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Product yield and value, financial rotations and biological relationships of good site Douglas fir Dobie, J. 1966

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PRODUCT YIELD AND VALUE, FINANCIAL ROTATIONS AND BIOLOGICAL RELATIONSHIPS OF GOOD SITE DOUGLAS FIR by J . DOBIE B.S.F., U n i v e r s i t y o f B r i t i s h Columbia,  1959.  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF Master o f F o r e s t r y i n the Department of Forestry  We a c c e p t t h i s t h e s i s as conforming to the r e q u i r e d s t a n d a r d  The U n i v e r s i t y o f B r i t i s h April,  1966.  Columbia  In p r e s e n t i n g t h i s t h e s i s  in p a r t i a l  f u l f i l m e n t of  requirements f o r an advanced degree at the U n i v e r s i t y of Columbia, for  I agree t h a t the L i b r a r y  r e f e r e n c e and s t u d y .  I further  s h a l l make i t  freely  the  British available  agree that p e r m i s s i o n f o r  ex-  t e n s i v e c o p y i n g of t h i s t h e s i s f o r s c h o l a r l y purposes may be gran by the Head of my Department o r by h i s  representatives;  understood t h a t c o p y i n g o r p u b l i c a t i o n of t h i s t h e s i s f o r cial  g a i n s h a l l not be a l l o w e d w i t h o u t my w r i t t e n  Department  of  The U n i v e r s i t y of B r i t i s h Columbia Vancouver 8, Canada Date  5""—  >JA*~0^f  /?£  &  It  is  finan-  permission.  i.  ABSTRACT The p r a c t i c e o f s u s t a i n e d - y i e l d  forest  management r e q u i r e s the f o r m u l a t i o n o f management p l a n s designed t o ensure the economic the f o r e s t e n t e r p r i s e .  e f f i c i e n c y of  Consequently a knowledge o f  the volume and value of timber i n f o r e s t stands i s o f the utmost  importance t o f o r e s t e r s engaged i n s u s t a i n e d -  y i e l d management. In t h i s t h e s i s an a n a l y s i s o f the q u a n t i t y and v a l u e o f the product y i e l d from f o u r n a t u r a l stands o f Douglas f i r  (Pseudotsuga m e n z i e s i i  i n B r i t i s h Columbia has been made. were 63,  86,  106 and 145  y e a r s o f 160, 165,  (Mirb.) Franco)  Average  stand ages  y e a r s w i t h h e i g h t s a t 100  175 and 165  feet,  respectively.  Logging and m i l l i n g c o s t s f o r what i s regarded as t y p i c a l c o a s t a l B r i t i s h Columbia o p e r a t i o n s were d e r i v e d from the l i t e r a t u r e and from l o c a l sources.  Lumber  y i e l d s and v a l u e s presented were o b t a i n e d from the r e s u l t s o f f o u r m i l l s t u d i e s of sample l o g s from the above s t a n d s .  Value and volume o f plywood and  piling  products o b t a i n a b l e were a s c e r t a i n e d from the l i t e r a t u r e and from l o c a l sources.  ii. L i n e a r programming t e c h n i q u e s were used to determine the optimum j o i n t - p r o d u c t y i e l d from each o f the stands.  F i n a n c i a l r o t a t i o n s a t two  establishment  c o s t s , and  l e v e l s of  t h r e e i n t e r e s t r a t e s , were  examined and mathematical models o f the r e l a t i o n s h i p between t r e e v a l u e , t r e e volume and v a r i a b l e s are  biological  presented.  I t was  found t h a t the net v a l u e per  cubic  f o o t o f t r e e i n c r e a s e d w i t h t r e e s i z e because o f reduced h a n d l i n g  c o s t s per u n i t volume and  q u a l i t y y i e l d i n the l a r g e r t r e e s .  better  At the l e v e l o f  c o s t s and v a l u e s used, and w i t h i n l i m i t s o f grade s p e c i f i c a t i o n s , i t i s more p r o f i t a b l e t o produce p i l i n g from s m a l l t r e e s , and plywood from l a r g e t r e e s , r a t h e r than lumber.  The  l i n e a r programming s o l u t i o n  t o optimum product y i e l d i n d i c a t e d t h a t optimum conversion  r e t u r n f o r a l l stands was  5 cents per  f o o t g r e a t e r than the lumber c o n v e r s i o n  return.  F i n a n c i a l r o t a t i o n s , a t 3 per cent i n t e r e s t on establishment  cubic  compound  c o s t s and on the value  of  the  growing stock, are between 60 and 70 y e a r s f o r these sites.  At 65 y e a r s the margin f o r p r o f i t and r i s k i n  iii. these stands v a r i e d from  $1400  to  $2000  i n c r e a s i n g w i t h degree o f s t o c k i n g . establishment but reduced  per a c r e ,  An i n c r e a s e i n  c o s t s d i d not a f f e c t the r o t a t i o n  the net value per acre o f the  I n c r e a s i n g the i n t e r e s t r a t e reduced  age  stand.  both the r o t a t i o n  age and the net value per a c r e o f the  stand.  Many b i o l o g i c a l v a r i a b l e s were found to be s i g n i f i c a n t l y c o r r e l a t e d w i t h t r e e value and volume. However, r e g r e s s i o n models u s i n g o n l y two  or three  v a r i a b l e s were s t a t i s t i c a l l y as good as, and,  from a  p r a c t i c a l p o i n t o f view, much b e t t e r than more i n v o l v e d models.  Combinations o f dbh,  c l a s s were the best two value p r e d i c t i o n .  b u t t - l o g grade and  crown  o r t h r e e v a r i a b l e models f o r  Tree dbh and D H rendered  similar  e s t i m a t e s o f board-and c u b i c - f o o t volumes. I t i s c o n s i d e r e d t h a t the volume and of  timber from these s i t e s c o u l d be  value  substantially  i n c r e a s e d by i n t e n s i v e f o r e s t management and  complete  u t i l i s a t i o n o f the p r o d u c t i v e c a p a c i t y o f the l a n d .  J.H.G. Smith.  TABLE OF CONTENTS INTRODUCTION RELEVANT INFORMATION Stand D e s c r i p t i o n s Study procedures Sample and stand t r e e diameter d i s t r i b u t i o n s COSTS AND VALUES OF PRODUCTS Logging c o s t s Milling  costs  Lumber v a l u e s Value o f pulp c h i p s from sawmill  residue  Plywood manufacturing c o s t s and r e t u r n s Value o f pulp c h i p s from p e e l e r l o g s Production  c o s t s and v a l u e o f p i l i n g  LINEAR PROGRAMMING TO MAXIMIZE CONVERSION RETURNS PER ACRE Alternative  activities  Data i n p u t Optimum s o l u t i o n TREE AND STAND ANALYSIS Tree  values  Stand n o r m a l i t y and growth FINANCIAL ROTATIONS Criterion for financial R o t a t i o n ages  maturity  BIOLOGICAL  RELATIONSHIPS  Regression  analysis  Test o f b i o l o g i c a l  variables  Important v a r i a b l e s f o r v a l u e p r e d i c t i o n S e l e c t e d r e g r e s s i o n models Merchantable volume e q u a t i o n s F o r m u l a t i o n o f t r e e grades IMPLICATIONS FOR STAND MANAGEMENT CONCLUSION LITERATURE CITED  LIST  OF  TABLES  Sample and stand t r e e d i s t r i b u t i o n s by 3-inch dbh c l a s s e s f o r f o u r stands o f Douglas f i r Percentage l o g grade d i s t r i b u t i o n c u b i c volume r e c o v e r e d f o r f o u r stands o f Douglas f i r  by  U t i l i s a t i o n standards f o r f o u r stands o f Douglas f i r F a l l i n g and bucking times and c o s t s by t r e e dbh and volume f o r Douglas fir Average f a l l i n g and bucking times and c o s t s by log-volume f o r Douglas fir High-lead y a r d i n g times and c o s t s by two-log t u r n volumes f o r a t u r n d i s t a n c e o f 400 f e e t Loading times and c o s t s by l o g volume f o r mobile l o a d e r s Log weights per c u b i c f o o t and cubic f e e t per 50,000 pounds o f l o g s f o r Douglas f i r w i t h t r u c k - h a u l c o s t per Ccf l o g s a t $ 1 7 . 