Open Collections

UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

The influence of changing logging technology upon the economic accessibility of the forest Cottell, Philip Leroy 1967

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata


831-UBC_1967_A6 C68.pdf [ 3.97MB ]
JSON: 831-1.0075371.json
JSON-LD: 831-1.0075371-ld.json
RDF/XML (Pretty): 831-1.0075371-rdf.xml
RDF/JSON: 831-1.0075371-rdf.json
Turtle: 831-1.0075371-turtle.txt
N-Triples: 831-1.0075371-rdf-ntriples.txt
Original Record: 831-1.0075371-source.json
Full Text

Full Text

T H E I N F L U E N C E OF CHANGING LOGGING TECHNOLOGY UPON THE ECONOMIC ACCESSIBILITY OF T H E FOREST by PHILIP L. COT T E L L B. S. F. University of British Columbia, 1966 A THESIS SUBMITTED IN P A R T I A L F U L F I L M E N T O F TH E REQUIREMENTS FOR T H E DEGREE OF Master of Forestry in the Department of Forestry We accept this thesis as conforming to the required standard The University of British Columbia June, 1967 In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f t h e r e q u i r e m e n t s f o r an a d v a n c e d d e g r e e a t t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a , I a g r e e t h a t t h e L i b r a r y s h a l l m a k e i t f r e e l y a v a i l a b l e f o r r e f e r e n c e a n d s t u d y . I f u r t h e r a g r e e t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s may be g r a n t e d by t h e H e a d o f my D e p a r t m e n t o r by h i s r e p r e s e n t a t i v e s , I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l n o t be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . D e p a r t m e n t o f T h e U n i v e r s i t y o f B r i t i s h C o l u m b i a V a n c o u v e r 8, C a n a d a i A B STRACT Supervisor: Professor J. H. G. Smith The economic accessibility of the forest depends on the value of forest products in the market place and the total of all costs i n -volved in getting them there. Where these costs equal the value of the products, the margin of economic operation occurs. At any point in time, a certain set of technological, social, and economic conditions prevail, which serves to define this boundary. However, it is not always clear just what the effect on the economic margin will be if a change in any of these factors takes place. This in turn increases the difficulty experienced by those who seek to plan for the most efficient and beneficial long term use of the forest, since neither the physical amount nor the monetary value of the forest resource can be adequately determined in economic terms. This thesis has examined the nature of technological change in the logging sector of the forest industry, taking particular notice of both the rate of changeanHof its effect upon economic accessibility of the forest. The resulting need for more factual information for resource planning was discussed, with the emphasis being placed upon i i the area of logging costs. A mathematical model of the highlead logging system, suitable for simulation on electronic computers, was developed to illustrate the type of information required, and how it may be used in the determination of forest accessibility. Also, economic analysis was applied to the problem of logging layout and road spacing, where it was shown that the value of the marginal return from each input activity must be equal for the optimum, or least cost condition, to exist. The usefulness of the cost analysis techniques was demonstrated in an example comparing the performance of the highlead and skyline logging systems on a standardized setting. This demonstrated that the latter system was competitive at a road construction cost of about $ 6 per lineal foot and over, while the former was the more economical below that value. Also, it brought out the fact that skyline systems can contribute in the future to an extension of the margin of operations in coastal British Columbia, and especially so if various technical improvements can be anticipated. A method for combining inventory data, logging prdductivity and cost relationships, and log market prices through the use of logging models was described, using an example from the University of British Columbia Research Forest. It was observed that refinements of this method could lead to a satis-factorily accurate and flexible definition of the economically accessible timber resource. ACKNOWLEDGEMENTS I wish to acknowledge the encouragement and helpful c r i t i c i s m of my major advisor in this project, Dr. J. H. G. Smith. The thesis was reviewed by Messrs. R. Mills, L; Adamovich, and L. Valg, and their guidance and comment was greatly appreciated. Dr. A. Kozak and Mrs. H. Froese provided a good deal of assistance in developing the computer program and carrying out the subsequent analysis. The comment of several colleagues, notably Dr. J. Nautiyal and Mr. P. Boateng was both stimulating and useful in this work. Last, but not least, the assistance of my wife, Donna, in the drafting of the illustrations deserves special thanks. Philip L. Cottell iv CONTENTS Page INTRODUCTION 1 LOGGING - SOME CONCEPTS 5 LOGGING AS A S Y S T E M 10 A) The Characteristics of a System 10 B) Logging, from the Systems Viewpoint 11 C) Tools for Systems Analysis in Logging 14 THE D E V E L O P M E N T OF LOGGING TECHNOLOGY IN CANADA 18 A) Tree Felling and Cutting 18 B) Primary Transport of Timber 19 1) Tractive Systems 19 2) Cable Systems 21 3) Mechanized Systems 24 a) The Shortwood System 24 b) The Tree Length System 25 c) The F u l l Tree System 26 d) The Complete Tree System 27 C) Secondary and Major Transport of Timber 28 D) Technological Change and Timber Accessibility 31 DEVELOPING MATHEMATICAL MODELS OF LOGGING SYSTEMS 33 A) The Need for Models in Logging 33 B) Theoretical Bases for Logging Model Development 34 Page 1) Simple Mathematical Models 34 2) Computer Oriented Models 41 A COMPUTER ORIENTED MODEL FOR HIGHLEAD LOGGING 45 A) Major Highlead Logging Cost Centers 45 1) Fixed Costs 45 a) Road Construction Costs 45 b) Landing Costs 46 c) Yarding "Road" Changing Costs 47 2) Variable Costs 51 a) Yarding Costs 51 3) Total Costs 53 B) Simulation of the Highlead Logging System 54 A COMPARISON O F HIGHLEAD AND SKYLINE LOGGING SYSTEMS 68 A) Skyline System 68 B) Highlead System - Portable Steel Spar 70 C) Comparison of Highlead and Skyline Systems under Standardized Conditions 71 T H E DETERMINATION O F ECONOMIC ACCESSIBILITY ON T H E UNIVERSITY O F BRITISH COLUMBIA RESEARCH FOREST 75 CONCLUSION 83 L I T E R A T U R E CITED 88 VI ILLUSTRATIONS Figure Page 1 Determination of optimum logging road spacing, after Matthews, 1942 36 2 One quarter of highlead setting, i l l u s t r a -ting geometry of logging "road" calcul-ation 49 3 Logging cost functions: total log cost as related to road spacing (from the highlead logging model) 56 4 Bar graph of logging cost relationships (from Fig. 1): total logging cost against road spacing 57 5 Logging cost functions: total logging cost as related to road spacing (from the high-lead logging model) 58 6 Stand volume and turn volume as related to total logging cost and road spacing ( R = $300 per station) 59 7 Stand volume and turn volume as related to total logging cost and road spacing (R = $700 per station) 60 8 The influence of yarding crew and equip-ment charges, average turn volume, and road spacing on average yarding costs 61 9a Components of fixed cost as related to road spacing (R = $700 per station) 62 9b Components of fixed cost as related to road spacing (R = $300 per station) 63 Hypothetical skyline setting, after Binkley's (1965) example Same area as in Figure 10a, showing highlead settings for cost comparison THE I N F L U E N C E OF CHANGING LOGGING TECHNOLOGY UPON THE ECONOMIC AC C E S S I B I L I T Y O F THE FOREST INTRODUCTION If any definite statement can be made concerning man's way of l i f e , the things that he does, and the ways i n which he does them, it is that these w i l l change. This has been so throughout recorded history, although sometimes the rate of change has been so slow as to be unnoticeable to the people l i v i n g i n a given age. Backward steps have o c c u r r e d f r o m time to time, but on the whole this change has been progressive i n nature, as reflected i n the increasing effectiveness of man's productive* economic, and socia l institutions. Such evolutionary development can be given the general name of "technological change". Dunlop (1962) stated that "technological change, apart f r o m discovery, i s a complex economic and s o c i a l process which i s influenced by a range of decisions, by business enterprises, labor organizations, and workers, national and l o c a l governmental agencies, the educational system, households, and the values and attitudes of the whole community". In the course of technological change old methods are improved upon, or are replaced by newer methods, so as to effect a net' improvement i n the well-being 2 of man. T h i s i s as true of the f i e l d of f o r e s t r y as i t i s of any other facet of human endeavor. Mankind has h i s t o r i c a l l y depended upon the f o r e s t for shelter, protection, food, fuel, and bu i l d i n g m a t e r i a l s . However, with the development of grea t e r knowledge, i m p r o v e d methods of production, and a wider v a r i e t y of goods to s a t i s f y h i s needs, man's r e l a t i o n s h i p to, and use of the f o r e s t has undergone m a r k e d change. These changes have in t u r n effected others a c r o s s the b r o a d s p e c t r u m of f o r e s t r y a c t i v i t i e s , to be evidenced f i n a l l y at the most b a s i c l e v e l of f o r e s t activity, that of logging, or ti m b e r h a r v e s t i n g . It i s w e l l known that today many f o r e s t stands are being p r o f i t a b l y h a r v e s t e d that not long ago were c o n s i d e r e d uneconomic, that i s , they were p r e v i o u s l y " e c o n o m i c a l l y i n a c c e s s i b l e " . Techno-l o g i c a l change has widened the m a r g i n of economic operation through cr e a t i n g demands for goods and raw m a t e r i a l s where p r e v i o u s l y there were none, and through introducing into use many c o s t - r e d u c i n g innovations. The existence of economic l i m i t s to f o r e s t a c c e s s i b i l i t y can b e s t be p i c t u r e d through c o n s i d e r a t i o n of the functional concept of the f o r e s t r e s o u r c e . T h i s e x p r e s s e s the view that f o r e s t s have no p a r t i c u l a r inherent value to man. Rather, to acquire value they must be available for use by man; it must be p o s s i b l e to combine them with other f a c t o r s of production (capital, labor) to create wanted goods, and at a p r i c e that the consumers w i l l w i l l i n g l y pay. Thus, the economic r 3 m a r g i n of operation, c o i n c i d i n g with the functional l i m i t of the f o r e s t r e s o u r c e , i s found where l o g p r i c e s equal t h e i r costs of extraction (which includes a r e t u r n on investment) and the subsequent p r o f i t to the logging e n t e r p r i s e is n i l . The questions a d d r e s s e d i n this thesis c o n c e r n the nature of t e c h n o l o g i c a l change with s p e c i f i c r e f e r e n c e to the logging sector of the industry, and the effect of these changes upon the economic a c c e s s i b i l i t y of the f o r e s t i n t e r m s of log production. Though innovation at e v e r y stage i n the manufacture of f o r e s t products i s important i n this respect, such l i m i t a t i o n of the subject i s n e c e s s a r y to develop adequately the t h e o r e t i c a l background and the r e l a t i o n s h i p s i n v o l v e d i n the f i e l d of logging. Of course, this whole question could be p h r a s e d i n t e r m s of the production of benefits other than wood, for example r e c r e a t i o n , water, and game. U l t i m a t e l y these should be given a place i n the determination of the value of the f o r e s t to society. However, at the p r e s e n t t i m e these other benefits are e x t r e m e l y d i f f i c u l t to measure, and t h e i r i n c l u s i o n would r e s u l t i n a much more i n t r a c t a b l e p r o b l e m than i s faced when only wood production is considered. In the approach to this subject, the b a s i c nature and objectives of the logging operation have f i r s t to be examined, both f r o m a broad, rather p h i l o s o p h i c a l viewpoint and f r o m the p r a c t i c a l l e v e l of the logging operator. T h i s involves a r e v iew of the place of logging, i t s e l f a complex s y s t e m c o m p r i s i n g numerous i n t e r a c t i n g subsystems 4 and v a r i a b l e s , as a component of the much l a r g e r economic and s o c i a l environment. To gain p e r s p e c t i v e with r e s p e c t to the timing, speed, and d i r e c t i o n of tech n o l o g i c a l change i n logging, the major h i s t o r i c a l developments i n logging methods i n Canada are b r i e f l y described, together with t h e i r effects upon the economics of timber h a r v e s t i n g . Two p r i n c i p a l f a c t o rs influence the establishment of the l i m i t of economic a c c e s s i b i l i t y i n the fo r e s t : the value of the logs i n the ma r k e t place, and the cost of getting them there. In o r d e r to estimate the a c c e s s i b i l i t y of a given f o r e s t a r e a or stand, then, i t is n e c e s s a r y to be able to determine the probable total logging costs, per unit volume of logs produced, with reasonable accuracy. Thus, the thesis deals also with the theory, development, and opt i m i z a t i o n of logging cost models, combining the " c l a s s i c a l " approach, where appropriate, with computer s i m u l a t i o n techniques. The study of these models, involving p r i n c i p a l l y the highlead cable yarding s y s t e m common i n coast a l B r i t i s h Columbia, p r o v i d e s c o n s i d e r a b l e i n f o r m a t i o n with r e s -pect to the behaviour of the logging s y s t e m under different conditions. The i n v e s t i g a t i o n furnishes a c e r t a i n degree of insight into the range of a p p l i c a b i l i t y of this system, as w e l l as into the economic effect of some improvements that might a r i s e through t e c h n o l o g i c a l b r e a k -throughs i n highlead y a r d i n g and other potent i a l l y competitive systems, with p a r t i c u l a r r e f e r e n c e to the a c c e s s i b i l i t y of the forest. 