rectangle (efgh) is inscribed in the circle, dividing the circumference of the circle into four equal parts. The inscribed rectangle is oriented in such a way that its 41 \X i // XX h 180° of : A f'g': B f9: C g’h’u D Fig. 5. The F our Sawing Faces of the Logs Used in this Study, and the Starting Point for Each F ace 42 top and bottom sides are parallel to the X axis and the left and right sides are parallel to the Y axis. Thus the projections of the three marks are located at the centers of the three respective sides of this rectangle. « The face (ef) denoted by the left side of the rectangle is the first face to be sawn. Starting from the zero degree point, the log is sawn completely. By rotating the log counterclockwise 90 degrees , the tOp side of the rectangle (fg) is brought into a vertical position, thereby putting the second mark at zero degrees. This point now becomes the reference for sawing the log in the second position. If instead, the log is rotated counterclockwise 45 degrees , the top side of the initial rectangle is brought into a position (f‘g') where the second mark is placed at 45 degrees on thecircumference of the circle. This side describes a new rectangle (e’f'g’h' in Figure 5) which designates the new sawing position of the log. In this manner any other selected sawing face is represented as the side of a rectangle. The center point of this selected face, projected on the circumference of the log, gives a point to which an angle is assigned, measured from the point designated as zero degrees. In this study, for programming convenience, the logs were sawn at 0, 45, 90, and 135 degrees, which represented four sawing faces given ' by the two rectangles of Figure 5. The 0 and 90 degree positions are given by the rectangle efgh, and the 45 and 135 degree positions by the rectangle e'g'g'h‘. For simplicity of notation, positions ef, f'g” , fg, 43 and g'h' will be referred to as A, B, C, and D respectively. In the sim— ulated sawing, any rotation angle can be assigned, and any face can be sawn. Assigning the rotation angle in increments of one degree, for ex- ample, will give 360 sawing faces. The above described sawing faces were used for all logs when using 1 Methods 1 and 2. The logs were sawn live in both methods. In Method 2, however, a cant was left after each sawing. The size of this cant was measured from the center of the log as given by the coordinates X=50 and Y=50 (Figure 3). One-half of the cant size was measured to the left of that point and the other half to the right of it. Since the sawing starts from the left side, the left half of the cant may fall within the board limits of the last board before the cant. In such cases , the position of the cant was shifted to the right at a distance equal to the overlapping, plus the kerf size, and the board was cut to full‘size. The computer then, is in— structed to jump the assigned cant size and continue the sawing process to the right by leaving a kerf. The remaining cant is sawn by rotating the log 90 degrees. Method 3, the simulation of present sawing practices, was carried out by "sawing" the log live twice. First, the best sawing face was chosen among the four faces described earlier. Starting from the selected face, cuts were made parallel to the Y axis. * Then, turning the log 90 *Starting points for the sawing of these faces were: log 1.1, 1350: log 1.2, 0°; log 2.1, 135°; log 2.2, 0°; log 3.1, 90°; and log 3.2, 45° (Figures 1 and 5). 44 4 degrees, it was sawn again. Thus the quality of each set of boards was revealed, as sawn with respect to the X and Y directions. After the produced boards were graded manually, they were used to synthesize a basic sawing pattern equivalent to the actual practice fol- lowed by sawyers as they work their way into a log. That is , the initial choice was made among the four boards—the first and last one from each live sawing. In each case, the board of the highest grade was identified and selected. Next a comparison was made between the grades of the remaining three boards and the board immediately alongside the one se- lected. This process was continued to the last board, always by "turning” the log and selecting the best remaining complete board or—where previous sawing had removed some of the width—the best remaining partial board. In cases of equal grade boards, the wider was chosen. If there was equal grade and width, the choice was made arbitrarily. Thus a sawing pattern was developed which came close to the one that would havebeen followed if this log actually had been sawn. The simulated sawing process can be described briefly as follows. The computer program first locates the starting point or zero degree angle. Then, perpendicular from the zero degree center of the assigned sawing face, it proceeds in Opposite directions with one-quarter of an inch in— crements until it reaches the limits of the log Cylinder. The two Opposite limiting points specify the width of the board. Next, the scanning pro— ceeds inward in increments of one-quarter of an inch until it reaches the 45 assigned board thickness of one and one-eighth inch, and allowing for the specific kerf size, recycles the entire process further into the log. When the log is rotated, by any assigned rotation angle, the same process is repeated, just as if we were dealing with a new log. The