4 0 f o r a 20-mile truck haul T o t a l o f h a u l i n g c o s t s and d e l a y c o s t f o r a r o u n d - t r i p t r u c k haul o f 10 m i l e s on g r a v e l and 30 m i l e s on pavement Booming and towing cost i n $/Ccf by l o g top diameter and l e n g t h on the b a s i s o f a c o s t o f $2.80 per M fbm f o r an average l o g o f 600 fbm and a tow d i s t a n c e o f 20 m i l e s  vii. Page  Table XI  XIII  XIV  XV  XVI  XVII  XVIII  XIX  XX  Road c o n s t r u c t i o n and maintenance c o s t s i n $/Ccf by l o g t o p diameter and l e n g t h on t h e b a s i s o f $6.50 p e r M fbm f o r an average l o g o f 350 fbm  25  T o t a l l o g g i n g c o s t s i n $/Ccf f o r Douglas f i r Hinder c o n d i t i o n s s t a t e d f o r the cost components  26  Saw-time i n min. p e r C c f o f l o g s by l o g t o p diameter and l e n g t h f o r a band-mill  29  M i l l i n g costs i n d o l l a r s per C c f of l o g s by l o g top diameter and l e n g t h on b a s i s o f $4*90 p e r C c f p e r minute o f saw-time  30  Percentage lumber y i e l d by lumber grade, value by l o g grade and mercha n t a b l e volumes per acre f o r 145and 106- y e a r - o l d Douglas f i r  33  Percentage lumber y i e l d by lumber grade, value by l o g grade and mercha n t a b l e volumes p e r acre f o r 86- and 63- y e a r - o l d Douglas f i r  34  Gross and n e t lumber v a l u e s p e r c u b i c f o o t o f l o g s c a l e from f o u r stands o f Douglas f i r  35  Volume, manufacturing c o s t and v a l u e o f Douglas f i r pulp c h i p s from band sawmill r e s i d u e . B.C. Coast u n i t s ( e q u i v a l e n t o f 80 cu. f t . s o l i d wood)  37  Douglas f i r plywood grades and component veneers. Standard 0121-1961. Canadian Standards A s s o c i a t i o n  41  Percentage veneer y i e l d by p e e l e r grade, average percentage veneer y i e l d by veneer grade and a l l o c a t i o n o f manufact u r i n g c o s t s by veneer grade f o r f o u r stands o f Douglas f i r  42  viii.  ix. Page  Table Conversion r e t u r n per cubic f o o t and per t r e e by dbh c l a s s e s f o r combined ages of s i t e c l a s s I I Douglas f i r  72  A d d i t i o n a l cubic volume per acre i n stumps and tops f o r f o u r stands of Douglas f i r  79  Comparison of normal stand data w i t h a c t u a l stand data f o r f o u r stands of Douglas f i r  80  XXXV  Past stump-height diameter growth f o r two stands of Douglas f i r  81  XXXVI  Current and past stand t a b l e s f o r 63- and 86- y e a r - o l d Douglas f i r  82  XXXVII  "Growth" and "normal* estimates of stand merchantable volume - cu. f t . per acre - by stand age f o r Douglas fir  83  "Normal" estimates of stand merchantable volume - cu. f t . per acre - by stand age f o r Douglas f i r  84  Margin f o r p r o f i t and r i s k - $/acre f o r lumber and optimum product based on growth and normal y i e l d volume estimates of f o u r stands of Douglas f i r  95  XXXII  XXXIII  XXXIV  XXXVIII  XXXIX  1  XL  Financial rotation calculation for 63-year-old Douglas f i r at a 3 per cent i n t e r e s t r a t e ; establishment cost of $20.00 per acre and annual maintenance of $1.00 per acre 96  ZLI  Financial rotation calculations for 86-year-old Douglas f i r at a 3 per cent i n t e r e s t r a t e ; establishment cost of $20.00 per acre and annual maintenance of $1.00 per acre 97  Financial rotation calculations f o r 63- and 8 6 - y e a r - o l d Douglas f i r a t 3 and 5 p e r cent i n t e r e s t , and $20 and $ 5 0 p e r a c r e e s t a b l i s h m e n t costs  98  Mean v a l u e s , s t a n d a r d d e v i a t i o n s and c o r r e l a t i o n c o e f f i c i e n t s o f independent and dependent t r e e v a r i a b l e s f o r combined ages and f o r 63-yearo l d Douglas f i r  116  Mean v a l u e s , s t a n d a r d d e v i a t i o n s and c o r r e l a t i o n c o e f f i c i e n t s o f independent and dependent t r e e v a r i a b l e s f o r 86-, 106- and 145-year Douglas f i r  117  R-squared v a l u e f o r r e g r e s s i o n o f c o n v e r s i o n r e t u r n lumber ( Y l ) and c o n v e r s i o n r e t u r n optimum (Y2) on selected biological variables f o r combined ages and 6 3 - y e a r - o l d Douglas fir 118 R-squared v a l u e s f o r r e g r e s s i o n o f c o n v e r s i o n r e t u r n lumber ( Y l ) and c o n v e r s i o n r e t u r n optimum (Y2) on selected biological variables-for 86- and 106- y e a r - o l d Douglas f i r  119  R-squared v a l u e s f o r r e g r e s s i o n o f c o n v e r s i o n r e t u r n lumber ( Y l ) and c o n v e r s i o n r e t u r n optimum-(Y2) on selected biological variables-for 1 4 5 - y e a r - o l d Douglas f i r  120  F r e q u e n c y o f o©c\a?rence o f e i g h t s e l e c t e d independent v a r i a b l e s i n r e g r e s s i o n o f lumber and optimum c o n v e r s i o n r e t u r n s on b e s t combinat i o n a o f 4 and 3 v a r i a b l e s and on t h e t h r e e h i g h e s t r f o r 10 a n a l y s e s o f Douglas f i r  121  xi. Table XLIX  L  LI  LII  Page Equations f o r r e g r e s s i o n o f lumber c o n v e r s i o n r e t u r n i n cents per c u b i c f o o t ( Y l ) on s e l e c t e d independent v a r i a b l e s f o r combined stands o f 6 3 - , 86-, 106-, and 145- y e a r - o l d Douglas fir  122  Equations f o r r e g r e s s i o n o f optimum c o n v e r s i o n r e t u r n i n cents p.er c u b i c f o o t (Y2) on s e l e c t e d independent v a r i a b l e s f o r combined stands o f 63-, 86-, 106-, and 145- y e a r o l d Douglas f i r  123  S t a t i s t i c s of p r e d i c t i o n of value equations f o r r e g r e s s i o n o f lumber c o n v e r s i o n r e t u r n ( Y l ) and optimum c o n v e r s i o n r e t u r n (Y2), i n cents per cubic f o o t , on s e l e c t e d independent v a r i a b l e s f o r a l l ages and i n d i v i d u a l stands o f Douglas f i r  124  E q u a t i o n s f o r r e g r e s s i o n o f mercha n t a b l e board f o o t and cubic f o o t volume f o r combined 63-, 86-, 106-, and 145- y e a r - o l d Douglas f i r  125  LIU - .•.  E q u a t i o n s f o r the r e g r e s s i o n o f l i n e a l f e e t o f t r e e r e q u i r e d per M fbm lumber and per C c f l o g s on dbh, h e i g h t , age and s i t e i n d e x f o r combined and i n d i v i d u a l a g e - c l a s s e s o f Douglas fir 126  LIV  D i s t r i b u t i o n o f t r e e grades by crown c l a s s , b u t t - l o g grade and dbh f o r combined stands o f Douglas f i r  127  xii.  LIST OF FIGURES Figure 1.  Page R e l a t i o n s h i p between c o n v e r s i o n r e t u r n s , ($/Ccf) from lumber and optimum product, and stand age f o r Douglas f i r  63  R e l a t i o n s h i p o f double-bark t h i c k n e s s o f Douglas f i r t o D.B.H.  85  3.  R e l a t i o n s h i p between D.B.H. and D.I.B. decrement f o r Douglas f i r  86  4.  Stand values and c o s t s ($/acre) by stand age (years) f o r Douglas fir. E s t a b l i s h m e n t c o s t o f $20.00 per acre and annual maintenance o f $1.00 p e r acre compounded a t 3, 5 and 7 p e r cent i n t e r e s t  99  2.  5.  Stand v a l u e s and c o s t s ($/acre) by stand age (years) f o r Douglas f i r . E s t a b l i s h m e n t c o s t o f $50.00 p e r acre and annual maintenance c o s t o f $1.00 per acre compounded a t 3, 5 and 7 p e r cent i n t e r e s t 100  xiii. ACKNOWLEDGEMENT  The  co-operation  and a s s i s t a n c e o f t h e  U n i v e r s i t y o f B r i t i s h Columbia Research F o r e s t at Hahey, B.C., Jayvee Logging Co., Haney, B.C., and  B.C. Crossarms L t d . , Surrey,  B.C., i n the  p r o v i s i o n o f study m a t e r i a l and f a c i l i t i e s i s g r a t e f u l l y acknowledged. The  financial  a s s i s t a n c e o f t h e Department  o f F o r e s t r y , Canada, and o f the U n i v e r s i t y o f B r i t i s h Columbia, as w e l l as the a d v i c e and a s s i s t a n c e o f the s t a f f o f the F a c u l t y o f F o r e s t r y i n the p r e p a r a t i o n o f t h e t h e s i s , i s noted w i t h  thanks.  1.  INTRODUCTION  U n t i l r e c e n t l y the h i s t o r y o f f o r e s t e n t e r p r i s e i n B r i t i s h Columbia has been one o f e x p l o i t a t i o n of a n a t u r a l resource. was c o n d i t i o n e d  This e x p l o i t a t i o n  by the abundance o f a c c e s s i b l e  timber  so t h a t the e f f o r t s o f those engaged i n the p r a c t i c e o f f o r e s t r y were d i r e c t e d p r i m a r i l y t o h a r v e s t i n g and processing  timber a t c o s t s l e s s than revenues.  Their  success i n t h i s endeavour i s evidenced by the p r e s e n t importance o f the i n d u s t r y t o the economy o f B r i t i s h Columbia. The  introduction of sustained-yield f o r e s t  management and t h e concept o f terminology such as management p l a n s , working p l a n s ,  allowable  c u t and  f i n a n c i a l r o t a t i o n s , have somewhat changed t h e r o l e o f the p r a c t i s i n g f o r e s t e r .  