5 LOGGING - SOME CONCEPTS "Logging", as most broadly defined, encompasses all the activities of manufacturing logs from the standing tree and the subsequent transportation of those logs from the forest to the "final landing" (Bennet and Winer, 1966). This final landing is usually a transfer point to a major transportation network, such as a booming ground, railway siding, or river bank. Where logs are transported directly from the woods to the conversion plants, the m i l l yard becomes the final landing. The actual transportation of logs may be subdivided into the "primary transport phase", carried out by "skidding", "yarding", or "forwarding" the logs to a primary landing, and the "secondary transport phase", whereby the logs are moved to the final landing. The Emajor transport phase" is the movement of logs from the final landing to the conversion center. Widely varying logging methods have been employed at different times and in different parts of the world. A l l of these, however, can be described in terms of the basic operations outlined above. Each logging method is most suitable under some set of conditions; none is universally practicable. To better understand how 6 each relates to the overall state of logging technology, a simple outline of the evolutionary stages of technology in general is useful. Silver-sides (1964) has aptly related the concepts of Mumford (1934) regarding technological development to the pattern of development exhibited by the logging industry. The earliest stage, labelled the "eotechnic phase", constitutes the period during which only simple tools are available, manipulated by human hands and energy, and aided by animal power where possible. The next stage, the "paleotechnic phase", is characterized by the direct substitution of mechanical power for human and animal energy, but with little basic change in methods. Finally, the "neotechnic phase" is the stage of mechanization, where advanced machines operated by skilled workers perform a well controlled industrial process. It is readily appreciated that logging is, in most major wood producing areas of the world, well into the paleo-technic and - notably in eastern Canada - rapidly entering the neotechnic stage. Scott (T962) expressed these fundamental ideas within the context of the stagesoof development observable in the forestry sector of the economy. The "primitive stage"; by his terminology, is characterized by the exploitation and use of whatever timber is available, employing a high proportion of unspecialized labor and little capital. The "capital intensive stage" is a period of improving tech-nology during which markets and institutional organizations are rapidly 7 developed. It is still distinguished, however, by the essentially exploitive use of a naturally provided resource, even though the scale and methods of operation have greatly changed. The third stage, the "controlled stage", is attained when the source of supply has been brought under control, and natural processes are moulded to suit man's needs. While Scott's concepts are not exactly parallel to those of Silver sides with regard to technological development - Scott spoke of the forest industry as a whole, while Silversides was concerned mainly with the logging sector - it is evident that their thoughts have followed the same general trend. They both dealt with the nature of technological change, its direction and goals, and the impact of these factors on the way in which forests are managed, harvested, and utilized. The factors responsible for such change, and the effects these changes produce, are of utmost concern to all engaged in the logging industry. Mechanization, the replacement of animal and human effort by mechanical effort, must be distinguished from automation, which is considered to exist when sophisticated controls actually make decisions, and feed these decisions back so as to automatically regulate the operation (Silversides, 1964). However, it must be recognized that both mechanization and automation are manifestations of techno-logical change. Even where total mechanization has been introduced, this is s t i l l far from being an automated system. Silversides (1966 b) 8 stated that total mechanization in logging is considered to exist when a standing tree can be harvested and delivered to the mill "untouched by human hands or hand tools". The introduction of mechanization to logging represents a true innovation, that is, a purposeful, directed, and organized change (Bennet and Winer, 1966). Innovation follows creative invention and is the process of bringing the invention into commercial use. Diffusion refers to the spread of the innovation throughout the industry. The term innovation as used in this context and in this thesis, then, must be distinguished from the broader concept of innovation as understood by the economist. Schumpeter (1961) expressed the view, for example, that innovation comprises five distinct cases: i ) the introduction of a new good, or a new quality of good; ii) the introduction of a new method of production, not necessarily founded on a scienti-fically new discovery; iii) the opening of a new market; iv) the conquest of a new source of supply of raw materials; and v) the re -organization of the corporate structure of an industry. In other words, innovation can be anything which acts to increase productive efficiency. Of the five areas of innovation cited, a segment of the second case is of prime concern to this study. That is, we are interested in changes in the methods of production, specifically those which are "embodied" changes, utilizing fundamentally new mechanical discov-eries and processes. 9 Distinct differences exi st between the economic character-istics of labor intensive logging operations and mechanized, capital intensive ones. These arise primarily through the differences in the relative levels of fixed versus variable (or direct) costs. A logging method utilizing a high proportion of labor has relatively greater variable costs than does the more mechanized system. However the capital costs (or indirect costs) of the former are relatively lower. For these reasons, labor intensive systems are said to be flexible, although they maybe inefficient (Silversides, 1966 a; Bennet and Winer, 1966). That is, the cost of the operation will fall nearly proportionally to decreases in output, which could be necessitated by poor market conditions, for example. A mechanized system, on the other hand, is more rigid, being unable to expand or contract rapidly with changing economic conditions. Since the greatest proportion of the total cost is independent of the level of production, costs per unit of output can rise significantly if the output level drops in response to market signals. In spite of this problematic cost characteristic, mechanization of logging affords the only possibility of achieving" significant reduc-tions in the overall cost of production. Labor intensive operations do not allow for any major reductions in cost, as output is controlled by the capacity of human energy and this imposes definite limitations on improvement (Silversides, 1966 a). LOGGING AS A SYSTEM A) The Characteristics of Systems A system is a set of objects, together with the relationships between those objects and their attributes (McMillan and Gonzalez, 1965). Objects can include any concrete or abstract entities imaginable, which are described by their so-called attributes. The relationships existing between the various entities and their attributes unify the whole into a meaningful system. The system environment is the set of all external objects which can affect, and be affected by, the system if a change in attributes occurs. For the purposes of this thesis, the concept of the system can be limited to those that are man made (but which involve interaction with natural systems) and that are under the conscious control of men, directed toward the achievement of some specified human goal. The description of a system requires specification of several points: 1. the nature of the inputs; 2. the nature of the outputs; 11 3. the s y s t e m "phase space", or the total of a l l conditions the s y s t e m can assume; 4. a d e s c r i p t i v e model r e l a t i n g inputs, outputs, and the s y s t e m states i n time ( E l l i s and Ludwig, 1962). S y s t e m a n a l y s i s involves studying the system, its objectives, and the a r r a y of p o s s i b l e configurations i t can assume. E c k m a n (1961) s u m m a r i z e d the steps involved: 1. define the problem, and s y s t e m objectives; 2. define the s y s t e m environment; 3. define the subsystems, or components of the m a i n system; 4. analyse the subsystems us i n g appropriate techniques; 5. study and define the i n t e r - r e l a t i o n s h i p s between sub-systems. B) Logging, f r o m the Systems Viewpoint C o m p a r i s o n of the above c h a r a c t e r i s t i c s of systems i n general to the known r e a l i t i e s of logging operations r e v e a l s that logging i s , indeed, a system, and a complex one. To follow Eckman's (1961) p r o c e d u r e of analysis, the objective may f i r s t be defined as the manufacture and t r a n s p o r t of logs f r o m the f o r e s t to the f i n a l landing, i n such a manner as to i n c u r the l e a s t p o s s i b l e total cost per unit volume of wood harvested, and at the same time comply with r e s t r i c -tions r e g a r d i n g the size, condition, and quantity of logs i m p o s e d by the e s t a b l i s h e d u t i l i z a t i o n f a c i l i t i e s . These r e s t r i c t i o n s f o r m one p a r t of the logging system environment, which is an extremely complex hierarchy comprising such influences as government policy and law, social conditions and attitudes, the overall economic climate, and specifically the markets for forest products (Cottell, 1967c). Forestry as a whole, of which logging is one subsystem, is a large and compli-cated system composed of both natural and man-made sectors (Seale, 1966). It functions to combine forest resources and others, trans-forming them into goods and services with the attendant creation or enhancement of utility. Turning to the subsystems of logging activity, these convention-ally include: 1. construction of access routes and log landing such as necessary to enable logging to continue; 2. felling of the trees; 3. topping, branching, and cutting the trees into suitable log lengths; 4. skidding, yarding, or otherwise forwarding logs to a primary landing (primary transport); 5. loading the logs, or otherwise embarking them upon the secondary transport phase; 6. unloading at the final landing; These functions may be performed in many different ways, and, especially with the more modern mechanized procedures, may be carried out in a different order from that shown above. 13 Each of these subsystems, though a definable work and cost component of the whole chain of logging activity, is dependent in some way upon one or more of the others. The specific subsystem inter-relationships vary widely depending upon the logging system design employed. A system design is a specific ordering of men, materials, equipment, and methods for attaining the stated objective; for example in coastal British Columbia highlead logging with portable steel spars, together with truck transport of logs, is the most common present design of the logging system. Logging is characteristically affected by many variables, the more important of which are not usually amenable to the direct influence of man. The following is a l i s t of the most significant variables requiring consideration. 1. Physical environment: a) terrain factors - slope - roughness - soil moisture - elevation b) climatic factors - precipitation: amount, form, and distribution - temperature: extremes of heat and cold c) location, affecting distance of transport 2. Forest stand: a) tree size: diameter, height, volume, and weight b) stand density c) proportion of cull 3. Economic factors: a) products required, and log form arising from this b) type and cost of equipment and labor. These factors all contribute to the determination of the input-output functions specific to any given logging system design. The precise relationships, however, may vary widely from place to place and from day to day. C) Tools for Systems Analysis in Logging Reliable estimates of the relationships within a given logging operation must be established before meaningful analysis of the system can proceed. Several powerful, and relatively new, tools are available to aid in this task. Lussier (19 59) has shown how this may be accomplished through the application of the methods of "Forest Operations Research" (FOR), a scientific method by which manage-ment problems of forest exploitation are defined, and solved in an optimum manner. This involves the collection of data for production control in logging through sampling of operations and the statistical evaluation of the results. If a large enough sample is obtained, such as will achieve statistical stability of the observed data, a mathe-matical model for the specific set of operating conditions - and the inherent variability of the operation - can be defined. In this way 15 the relationships can be established between variables within sub-systems, and between the subsystems themselves, as required for the system analysis. The techniques which form the basis for the data collection procedures have been recently analyzed and reported by Pfeiffer (1967). Modeling, another important tool of systems analysis, has been defined by Chestnut (1965) as the representation of a system or part thereof in a mathematical or physical form suitable for demon-strating the way in which the system behaves. Modeling has been used by Matthews (1942) and later by Lussier (1961) in the planning of logging operations. Modeling can be advantageously combined with simulation, whereby varying inputs and environmental situations are introduced so as to explore the model's reactions under different conditions. This is usually done in conjunction with the use of computers, and Lussier (1963) has demonstrated how this can be applied to logging situations. Some of the hazards to be avoided in the use of logging models, such as poorly defined terminology and statistical units, and projection of a model beyond the limits for which it was originally designed, have been described by Lussier (1965). There are several other techniques that have been found useful in the analysis of logging problems. Two of the most important of these are mentioned briefly here, although they are not further expanded in this thesis. Dane (1965) and Donnelly (1967) have demonstrated applications of statistical decision theory to the problems of logging and forest engineering. This procedure is used to help make rational decisions in the face of risk and uncertainty, where the problem can only be phrased in statistical terms. Applications of linear programming (LP) in the field of logging have been described at several different conceptual levels of operation. Briefly stated, L P is a mathematical technique for determining the most efficient allocation of scarce resources to competing '.demands, where the system relationships can be expressed in terms of linear equations, inequalities, and restraints. Smith and H a r r e l l (1961) showed how L P could be used in determining optimum log making practise. Lussier (1961) presented an application of the L P technique in the maximization of logging profits under conditions of varying timbe type and associated machine productivity. The integration of various logging subsystems with the overall forest management problem has been discussed by Donnelly (1963) and Winer and Donnelly (1963), who particularly stressed the value of L P in helping to organize information, and in providing a basis for greater understanding and exploration of policies and objectives. More locally, Valg (1962) has applied L P to the determination of the economically marginal tree size at the University of British Columbia Research Forest. Pearse and Sydneysmith (1966) have demonstrated optimum log allocation procedures through L P for distributing raw materials to conversion plants, with a specific example involving the British Columbia coastal log supply for the year 1962. A modification of their model could b used to determine the individual contribution of various types of log to the total profit of a f i r m or industry. Dobie (1966) employed L P techniques to determine maximum conversion returns per acre at the UBC Research Forest, by achieving most efficient allocation of logs to conversion processes. 