model also scans the log for defects and counts the number of all defect units, by quarter-inch squares, in a sequential order. It starts from the first disk and one defect unit, and penetrates through the cylin- der of the log until all disks are explored for defects in a position given (by the coordinates of the first unit defect. The process is repeated until all unit defects appearing in any disk's face are checked and counted. The output of this searching is printed under the printout of the board produced from the log. Each board includes the defects encountered in the area occupied by this board inside the log. For all three sawing methods, to handle the problem of taper, the circumference of each log was rounded in the shape of a cylinder. . This rounding was accomplished by using the four Opposite circumference points of the small-end disk. Thus taper adjustment during the operation was avoided. Another factor considered was the size of the kerf. The two kerf sizes used for each method and log were introduced into the [model so that comparisons of the influence of kerf on the grade of the resulting boards could be made. The effect of cant production was investigated by introducing two 46 cant sizes on all logs sawed. Although maximum lumber grade is the con- trolling factor in grade sawing, producing cants from the heart portion of ' lower grade logs may increase their overall dollar return. Finally, to bring the simulation still closer to industry practice, the boards produced by all methods and from all logs were edged to the? width of the small end and trimmed one inch at both ends. Operating Characteristics of the Model In order to simplify the problem certain limits were introduced in the simulated break-down Operation. These limits—in the form of model ele- ments, and policies for the execution of the work, and sawing rules—were: 1. Elements: (a) cut the log into lumber; (b) rotate the log, or coordinate system, by 45 degrees; and (c) rotate four times. 2. Policies: (a) use one particular method at a time; (b) repeat it with all methods assigned; (0) leave two cant sizes when sawing with Method 2; (d) saw first on circular saw and next on sash gang saw; and (e) shift cants sawed with Method 2 to sash gang saw by turning them 90 degrees, and saw in one pass. , 3. Rules: (a) saw one and one-eighth of an inch thick lumber only, and accept boards three inches wide or more; (b) change sawing method after the log is completely ‘sawn; (C) out log completely with all methods before shifting into another log; ((1) out only in X or Y directions; and (e) change design (machine) when each cut is completed. The simulated rotation of the log was accomplished by rotating the X—Y coordinate system, using the general mathematical formula: X1 Xcos9+Ysin9 Y1=-Xsin9+YcosG Where X1 and Y1 are the coordinates of the new system having the same 47 origin as X and Y. A given defect unit will have two pairs of coordinates, and the relationship between these coordinates involves the angle 9. The new X1 ,Y1 system is obtained from the X,Y system by rotation through the angle 9. In this program 9 was equal to 45 degrees (Figure 6). With the use of this formula, the defect location on the plane of each disk was rotated to new positions as the requirements of the log’s positioning de- manded. Finally, a test is built into the program for checking the accuracy of the output. This check is accomplished by printing out the following three characteristics for comparison with the measurements obtained from the actual cutting of the logs: l. Coordinates of the end section of the log circumference 2. Coordinates of each board produced from the log 3. Coordinates of a unit defect on the face of the board. Lumber Grading The lumber produced by the simulated sawing was graded manually. A modified version of the National Hardwood Lumber Association grading system was used. Under the modified system, the grades of "select" and "sound wormy" were not considered. All boards were graded on the basis of defects with no allowances madefor pith, wane, or split. Any kind of defect appearing on the face of a board—including mineral streaks and spots—was considered the same as any other non-acceptable defect. The minimum sizes of the boards under this modified system were the same 48 X1 Y1 \ $5 P (X,Y) in XY-System X1,Y1)in X1Y1-System Fig.6. Simulation of Log Turning by Turning the X-Y Coordinates 49 as in the N. H.L.A. rules. All the boards were measured for their width to the nearest one-quarter of an inch. The simplified grading system used in this study was chosen purely as a matter of convenience, to achieve the kind of analysis attempted here. It would be recalled that during the investigation of the interior . defects of the log all defects were recorded in the same manner, with no distinction made for defect types. Thus not only was defect recording simplified, but it was possible—in projecting the defects from the disks onto a board face—to'use the same technique for all defects. All defects therefore appeared as being of the same quality. The grading system of this study is not associated with the model and is not an inherent limitation of it. In cases where the N. H. L...A. rules should be used, defect types could be coded individually using a larger set of data columns to record the observations , so that they may appear on the face of the board. Therefore, any yield figures derived from the produced boards and graded with the presented system should be con- sidered for their value as related to this study only. They may not be applicable elsewhere . Yield Evaluation The evaluation of sawing methods was done by computing the grade volume recovery by each method, separately for each log. A price-grade ratio was used in order to put the results of all alternative sawing methods on the same basis. The monetary values used were based on the July 22, 1967 50 Hardwood Market Report for plain sawed 4/4" red oak (F: 0.8. Mills— Wausau, Wisconsin area). They were as follows, in thousand board feet: PAS, $230; No. 1C, $140; No. 2C, $80; No. 3A, $60; and No. 3B, 354. The total sum, estimated by adding the value of all grades recovered by each method, was standardized to an equivalent value in thousands of board feet based on log scale. (The tabulated results of these evalua-- tions are presented in Appendix A.) Analysis of Variance The yield value results of the sawing methods for each log grade, and for all grades, were tested with an analysis of variance which com- pared methods and grades and their interaction. The purpose of this test was to find if the mean yields for the sawing methods tested differed sig- nificantly. In this way, it may be determined whether the interaction of 10g grades used and sawing methods is important affecting the results. The results of this test, although severely limited by the very small number of observations, are discussed in the following section. IV. RESULTS AND DISCUSSION Evaluation of the Model Model Characteristics In a sawing Operation, the most important consideration is the effect which various judgments, made in the form of sawing methods , will have on total profits. A simulation model offers the possibility of testing these decisions Outside of the real system and of measuring the effects on total yield of various log grades. The various sawing methods chosen to be tested become parameters in the simulation model. Two sets of data are introduced into the model. The first consists of data describing the raw material being processed. The second, consisting of data corresponding to decisions previously made , sets the parameters of the model. It is the second set of data which causes changes in the variables, reflected in the output which is used for analysis and evalua- tion. The output data are measurements Of the effect of the interactions between the raw materials and the sawing methods. Therefore, essential characteristics of the model are the type of input data and the form of the output data. In order to run the model, instructions are needed for proces- sing the input data and producing the output data. If the purposes of the simulated model are to be fulfilled, the greatest advantage will be an in- creased understanding Of the complete Operation cycle. 51 52 The Experimental Model It will be recalled that the main objective of the study is to construct and test a model which would provide a means for the same log to be sawed with‘different methods. The model has been tested for its workability and '. has been proven to fulfill the purpose set for this study. The interaction of elements, policies and rules introduced into the model to accomplish the sawing program outlined under Methods and Procedures achieved the first objective of this study. A schematic representation of the model in the form of a flow diagram is given in Figure 7. The output Of the sawing program includes, for each sawing, a cal— culation of the resulting sizes and volumes of individual boards , and the total yield. Also presented are the number of clear cuttings and cutting units required for each grade Of lumber, based on the surface measure of the individual boards (Figure 8). Thus, the first step in demonstrating the workability Of the model was accomplished. The model has been used to saw one-inch thick lumber. Yet the form is such that it allows for any other thickness , or combination of thick- nesses, which may be desired. The same holds true for the cant sizes. Although four- and six—inch cant sizes have been assigned in the pilot runs, the model is written in a form such that any size can be assigned. Increments for both thickness of lumber and cant size can be used from one-quarter of an inch and up.) S3 Gawain: 5m) {Wiggins} READ DATA SET NUHBERS FROM CARDS FOR LABELING 1 'F 0‘” Is BOARO CONTAINS A1 I FIRST OOLUNN WIDER THAN 3%??ng XPAND T016 3 'NCHES YES <——— CALL BOARD FIND TOP ANO + BOTTOM OF BOARD CALL CUT L r IS BOARO LESS THAN 3 INCHE "0 \ ON RIGHT sum-z ’ CALL ROT J RETURN —>— Fig. 7. Flow Chart of the Simulated Log Breakdown 54 a READ A DISK ] 1 OF DEFECTs INRITE HEADINOs FOR LOOK AT FIRST BOARD DEFECT > 0053 '7 PLACE A FALL INSIDE YE DASH IN THE CURRENT BOARD ou'rpu‘r PLANK READ NEXT BEING CUT OTHERwISE DEFECT FRONI LOOP no , € J NO HAVE ALL DEFECTS BEEN CHECKED YES HAVE DISKs BEEN "0 CHECKED YES PRINT THE OUT PUT J COMPUTE WRITE FINAL INCREASE BY BOARD FEET e STATEHENTs 5/4 INCH TOTAL ALONG LOO 55 SUBROUTINE ROT ROTATE EACH DEFECT 45° ROTATE BORDER OF LOG 45° I l 56 l A rectangle indicates any processing f operation except a decision. A diamond indlcates a decision. 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