There i s s t i l l the n e c e s s i t y ,  as i n any b u s i n e s s e n t e r p r i s e , t o ensure t h a t t h e operation  i s functioning at a p r o f i t .  However, the  f o r e s t e r engaged i n s u s t a i n e d - y i e l d management must consider  the f u t u r e and, i n the l i g h t o f h i s p r e s e n t  knowledge and p r e d i c t e d t r e n d s ,  f o r m u l a t e management  p l a n s t o ensure the f u t u r e p r o f i t a b i l i t y o f h i s e n t e r p r i s e .  2. I t i s p o s s i b l e t o s p e c u l a t e on forthcoming market requirments  f o r f o r e s t products and time  w i l l judge t h e accuracy o f the p r o g n o s i s .  alone  However, no  s p e c u l a t i o n i s r e q u i r e d by the f o r e s t e r as t o the p o t e n t i a l i t y o f the r e s o u r c e s a t h i s d i s p o s a l . h i s managed f o r e s t t h e r e i s a c e r t a i n acreage  Within of land  stocked w i t h , o r capable o f producing, a v a r i e t y o f s p e c i e s o f timber.  Each t r e e o f each s p e c i e s has, o r  w i l l have, a c e r t a i n v a l u e as one product o r another. By a c r i t i c a l e v a l u a t i o n o f the p r o d u c t i o n  possibilities  o f h i s f o r e s t , t h e f o r e s t e r can p r o v i d e h i m s e l f w i t h a d e f i n i t e knowledge o f h i s product  potential.  S p e c i f i c d e t a i l s r e g a r d i n g the q u a l i t y o f t r e e s , volume and grades o f l o g s from these t r e e s , and value o f product from the l o g s a r e o f v i t a l i n t e r e s t t o the forester.  P r o v i d e d with such i n f o r m a t i o n , t h e t a s k o f  p l a n n i n g f o r the f u t u r e can be somewhat f a c i l i t a t e d . In t h i s t h e s i s an attempt has been made to p r o v i d e data and i n f o r m a t i o n which may be o f i n t e r e s t t o the f o r e s t i n d u s t r y i n B r i t i s h Columbia.  An a n a l y s i s  o f t r e e and stand v a l u e s o f f o u r n a t u r a l stands o f Douglas f i r (Pseudotsuga  m e n z i e s i i (Mirb.) Franco) has  3.  been made.  The a c t u a l grades and value o f the lumber  r e c o v e r e d from the stands a r e presented w i t h a t h e o r e t i c a l assessment o f the value o f the optimum product as d e f i n e d by l i n e a r programming s o l u t i o n s . F i n a n c i a l r o t a t i o n s o f the stands a r e e s t i m a t e d and r e l a t i o n s h i p between t r e e v a l u e and b i o l o g i c a l v a r i a b l e s i s examined. On the t h e o r y t h a t t r e e q u a l i t y s h o u l d be d e f i n e d i n terms o f a net money standard, the n e t v a l u e per c u b i c f o o t o f t r e e o r l o g i s the b a s i s f o r most o f the d i s c u s s i o n .  Logging  c o s t s and product  v a l u e s have been d e r i v e d from a review o f the l i t e r a t u r e and from l o c a l sources.  They a r e thought  t o be  r e p r e s e n t a t i v e o f c u r r e n t c o s t s and v a l u e s on the coast o f B r i t i s h Columbia.  The data on lumber y i e l d s  here were o b t a i n e d from m i l l s t u d i e s conducted  presented by the  author under the a u s p i c e s o f the F o r e s t Products Laboratory o f the Canada Department o f F o r e s t r y , Vancouver, B r i t i s h Columbia.  RELEVANT INFORMATION Stand D e s c r i p t i o n s The 86-, 106- and 145- y e a r - o l d stands were l o c a t e d on the Research F o r e s t o f the U n i v e r s i t y of B r i t i s h Columbia a t Haney, B.C.  The 63- y e a r - o l d  stand was l o c a t e d on the campus f o r e s t o f the above university.  A l l o f the stands were composed of  Douglas f i r , western hemlock (Tsuga h e t e r o p h y l l a (Raf.) Sarg.) and western r e d cedar (Thu.-ja p l i c a t a Donn, ). Sampled p o r t i o n s o f the stands contained more than 90 per cent Douglas f i r by volume. Average s i t e i n d i c e s f o r the stands, based on the average height o f dominant and co-dominant t r e e s , were 160, 165, 175 and 165 a t 100 years i n order of ascending stand age.  Thus, a l l of the stands came  under the broad grouping of s i t e c l a s s I I Douglas f i r as designated by McArdle, Meyer and Bruce (1949). Ages of the sampled t r e e s w i t h i n each stand were remarkably uniform.  C o e f f i c i e n t s o f v a r i a t i o n of  age f o r the 63-, 86-, 106- and 145- y e a r - o l d groups were 4, 5, 3 and 5 per cent r e s p e c t i v e l y .  5. Study procedures Sample t r e e s were s e l e c t e d a t random, w i t h i n t h r e e - i n c h diameter c l a s s e s , from each s t a n d . Data on t r e e diameter, h e i g h t s and o t h e r b i o l o g i c a l v a r i a b l e s were c o l l e c t e d f o r each t r e e .  The b u t t  34-^oot s e c t i o n s o f each t r e e were graded f o r p e e l e r l o g o r saw l o g q u a l i t y .  Estimates of s u i t a b i l i t y of  t r e e s and t r e e - s e c t i o n s f o r use as p i l i n g were made. The l o g s c u t from each t r e e were i d e n t i f i e d w i t h t r e e number, then s c a l e d and graded a c c o r d i n g t o the s p e c i f i c a t i o n s o f the B.C. board and c u b i c f o o t  rules.  A l l o f the study l o g s were manufactured rough lumber.  into  Circumstances n e c e s s i t a t e d the use o f  t h r e e d i f f e r e n t sawmills f o r the m i l l s t u d i e s .  Each  sawmill was equipped w i t h a c i r c u l a r head-saw and an edger as t i t s - b a s i c l o g c o n v e r s i o n equipment and a l l t h r e e manufactured a s i m i l a r product.  The lumber from  each l o g was i d e n t i f i e d by l o g number and t a l l i e d a c c o r d i n g t o grade and dimension.  Grade s p e c i f i c a t i o n s  used were those o f t h e B r i t i s h Columbia Lumber Manuf a c t u r e r ' s A s s o c i a t i o n Standard Grading and D r e s s i n g Rules No. 59 f o r Douglas f i r .  The percentage o f lumber  6. volume recovered by thickness f o r each age c l a s s was as follows: Stand age (years)  Lumber volume per cent by t h i c k n e s s , 1» 2" 3" t o 5" 6" and over  63  18  14  39  29  86  8  19  44  29  106  11  27  55  7  145  9  23  35  33  The lumber was evaluated using 1965 market p r i c e s f o r rough, unseasoned Douglas f i r which averaged as f o l l o w s : Lumber grade  F.Q.B. m i l l p r i c e $/M fbm  B and B e t t e r Clear  175  C Clear  165  D Clear  125  Select Structural  105  Construction  95  Standard  85  Utility  70  Economy  40  7. Sample and stand t r e e diameter  distribution  The d i s t r i b u t i o n s o f sample t r e e s and o f t r e e s p e r acre by t h r e e - i n c h diameter shown i n Table I .  c l a s s e s are  Volumes per a c r e r e c o v e r e d a r e  shown i n Table I I w i t h t h e d i s t r i b u t i o n o f volume by log  grade.  I t w i l l be noted i n Table I t h a t t r e e s o f  the s m a l l e r diameter  c l a s s e s were not sampled.  This  was not by c h o i c e but was d i c t a t e d by the p h y s i c a l n e c e s s i t y o f having sample t r e e s i n f a i r l y c l o s e p r o x i m i t y t o each o t h e r i n order t o f a c i l i t a t e h a r v e s t and t r a n s p o r t en masse t o the study Lumber v a l u e s f o r those diameter  their  sawmills.  c l a s s e s present i n  the stands, but not sampled, were o b t a i n e d by v a l u e p r o j e c t i o n o f the sampled m a t e r i a l .  Data from t r e e s  o f 12 i n c h e s and over i n diameter o n l y were used f o r t h i s a n a l y s i s , as these were c o n s i d e r e d the merchantable component o f the stands. Standards o f u t i l i s a t i o n p r a c t i s e d were somewhat poorer t h a n t h e rough u t i l i s a t i o n  standards  s p e c i f i e d i n the B.C. F o r e s t S e r v i c e Standard F o o t Volume Tables o f 1962.  The average  Cubic-  u t i l i s e d top  diameters and l e n g t h s f o r the f o u r stands were as shown  8. i n Table I I I . the average  I t i s worthy o f note a t t h i s time t h a t  percentage  o f h e i g h t u t i l i s e d d i d n o t vary  a p p r e c i a b l y among age c l a s s e s , being 64 p e r cent i n t h r e e o f the stands and 66 per cent i n the o t h e r . The primary reason f o r the i n c r e a s e w i t h stand age i n top diameter r e c o v e r e d , shown i n Table I I I , was f a l l i n g breakage i n the t a l l e r  trees.  