18 T H E D E V E L O P M E N T OF LOGGLNG TECHNOLOGY IN CANADA The following discussion is by no means intended as a comprehensive historical treatment of the many technological develop-ments that have occurred in logging. Rather, the emphasis has been placed upon describing the most significant and far-reaching of these innovations, and their impact on the established patterns of timber harvesting. Particularly, the period between innovation and wide-spread industry acceptance has been stressed in this discussion so as to gain an impression of the pace of technological change over the long term. The limitations of each logging system or subsystem, and the ways in which these were overcome by subsequent developments are of primary importance in understanding the reasons and incen-tives for invention and innovation in the industry. A) Tree Felling and Cutting The major events in the development of methods for felling and cutting timber have been documented by Silversides (1966 b). An ever increasing rate of change is shown in the analysis of the tools available: the crosscut saw replaced the axe within 50 years of its innovation, the bucksaw replaced the crosscut over a period of about 45 years, the power saw took the place of the bucksaw within 30 years of its innovation, and the mechanical shear of the processing machine is now replacing the power saw in many eastern Canadian operations. This last development marks the emergence of the neotechnic phase in the performance of the tree cutting function. British Columbia is just now verging upon entering this neotechnic phase with certain experimental operations in second growth coastal timber, where mechanical falling shears are being investigated (Anonymous, 1967). B) Primary Transport of Timber In the primary transport of timber, a pattern of development similar to that of the timber cutting operation is evident, although it is considerably more complicated because of the multitude of methods that have been devised, and because of the differences in logging system requirements and suitability between forest regions. 1) Tractive Systems Animal power, including oxen and mules and, most commonly, horses, has been widely used in the past for skidding. Even today an estimated 2, 500 horses are being used in logging in eastern Canada, although animal power has been replaced rapidly there over the past 10 to 12 years by the wheeled skidder (Silversides, 1966 b). The severe limitations of the level of sustainable animal and human effort, and their rapidly decreasing efficiency with increasing skidding distan were the prime reasons for this substitution. The first wheeled skidder introduced in the east in 1954, was little more than a four wheel drive truck. Five years later, in 1959, the first model of the rubber-tired articulated frame wheeled skidder was produced. Its diffusion throughout the industry is now essentially complete, after a period of only 10 to 13 years since its innovation. Its use in logging has enabled increases in man-day productivity, reduction of the total labor requirement of the industry, and reduction of the costs of wood procurement. It has lent a much greater degree of flexibility to the planning of operations with respect to such factors as terrain conditions, brush and ground cover, ground moisture, weather, and skidding distance (Bartholomew, Bennett, and Winer, 1965). A l l three of the basic mechanized logging systems as currently conceived depend upon machines of this type, as will be discussed in part 3 below. The use of track-type tractors in the woods on a large scale did not occur until ::just after the F i r s t World War. P r i o r to that time, steam powered wheeled tractors had been used as early as 1893 in California (Brown, 1936). With the development of tracks (1904) and the replacement of steam by gasoline and diesel power, the tractor rapidly became a successful logging innovation. The development of the Fairlead arch and winch (1928) eliminated the necessity for bunching the logs for the tractor, with the resultant displacement of the remaining horses that had been used for that purpose. Tractors also replaced cable yarding and skidding systems where gentle topo-21 graphy favored their use. The advantages displayed by the tractor as compared to animal skidding include greatly improved speed and power, ability to work on steeper grades and rougher and wetter topo-graphy, and efficient operation over considerably greater skidding distances. Tractors have been in common use in Br i t i s h Columbia both in coastal and interior operations, although they are more pre-dominant in the latter. The smaller tree sizes and easier topography of the interior favor the use of tractors over cable systems because a more optimum turn size may be easily assembled for the tractor, whereas cable yarding is largely limited as to number of pieces that can be handled per turn. The past 10 years has seen considerable replacement of tractors by the faster, more mobile, and less costly wheeled skidder in the interior and in second growth operations on the coast. 2) Cable Systems In western Canada, the widespread replacement of animal power by steam powered cable systems occurred just prior to, and during,the early part of the twentieth century. F r o m the time of their earliest introduction to the woods in California in 1881, steam powered cable yarding methods rapidly evolved in British Columbia and in the United States, from the simple groundlead to highlead (c. 1905), slackline skidder (1909), and skyline (1914) systems (Bryant, 1923; 22 Brown, 1936; Andrews, 1956). The great size and weight of the logs in the Pacific region, together with the ever increasing distances of transport required provided the incentives for this development. Cable systems offer important advantages over other methods of logging. During operation the power unit remains stationary, thus freeing the system from the influence of ground conditions, and enabling the use of large, highly powered equipment. This in turn allows for greatly increased effective yarding effort, and greater speed of log movement. Adverse slopes are not a limiting factor, since the same power can be transmitted through the cable regardless of whether yarding is uphill or downhill - a major advantage over tractive systems. Some of the disadvantages of cable yarding are: the high fixed costs of equipment, rigging up and moving spars, and changing lines during yarding; requirement of large amounts of skilled and costly labor; and the limitations to efficient yarding distance because of decreasing lift angle (highlead) or excessive line deflection (skyline systems). Recent improvements in cable yarding have included increased yarding engine power, and a reduction in labor requirements and fixed costs through the introduction of the portable steel spar. The diffusion of the steel spar throughout the industry in the Pacific region has covered some 15 years, enabling lowered total logging costs and increasing the supplies of timber available for profitable exploi-tation. For short distance yarding on the coast of British Columbia, 23 special "snorkel" (extension) attachments and log grapples on power shovels and loaders are being widely used. These are especially economical for right-of-way pickup along the sides of newly constructed roads, where the logs can be windrowed or loaded directly onto trucks (Spiers, 1956). The balloon yarding system, which is basically a cable yarding system where the lifting force is always located directly above the load must sti l l be considered to be in the stage of active development, since many of the obstacles have yet to be overcome (Lysons et al. , 1966). It offers promise, however, for application on the Pacific coast because of the aforementioned lifting characteristic and the resultant potentially great yarding distance and speed (Anon. , 1966). Although capital costs would be high, the possibilities for increases in productivity, and reductions in fixed costs and road building costs per unit volume of logs produced are significant. Cable systems have never been used to a great extent in eastern Canada, partly because of the easier terrain, but mostly because of the small size of the material to be handled which greatly curtails productivity in cable yarding. A e r i a l logging with helicopters has been experimented with in recent years, but a satisfactory system has not yet been devised. The high capital and operating costs would have to be offset by rapidly transporting large numbers of maximum payloads from areas inaccessi-ble by road. Difficulties in estimating optimum load sizes, corres-ponding to their lift capability, and in machine reliability, safety, and weather dependence have so far precluded the use of helicopters. 3) Mechanized Systems It has been stated that the neotechnical phase of logging development is entered when men no longer are working on the ground, performing hand labor. It is the phase of total mechanization of operations, from the stump to the final landing. An intermediate stage of partially mechanized logging commonly occurs during the transition period. Three principal mechanized logging systems have evolved in eastern Canada: the shortwood system, the tree length system, and the full tree system (Silversides, 1964). Without going into the specific descriptions of the equipment used, the basic operational characteristics of each of these are discussed below. a) The Shortwood System This method consists of processing trees into bolts of uniform length at the stump area and transporting or forwarding the processed wood to the truck road (Bell, 1965). The partially mechanized system requires manual cutting and piling of the bolts, the forwarding being carried out by tractor or wheeled skidder. If fully mechanized, two machines are employed in the system: a stump area processor and a self-loading forwarder. According to Bell (1965) the basic design requirements for the latter system are: 25 - high mobility off-road vehicles - forwarder: . . efficient self loader system . . large payload capacity - processor: . . tree cutting boom, with long reach multi-function capacity (semi-automatic) . . accumulating capacity for processed wood - continuous year-round operation, day and night - machines operate independently of one another. Cross (1965) has pointed out that the factors which would govern the applicability of a given mechanized logging system are: terrain and stand characteristics, labor cost and availability, equipment cost and availability, and the cutting and delivery method (form of product) in use. Of these the labor requirement is the most important with respect to the decision between partial and total mechanization. The chief limitation of the shortwood system is its relatively high labor content, except in its ultimately mechanized form. Low density stands, scattered mixed wood stands, and selective cut systems would mitigate against the shortwood method. b) The Tree Length System With this method, trees are felled, limbed, topped, and possibly barked at the stump before being forwarded to a haul road (Silversides, 1964). Under partial mechanization the work at the stump, and generally bucking and piling at the landing, are done manually, while skidding is done by machine. Total mechanization employs two, or possibly three machines: the stump processor, the forwarding vehicle, and perhaps a machine at the landing to slash to length and pile. The major limitations at present include the difficulty of efficiently gathering an optimum skidder load of tree lengths, and the restriction of the processor to operation on slopes not greater than 15% to 20%. Stand density and tree size again constitute the main determining factors in the economy of the operation, the former influencing primarily the productivity of the skidder, and the latter influencing mainly the productivity of the stump area processor (Dibblee, 1965). Requirements of the processor emphasize good off-road mobility, low ground pressure, and high ground clearance. c) The F u l l Tree System Full tree logging involves the transportation of the entire tree, comprising bole, top, and limbs from the stump to a landing where it is processed into logs or chips (Horncastle, 1965). Although the method is in an early stage of development, its use is likely to be favored where: - rough terrain would impede a processing unit - trees are particularly small and a low processing time per tree is necessary - partial cutting is necessary - roadside barking is desirable - slash removal as a silvicultural or fire preventive step is necessary - logging residues maybe used for byproducts. Some form of high capacity roadside processor is required, together with a feller-skidder in the fully mechanized version of the system, or manual falling with chain saws followed by machine forwarding where it is partially mechanized. Mechanical reliability is the most pressing current problem with this system, whereas its greatest single advantage is that a wide variety of felling and skidding technique and equipment can be employed to contend with the wide variety of natural conditions in the forest (Hamilton, 1965). d) The Complete Tree System Although the complete tree system does not presently exist, it is possible that the world's future demand for wood fiber will bring about its development (Young, 1966). For this logging method a mobile complete tree harvester would be required. Such a device would remove the tree from the earth, eliminate the soil and stones from the roots, and reduce the tree (save for the small branches and small roots) to chips. The chips would then be moved directly to the m i l l . The assessment of the economic feasibility of such a procedure is beyond the capabilities of current knowledge. However, the concept does serve as a reminder to those who would claim that logging techniques are already approaching their greatest possible refinement, that, in actuality, the ultimate still lies far beyond present abilities and technology. C) Secondary and Major Transport of Timber In the area of secondary and major log transport methods progress and innovation have kept pace with, and complimented, developments in the primary phase of logging. Railroad logging developed, in the West, concurrently with cable yarding systems, and together they enabled huge tracts of timber to be made accessible that had earlier been considered to be beyond economic reach. Though fixed costs were high, the railroads