9. Table I .  Sample and Stand Tree D i s t r i b u t i o n s by 3-Inch D.B.H. C l a s s e s f o r F o u r Stands o f Douglas F i r , Stand Age  DBH, Class (inches)  12 15 18  21 24  27 30 33 36 39  62 8_6 106 145 No. Trees Sampled  7 10 11 13  5 3 1  4 5 9 6 4 6 1  42  45 48 Total  (1)  50  35  4 5 4 4 8 4 6 4 3 1 43  4 6 3 6 6 3 2 3 1 34  (Years)  §1  M  12" and 10 20 37 23 35 10 16  5 3 1  23  30 3 10 7  107 126  106  145  over DBH(1  8 2 12 9 6 3 9 10 3 5 2 2 71  E s t a b l i s h e d from Data on l / l O t h - a c r e sample i n each area.  . . . . .  10 2 1 8" 7 4 9 14 2 7  1 65  plots  10, Table I I . Percentage Log Grade D i s t r i b u t i o n by Cubic Volume Recovered f o r Four Stands of Douglas F i r  Stand Age (Years) Log Grade  63 86 106 145Percentage Log Grade D i s t r i b u t i o n by Cubic Volume  No. 3 Peeler No. 4 Peeler or S.F.P.U)  8  No. 2 Sawlog No. 3 Sawlog  92  T o t a l Volume per Acre Recovered (cubic f e e t ) 7,235  (1)  3  13  18  10  12  6  40  27  76  47  48  14,208 13,800  Suitable f o r peeling.  16,600  11. Table III.  U t i l i s a t i o n Standards f o r F o u r Stands o f Douglas F i r  Stand Age  Average Stump Height (years) ( f e e t )  Average Top Diameter (inches )  Average Utilised Length (feet)  Percentage o f T o t a l Height Utilised  63  2  8.4  75  64  86  2  9.7  96  64  106  2  11.5  114  66  145  2  12.7  110  64  12. C o s t s and  Values o f Products  A l l c o s t s and v a l u e s summarized i n t h i s t h e s i s were d e r i v e d i n d e t a i l by Dobie (1966). some o f the phases o f l o g g i n g , p r o d u c t i o n obtained  from the l i t e r a t u r e and  For  times were  c o s t s per u n i t  time were c a l c u l a t e d from c u r r e n t equipment l a b o u r c o s t s i n B r i t i s h Columbia.  of  and  In these cases  20  per cent o f l a b o u r c o s t s have been added f o r p a y r o l l overhead and  an a d d i t i o n a l 10 per cent o f p a y r o l l  machine c o s t s added f o r g e n e r a l and expense. no  and  administrative  Because o f the d i f f i c u l t y o f d e f i n i n g them  c o s t s have been added f o r taxes and  laneous overhead. miscellaneous  other  miscel-  Smith et a l . (1961) i n d i c a t e d t h a t  c o s t s accounted f o r 51 per cent o f  t o t a l c o s t o f primary l o g g i n g and t h i n n i n g c o s t per M fbm  Scribner.  23 per cent o f  the the  These i n c l u d e d  road  and booming and towing c o s t s which have been d e r i v e d s e p a r a t e l y here.  The  allowance here f o r  miscellaneous,  i f road c o s t s and booming and towing c o s t s are would l i e somewhere i n between the two  included,  percentages  shown above.  Lumber and plywood manufacturing and  piling  13. production  c o s t s were o b t a i n e d  and from l o c a l i n d u s t r y .  from the l i t e r a t u r e  No p a y r o l l overhead o r  a d m i n i s t r a t i v e c o s t s were added t o these e s t i m a t e s  as  i t was assumed t h a t they were a l r e a d y i n c l u d e d i n the quoted c o s t s . Many o f the l o g g i n g and m i l l i n g time and cost curves were o f a logarithmfe-, nature w i t h the s t r a i g h t l i n e form o f y = a + b l o g x.  The r e l e v a n t  equations and t h e i r s t a t i s t i c s a r e shown i n the appropriate  tables.  Logging c o s t s Logging c o s t s used i n t h i s t h e s i s a r e f o r s p e c i f i c p i e c e s o f equipment working under c e r t a i n assumed c o n d i t i o n s .  Yarding  costs are f o r a portable  s t e e l span y a r d i n g over an average t u r n d i s t a n c e o f 400 f e e t .  Loading c o s t s a r e f o r a mobile l o a d e r and  t r u c k - h a u l i n g c o s t s f o r a 50,000-pound l o a d t r u c k e d  over  a r o u n d - t r i p d i s t a n c e o f 10 m i l e s on g r a v e l and 30  miles  on pavement.  The assumed water-towing d i s t a n c e i s 20  miles. (a)  F a l l i n g and bucking c o s t s . Average f a l l i n g and bucking times p e r t r e e were  14  estimated from t h e work o f V a l g ( 1 9 6 2 ) , t h e U n i t e d S t a t e s Bureau o f Land Management ( 1 9 6 4 ) , and Nixon and Gunn ( 1 9 5 7 ) . to  F a l l i n g and bucking c o s t s were c a l c u l a t e d  be 17 c e n t s per minute.  Costs f o r i n d i v i d u a l l o g s  were a s s i g n e d on the b a s i s o f p r o p o r t i o n a t e time by volume.  The d e t a i l s o f f a l l i n g and bucking times and  c o s t s f o r t r e e s and l o g s a r e presented i n T a b l e s IV and V.  R e g r e s s i o n equations f o r f a l l i n g and bucking  times  and t r e e volumes r e c o v e r e d a r e presented i n the appropr i a t e t a b l e s with t h e i r r e l e v a n t (b)  statistics.  High-lead yarding costs. Y a r d i n g times f o r a two-log t u r n over an  average  y a r d i n g d i s t a n c e o f 400 f e e t were d e r i v e d from  the work o f V a l g ( 1 9 6 2 ) , t h e Bureau o f Land Management (B.L.M.) ( 1 9 6 4 ) , Tennas e t a l . (1955) and Adams ( 1 9 6 5 ) . Y a r d i n g c o s t s were estimated t o be 60 c e n t s p e r minute. Times and c o s t s by t u r n volume a r e g i v e n i n Table VI w i t h a p r e d i c t i o n equation f o r y a r d i n g time by t u r n volume. (c)  Loading c o s t s Average l o a d i n g times f o r mobile l o a d e r s were  estimated from t h e work o f V a l g ( 1 9 6 2 ) , Adams ( 1 9 6 5 ) , the B.L.M. (1964) and Mcintosh  (I960).  Current loading  c o s t s were estimated a t 29 c e n t s per minute.  Loading  15. t i m e s and  c o s t s by l o g volume are p r e s e n t e d i n T a b l e  V I I w i t h the a p p r o p r i a t e  r e g r e s s i o n equation  of  l o a d i n g time on l o g volume. (d)  Truck-hauling  cost  E s t i m a t e s o f r o u n d - t r i p time f o r the of surfaces considered o f the B.L.M. ( 1 9 6 4 )  types  here were d e r i v e d from the work  and  Byrne e t a l .  (I960).  t o be 2 1 cents per minute  Operating  c o s t s were estimated  and  delay  c o s t s t o be 1 5 cents per minute f o r l o a d i n g  and  unloading.  f o r Douglas f i r ,  Table V I I I shows assumed l o g weights the r e s u l t i n g c u b i c volume f o r a  5 0 , 0 0 0 - p o u n d l o a d and  the c o s t per C c f o f l o g s f o r a  2 0 - m i l e haul at a cost of $ 1 7 . 4 0  per round  trip  t r a v e l l i n g time o f approximately 82 minutes. c o s t s , added to the d e l a y h a u l i n g c o s t s o f Table (e)  Booming and  equation theory  the  total  IX.  towing  Booming and  costs, provide  These  costs  towing c o s t s and  relative  cost  presented i n Table X have been developed on  t h a t c o s t s per u n i t volume o f l o g s should  the  be  a l l o t t e d on the b a s i s o f a r e l a t i o n s h i p s i m i l a r to those g i v e n f o r the o t h e r phases o f l o g g i n g . times per C c f o f l o g s boomed and  Handling  towed i n c r e a s e  with  16. decreasing  l o g volume, consequently c o s t s i n c r e a s e  accordingly.  The  data presented  on i n f o r m a t i o n o b t a i n e d contractors. s i z e o f 600 and 15  i n Table X are based  from l o c a l booming and  Cost per M fbm o f booming an average l o g fbm  i n t o 5 s o r t s would be $1.25  cents per s o r t , o r $2.00 per M fbm.  would be 80 cents per M fbm  per M  f o r a 20-mile tow.  (f)  f o r a l o g volume o f 600  fbm  Towing c o s t s  the t o t a l booming and towing c o s t i s estimated per M fbm  towing  Thus a t $2.80  fbm.  Road c o s t s Road c o s t s per Ccf o f l o g s are t r e a t e d here  i n a f a s h i o n s i m i l a r to the c o s t s per u n i t volume f o r the o t h e r phases o f l o g g i n g .  Although the c o s t o f  making does not depend to a g r e a t extent o f timber s e r v i c e d by the road, per C c f o f l o g s does.  road-  on the volume  the c o s t o f road-making  I f the road  s e r v i c e d a heavy  volume o f l a r g e t r e e s then c o s t s per Ccf would be  less  than i f i t s e r v i c e d a s m a l l e r volume o f s m a l l t r e e s . Consequently road c o n s t r u c t i o n and maintenance c o s t s have been a s s i g n e d decreasing  at an i n c r e a s i n g r a t e per C c f o f l o g s  with  l o g volume. Information  obtained  from l o g g i n g  c o n s t r u c t i o n companies on the B.C.  road  coast i n d i c a t e d t h a t  17. r o a d c o s t s can vary from M fbm  $1.00  $10.00  depending on topography, base m a t e r i a l  volumes o f timber s e r v i c e d .  $6.50  to over  per M fbm  f o r the average study l o g o f  Total logging  and  An a r b i t r a r y c o s t o f  i s used here to a s s i g n the c o s t s presented (g)  per  350  fbm  i n Table  XI.  costs  A l l o f the f o r e g o i n g components o f l o g g i n g c o s t s have been t o t a l l e d to r e n d e r the c o s t s i n Table  XII.  presented  18.  Table IV. F a l l i n g and Bucking Times and Costs by Tree UBH and Volume f o r Douglas F i r Tree DBH (inches) 8 10 12 14  16 18 20 22 24 26 28 30  32  34 36 38 40  42 44 46 48 50  F . and B. F. and B. Cubic Feet F. and B. Time per Cost per Recovered Cost per Tree v D Per Tree (3) Ccf Tree 12) (Mn.) (Dollars) (Dollars) 3.8 4*4 5.3 6.4 7.8 9.2 10.7 12.0 13.5 15.0 17.0 18.8 20.5 22.5  24.5 26.5  29.0  31.0 33.0 35.0 37.5 40.0  .65 • 75 .90 1.09 1.33 1.56 1.82 2.04 2.30 2.55 2.89 3.20 3-48 3.82  4.16  4.50 4.93 5.27 5.61 5-95 6.37 6.80  20 25  32  42 56 71 90 110 138  168  196 230 270 310 355 400 450 500 550  600 655 710  3.25 3.00 2.80  2.60  2.38 2.20 2.02 1.85 1.67  1.52  1.47 1.39 1.29 1.23 1.17 1.12 1.10 1.05 1.02 .99 .97 .96  (1)  y = -46.334 + 20.189 Log ( x ) : r = .942** : See =+4.04 where y i s F. and B. time i n min. per t r e e . x i s D.B.H. o f t r e e .  (2) - -  On the b a s i s of 17 cents per min. o f F. and B. time.  (3)  Based on a c t u a l recovery data on 162 Douglas f i r trees from Haney, B.C. y - 19.289 - 3.172 x +.344 x 2 R- = . 9 9 9 * * \ s =+4.70 where y i s cubic volume recovered x i s DBH o f t r e e . r and R - simple and- m u l t i p l e c o r r e l a t i o n c o e f f i c i e n t ** - s i g n i f i c a n t a t 99% l e v e l o f p r o b a b i l i t y . See -standard e r r o r of estimate. :  e e  19. Table V.  Average F a l l i n g and Bucking Times and Costs by Log Volume f o r Douglas F i r  Log Volume (cu. f t . )  5 10 15 20 25 30 50 75 100 125 150 175 200 225 250 275 300 325 350  (1)  F. and B. Time (Min.)  0.8 1.5 2.2 2.8 3.3 3-5 4.8 6.4 8.0 9.5 11.2 12.9 14-4 16.0  17.7 19.2 20.8 22.5 24.2  F. and B. Time ... (Min./Cc£)t ) 1  16.0 15.0 14.7 14.0 13.2 11.7 9.6 8.5 8.0 7.6 7-5 7.4 7.2 7.1 7.1 7.0 7.0 6.9 6.9  F. and B. Cost ($/Ccf)  2.72 2.55 2.50 2.38 2.24 1.99 1.63 1.44 1.36 1.29 1.27 1.26 1.22 1.21 1.21 1.19 1.19 1.17 1.17  y = 20.310 - 2.444 Log (x) : r = .975** .* See = + .775 where y i s F. and B. Time min./Ccf o f Logs, x i s cubic volume o f l o g .  20. Table VI. High-Lead Yarding Times and Costs by Two-Log Turn Volumes f o r a Turn Distance of 400 Feet  Turn Volume (cubic f e e t )  5 10 15 20 25 30 50 75 100 125 150 175 200 225  250  275  300 325 350  Yarding Time Min./Ccf(l)  Yarding Cost(2) $/Ccf  70.0 45.0 30.5 22.0 17.5 15.0 8.7 6.2 4.7 3.8 3.3 2.9 2.6 2.2 2.0 1.9 1.8 1.7 1.7  42.00 27.00  18.30  13.20 10.50 9.00 5.22 3.72 2.82 2.28 1.98 1.74 1.56 1.32 1.20 1.14 1.08  1.02 1.02  (1) -  y = 67.02 - 12.368 Log (x) : r = .897** : See +8.34 where y i s yarding-time i n min./Ccf over 400 f e e t x i s two-log t u r n volume i n cubic f e e t .  (2)  On the b a s i s of 60 cents per minute.  21. Table V I I .  Loading Times and C o s t s by Log Volume f o r Mobile  Log Volume (Cubic F e e t )  5 10 15 20 25 30 50 75 100 125 150 175 200 225 250 275 300 325 350  Loaders  Loading Time^ ^ (Min./Ccf) 1  11.4 9.8  8.3 7.2 6.1 5.4 3.7 2.9 2.6 2.6 2.6 2.6 2.6 2.6 2.6 2.6 2.6 2.6 2.6  Loading C o s t ^ ) (£/Ccf) - 2  3.31 2.84 2.41 2.09 1.77 1.57 1.07 .84 .75 .75 .75 .75 .75 .75 .75 .75 .75 .75 • 75  (1) - -  y = 13.206 - 2.012 Log ( x ) : r = .940** : See = + 1.01 where y i s l o a d i n g time min./Ccf o f l o g s , x i s c u b i c volume o f l o g .  (2)  On the b a s i s o f 29 cents per  minute.  22. Table V I I I .  Log Weights Per Cubic F o o t and  Cubic  F e e t per 50.000 Pounds o f Logs f o r Douglas F i r w i t h Truck-Haul Cost per Ccf Logs a t $17.40 f o r a 20-Mile Truck  Log Top Diameter (inches) 6 8  Log Weight (Pounds per Cubic Foot)  62 61  10 12 14  60 59  20  55  16 18 22  24 26  28  30 32 34 36 38  40  Haul  58 57 56  54 53  52  51 50 49 48 47 46 45  Cubic F e e t  Per 50,000 Pounds 806  820 833 847 862 877 893 909 926 943 962 980 1000 1020 1042 1064 1087  1111  Truck-Haul Cost (*/Ccf) 2.16  2.12 2.09 2.05 2.02 1.98 1.95 1.91  1.88  1.85  1.81  1.78 1.74 1.71 1.67 1.64 1.60  1.57  23Table DC.  T o t a l o f Hauling Costs and Delay C o s t s f o r a Round-Trip  Truck Haul o f 10 M i l e s on  G r a v e l and 30 M i l e s on Pavement  Log Top Diameter (inches)  16  6 8 10 12 14 16  4.68 4.38 4.10 3.82 3-55 3.28  20 22  2.87 2.72  18  24  26  28  30 32  34 36 38 40  3.09 2.60  2.48 2.39 2.31 2.25 2.21 2.18 2.14 2.11  Log Length (Feet) 24 32 -40 T o t a l C o s t s - $/Ccf  4.35 4.05 3.68 3.40 3.11 2.88 2.73 2.60  2.49 2.42  2.35 2.32 2.28 2.25 2.21 2.18 2.14 2.11  R e l a t i v e c o s t index:-  y = 524-588 - 80.485 = ± 39.71  4.09 3.68 3.33 3.05 2.86 2.70 2.58 2.48 2.42 2.39 2.35 2.32  2.28 2.25 2.21 2.18  2.14 2.11  3.79 3.38  3.08  2.87 2.71 2.59 2.52  2.45 2.42 2.39 2.35  2.32 2.28 2.25  2.21 2.18  2.14 2.11  Log (x): r = .942** : See  where y i s r e l a t i v e c o s t o f h a u l i n g . x i s c u b i c volume o f l o g . Based on an index o f 100 f o r l o g volumes o f 100 c u b i c f e e t and over.  Table X.  Booming and Towing Cost i n $/Cef by Log Diameter  and Length on the B a s i s o f a Cost  o f $2.80 per M fbm f o r an Average Log o f fbm and a Tow  Log Top Diameter (inches) 6 8 10 12 14 16 18 20 22 24 26  28  30 32 34 36 38 40  16 9.00 8.10 7.00 6.20 5.40 4-50 4.00  Log Length (Feet) 32 24 Costs - $/Ccf 6.80  5.90  6.70  5.70 4.50 3.70  4.50  1.78  1.58  2.70 2.40  1.82  40  7.70  2.20 2.10 2.00 1.92 1.87  3.00  600  D i s t a n c e o f 20 M i l e s  5.75 4.80 3.90 3.35 2.85 2.50 2.25 2.10 1.95 1.90 1.85 1.78 1.73 1.68  3.40  Top  1.62  3.10 2.60 2.30 2.10 1.95 1.90 1.80 1.75  3.60 3.00 2.45 2.10 2.00 1.90  1.82  1.70  1.75 1.70 1.65 1.58  1.50  1.40  1.63 1.58  1.44  1.40  1.50 1.45  1.35 1.32  R e l a t i v e Cost Index  y = 762.034 - 121.885 Log (x): r = .964** : See = + 46.83 where y i s r e l a t i v e c o s t o f booming and towing  x i s the c u b i c volume o f the l o g . Based on an index o f 100 f o r a 350 cu. f t . l o g .  25. Table X I .  Road C o n s t r u c t i o n and Maintenance C o s t s i n $/Ccf by Log Top Diameter and Length on the B a s i s o f $6.50 per M fbm f o r an Average Log o f 350  Log Top Diameter (inches)  6 8  10 12 14 16 18  20 22  24  26 28 30  32  34 36 38 40  fbm.  16  14.60  13.20 11.36 10.05 8.78 7.30 6.50 5.53 4.88 4.40 3.90 3.58 3.42  3.25 3.12 3.04 2.96 2.90  Log Length (Feet) 32 24 Road Cost -- $/Ccf  12.50 10.90 9.35 7.80  6.44 5.45 4.64 4.06 3.66 3.42 3.17 3.09 3.00 2.90 2.81  2.74 2.64 2.57  11.00 9.28 7.30 6.02 5.04 4.23  3.74 3.42 3.17 3.09 2.93 2.84 2.76 2.65 2.57 2.44 2.34 2.28  40 9.60  7.32 5.85 4.88 3.98 3.42 3.25  3.09 2.96 2.84 2.76 2.68 2.57 2.44 2.36 2.28 2.20 2.15  R e l a t i v e Cost Index:y =  739.651 - 118.123 Log (x) : r = .962** : See where y i s r e l a t i v e . c o s t o f road c o n s t r u c t i o n and maintenance. x i s the c u b i c volume o f the l o g . Based on an index o f 100 f o r a 350 c u b i c f o o t l o g .  = + 46.85  26. Table X I I .  T o t a l Logging Costs i n $/Ccf f o r Douglas F i r under C o n d i t i o n s S t a t e d f o r the Cost Components  Log Top Diameter (inches)  6 8  10 12 14 16 18  20 22 24 26 28 30 32  34 36 38 40  16 "~  64-16  50.86 40.49 34.01 28.87 24-12 21.22 18.57 16.46 14-86 13.33  12.38 11.81  11.30 10.84 10.41 10.16 9.89  Log Length (Feet) 2]± -32 Logging Cost - $/Ccf  47.17 37-72 30.84 25.42 21.13 18.10 15.75 14.07 12.76 11.92  11.19 10.76 10.37 10.03 9.77 9.54 9.27 9.12  38.08  30.59  24-06  19.96  16.76 14.55 13.07 11.98 11.19  10.76 10.31 10.00 9.75 9.46 9.21 8.96 8.75 8.61  ^0  31.75 24.16  19.63  16.56  14.05 12.30 11.60  10.83 10.44 10.13 9.88 9.64 9.34 9.03 8.85 8.68 8.51 8.39  27. M i l l i n g costs For the d e r i v a t i o n o f m i l l i n g c o s t s , a h y p o t h e t i c a l band m i l l with a capacity of 100 M fbm per 8 hours has been assumed.  