provided economical transpor-tation where the volume of logs to be hauled was great, and where relatively long hauling distances were involved. They were especially suited for combination with the far reaching skyline systems, which could log huge areas from one spur line. In the 1930's, however, the improvements that had taken place in truck logging, the increasing scarcity of high volume valley-bottom stands, and the increasing cost of r a i l line construction as operations moved into more difficult terrain marked the waning of the railroad era. Truck transport of logs offered greater flexibility of operation with respect to slopes and stand volumes, and lower investment costs for both equipment 29 and the construction of transportation arteries. Such innovations as pre-load trailers, t rpup u trailers, fast, mobile loading machines, and self-loading pulpwood trucks have also contributed to flexibility of operations and reduction of costs. Logging became feasible in stands of smaller volume, where terrain conditions would rule out any possibility of economical railroad operation. There are st i l l a few logging railroads in use; however, where the major investments had been made prior to the widespread introduction of truck logging, and where it has since been possible to convert them to provide a main transport function. In road construction important improvements have occurred to reduce the costs of providing transport facilities. Powerful shovels and tractors are in use in subgrade construction; rockdrilling has become more efficient with the introduction of track mounted self-propelled d r i l l rigs; and the development of explosives of low cost has further decreased the expense of rock work in the increasingly rough terrain. These improvements work to reduce the cost burden of road Building, thereby extending the limits of timber accessibility. Water has long been important in both the secondary and main transportation phases in logging. In eastern Canada, stream driving is sti l l a major method of moving logs from the woods, although truck transport has made substantial inroads recently. According to McNally (1963) over 85% of the pulpwood logged in e a s t e r n C a n a d a i s m o v e d at l e a s t s o m e p a r t o f t h e d i s t a n c e t o t h e m i l l b y t r u c k . P r o b l e m s o f h i g h l a b o r i n p u t , s i n k a g e l o s s , d e p e n d e n c u p o n s e a s o n a l a n d w e a t h e r f a c t o r s , t h e f i n a n c i a l b u r d e n o f h o l d i n g l a r g e i n v e n t o r i e s o f w o o d w h i l e w a i t i n g f o r t h e r i v e r o r s t r e a m to b e c o m e d r i v e a b l e , a n d t h e d e m a n d f o r c l e a n f r e s h w o o d h a v e w e i g h e d h e a v i l y a g a i n s t t h e s t r e a m d r i v e . R a f t i n g h a s a l w a y s b e e n i m p o r t a n t a l o n g t h e P a c i f i c c o a s t , p r o v i d i n g i n e x p e n s i v e m o v e m e n t o f l o g s f o r c o n s i d e r a b l e d i s t a n c e s . O v e r t h e p a s t 10 y e a r s l o g b a r g e s - s e l f l o a d i n g a n d s e l f - d u m p i n g -h a v e r e v o l u t i o n i z e d l o n g d i s t a n c e t r a n s p o r t i n t h i s r e g i o n b y p r o v i d i n g g r e a t e r s p e e d , r e d u c i n g l a b o r i n p u t r e q u i r e m e n t s , a n d b y d e c r e a s i n g t h e r i s k o f l o s s . R a f t i n g i s s t i l l t h e m o s t c o m m o n l y u s e d m e t h o d o f m o v i n g l o g s i n t h e q u i e t e r w a t e r s , a n d w h e r e t h e t r a n s p o r t d i s t a n c e i s n o t g r e a t e n o u g h t o j u s t i f y t h e e x p e n s e o f l o a d i n g o n t o b a r g e s . A l t h o u g h d i s c u s s i o n o f t h e u s e o f p i p e l i n e s g o e s s o m e w h a t b e y o n d t h e t o p i c o f l o g g i n g , a b r i e f m e n t i o n o f t h i s m e t h o d o f w o o d t r a n s p o r t i s p e r h a p s a p p r o p r i a t e . T h e s e a r e i n a s t a g e o f a d v a n c e d t e c h n o l o g i c a l d e v e l o p m e n t , a n d a c t i v e i n n o v a t i o n i s c u r r e n t l y t a k i n g p l a c e . T h e e c o n o m i c a c c e s s i b i l i t y o f f o r e s t s o n s i t e s f a r f r o m e x i s t i n g m i l l s m u s t b e g r e a t l y e x p a n d e d b y t h i s d e v e l o p m e n t t h r o u g h t h e r e d u c t i o n o f o v e r a l l t r a n s p o r t a t i o n c o s t s , e l i m i n a t i o n o f t h e n e e d f o r l o g s t o r a g e a n d i n v e n t o r y , a n d l i b e r a t i o n o f t h e o p e r a t i o n f r o m t h e r e s t r i c t i o n s o f w e a t h e r a n d t e r r a i n ( T h i e s m e y e r , 1964). D) Technological Change and Timber Accessibility The foregoing discussion has indicated something of the nature and pace of technological development in the logging industry. Predominant trends of these changes have included the reduction of overall labor input, but with an attendant increase in skill require-ments, the movement toward heavier capital investment in machinery of all types, and the increased rate of acceptance of new methods and equipment. The prime incentive for this has been the wish to increase profits through reducing the costs of production. Meanwhile, continued logging in the virgin stands of high quality timber, close to population centers and conversion facilities, has continued apace with the result that loggers have had to go ever farther away to obtain timber supplies of ever decreasing quality. Technological improvement thus performs two related functions at the same time; profits on current-ly accessible timber are increased (an economic "rent"), and reduced costs of operation make it attractive to utilize stands of lower quality or requiring greater distance of transport, that were uneconomic before. The economic margin of operation depends upon many factors which go to make up the overall profitability of the logging enterprise, e. g. the market price for logs of various species and quality, the distance, mode, and resultant cost of transport, terrain factors influencing the cost of access route construction,and stand factors i n f l u e n c i n g l o g g i n g p r o d u c t i o n . B e c a u s e o f t h e v a r i a b i l i t y o f t h e s e f a c t o r s a c c e s s i b i l i t y c a n o n l y b e a c c u r a t e l y j u d g e d o n a s t a n d b y s t a n d b a s i s , a n d i n r e l a t i v e t e r m s w i t h r e s p e c t t o t i m e , e c o n o m i c c o n d i t i o n s , a n d t h e e x i s t e n t l e v e l o f t e c h n o l o g y . 33 DEVELOPING MATHEMATICAL MODELS OF LOGGING SYSTEMS A) The Need for Models in Logging If logging managers are to understand the factors influencing the productivity of the logging phase of woods operations, and control them in such a way as to maximize overall efficiency, an appreciation of the working of the entire system is required. The complexity of the real situation necessitates the use of simplified mathematical models which can incorporate the most significant variables and relationships influencing the system behaviour. Some of these variables are probabilistic, or stochastic in nature, being subject to random influences. Others are deterministic, capable of precise definition and analysis. Both types can be included in the model, using regression techniques or mathematical expressions. For different methods of logging, the approach to the task of model construction must, of course, differ also. As an example, the necessity of integrating the operations of timber felling and cutting with skidding is much greater if a totally mechanized system is being used than where a cable system is in use, because the interdepen-dency between these two subfunctions in logging is very pronounced in the former system, but is of lesser significance in the latter. Accordingly, the following discussion of the development of logging systems may require modification here and there to take account of such dissimilarities. B) Theoretical Bases for Logging Model Development 1) Simple Mathematical Models An early application of mathematical modeling to logging was performed by Matthews (1942), in which he approached the problem of optimizing (minimizing) the cost of logs, per unit volume, delivered at the primary landing considering the total of skidding costs and road construction costs. This, in effect, reduced to a problem of determining the optimum road spacing and landing spacing combination for the particular set of cost schedules, stand volumes, and produc-tivity functions involved. Skidding costs (Matthews was concerned with horse and tractor skidding) were assumed to vary in a linear way with skidding distance, being equal to zero at zero distance. Road construction costs per unit volume, however, were pictured as declining with increasing skidding distance, since these fixed costs could be applied to increasingly larger volumes of timber. These relationships are shown in Figure 1. On the basis of an empirical example, Matthews concluded that the road spacing which corresponded to the lowest overall total cost was found at the intersection of the two cost curves. The optimum spacing of roads is thus seen to be dependent primarily upon stand volume per unit area, road cost per unit of lineal distance, and skidding cost per unit volume, per unit of distance that it isskidded. Mathematically, Matthews expressed this by: A T C = AVC + A F C C S + 1. K 1 V S where: A T C average total cost, per unit volume of logs, of skidding and road construction; AVC = average variable cost, per unit volume of logs, A F C = average fixed cost, per unit volume of logs, representing the shared road construction cost C = variable cost of skidding, e. g. $ /100 cubic feet ( C C F ) / 1 0 0 foot station (sta.); S = road spacing, e. g. in sta. ; R = road construction cost, e.g. $/sta. ; V = stand volume, e.g. CCF/acre; D = average skidding distance, e. g. sta. ; = the ratio S/D, which varies to take account of the presence or absence of central landings, and the distance between them; K = a constant conversion factor for area units, representing primary transport cost; 2 e. g. K ? = 4. 356 sta. /acre. 34 o Skidding Distance or Road Spacing D = f ( S ) Figure 1. Determination of optimum logging road spacing, after Matthews, 1942 Figure 1 states that at the optimum road spacing: C S -K 1 V S or S = C V Z. The value S represents the road spacing which will result in the lowest total cost of wood at the primary landing under the foregoing assumptions. A similar analysis was done by McNally (1963) with respect to more mechanized systems. because of the underlying assumptions that the skidding cost function is linear, and that it goes through the origin. That is, Matthews has neglected the fixed costs in the skidding function, which must, of course, appear somewhere in the total cost equation (1). Lussier proposed an alternative solution in which he replaced the value C in the Matthews formula with a skidding function of the form: Lussier (1961; 1965) has criticized this solution, primarily Y = a + bD and so C = Y (T) where Y = average skidding cycle time, determined by operations research methods, a and b being 3 8 r e g r e s s i o n c o e f f i c i e n t s ; D = a v e r a g e s k i d d i n g d i s t a n c e ; T = c o s t o f s k i d d i n g c r e w a n d e q u i p m e n t p e r u n i t t i m e ; C = a v e r a g e s k i d d i n g c o s t , e.g. $ / C C F . F r o m t h i s i t c a n b e s e e n t h a t C i s i t s e l f a f u n c t i o n o f D a n d t h e r e f o r e o f S, t h e r o a d s p a c i n g . T h e o p t i m a l a n s w e r f o r S m u s t t h e r e f o r e b e o b t a i n e d t h r o u g h i t e r a t i v e s o l u t i o n a n d s e l e c t i o n o f t h e b e s t r e s u l t , as a d v o c a t e d b y L u s s i e r ( 1 9 6 1 ) . H o w e v e r , L u s s i e r d o e s n o t go t o t h e b a s i c f a u l t o f M a t t h e w s ' a n a l y s i s , a l t h o u g h h e c i r c u m v e n t s i t . T o do t h i s , t h e t r u t h o f M a t t h e w s ' m o s t b a s i c a s s u m p t i o n m u s t b e c h a l l e n g e d . T h a t i s , d o e s t h e m i n i m u m t o t a l c o s t a c t u a l l y o c c u r a t s u c h a r o a d s p a c i n g t h a t v a r i a b l e s k i d d i n g c o s t , a n d f i x e d r o a d c o s t , p e r u n i t v o l u m e o f l o g s p r o d u c e d , a r e e q u a l ? A c o n s i d e r a t i o n o f s o m e o f t h e p r i n c i p l e s o f e c o n o m i c s i n d i c a t e s t h a t i t i s n o t . O n e o f t h e b a s i c t e n e t s o f e c o n o m -i c s s t a t e s t h a t f o r e f f i c i e n t r e s o u r c e a l l o c a t i o n ( i n t h i s p r o b l e m t h e p r o p o r t i o n a t e a l l o c a t i o n o f d o l l a r i n p u t s t o s k i d d i n g a n d r o a d c o n s t r u c t i o n ) t h e v a l u e o f t h e m a r g i n a l r e t u r n f r o m e a c h i n p u t m u s t b e e q u a l . T h a t i s , t h e r e t u r n f r o m t h e l a s t u n i t o f s k i d d i n g i n p u t m u s t e q u a l t h e r e t u r n f r o m t h e l a s t u n i t o f r o a d c o n s t r u c t i o n i n p u t . I n o t h e r w o r d s , a t t h e o p t i m u m c o m b i n a t i o n o f t h e two, t h e r a t e o f c h a n g e o f s k i d d i n g c o s t w o u l d b e e q u a l t o t h e r a t e o f c h a n g e o f r o a d c o s t , p e r u n i t v o l u m e o f l o g s . I n t e r m s o f F i g u r e 1, t h i s m e a n s t h a t t h e o p t i m u m c o m b i n a t i o n o f s k i d d i n g c o s t s a n d r o a d c o s t s o c c u r s w h e r e t h e s l o p e s o f t h e t w o cost curves are opposite but equal, a condition which has no particular relationship to their point of intersection. Although this concept has never, to the author's knowledge, found its way into the forestry literature of road spacing, it was mentioned as early as 1917 by Williams, in a discussion of the economics of railroad construction. A general solution using simple calculus supports this view: let x = road spacing (S) AVC = f (x) A F C = f (x) A T C = y = AVC + A F C or y=f1 (x) + f 2 (x) dy dx dy where average total cost is minimum, _ dx therefore 0 = f' + f ' 1 -* and - f 1 = + f i 1 2 Therefore, at minimum average total cost, the first derivative of average variable cost is equal to that of average fixed cost, but is opposite in sign. The slopes of the cost curves are equal, in absolute terms, at that point. 