Sawmilling costs per  M fbm o f l o g s o r lumber are normally a l l o c a t e d to l o g s i z e s on the b a s i s o f time taken a t the head-saw t o process o r produce the u n i t volume o f i n t e r e s t . Sawing time per l o g normally increases w i t h l o g diameter and l e n g t h , but sawing time per u n i t volume of logs o r lumber normally decreases as l o g diameter and length i n c r e a s e . M i l l i n g times and costs were derived from the work o f Matson (1952), Lodewick (1941) and Rankin  (1963).  The estimated average m i l l i n g costs were  $26.00 per M fbm o f l o g s .  The average study l o g  scaled 350 fbm and had a conversion f a c t o r o f 5.7 fbm per cubic f o o t o f l o g s c a l e .  Thus, average m i l l i n g  costs were $14.52 per Ccf o f l o g s f o r the average l o g . Sawing time per Ccf o f l o g s f o r the average l o g o f 350 fbm o r 61 cubic f e e t was estimated a t approximately three minutes.  The derived average sawing cost was  $4.88 per C c f o f l o g s per minute o f head-saw time.  28. Saw-time per C c f o f l o g s , by l o g top diameter  and  l e n g t h , are presented i n Table X I I I w i t h d e r i v e d relationships.  M i l l i n g c o s t s are g i v e n i n Table  XIV.  29. Table X I I I .  Saw-Time i n M i n . p e r C c f o f Logs by Log Top Diameter and Length f o r a B a n d - M i l l  Log Top Diameter (inches) 6 a 10 12  14  16 18 20 22 24 26  16(D 11.35  7.62 5.61  4.70  4-04 3.76  3.50  i2  3.32 3.14 3.02 2.94 2.86 2.80 2.75  3a 40  2.68 2.67 2.66  28  30  34 36  2.70  -  Log Length 40(4) 24(2) Saw-Time i n M i n . / C c f o f Logs 10.12 7.02 5.22 4-35 3-72 3-40 3.11 2.96 2.80 2.69  8.91 6.32 4.80 4.00 3.44 3.13 2.86 2.72 2.57 2.48  2.54 2.46  2.35  2.62  2.41  2.39 2.36 2.35 2.34  7.78  5.70  4.41  3.71  3.20 2.92 2.67 2.54 2.42 2.33 2.26 2.20 2.14 2.10  2.41  2.26  2.20 2.19 2.18 2.18 2.17  2.07  2.06 2.06 2.06  (1)  y = 14.577 - 3.516 Log ( x ) : r =.882**: See =+1.09  (2)  y = 13.368 - 3.248 Log ( x ) : r  (3)  y = 11.916 - 2.870 Log ( x ) : r  (4)  y = 10.520 - 2.489 Log ( x ) : r =.910**: See =+  =.896**: =.904**:  See =± .94 See =+ .79  where y i s saw-time i n min./Ccf o f l o g s x i s l o g top diameter i n inches.  .66  Table XIV.  M i l l i n g C o s t s i n D o l l a r s p e r C c f o f Logs bv Log Top Diameter and L e n g t h on B a s i s o f $4.90 p e r C c f p e r M i n u t e o f Saw-Time  Log Top Diameter (inches) 6 8 10 12  14  16 IS 20 22 24  26 28  30 32 34 36 38 40  16  Log L e n g t h ( F e e t ) 24 32 M i l l i n g C o s t $/Ccf o f Logs  55.51  37.27 27.44 22.99 19.76 18.39 17-12 16.24  15-36  14.77 14.38 13.99 13.69 13.45 13.21 13.11 13.06 13.01  49.50  34-33 25-53  21.28  18.19 16.63 15.21 14.48 13.69 13.16 12.81 12.42 12.03 11.79 11.69 11.54 11.49 11.44  43.58 30.91 23.48 19.56  16.82  15.31 13.99  13.30  12.57 12.13 11.79 11.49 11.05  IO.76 10.71  10.66 10.63 10.61  40  38.05  27.88 21.57  18.15  15.65  14.28  13.06 12.42  II.84  11.40  11.05  10.76 10.47 10.27 10.12 10.08 10.08 10.08  31. Lumber v a l u e s The percentage  o f lumber volume r e c o v e r e d  by lumber grades i s shown i n Tables XV the v a l u e s by l o g grade, percentage stand.  and XVI  volumes per a c r e ,  with  and  volume d i s t r i b u t i o n by l o g grade f o r each  Lumber v a l u e s i n c r e a s e d c o n s i s t e n t l y w i t h  l o g q u a l i t y i n a l l stands except the 145-year, where the grade 2 sawlogs had a h i g h e r lumber v a l u e  than  the grade 4 p e e l e r l o g s but lower than t h a t o f the grade 3 p e e l e r l o g s . The average g r o s s and net lumber v a l u e s per acre are presented i n Table XVII f o r the f o u r stands. The  c o n v e r s i o n r e t u r n s shown are the amounts a v a i l a b l e  f o r stumpage and p r o f i t .  Table XVII shows t h a t the  average lumber value per c u b i c f o o t o f r e c o v e r e d volume d i d not vary much among the t h r e e younger stands, i n c r e a s e d by  12  but  cents per cubic f o o t from the 106-to the  145-year-old stand.  T h i s i s accounted  f o r by the h i g h  volume o f grade 3 p e e l e r l o g s i n the 145-year stand  and  the h i g h q u a l i t y o f lumber o b t a i n e d from them. I t i s a l s o apparent  from Table XVII t h a t l o g g i n g  and m i l l i n g c o s t s per cubic f o o t o f l o g s , d e r i v e d e a r l i e r  32. i n t h i s t h e s i s , d e c r e a s e d w i t h s t a n d age.  Average l o g  s i z e i n c r e a s e d w i t h s t a n d age.  average  Therefore,  l o g g i n g and m i l l i n g c o s t s per u n i t volume d e c r e a s e d . As a r e s u l t the net lumber v a l u e s p e r c u b i c f o o t o f l o g increased f a i r l y uniformly w i t h stand  age.  Table XV.  Percentage Lumber Y i e l d by Lumber Grade, Value by Log Grade'"and Merchantable Volumes Per Acre f o r 145- and 106-Year-old Douglas F i r Stand Age 145 y r .  Lumber Grades  3P  B and B t r C l e a r C Clear D Clear Select S t r u c t u r a l Construction Standard Utility Economy  59 1 1 28 4 2 3 2  Lumber value $/ fbm $/cu.ft.log  141 1.12  Volume/acre Lumber recovery f a c t o r Percent d i s t r i b u t i o n by l o g grade * 3P Grade - 4P(SFP)Grade 2 3 --. Grade 3S Grade  3 4 2 3  106 y r .  AV. 3P 4P ,, 2S 28 38 4P (S.F.P.) (S.F.P.) Percentage Volume Recovery 36 3 1 23 9 3 16 9 115 0.78  31 2 1 46 9 3 5 3 127 0.95  7 1  -  53 25 5 7 2 107 0.79  24 1 1 45 17 4 5 3 117 0.87  12  27  AV  7 3 2 28 41 12 6 1  16 13 4 27 26 12 2 —  20 5 5 36 24 6 3 1  11 5 4 31 34 9 5 1  1 1 1 24 49 15 8 1  122 0.99  116 0.86  109 0.80  95 0069  13,800 cu. f t . 7.3  16,600 cu. f t . 7.4 13  3S  48  peeler l o g . peeler l o g or s u i t a b l e f o r peeling. sawlog. sawlog.  3  10  40  47  103 0.75  Table XVI. Percentage Lumber Y i e l d by Lumber Grade Value by Log Grade and Merchantable Volumes per Acre f o r 86- and 63-year-old Douglas F i r  Lumber Grades  B and B t r Clear C Clear D Clear Select Structural Construction Standard Utility Economy Lumber value f / fbm $/cu.ft.log Volume/acre Lumber recovery factor Percent d i s t r i b u t i o n by l o g grade (1)  Stand Age  63 Log Grades 33 'AV. (4P.2S)^ ) 3S (S.F.P.) Percentage Volume Recovery  86 y r .  yr,  4P (S.F.P.)  25  0.3 3.4 1.4 43.6 41.7 7.7 1.9  —  0.4 2.1 1.1 41.6 39.2 12.6 2.3 0.7  0.1 0.5 0.1 47.2 38.1 8.5 4.9 0.6  0.2 0.9 0.4 45.8 38.4 9.5 4.2 0.6  3.9 9.7 17.2 51.3 17.1 0.6 0.2  0.6 1.4 6.4 59.8 27.3 3.6 0.9  1.0 2.3 7.6 59.0 26.1 3.2 0.8  104 0.79  102 0.77  99 0.73  100 0.74  114 0.80  104 0.74  105 0.74  1  14,208 cu. f t .  —  6  —  7, 235 cu. f t .  7.4 18  —  AV,  7C0 76  8  92  A l l o f the grade 2 sawlogs i n t h i s age c l a s s were also grade 4 peeler l o g s o r S.F.P.  35. Table XVII.  Gross and Net Lumber Values per Cubic Foot o f Log Scale from Four Stands o f Douglas F i r  Stand Age (years)  Gross Lumber Value ($/cu.ft.)  Logging and Milling Costs ($/cu.ft.)  Net Volume Lumber Lumber Per ConverValue Acre sion ( $ / c u . f t . ) (cu.ft.) Return er acre _$)  ?  63  .73  137  .36  7,235  2,600  86  .74  .31  • 43  14,208  6,100  106  .75  .25  .50  13,800  6,900  145  .87  .25  .62  16,600  10,300  36. Value of pulp chips from sawmill residue An a d d i t i o n a l source of revenue f o r sawmill owners i s created by the manufacture and s a l e of pulp chips from t h e i r residue.  A u n i t of pulp c h i p s ,  as recognised on the coast of B r i t i s h Columbia, i s volumetric and the same f o r a l l species.  I t i s that  volume of chips which occupies 200 cubic f e e t of space and, depending on degree of compaction, i s estimated to contain 7 0 to 9 0 cubic f e e t of s o l i d wood.  A conversion of 80 cubic f e e t of s o l i d wood per  u n i t of chips i s used here. Dobie (1966) estimated the cost of  producing  chips from residue f o r the type of m i l l envisaged $4.55 per u n i t .  as  Douglas f i r pulp chips from sawmill  residue are c u r r e n t l y s o l d f o r 27 per cent of the p r i c e of grade 3 hemlock sawlogs, or (27 per cent of $60.00 per M fbm) $16.20 per u n i t .  Estimates of u n i t s of chips  produced from Douglas f i r band sawmills (Dobie and Parry, 1965)  are presented i n Table X V I I I , w i t h the manufactur-  i n g c o s t s and gross and net values of chips per Ccf of logs.  37. Table X V I I I .  Volume, Manufacturing c o s t and v a l u e o f Douglas F i r Pulp Chips from Band Sawmill Residue.  B.C. Coast U n i t s ( E q u i v a l e n t  o f SO cu. f t . S o l i d Wood)  Log Top Diameter (inches)  6 8  10 12 14 16 18  20 22  24  26 28 30 32 34 36 38 40  Units of P u l p Chips Per C c f Logs • 57 .48 • 41 .38 .34 .31 .30 .29 .29 .29 .29 .29  .29  .29 .29  .29 .29 .29  Manufacturing Cost a t $4.55 Per U n i t ($) 2.59 2.18 1.87 1.73 1.54 1.41 1.36 1.32 1.32 1.32 1.32 1.32 1.32 1.32 1.32 1.32 1.32 1.32  Gross Value a t $16.20 >er u n i t per  Net Value Per C c f Logs  111  9.23  7.78 6.64 6.16 5.50 5.02 4.86 4.70 4.70 4.70 4.70 4.70 4.70 4.70 4.70 4.70 4.70 4.70  6.64 5.60 4.77 4.43 3.96 3.61 3.50 3.38 3.38 3.38 3.38 3.38 3.38 3.38 3.38 3.38 3.38 3.38  38.  Plywood m a n u f a c t u r i n g  c o s t s and  returns  F a c t o r s w h i c h a f f e c t the c o s t o f f i n i s h e d plywood are l o g c o s t s and m a n u f a c t u r i n g Manufacturing  costs.  c o s t s i n c l u d e the cost of b a r k i n g  and  p e e l i n g l o g s , o f d r y i n g , l a y - u p and p r e s s i n g o f v e n e e r s and o f t r i m m i n g , The  p a t c h i n g and s a n d i n g o f plywood p a n e l s .  c o s t o f p a n e l manufacture i s q u i t e v a r i a b l e and i s  a f f e c t e d by the t h i c k n e s s o f t h e p a n e l and t h e number o f component v e n e e r s .  The grade o f p a n e l produced i s  c o n t r o l l e d by the grade o r grade p o t e n t i a l o f v e n e e r s available.  The Canadian S t a n d a r d s A s s o c i a t i o n Douglas  f i r plywood and component veneer g r a d e s a r e l i s t e d i n Table XIX. C o s t s f o r plywood manufacture i n B r i t i s h Columbia are n o r m a l l y quoted on t h e b a s i s o f one square f e e t o f plywood, (M  3/8ths).  3/8ths  thousand  o f an i n c h i n t h i c k n e s s  These c o s t s are d e r i v e d by d i v i d i n g  total  p r o d u c t i o n c o s t s by t o t a l p r o d u c t i o n o v e r a p e r i o d o f time.  Few companies a t t e m p t t o a l l o c a t e c o s t s t o p l y -  wood by grade and p a n e l s i z e because o f the i n h e r e n t i n such a p r o c e d u r e . t h a t s e l l i n g p r i c e was  Mayhew  (1958)  complications suggested  a f u n c t i o n o f c o s t s and t h a t  the  c o s t r a t i o s f o r veneer manufacture s h o u l d be a p p r o x i m a t e l y  39. 1.5 f o r A veneer and 1.25 f o r B veneer i f C i s used as the base of 1.0.  This procedure has merit where  increased expenditure i s required to r e a l i s e the f u l l potential of A and B veneers (e.g. patching).  Because  the peeler logs discussed here were of low quality, the cost r a t i o procedures are used here to a l l o c a t e manufacturing costs to veneers by grade. Average manufacturing costs derived by Dobie (1966) from the work of Rankin (1963), Herstrom ( I 9 6 0 ) , and from information obtained from the Plywood Manufacturers Association of B.C., were $40.00 per M 3/8ths f i n i s h e d plywood.  Industry average veneer  grade recovery from the c l a s s of peeler logs discussed herein are shown i n Table XX f o r the four stands.  To  f a c i l i t a t e the denrisration of manufacturing costs by veneer grade, the cost r a t i o s previously noted were applied to the average percentage of veneer p o t e n t i a l estimated from the t o t a l population of peeler logs i n the four stands.  Average veneer p o t e n t i a l and  estimated manufacturing costs by veneer grade are shown also i n Table XX. The green veneer input per unit volume of f i n i s h e d plywood and the r e s u l t i n g manufacturing costs  40. per M 3/8ths of plywood by grade are presented i n Table XXI. Veneer recovery i s u s u a l l y quoted as a r a t i o of square f e e t per M fbm l o g s c a l e , or as a percentage of the l o g s c a l e .  For example, a r a t i o of 2.67 M 3/8ths  i s the equivalent of 1000 board f e e t (2 2/3 M s q . f t . x 3/8" = 1000 board f e e t ) o r 100 per cent recovery,  A  recovery r a t i o of 2.3 M 3/8ths quoted by s e v e r a l manufacturers of plywood i n B.C. agree e x a c t l y w i t h the i n d u s t r y average quoted by Clarke and Knauss (1957) f o r western Washington, north-western and south-western Oregon.  A recovery r a t i o of 2.3 M 3/8ths plywood per  M fbm l o g scale i s used here as the b a s i s f o r recovery calculations.  The transformation of t h i s r a t i o to  recovery i n terms of cubic scale i s shown i n Table X X I I . November 1965 car-load p r i c e s f o r plywood i n Vancouver were as f o l l o w s : Plywood Grade G 2 S G Solid G 1 S Solid 2 S Solid 1 S Sheathing  D o l l a r s Per M 3/8ths 186.45  168.70 150.95  165.40 147.65 88.80  41. U s i n g the data p r e s e n t e d i n T a b l e s  XX,  XXI and XXII, and the above p r i c e s , an optimum plywood y i e l d from each stand o f timber was by l i n e a r programming a n a l y s i s .  derived  These are shown  i n Table XXIII w i t h the net v a l u e o f plywood per Ccf of l o g s .  Table XIX.  Douglas F i r Plywood Grades and Component  0121-1961.  Veneers.  Standard  Standards  Association,  Plywood Grades 1.  2.  Component Veneers  Sanded Good Two S i d e s (G2S) Good/Solid ( G / S o l i d ) Good One Side (G1S) S o l i d Two S i d e s ( S o l i d 2S) S o l i d One Side ( S o l i d IS) Marine Unsanded S e l e c t Sheathing Sheathing  Canadian  Face A C A C A C B B A  C Improved C  Inner  C C B C C  Back A B C B C A C  c  42, Table XX.  Percentage Veneer Y i e l d by P e e l e r Grade, Average Percentage Veneer Y i e l d by Veneer Grade and A l l o c a t i o n o f M a n u f a c t u r i n g C o s t s by Veneer Grade f o r F o u r Stands o f Douglas Fir  A. Stand Age (years) 145 145 106 106 86 63 B.  C.  Percentage Veneer Y i e l d by P e e l e r Grade and Stand Age Percentage Veneer Y i e l d Peeler Grade B 8 12 3 5 4 8 3 4 5  4 4  80  95  88  95  100 100  Average T o t a l Percentage Veneer Y i e l d by Grade from a l l Ages Veneer Grade Percentage A 5 B 2 C 93  Manufacturing C o s t s A l l o c a t e d Average Cost  by  $40.00/M 3/8ths Plywood  $40.00 = . 0 5 ( 1 . 5 cost C)+.02(1.25 Cost C)+ .93(Cost C) = (.075 + .025 + .93) = 1 . 0 3 Cost C  Cost C = 40.00/1.03  Cost B = 1.25 Cost C Cost A = 1.5 Cost C  Cost C  = $39.20  = {J49.00 = $58.80  43. Table XXI.  Green Veneer Input per U n i t Volume o f F i n i s h e d Plywood and Manufacturing C o s t s per M j / 8 t h s Plywood by Grade  A. Veneer Grade A B C  Green Veneer Input by Plywood Grade G2S .66  .50  Plywood Grade G / S o l i d G1S S o l i d 2S S o l i d IS Green Veneer Input R a t i o s .33 .33 .33 .66 .33 .50 .83 -50 .83  Sheathing  1.06  The above r a t i o s are based on an i n p u t o f 7 / l 6 t h s o f green veneer f o r 3 / 8 t h s o f sanded plywood w i t h a 3 / l 6 t h core.  B.  Shrinkage allowance i s 6 per cent.  Manufacturing C o s t s p e r M 3 / 8 t h s Plywood Based on Percentage Input o f Green Veneers  Plywood Grade G2S Manufacturing Cost- $ 50 (Log - cost excluded)  G/Solid  47  G1S  45  S o l i d 2S  45  S o l i d IS  42  Sheathing  39  44.  Table X X I I .  Plywood Recovery (M 3/8ths) i n Terms of Log Cubic Scale f o r Four Stands of Douglas F i r  1.  Recovery per M fbm Logs  2.  FEM/Cu.Ft. Ratios Stand Age (years) 145 106 86 63  3.  -  2.3  Peeler Grade 3 4_ fbm/cu.ftT  S77  6.6  oTT  6.1 5.9  5.6  H 3/8ths Plywood per Ccf Log Scale Stand Age P e e l e r Grade (years) 3 4_ M 3/8ths/CcF 145  106 86 63  1.54 1.52  1.40 1.40  1.36 1.29  45. Table X X I I I .  Optimum M i x t u r e o f Plywood Grades t o Maximise Returns from A v a i l a b l e Veneers i n F o u r Stands o f Douglas F i r  Plywood Grades  145  3 340  Stand Age (Years) 86 106P e e l e r Grades 3 4 4 4 Plywood Y i e l d - Sq.Ft . 