40 It would appear that this finding invalidates the theoretical basis of Matthews' logging cost analysis. Also, Lussier's objection based on the fact that the function does not go through the origin is not a wholly correct criticism. Only the relative slopes of the variable and fixed cost curves are relevant to the analysis, inter-section points or 'a' constants are not. This will become clearer after an examination of the results of experiments with the models developed in a later section of this thesis. Mention is also made here of Matthews' (1942) treatment of logging road standards through the use of another simple mathematical model. The road standard is an expression of the quality of the road with respect to ease and speed of movement of vehicular traffic. Lower standards are characterized by low investment in construction, but high log hauling costs because only slow truck speeds are possible. Higher standards, on the other hand, are more costly to construct, but provide for higher operating speeds and reduced maintenance costs, thus decreasing the cost of the hauling phase. At some road standard there is a "break even" point in costs, under the given set of conditions which include the total wood volume to be hauled over the road, the relative levels of hauling and construction costs for the different standards, and the haul distance involved. Larsson (1965) discussed the interaction between road standards and optimum road spacing, a feature which necessitates an iterative solution method to a r r i v e at an o p t i m a l a n s w e r f o r t h e o v e r a l l t r a n s p o r t a t i o n s y s t e m . T h a t i s , f o r e a c h s p e c i f i e d r o a d s t a n d a r d t h e r e i s a n o p t i m u m s p a c i n o f r o a d s , o f w h i c h s o m e o n e c o m b i n a t i o n w i l l r e s u l t i n m a x i m u m o v e r a l l e c o n o m y . C o m p u t e r m e t h o d s a r e q u i t e o b v i o u s l y i n d i c a t e d f o r t h i s t a s k , a p r o j e c t i n w h i c h L a r s s o n ( 1 9 6 5 ) h a s r e p o r t e d t o b e c u r r e n t l y e n g a g e d . T h e m a j o r d i f f i c u l t y w i t h a t t e m p t i n g s u c h a n a l y s e i n B r i t i s h C o l u m b i a ; a t t h e p r e s e n t t i m e i s t h e l a c k o f f a c t u a l d a t a r e g a r d i n g t h e e f f e c t o f c h a n g i n g r o a d s t a n d a r d s o n l o g h a u l i n g c o s t s , a n d w h a t r e s u l t a n t s a v i n g s m i g h t b e a c h i e v e d . R e s e a r c h i n t o t h e s e r e l a t i o n s h i p s w o u l d p r o v i d e v a l u a b l e i n f o r m a t i o n n e c e s s a r y t o t h e i m p r o v e m e n t o f l o g g i n g p l a n n i n g , e s p e c i a l l y f o r a l o g g i n g c o m p a n y w h i c h d o e s i t s o w n t r u c k i n g . 2 ) C o m p u t e r O r i e n t e d M o d e l s C a r e f u l s t u d y o f t h e p r o b l e m o f c o n s t r u c t i n g m o d e l s o f t h e l o g g i n g s y s t e m a d e q u a t e f o r u s e i n p l a n n i n g o p e r a t i o n s a n d i n d e t e r m i n i n g t h e e c o n o m i c l i m i t s o f t i m b e r a c c e s s i b i l i t y r e v e a l s t h e i n a d e q u a c y o f o v e r - s i m p l i f i e d m a t h e m a t i c a l r e l a t i o n s h i p s . T h e c o s t o f p r i m a r y t r a n s p o r t , f o r e x a m p l e , i s d e p e n d e n t u p o n m a n y f a c t o r s , i n c l u d i n g t h e t y p e a n d p o w e r o f th e m a c h i n e , t h e o p e r a t o r ' s s k i l l a n d m o t i v a t i o n , t h e t r a n s p o r t d i s t a n c e t o t h e p r i m a r y l a n d i n g , t h e d e n s i t y o f t h e s t a n d , t h e s i z e o f t h e i n d i v i d u a l t r e e s a n d l o g s , a n d v a r i o u s t e r r a i n a n d w e a t h e r c o n d i t i o n s . I t w o u l d b e i m p o s s i b l e a n d u n n e c e s s a r y t o a t t e m p t to a c c o u n t f o r a l l o f t h e s e i n a m o d e l . Instead, FOR techniques, as described by Lussier (1963) and Pfeiffer (1967) can be employed to discover the most important variables affecting each phase or subsystem of the operation, their quantitative relationships as regards productivity, time, and/or cost, and the degree of variability which may be expected in this relationship under normal circumstances. The resulting relationship generally takes the form of a regression equation, together with its associated standard error of estimate (SE ) as the expression of the dispersion E of the observed data, and the associated correlation coefficient (R) 2 or coefficient of determination (R ) describing the amount of the total variability in the dependent variable that is explained by the expression. Then the model of the total logging system can be built up, using the relationships that have been worked out for each of the subsystems as components. The possibility of interaction and non-additivity of component relationships must be always kept in mind. The objective sought from the use of the model has also to be kept to the fore, so as to avoid including irrelevant costs and data, or excluding relevant ones. For the purposes of this paper, the total of all costs involved in harvesting a given block of timber is important, since accessibility hinges upon the excess of total value over total costs of extraction. In other problems of a more operational nature, variable costs maybe the only relevant consideration (direct costs). In general, once the model has been constructed as outlined above, it is no longer in a form amenable to the determination of the economically optimum combination of conditions by ordinary mathe-matical procedures such as discussed by Matthews (1942) and Lussier (1961). It becomes necessary to employ simulation techniques to determine how the model reacts to various inputs, followed by the selection of the best set of input conditions in such a manner as is established by the objective criteria. Using electronic computers, great numbers of possible factor combinations can be explored quickly and inexpensively, although there are sti l l certain limitations to present machine capacity and speed in problem solving which need to be borne in mind. Graphical summaries of these investigations can be of help in providing easier understanding of the behaviour of the system and in determining the relative importance of individual factors, a benefit which may lead to further simplification of the model without loss of realism (Smith, 1967). In all such work it is important to be aware of, and allow for, the assumptions and unknowns built into the model, as well as the aforementioned variability existing in the statistical data. The model should be tested against reality under varying conditions, and in use it should act as a guide, or aid to be modified by experienced judgment, rather than as a rule. Wherever feasible, its results should be phrased in statistical terms rather than in absolutes. "Sensitivity analysis", wherein high, low, and most probable values for requested information are reported together with some estimate of their probability of occurrence gives the logging planner some rational basis for choosing among alternatives. This choice could be either an informal weighing of the pros and cons, or it could take the shape of the more formal decision theory approach. 45 A COMPUTER ORIENTED MODEL, FOR HIGHLEAD LOGGING Because of the several unique characteristics of cable yarding systems in general, and of the highlead system in particular, a model quite specific to this logging technique is necessary. The following discussion describes the theoretical basis of one such model which has been recently developed (Cottell, 1967 b), including the nature of the model itself, the computer simulation to which it was subjected, and the behaviour observed in the model under the simulated conditions. A) Major Highlead Logging Cost Centers 1) Fixed Costs a) Road Construction Costs For the purposes of logging planning it must be assumed that the average cost of road construction, per unit length of road built, can be adequately estimated on the basis of known facts concerning terrain type, soil characteristics, degree of slope, the available labor and equipment and their cost (Cottell, 1967 a). Further, the timber volume, per unit area, must be known within reasonably accurate 46 limits. The road cost to be applied to the timber may be determined from: K R RCOST = 2 S V where: RCOST = road construction cost, dollars per 100 cubic feet (CCF) of logs; R = road construction cost, dollars per 100 feet (sta.) for an assumed road standard; V = timber volume, C C F per acre; S -- = road spacing, in 100 foot stations; 2 = area conversion factor, 4. 356 sta. per acre, (Matthews, 1942; Lussier, 1961). In coastal British Columbia, R varies most commonly from about $200/sta. for the best work situations to about $700 or $800/sta. for the worst, with the average being in the area of $300 to $400/sta. (Cottell, 1967 a). b) Landing Costs Landing costs are fixed costs whose amount, per unit volume of logs served, declines with increasing setting size and stand density. That is, landing costs, like road costs, fall as road spacing and inter-landing distance increase. Correspondingly, the expression describing landing costs is quite similar to that for roads: LCOST = K 2 L S W V where: LCOST = landing cost, dollars per C C F of logs produced on the setting; L = cost of landing construction, moving the spar, and rigging up, dollars: K^, S, V = as defined above; W = inter-landing spacing, 100 foot stations; (Matthews, 1942; Lussier, 1961). For this model, L has been calculated from: L = R + 240 C where: L = as defined above; R = cost of 1 - 100 foot station of road, dollars; C = cost of the yarding equipment and crew, dollars per minute (4 hours, or 240 minutes are required to move and rig up the mobile spar on the average (Rasmussen, 1965). c) Yarding r,Roadl>r Changing Cost As the logging proceeds on a highlead operation the location of the yarding cables must be changed from time to time, progressing 48 around the setting until all of the logs have been yarded to the landing-Each such position of the cables is commonly termed a "road". Though the time and cost of changing yarding roads are generally not separated from the yarding cost, it is more properly considered a fixed cost, as has been done in this model. The number of yarding roads varies with the setting size. To determine this relationship, two simplifying assumptions were made: i) a constant distance of 60 feet between roads at the farthest point from the spar is maintained; ii) slight over estimation of the average yarding distance has a negligible effect upon overall accuracy (exact formulae have been reported by Suddarth and Herrick, 1964, however they would unnecessarily complicate this model at its present stage of development). Figure 2 shows the geometrical features of the highlead setting. F i r s t the average maximum yarding distance is obtained, and the corresponding average angle, oL , subtended by the two adjacent roads at that point is found. The approximate number of roads needed to log the setting is determined from the number of O C 's required to complete a full circle. E = 3 49 Figure 2 . One quarter of highlead setting, illustrating geometry of logging "road" calculation -50 where: S, W = as defined previously, E = average maximum yarding distance per yarding road, sta. 0. 60 tan OC -E where: (X = the mean angle between contiguous yarding roads, in radians. N = 2 ? r 2 ^ or: N = arctan OC where: N = number of yarding roads per setting (i. e. 2 7T radians in the full circle). N T C CRCOST = S W V where: CRCOST = the overall cost of changing yarding roads, dollars per CCF; T = time taken per road change (an average of 18 minutes has been used here); C = cost of the yarding equipment and crew, dollars per minute. 51 2) Variable Costs a) Yarding Costs Several factors influence highlead yarding costs: log and turn volumes, yarding distance ( a function of road spacing and inter-landing spacing), the crew size, experience and motivation, the type and power of available equipment, and the cost of labor and equipment. Terrain effects are seldom significant within a given setting; however they are probably significant between settings. Several studies of highlead operations have been undertaken to determine the influence of these variables on the production function (Tennas, Ruth, and Berntsen, 1955; Mcintosh, 1963; USBLM, 1965; Adams, 1965; Rasmussen, 1965; and Pfeiffer, 1967). These are difficult to judge on a comparative basis, since each was carried out under quite different conditions of timber type, terrain, and equipment character-istics. Despite some drawbacks, notably the omission of the 2 associated R and SE in his report, the regression equations of E Adams (1965) were accepted as most appropriate for use in this model. Also, his estimates of labor, equipment, and other highlead operating costs were used throughout this examination. Yarding costs may be expressed by: YCOST = Y C where: YCOST = highlead yarding cost, dollars per C C F of logs produced; Y = yarding time in minutes per CCF; C = cost of yarding equipment and crew, dollars per minute. The valine Y is a function of several variables, as expressed by the regression equations: 2 Y = 1.471 + 0.007237D - 0. 000003448D + 0.003771V + + 0. 000008633DVt - 0.1402N Y 2 = 0. 2827 + 0.1150C + 0. 001519Vt + 0. 05806N where: Y^ = round trip turn time (yarding cycle time) in minutes, but excluding unhooking time at the landing; Y^ = minutes unhooking time at the landing; D = slope distance in feet; V = volume per turn, cubic feet; t N = number of logs per turn; C = number of chokers used, (Adams, 1965). Assuming C = 2 and N = 2 throughout, these terms can be combined with the constant in Y . Total yarding cycle time in minutes per turn can then be expressed by: = 1.8197 + 0.007237D - 0. 000003448D 2 + 0.005288Vt + . + 0. 000008633DV Yarding time, in minutes per C C F produced, is therefore: Y = 1. 1 ( Y o which is used in the YCOST expression for estimating total yarding cost. An additional 10% for unnecessary delay time has been added, since the regression does not allow for this internally. cost components would theoretically be a more correct approach to this problem. However such attempts meet with insurmountable difficulties of identifying and partitioning the two, other than on an arbitrary basis, and results in no improvement over the combined cost approach used here. 3) Total Costs Separation of the yarding function into its fixed and variable By combining all of the foregoing cost components into a single expression, an essentially complete model of the productivity and cost relationships of a highlead logging system is obtained. This model while admittedly making use of a number of important assumptions which undoubtedly influence its performance, would appear to be as complete and detailed as is worthwhile on the basis of presently available information. Total cost, as defined here, represents the sum of all costs of logs at the primary landing, excluding falling and bucking. Total cost = TCOST = RCOST + LCOST + CRCOST + YCOST TCOST = K 2 R + K 2 L + N T C + Y C S V S W V S W V B) Simulation of the Highlead Logging System Behind each of the terms in the model discussed above lie the relationships described in parts 1) and 2). Therefore, computer simulation can be easily carried out by varying the assumptions concerning the variables: R, V, V , S, and C. The model's behaviour can then be observed to help clarify our understanding of its cost-wise response to different physical and economic conditions. This was carried out on the I. B. M. 7040 computer at the University of British Columbia, and results, selected for their value in demon-strating the principles involved, are presented here graphically. Using several "loops", the model equations were solved for over 15, 000 combinations of the major variables, which were allowed to take on 55 the following values: W: 400 feet to 1000 feet, by 200 foot intervals; S: 800 feet to 2000 feet, by 200 foot intervals; VT: 50 cf to 125 cf by 25 cf intervals; V: 50 C C F to 125 C C F by 25 C C F intervals; R: $100 to $900 per station, by $200 intervals; C: $0. 50 to $1. 00 per minute, by $0. 25 intervals. This was accomplished using about 15 minutes of computer time. The companion notes in the text below point out the nature and significance of the model's reactions to the various input conditions. defining the optimum road spacing under given conditions may be observed in Figures 3, 4, and 5. Figure 3 shows yarding costs and fixed costs (including road construction, landing, and yarding road changing costs) plotted against road spacing (road construction cost, R, is $300 per station of 100 feet). It is apparent that minimum total cost occurs at about S = 1400 feet, where the rate of decrease in fixed costs equals the rate of increase of yarding costs. This is perhaps more readily appreciated upon examination of the bar graph (Figure 4), which depicts logging costs under the same conditions as in Figure 3. It shows principal components of total cost for various road spacings, and the way in which the costs change as spacing increases. It is evident that total costs must fall as long as the rate F i r s t of all, the validity of the marginal cost analysis for 1 56 Road Spacing ( S ) - Feet Simulation Conditions: C = $0. 50 per minute VT = 50 cubic feet per turn R = $300 per 100-foot station V =75 C C F per turn W = 600 feet Figure 3. Logging cost functions: total log cost as related to road spacing (from the highlead logging model) "7\ 7-h U U Sh ui rt i—i o Q fl fl in o U ha fl 3-o K e y : BOO I90O 1200  / 4 o ° R o a d S p a c i n g - F e e t ZSO 29o 335 Jdo 430 M e a n Y a r d i n g D i s t a n c e - F e e t C o m p o n e n t s o f T o t a l C o s t Y a r d i n g c o s t s R o a d c o n s t r u c t i o n c o s t s L a n d i n g c o s t s C h a n g i n g " r o a d s " c o s t F i g u r e 4. B a r g r a p h o f l o g g i n g c o s t r e l a t i o n s h i p s ( f r o m F i g u r e 1. ): t o t a l l o g g i n g c o s t a g a i n s t r o a d s p a c i n g . 58 14 i i * ! 1 600 1000 (200 HCO IbOO [BOO ZOOO Road Spacing ( S ) - Feet Simulation Conditions: C = $0. 50 per minute VT = 50 cubic feet per turn R- = $700 per 100-foot station V =75 C C F per acre W = 600 f e e t Figure 5. Logging cost functions: total logging cost as related to road spacing (from the highlead logging model) 14 59 800 100O l2oo 1400 ((oOO i BOO 2t)oo Road Spacing ( S ) - Feet Simulation Conditions: C = $0. 50 per minute VT = volume per turn, cubic feet R = $300 per 100-foot station V = volume per acre, C C F W = 600 feet Figure 6. Stand volume and turn volume as related to total logging cost and road spacing (R = $300 per station) 60 Simulation Conditions: C = $0. 50 per minute; VT R = $700 per 100-foot station V W Figure 7. volume per turn, cubic feet volume per acre, C C F 600 feet Stand volume and turn volume as related to total logging cost and road spacing (R = $700 per station) So too tes Average Turn Volume - Cubic Feet Simulation Conditions: R = $300 per 1000 foot station V = 75 C C F per acre W = 600 feet Figure 8. The influence of yarding crew and equipment charges, average turn volume, and road spacing on average yarding costs 6? Road construction costs Landing costs Changing "roads" costs I boo Road Spacing ( S ) - Feet Simulation Conditions: C = $0. 50 per minute R = $700 per 10P-,foot station VT = 50 cubic feet per turn V =75 C C F per acre W = 6 0 0 feet Figure 9a. Components of fixed cost as related to road spacing (R = $700 per station) Key: Road construction costs Landing costs Changing "roads" costs 1000 i20o wo Road Spacing ( S ) iboo Feet Simulation Conditions: C = $0. 50 per minute VT = 50 cubic feet per turn R = $300 per 100-foot station y =75 C C F per acre W = 60Q feet i Figure 9 b. Components of fixed cost as related to road • spacing (R = $300 per station) of decrease of fixed costs is greater than the rate of increase of yarding costs. Similarly, total cost ceases to fall (reaches a minimum) where the two change at an equal rate, and begins to rise again when the rate of yarding cost increase becomes greater than that of fixed cost decrease. Thus, the model does bear out the conclusions of the earlier discussion regarding the behaviour of logging costs, and the conditions for optimal logging layout. It must be pointed out that in practise the precise achievement of optimum spacing is not really a cr i t i c a l requirement. Examination of the total cost curves of Figures 3 and 4 reveals that a very broad, shallow minimum area is involved here. For this example, estimated total cost varies less than $0.15/CCF from that of the optimum condition over a range of road spacings extending from 1000 feet to 1800 feet. This allows a great deal of leeway about the optimum in logging layout and planning without incurring significant cost penalties. Figure 5 simply depicts logging costs as in Figure 3, the only difference in conditions being that road construction cost has here been assessed at $700 per 100-foot station. A minimum cost is not reached within the physical limitations of the highlead system, indicating that the settings should be as large as practically possible for best overall economy. In Figure 6 an example illustrating the relationships of turn volume and stand volume to overall logging cost is examined. Yarding cost per minute, ro a d c o n s t r u c t i o n cost, and setting width are held constant, while r o a d spacing i s allowed to vary. It i s apparent that t u r n volume has a m ore sig n i f i c a n t effect upon total logging cost than does stand volume, although the la t t e r i s also important. T h i s r e s u l t s f r o m the fact that t u r n volume d i r e c t l y influences y a r d i n g costs, v. the l a r g e s t component of total cost under these conditions. Stand volume and t u r n volume are seen to have opposing effects upon optimum r o a d spacing: i n c r e a s i n g stand volume reduces optimum spacing, while i n c r e a s i n g t u r n volume i n c r e a s e s optimum spacing. The f i r s t effect can be understood f r o m a c o n s i d e r a t i o n of the behaviour of the f i x e d cost curve ( F i g u r e 3) which both flattens out and drops to a lower l e v e l as stand volume i n c r e a s e s . Though the absolute f a l l i n cost has no effect on the optimum spacing, the change i n the slope of the l i n e does, shifting the point at which the slopes of the y a r d i n g cost curve and the fixed cost curve become equal to the left, and so red u c i n g the optimum spacing. The i n c r e a s e i n optimum spacing with i n c r e a s i n g t u r n volume o c c u r s because this factor becomes of r e l a t i v e l y g r e a t e r importance i n the y a r d i n g equation as compared to the y a r d i n g distance. Thus the rate of yarding cost i n c r e a s e with i n c r e a s i n g y a r d i n g distance i s reduced, i . e. the slope of the ya r d i n g cost curve becomes s m a l l e r , causing the optimum condition to be shifted to the right. In F i g u r e 7, a r o a d c o n s t r u c t i o n cost of $700 pe r 100-foot station has been assumed, a l l other f a c t o r s r e m a i n i n g the same as for F i g u r e 6. The r e l a t i o n s h i p s also r e m a i n the same as was observed in Figure 6; the only change is in the absolute levels of cost. This is the same as the effect obtained when C, the cost of the yarding equipment and crew per unit.of time, is varied. The relative curve positions remain the same, but absolute yarding costs vary in direct proportion to the change in C, for a given average turn size as shown in Figure 8. However the same graph shows that this proportion will vary with turn size, with a higher C producing a relatively greater increase in yarding costs where small turn volume are the case than where large average turns are possible. Figures 9a and 9b show the relative importance of each of the components of fixed logging costs under different assumptions regard: the value of R, road construction cost. All.behave much alike, with road construction consistently contributing the highest proportion to total fixed cost. Comparing the slopes of the cost curves of Figure 9a to those of Figure 9b, it is evident that those of the first mentioned are somewhat steeper. Following the reasoning of the marginal cost analysis, this would indicate that lower road costs, producing a lower slope of the fixed cost line, would favor smaller settings and closer road spacing than a higher road cost - a formal statement of what would appear intuitively to be the case. It should be noted, then, that it is not the change of fixed cost in absolute terms which is important to the determination of the optimum spacing, but rather it is the altered rate of change of fixed cost which should be considered. These illustrations indicate the important influences at play-in the establishment of highlead logging costs, and how changes in these can alter the layout requirements for optimum efficiency. When a comparison of the highlead system with any other system is being done so as to judge their respective advantages for logging a given area, this should ideally be done in such a way that each is presented in its most efficient layout configuration. In a similar way, when attempts are made to estimate logging costs for determining the economic accessibility of a forest area, these costs should be based on the use of the most suitable logging system for the area, with the controllable variables optimized. A COMPARISON OF HIGHLEAD AND SKYLINE YARDING SYSTEMS To compare the economics of highlead and skyline cable yarding systems a simple example, considered representative of conditions that commonly obtain in coastal British Columbia, was selected. The same hypothetical forest area was "logged" by each method and the resultant wood costs at the primary landing were evaluated to determine which was the more economical, and why. A) Skyline System Binkley (1965) has presented an example of skyline logging cost calculations on a hypothetical setting based on his study of operations in Oregon, where a radio controlled carriage was used. The conditions chosen were reasonably advantageous for the use of the skyline method, and are summarized below, and in Figure 10a. - setting 800 feet wide by 2 500 feet long; this corresponds closely to his maximum recommended external yarding distance; - single span skyline; - skyline gradient = 30%; - lateral slope = 0% under skyline; 69 - volume per acre = 45, 000 fbm Scribner (at a conversion factor of 8 fbm per cubic foot, this is about 56 CCF/acre); - cull = 13%, (.87 (56) = 49 CCF/acre, net); - average log size = 300 fbm (37.5 cubic feet) gross; - average turn size = 1500 fbm, 5 logs (187 cubic feet); - 5 man crew; - chokers preset to reduce yarding cycle time; - 50 minutes effective operating time per hour; - average skyline yarding distance = 1300 feet; - average lateral yarding distance =100 feet. Using these assumptions and supplying the regression equations for cycle time components as reported in an earlier part of his paper, a time of 9. 02 minutes per turn was calculated. This indicated a production rate of 57, 838 fbm (72. 3 CCF) per 8-hour day. On this basis, the total costs of wood to the landing were estimated as follows: Labor (@ $18.75 per hour, or $150 per day) $2.08 per C C F Rigging (4 spars, 4 tailholds, move in etc. , for a total of $7100 on a total volume of 2240 CCF) $3. 18 ti Yarding machine cost (@ $19- 32 per hour) $2.14 tt Road construction cost: - haul road, 800 ft. @ $4 per lineal ft. , $3200 - tote road, 1000 ft. @ $1 per lineal ft. $1000 - 1 landing, @ cost of 100 ft. of road 400 70 $4600 2.06 per C C F Total Cost: $9. 46 per C C F B) Highlead System - Portable Steel Spar To log the same setting by highlead, a second portion of road would have to be constructed, as shown in Figure 10b, uphill from the main valley road. The area could then be logged to four landings without exceeding the distance capabilities of the system although some trouble on the long corners could be expected. On a 2-log turn basis, turn volume would be about 7 5 cubic feet. Average yarding distance would be about 410 feet. Using the previously devised highlead logging model, which makes use of Adams' (1965) yarding regression equation and labor and machine costs, costs by this system approximate: Labor and machine (@ $30 per hour) $3. 58 per C C F Rigging: - 4 setups, 4 hours each, occupying machine and crew @ $30 per hour, on total volume of 2240 C C F . 22 ir - changing yarding roads (from model) . 80 tt 71 Road construction: - haul r o a d 1, 800 feet @ $4/foot: $3200 - haul r o a d 2, 800 feet @ $6/foot: 4800 - landings 1 & 2, est. as cost of 1 station of r o a d each: 800 - landings 3 & 4 est. as cost of 1 station of r o a d each: 1200 $10,000 4.47 per G C F T o t a l cost: $9. 07 per C G F C) C o m p a r i s o n of Skyline and H i g h l e a d Systems under Standardized Conditions Throughout the above analysis, y a r d i n g to only one side of the lower haul r o a d has been considered. The higher cost of haul r o a d 2 i n the highlead layout takes account of the p r o b a b i l i t y of g r e a t e r t e r r a i n d i f f i c u l t y at higher elevation, and thus greater expense. The tote r o a d for the skyline layout i s of low quality and cost, being suited only for use by t r a c k e d v e h i c l e s . It i s u s e d for c a r r y i n g the snubbing machine to the top end of the setting. i t would appear that the cost of skyline logging is not a great deal m o r e than that of the highlead system. It must be recognized, however, that the example was somewhat b i a s e d against the highlead s y s t e m C o m p a r i n g the costs of the two systems as c a l c u l a t e d above Figure 10a. Hypothetical skyline setting, after Binkley's (1965) example Key: Landing @ Road r e -setting boundary -Yarding road Scale: 1 inch = 500 feet Figure 10b. Same area as in Figure 10a, settings for cost comparison showing highlead because it was difficult to divide the study area into the most suitable highlead setting dimensions. This resulted in higher landing construction and rigging charges than would normally be the case (about $0. 37/CCF extra on the basis of a setting width of 600 feet). This would indicate something in the order of $0. 7 5/CCF overall extra logging cost using a skyline, rather than highlead under these conditions. The important questions here are: under what conditions would the skyline system offer greater economy than highlead, and could this lead to a general expansion of the economic margin of logging operations, considering the conditions currently facing the industry? Among the possibilities examined, the cost of road construction stands out as the most sensitive variable. If, in the above example, road construction cost were increased by as little as a dollar per lineal foot (but keeping the tote road cost the same), the indicated logging cost would become $9. 86/CCF for the skyline layout, and $9- 96 /CCF for the highlead operation (on basis of setting width of 400 feet). This represents a rate of cost increase for the latter of more than twice that of the former system as road costs rise. It also shows that the break-even point between the two systems occurs in the region of $6 per lineal foot average road construction cost, or somewhat more than $30, 000 per mile, under the example conditions. Although current road outlay in coastal British Columbia averages much less than this, some of the areas now being logged by highlead could probably be more profitably logged by skyline, because of road costs equal to, or in excess of this figure. Another factor worthy of consideration is the probability of basic improvements to each of these systems. However, these are very difficult to visualize beforehand, let alone evaluate. One development that could be conjectured upon is the possibility of a radical increase in line speeds, which would reduce the haul-in and haul-back portions of the yarding cycle. A differential improve-ment of this nature favoring the skyline method which could double the line speeds that were indicated by Binkley (1965), would produce a yarding cost reduction of about $0. 68/CCF, based on the example above. Though not a large saving, it is certainly significant, and could change the competitive situation between skyline and highlead systems in certain areas. When added to other improvements that could occur, but which are more difficult to foresee and assess theoretically, the skyline system does appear to offer potential cost advantages which could be important in the widening of the economic limits of logging operations in the future. Improvements in road construction techniques which could reduce this portion of logging costs would, of course, discriminate in favor of the highlead system in areas where highlead and skyline were actively competing. It would also lead to a general expansion of the economic margin, since even more difficult terrain would be brought within reach of the skyline by lowered scoad costs. This illustrates the double effect, well known in economics, which occurs as a result of a cost reducing innovation. The firs t effect, the 74 substitution effect, is evidenced by the replacement of costly yarding to some extent by the now relatively less dear input of roads. The second effect, the expansion effect, is evidenced by the overall widening of the economic limits of operation resulting from the net reduction of total logging cost (Watson, 1963). Another revolutionary concept in the phase of primary log transport is balloon logging, a development whose economic potential is as yet largely unknown. Mention is made of it here because of its unique position somewhere between the highlead and skyline systems in concept. Any attempt to produce numerical examples, or predictions of operating costs would be purely speculative at the present, and i l l -suited to a paper of this kind. Nonetheless, the possibilities of cost reduction through greatly extended yarding distance, more rapid line speeds, and the air-borne transport of logs during yarding are real enough to warrant continued interest in the improvement of this system. 75 T H E DETERMINATION O F ECONOMIC ACCESSIBILITY ON T H E UBC RESEARCH FOREST The need for more adequate definition and description of the true forest resource, i . e. that which is economically available for use by society under some given set of conditions, has frequently been felt by practising foresters. For example, Wilson (19 66) has studied the question of forest accessibility in Canada at the national level in an attempt to determine the available economic supply of timber, so that its adequacy to meet the demands that will be placed upon it in the foreseeable future may be judged. He determined the area of, and the timber volume within, the I960 timber drainage, i.e. the forest accessible in I960 as defined by log prices and costs of production. The form, product potential, and thus the value of the timber was not studied, however. Wilson stressed that these timber availability estimates were based on allowable cut calculations, which are not equivalent to economic supply functions. These functions could not be estimated on the basis of information available to him. The sub-marginal timber zone was also investigated to determine the availability of wood under conditions of higher price, but these efforts were hampered by lack of the information and tools necessary to estimate logging costs adequately. Zivnuska (1965), in defining the role 76 of North American forest resources in the world forest economy, also expressed the need for methods of attaching some economic meaning to the forest inventory, rather than allowing it to remain a simple stock-taking of a physical good. Long range national or regional planning of forest use, policy decisions regarding suitable tenure systems and cutting practises, and the broad planning of forest development and logging activities all require such knowledge. Also, measures of the economic resource must be phrased in dynamic, rather than static terms, so as to remain useful as environmental conditions and technology change. The economic limit of timber accessibility has been defined as the point at which the market value of logs from a given stand of timber just equals the sum of their costs of extraction. Thus, accessibility is determined by three major influences: the market for forest products, the costs of production, and the physical nature of the timber itself, which affects both of the other factors (Roitto, 1959; Cottell, 1967 a). Market demand, and the factors influencing demand, are taken in this paper as given, being reflected in the price of logs at the market place nearest to the standing trees. Production costs include those of both extraction and conversion. However, only the former are ofiinterest here, since the conversion costs are accounted for by the use of the market price for unprocessed logs in the determination of log value. Timber characteristics which influence 77 net log value include size, species, and quality, or grade. These have two main effects: log size, species, and quality influence the type and value of product which may be obtained through manufacture, and log size in particular influences the cost of extraction and con-version. Thus, economic accessibility can be suitably defined for the purposes of forest planning by combining facts regarding the timber characteristics which influence market value, and the costs of extraction, with the external characteristics of the market demand for forest products, and the factors of production by which that demand is to be satisfied. The earlier parts of this thesis have dealt with the determin-ation of yarding costs and fixed logging costs under varying conditions, using computerized models which are readily adaptable to change. The highlead logging system in particular was emphasized because of its widespread use in coastal British Columbia. The other activities which go to make up the total of timber extraction costs (including falling and bucking to length, yarding or skidding, road construction, loading, and secondary and major transportation to the market place or mill), have been recently investigated at the University of British Columbia Research Forest by Dobie (1966), who has reported cost relationships for each of these functions. When combined with information regarding the forest inventory and the appropriate schedule of log market prices, these relationships can provide a preliminary indication of the manner in which the economic 78 accessibility of forests may be determined. A preliminary study of this nature has recently been carried out at the University of British Columbia Research Forest (Cottell, 1967 a). The market pricesfor logs were established as of January, 1967 on the Vancouver log market. The recently completed UBC Forest inventory of 19 65 provided data on net stand volumes by species and diameter classes. This was further analyzed to estimate the average log sizes that could be expected from each stand. Stand volume by species and the market price for logs of each species together deter-mined the gross value of the stand in terms of wood products. Road construction records dating back to 1946, but covering principally the years 1957 - 67, were analyzed so that road building cost could be related to the topographic land classification system of Lacate (1965) . The highlead model could thus be applied to the determination of logging costs for each stand, as delineated by the inventory, depending upon its average volume per acre, the average expected turn volume, and the probable road cost as indicated by the land type in which it was located. The costs of preparing the logs and transporting them, other than those of yarding and the fixed costs of road construc-tion, landing construction, and changing yarding roads, were assigned according to log size, using the cost schedules reported by Dobie (1966) . Finally, the net value of the stand in total and on a per acre basis was established simply by subtracting the total costs of extraction from the estimated timber value. The net value thus obtained was taken as the measure of the economic accessibility of each stand, with a zero net value representing the outer limit of accessibility. On the basis of the information available, and the assumptions made, it appeared that only a few of the stands over 80 years of age on the UBC Research Forest were inaccessible for highlead logging. These few, as it developed, were composed mainly of low valued deciduous species. In all, 98 stands covering 3928 acres were examined. Their total net value was assessed at $3, 200, 000 on the basis of what their worth on the Vancouver log market of January, 1967 would have been if the Forest were all harvested in one year. The effect that this might have on market price was not taken into consideration, however. For the individual stands, the average net value ranged from - $125 to +$1674 per acre, with a mean of+$779 per acre. Logging costs (including all costs of log preparation and transport to Vancouver, save overhead costs) varied from $16 per C C F to $34 per CCF, with a mean of $22 per C C F (or $28 per C C F if an allowance of 15% were made for overhead charges). Applying this overhead allowance would reduce the net timber value to an average of $464 per acre, or a total of $1, 823, 000 for the 98 stands altogether. It is interesting to note that under a sustained yield policy which would return $80, 000 net profit to the Forest accounts annually, the net present worth of the Forest would amount to only $1, 333, 000, based on an interest rate of 6%. This would indicate a sacrifice in net present worth of some $490, 000 in timber value if sustained yield were elected rather than rapid liquidation. Other forest values have not been taken into account here, and could conceivably tend to offset this loss. It is doubtful whether these could fully compensate for the lost revenue from wood production, considering that the value of game, recreation, and water yields in that area would be relatively low compared to more populous areas nearer Vancouver or other major centers. This accessibility analysis provided information that should prove to be of value in management decisions at the UBC Research Forest and elsewhere. Firstly, it demonstrated that the determination of the economic accessibility of forest could be taken beyond the level of the "educated guess", provided factual information concerning a few of the most important variables was available. Secondly, it showed that while there is a great variability in stand value, very little of the total UBC Forest inventory is beyond economic reach, and that planning timber harvesting for the Forest as a whole is a realistic approach under the current conditions. Thirdly, it provided a summary of the road spacings and inter-landing spacings which should obtain to achieve the optimum, or least cost condition for highlead yarding, for each individual stand. Fourthly, and perhaps this was the most important development from the exercise, many gaps in present knowledge concerning timber value and logging productivity relation-ships were revealed. The realization that these must be more adequately investigated before truly accurate estimates of timber 81 accessibility can become a reality was strongly brought out. In this way, the preliminary study served as a guide to the type of research that is required to enable a more accurate determination of forest value for practical purposes. Some important topics requiring study in this respect include: methods for estimating log sizes and the numbers of logs which will be produced from a given stand; methods for grading trees during inventory according to some system which will reflect their value in use; and methods for obtaining better estimates of road construction costs through varying terrain. Also, the necessity for improved and localized productivity data would be indicated for each phase of the logging operation. Technological change in the methods of timber harvesting will naturally affect the answers to the questions raised in this section, as well as the pertinence of the questions themselves. Static models, or information contained in records which reflect past performance, are of little value when it comes to predicting the conse-quences of change. The most valid modeling procedures available are those which stress quick, efficient, and effective methods of data collection, supplemented by continual re-examination of the forest management and logging systems and their objectives. Computerized logging models can provide the flexibility required to cope with change by injecting an element of dynamism into an otherwise static approach. In other words, by studying the models under many different combin-ations of the input variables, and by revising the model relationships to keep pace with system improvements, a current picture of forest accessibility can be maintained. While this may still not solve our problems regarding the future, it at least allows us to know a great deal more about the present than has heretofore been possible. 83 CONCLUSION A l l human planning is both blessed and hampered by an inability to foresee the future and the developments that will come with it. The best that can be done is to analyse past performance, and project trends on the basis of data, intuition, and experience. Planning, to be rational and useful, must be based upon that which is known to exist. Plans must be flexible, capable of revision almost immediately as conditions change. Forestry planning, even though the long view is traditional and necessary, cannot escape the requirement that policies be based on present technological knowledge. Over relatively recent years, logging methods and transportation facilities have experienced a time of rapid evolution and improvement. The trend has been away from labor intensive systems, toward higher capital investment in powerful mechanical equipment. Projecting this trend, the eventual achievement of total mechanization of the logging industry of this country appears inevitable. Only in high volume virgin forest stands can the luxury of manual labor, employed in partially mechanized operations, be afforded. "When these are gone, areas not suitable to fully mechanized logging methods will likely become economically inoperable. However, mechanized systems themselves offer wide scope for improvement and development, suggest-ing that the terrain difficulties which limit the efficiency of present day equipment can be overcome, or their effects diminished to some degree. The problem of economic accessibility is, or should be, a major concern to all who must plan for, regulate, and actually carry out the development and use of the forest resource. In many instances, this problem has not been adequately realized, or, if realized, it has been put aside as too complex to allow for any attempt to analyse it in detail. The accessible forest has in the past been delineated by arbitrary lines drawn on a map at some specified elevation, or distance from the conversion center, or at the boundary of a change in timber type. In other cases, the question has been side-stepped with the assertion that eventually, under some set of conditions, all of the forest is accessible, and that therefore it is unnecessary to determine current economic boundaries, which are soon out of date. Quite clearly, this is untrue, since forest products can always be replaced by substitutes if their price becomes too high, a fact which sets a definite ceiling on the price for forest products and on the amount which can be spent in producing them. Also, at some price level intensive use of forest land close to population centers may become more attractive than expanding further the operations in naturally provided timber. Thus, it cannot be assumed that the entire physical inventory will ever become part of the forest resource in the economic sense. Admittedly, the determination of the economic boundary of the resource is a complicated undertaking. As yet the relationships involved in forest production activities have only been generally defined. Actual data concerning actual operations is scarce and highly variable. Enough is available, however, to enable demonstration of a possible approach to defining timber accessibility. Such an approach necessi-tates synthesis of pertinent information about the timber, terrain, and logging methods, as well as log transport costs and market prices. This can only be done on a current basis, since even current conditions are highly variable and incompletely known. Anticipating the future would be an impossible problem in this regard. For this reason, it follows that very fast, flexible, and high capacity procedures are needed to keep the accessible resource adequately defined in the face of constantly changing conditions. Thus, all individual stands in a given forest area and their economically important characteristics must be readily available for computer analysis. Their relationships to the economic environment and within the various production sub-systems should be capable of easy revision in a computer program, which could be used to simulate the response and condition of the whole forest system. As changes occur in the real system relationships, these could be redefined, remeasured, and finally introduced into the computer model in place of the outdated relationships. The entire analysis could then be reworked using the up-dated material, and the new economic boundaries would be so defined. In this way a contemporary picture of the size and worth of the forest resource could be maintained to provide a sound factual basis for planning and management decisions. This study can only claim to be a beginning attempt at the above described task. Its purpose has been to demonstrate the feasibility of the proposals made herein, and to bring out some of the major relationships requiring analysis. In particular, the influence of logging activities and the effect of technological changes in this field upon logging costs, and ultimately upon forest accessibility, were examined. It is an understatement to say that a great deal remains to be done. The discussion of the study at the UBC Research Forest specified in particular the need for better information concerning log sizes, quality, and market value from inventory data, road construction costs, and production functions and their variability for all phases of logging and the subsequent transportation of logs. Each of these leads inevitably to a further array of questions, all of which require a good deal of thoughtful consideration. For example, how could log sizes be determined with reasonable accuracy during inventory cruising; by what criteria should logs be graded as to quality, so as to reflect their value in oompeting uses; what simple terrain classification system would best indicate road building costs; and to what degree do non-additivity and variation occur in the relationships between and within logging subsystems, such that could affect the adequacy of logging cost estimates? 87 Investigations of these questions will probably take place, but it is apparent that this is a long term undertaking. Meanwhile, it should not be said that since information is incomplete, and in some cases lacking, no attempt should be made to refine the definition and understanding of the forest resource. Rather, it is necessary to do the best possible job with the information available, and constantly seek to improve it. Foresters have an important responsibility to manage the forest in" such a way as to achieve the greatest benefit to society. This task can only be lightened through the evaluation of the forest resource within an economic framework designed to reflect its true worth to the human community. 88 L I T E R A T U R E CITED Adams, T. C. 1965. Highlead logging costs as related to log size and other variables. Pacific Northwest Forest and Range Experiment Station, U. S. D. A. , Forest Service. Research Paper PNW - 23. 38 p. Andrews, R. W. 1956. Glory days of logging. Superior Publishing Co., Seattle, Wash. 17 6 p. Anonymous, 1966. Balloon logging development continues in U.S.A. operation. World Wood. Vol.7. No. 6. p 3-4, 40 Anonymous, 1967. Felling machine, Vancouver Province. May 24, 1967. (Photo and Caption) Bartholomew, A., W. D. Bennett, and H.I. Winer, 1965. Factors affecting the productivity of wheeled skidders. C.P.P. A. No. 2339. (B-8-a). 4 p. Bell, W. J. 1965. The short wood system: engineering features. Fundamentals of mechanical harvesting. Panel discussion, C.P.P.A. No. 2337 (B-l) p. 2-5 Bennett, W. D. and H. I. Winer, 1966. Cost analysis in logging. Paper presented at Sixth World Forestry Conference, Madrid, Spain. 15 p. Binkley, V. W. 1965. Economics and design of a radio controlled skyline yarding system. U.S. For. Service. Res. pap. P.N. W. - 25. P. N. W. For. and Range Exp. Sta. Portland, Oregon. 30 p. Bjerkelund, T. C. 1965. The tree length system: operating features. Fundamentals of mechanical harvesting. Panel discussion. C.P.P.A. No. 2337. (B-l) p. 5-7. Brown, N. C 1936. Logging - transportation. Wiley, New York. 327 p. 89 Bryant, R. C. 1923. Logging. The principles and general methods of operation in the United States. Wiley, New York. 556 p. Chestnut, H. 1965. Systems engineering tools. Wiley, New York, 646 p. Cottell, P.L. 1967 a. Forest inventory valuation. Forestry 581. Directed Study, U. B. C. 39 p. Cottell, P.L. 1967 b. An examination of highlead logging research and its application. Forestry 572. Directed Study, U.B.C. 37 p. Cottell, P.L. 1967 c. Systems analysis and its application in forestry. Forestry 560. Directed Study, U. B. C. 24 p. Cross, E. E. 1965. The Short wood system: operating features. Fundamentals of mechanical harvesting. Panel discussion. C P . P . A . No. 2337. (B-l)p.2. Dane, C. W. 1965. Statistical decision theory and its application to forest engineering. Jour, of For. , April, Vol. 63 p. 276-279. Dibblee, D. H. W. 1965. The effect of some stand factors on the performance of mechanical harvesting equipment. C.P.P. A. No. 2348. (b-1) p. 9-11. Dobie, J. 1966. Product yield and value, financial rotations and biological relationships of good site Douglas f i r . M. F. Thesis, U.B.C. 141 p. Donnelly, R. H. 1963. Mathematical programming in the management of logging operations. J Reprinted from Proceedings of Society of American Foresters. 3 p. Donnelly, R. H. 1967. A sample of decision theory in the forest products industry. Proceedings of "Chance and Change" a seminar of decision theory conducted at U. B. C. March 10, 1967. p. 29-36. Dunlop, J. T. 1962. Problems and potentials - automotive and techno-logical change. Prentice Hall. 90 Eckman, D.P. (Editor), 1961. Systems: research and design. Proceedings of the first Systems Symposium at Case Institute of Technology. Publication of the Systems Res. Center, Case Institute of Technology, Wiley. 310 p. Ell i s , D. O. and F. J. Ludwig. 1962. Systems philosophy. Prentice Hall, Space Technology series. 387 p. Hamilton, D. D. 1965. Fu l l tree system: a philosophical view. Funda-mentals of mechanical harvesting. Panel discussion. C.P.P.A. No. 2337. (B-l) p. 9. Horncastle, D. C. 1965. The full tree system: operating features. Fundamentals of mechanical harvesting. Panel discussion. C.P.P.A. No. 2337. (B-l) p. 8-9. L a c a t e , D. S. 1965. Forest land classification for the U. B. C. Research Forest. Dept. of For. Pub. No. 1107. 24 p. Larsson, G. 1965. The economic road standard, road spacing, and related questions. Discussion paper presented in the Symposium of the Planning of Forest Communication Net-works (Roads and Cables), Geneva, FAO/ECE/LOG/149. Vol. II. p. 253-260. Lussier, L . J . 1959. A statistical planning system for control of logging operations. For. Prod. Jour. June. Vol. 9. p. 192-195. Lussier, L . J . 1961. Planning and control of logging operations. The Forest Research Foundation, Laval University, 135 p. Lussier, L . J . 1963. A gambler's approach to logging problems. Pulp and Paper Mag. of Canada. Sept. p. WR-354-364. Lussier, L . J . 1965. Pitfalls in logging-cost analysis. C.P.P.A. No. 2351 (A-2-a), p. 28-32. Lysons, H.H., V. W. Binkley, and C. N. Mann, 1966. Logging test of a single hulled balloon. P. N. W. For. and Range Exp. Sta. U. S. F. A. , U. S. D. A. 20 p. Matthews, D. M. 1942. Cost control in the logging industry. McGraw H i l l Inc. 374 p. 9 1 Matthews, D. M. 1942. Cost control in the logging industry. McGraw-H i l l Inc. 374 p. Mcintosh, J. A. 1963. Prelogging in a West Coast cedar-hemlock stand. For. Prod. Res. Br., Dept. of For. Pub No. 1028. 39 p. McMillan, C. and R. F. 'Gonzalez. 1965. Systems analysis, a computer approach to decision models. Richard D. Irwin Inc. 336 p. McNally, J. A. 1963. Mechanized logging and road requirements. Pulp and Paper Mag. of Canada. Woodlands section index. No. 2258 (B-8-b) p.-WR- 377-382. Mumford, L. 1934. Technics and civilization. Harcourt, Brace and Co. New York. Cited in C. R. Silversides, Developments in logging mechanization in eastern Canada. H. R. MacMillan Lectureship delivered at U. B. C. 1964. p. 2. Newnham, R. M. 1966 (b) A simulation model for studying the effects of stand structure on harvesting pattern. For. Chron. 42 (1) 39-44 Pearse, P. H. and S. Sydneysmith. 1966. Method for allocating logs among several utilization processes. For. Prod. Jour. Vol. 16. No. 9. p 87-98. Pfeiffer, K. 1967. Analysis of methods of studying operational efficiency in forestry. M. F. Thesis, U.B.C. 94 p. Ramussen, C. R. 1965. Yarding study 1.. MacMillan Bloedel Ltd. private report. Kelsey Bay Division. Unpublished. Roitto, Yrjo" 1959. Inaccessible forests as a costing problem. Pulp and Paper Mag. of Canada. Woodlands Review Section. August. 5 p. Schumpeter, J. A. 1934. The theory of economic development. Trans-lation 1961 by Redvers Opic, Oxford University Press, New York. 255 p. Scott, A. D. 1962. The development of the extractive industries. C.J. E. P.S. February. Seale, R. H. 1966. Forestry as a system. Paper on a project conducted at Syracuse State University College of Forestry. 12 p. 92 Silversides, C. R. 1964. Developments in logging mechanization in Eastern Canada. H. R. MacMillan Lectureship delivered at U. B. C 29 p. Silversides, C. R. 1966 (a) The influence of mechanization on harvesting and transportation methods. Paper presented at Sixth World Forestry Conference, Madrid, Spain. 15 p. Silversides, C. R. 1966 (b) The rate of diffusion of new harvesting systems and machines in the pulpwood logging industry in Eastern Canada. C P . P. A. 2411 (B - l ) . Reprinted from Woodlands Review Section, Pulp and Paper Mag. of Canada. Nov. 1966. 13 p. Smith, CW. and C Harnell, 1961. Linear programming in log production. For. Prod. Jour. Vol XI. No. 1. p. 8-11. Smith J. H. G. 1967. Simulating stand growth and yield to improve decisions made by forest managers. Paper presented at Ninth Annual Meeting of the Canadian Operational Research Society, Ottawa. May 1967. 8 p. Smith, J.H.G-, J.W. Ker, and J. Csizmazia. 1961. Economics of reforestation of Douglas F i r , Western Hemlock and Western Red Cedar in the Vancouver Forest District. U.B.C. Faculty of Forestry. For. Bull. No. 3. p. 90-93. Spiers, J. J. K. 1956. Some considerations in planning a mobile logging operation. M. F. Thesis, U. B. C 100 p. Studdarth, S. K. and A. M. Herrick. 1964. Average skidding distance for theoretical analysis of logging costs. Purdue University, Agricultural Exp. Sta. Res. Bull. No. 780. 6 p. Tennas, L. R. , R.H. Ruth, and C M . Berntsen, 1955. An analysis of production and costs in highlead logging. P.N. W. For. and Range Exp. Sta., U. S.D. A. For. Ser. Res. Paper No. 11. 37 p. Thiesmeyer, L. R. 1964. Hydraulic wood-chip pipelinesfor the pulp and paper industry. Trend-publication of the Pulp and Paper Research Institute of Canada. No. 4. p. 4-8. 93 United States Department of the Interior, Bureau of Land Manage-ment, 1964. Logging costs. Valg, L. 1962. Determination of the economically marginal tree size through the application of conventional and linear -programming techniques. M. F. Thesis, U.B.C. 147 p. Watson, D. S. 1963. Price theory and its uses. Houghton Mifflin Co. 431 p. Williams, C. C 1917. Design of railway location. Wiley.p.471, 472. Wilson, D. A. 1966. Wood products - the supply of timber from Canadian forests. National Forestry Conference, Quebec 35 p. Windebank, W. J. , E. E. Grainger, F. A. Harrison, and F. A. Roberts. 1963. A Symposium on technical change and its conse-quences on woods operations. Pulp and Paper Mag. of Canada W.S.I. No. 2217 (B-2) p-WR-159-173. Winer, H. T. and R. H. Donnelly, 1963. Linear programming in woodlands decisions. Pulp and Paper Mag. of Canada. Sept. p. WR 350-354. Young, H. E. 1966. World forestry based on the complete tree concept. Paper presented at the Sixth World Forestry Conference Madrid, Spain. 5 p. Zivnuska, J. A. 1965. On defining the role of the United States in a world timber economy. Seminar on British Columbia's future in forest products trade in A s i a and the Pacific Area. U.B.C. Dept. of Extension, p. 125-138. 


Citation Scheme:


Citations by CSL (citeproc-js)

Usage Statistics



Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            async >
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:


Related Items