3/8ths 218 125 125  G2S S2S Sheathing  214 986  1275  Plywood Value $/Ccf Logs  121  81  Logging Cost(IT $/Ccf Logs  10  12  Conversion Return(2) $/Ccf Logs  111  69  107 1195  63  4  1275  1360  1290  81  68  64  10  12  13  14  92  69  55  50  102  (1)  Derived from l o g g i n g c o s t s e c t i o n o f t h i s  (2)  Amount a v a i l a b l e f o r stumpage and p r o f i t .  thesis.  46. Value o f pulp c h i p s from p e e l e r l o g s In a d d i t i o n t o plywood v a l u e from p e e l e r l o g s t h e r e i s the value o f c h i p p a b l e r e s i d u e .  Butler  (1965) estimated a r e c o v e r y o f 0.3 u n i t s o f c h i p s per H fbm o f l o g s from r e s i d u e o r 0.5 u n i t s i f the cores a r e chipped.  Chipping  c o s t s here a r e regarded  as being the same as those o f a sawmill  residue  c h i p p i n g o p e r a t i o n , o r $4.55 per u n i t o f c h i p s . the assumption t h a t t h e cores a r e chipped,  the y i e l d  and value o f c h i p s p e r C c f l o g s c a l e would be as shown i n Table XXIV.  On  47.  Table XXIV.  D e r i v a t i o n o f Chip Values per Ccf Log S c a l e o f P e e l e r Logs from Four  Stands  o f Douglas F i r  1.  Board F o o t / C u b i c Foot R a t i o s  Stand Age  P e e l e r Grade  (years)  3  4 fbm/cu.ft.  145 106 86 63  6.7 6.6  2..  Chip Y i e l d per C c f Logs on the B a s i s o f 0.5 U n i t s per M fbm. Logs  145  .33 .33  106 86 63  145 106 86  63  6.1 6.1 5.9 5.6  .30 .30 .29  .28 3.  Chip Value  -  $16.20 per U n i t .  4.  Chip Cost  -  $ 4.55 per U n i t .  5.  Net Value o f C h i p s - $/Ccf Logs 3.84  3.84  3.49 3.49  3.38 3.26  48. P r o d u c t i o n c o s t s and v a l u e o f  piling  The p r o d u c t i o n o f p i l i n g from a stand o f timber may  be regarded as a h i g h l y - s e l e c t i v e o p e r a t i o n ,  where those t r e e s w i t h p i l i n g p o t e n t i a l are removed w i t h a minimum o f d i s t u r b a n c e to the r e s i d u a l  stand.  I n o r d e r t h a t p i l i n g p o t e n t i a l be r e a l i s e d i n s i t u a t i o n s where a stand i s being c l e a r - c u t the • piling  should be removed before the g e n e r a l l o g g i n g  takes place. Because o f the nature o f the o p e r a t i o n , l o g g i n g f o r p i l i n g i s normally more c o s t l y conventional thinning. an average c o s t o f  (1952)  Joergensen  $13.87  than indicated  per C c f o f l o g s f o r two  t h i n n i n g o p e r a t i o n s i n Douglas f i r i n B r i t i s h Worthington and Shaw  $17.55  (1952)  Columbia.  quoted an average c o s t o f  per C c f o f l o g s f o r t h i n n i n g Douglas f i r i n  Washington.  Worthington  (1957)  t h i n n i n g Douglas f i r to be o f l o g s f o r two  found the c o s t o f  $24.15  and  $22.97  o p e r a t i o n s i n Washington.  c o n v e r s i o n f a c t o r o f 5.5  per M  fbm  Using a  fbm per c u b i c f o o t f o r the  s i z e o f m a t e r i a l , the corresponding  c o s t s would be  $13.30  Worthington  and $12.60 per C c f o f l o g s .  (1961)  a l s o quoted an average c o s t o f $13.33 p e r cord o f 83 c u b i c f e e t o r $16.10 p e r C c f o f l o g s f o r t h i n n i n g 40-  t o 7 0 - y e a r - o l d Douglas f i r i n Washington. P u b l i s h e d i n f o r m a t i o n on t h e c o s t o f  l o g g i n g f o r p i l i n g i s sparse but i n d i c a t i o n s a r e t h a t i t i s more expensive than the c o s t o f t h i n n i n g . Smith and T e s s i e r (1961) i n d i c a t e d a c o s t o f $26.60 per C c f o r 19 cents p e r l i n e a l f o o t i n a p i l i n g o p e r a t i o n a t Haney, B.C.  Warrack (1959) estimated a  c o s t o f $20.00 p e r C c f f o r l o g g i n g p i l i n g  i n a study  made a t Cowichan Lake, B.C. The  cost o f logging f o r p i l i n g  can vary  c o n s i d e r a b l y with t h e number o f p i l i n g p e r a c r e , the topography o f the area and the l e n g t h o f t h e p i l i n g . Logging c o s t s p e r l i n e a l f o o t normally  increase  with  l e n g t h o f p i l i n g because o f the a d d i t i o n a l care required to l o g long pieces.  Average c o s t s  should  decrease a s the number o f p i l i n g p e r acre increases;. Industry e s t i m a t e s o f c o s t s a r e t h a t t h e maximum should be about IS cents p e r l i n e a l f o o t i n o r d e r t h a t the o p e r a t i o n be p r o f i t a b l e .  Consequently,  a c o s t o f IS cents p e r l i n e a l f o o t has been a s s i g n e d  50. here t o a p i l i n g l e n g t h o f 90 f e e t and c o s t s a r e s c a l e d down with d e c r e a s i n g l e n g t h as i n d i c a t e d i n Table XXV. f.o.b.  A l s o presented  i n Table XXV a r e c u r r e n t  p r e s e r v a t i o n p l a n t p r i c e s , f o r unbarked  Douglas f i r p i l i n g ,  quoted by two major producers  o f Douglas f i r p i l i n g on the B.C. c o a s t . at  Apparently,  the present time, there i s no d i s t i n c t i o n made i n  grades o f p i l i n g ,  a t l e a s t t o t h e s u p p l i e r and the  o n l y premium p a i d i s f o r l e n g t h .  S e l l i n g prices at  the p l a n t l e s s l o g g i n g c o s t s a r e shown as n e t value o f p i l i n g i n Table XXV.  Table XXV.  Logging C o s t s and Value o f Douglas F i r Piling  Length o f Piling (feet)  30  to  55  50  60  65 70 75 80  85 90 and over  Logging C o s t s Per L i n e a l Foot Unpeeled (cents) 12 13 13  14  15 16  17 17 18  Value Per L i n e a l Foot Unpeeled F.O.B. P l a n t (cents)  37 40 42 43 44 45 47 48 50  Net Value Per L i n e a l Foot(cents)  25 27  29 29 29 29 30 31 32  52. L i n e a r Programming t o Maximize C o n v e r s i o n R e t u r n s Per Acre Alternative  activities  U s i n g t h e n e t v a l u e s d e r i v e d i n the  foregoing  s e c t i o n s o f t h i s t h e s i s f o r the v a r i o u s p r o d u c t s ,  the  maximum c o n v e r s i o n r e t u r n s p e r a c r e f o r t h e f o u r s t a n d s were o b t a i n e d by l i n e a r programming t e c h n i q u e s . From t h e volume o f l o g s a v a i l a b l e i n each s t a n d c e r t a i n alternative production p o s s i b i l i t i e s e x i s t .  In order  t o maximize t h e c o n v e r s i o n r e t u r n s p e r a c r e i t necessary  t o s e l e c t , from t h e a v a i l a b l e  is  alternatives,  t h o s e which w i l l r e n d e r the h i g h e s t n e t p r o f i t s . The a l t e r n a t i v e s t o be d e c i d e d among a r e whether  to: 1.  s e l l peeler  logs  2.  manufacture plywood from p e e l e r  3.  manufacture lumber from p e e l e r  4.  s e l l saw l o g s  5.  manufacture lumber from saw l o g s  6.  sell  7.  manufacture lumber from p i l i n g .  piling  logs logs  53. I n a d d i t i o n , t h e r e are two grades o f p e e l e r and l o g s a v a i l a b l e i n the two each o f these two  saw  o l d e r a g e - c l a s s e s , so t h a t  stands have n i n e a l t e r n a t i v e s  from  which to choose the optimum. A problem  such as d e s c r i b e d here c o u l d be  s o l v e d by l a b o r i o u s a c c o u n t i n g procedures, t o the t o t a l net revenue a v a i l a b l e from each  determine  alternative  and t o s e l e c t those, c o n s i s t e n t w i t h the r e s o u r c e s u p p l i e s , which would maximize p r o f i t s .  However,  l a r g e numbers o f a l t e r n a t i v e s would make c o n v e n t i o n a l a c c o u n t i n g procedures completely i m p r a c t i c a l .  The  technique o f l i n e a r programming t a k e s decision-making f o r such problems out o f the realms o f i n t u i t i o n o r educated guess-work. L i n e a r programming problems have t h r e e b a s i c components:1.  an o b j e c t i v e - i n t h i s case  maximising  c o n v e r s i o n r e t u r n per a c r e 2.  i n p u t r e s t r a i n t s - a v a i l a b l e l o g supply  3.  a l t e r n a t i v e interdependent a c t i v i t i e s -  l o g s e l l i n g , plywood and lumber manufacture, production.  piling  5 4 .  I n a l i n e a r programming maximisation problem  the  objective i s to: n Maximize S X j P j j=l Subject t o : (1)  m S  XjAij  Vi;  j = 1,2,  n  - i=l (2)  Xj  ^0  where S i s summation Xj i s the l e v e l o f a c t i v i t y j (lumber  or plywood manufacture,  etc.)  P j i s the net r e t u r n per u n i t o f a c t i v i t y j A i j i s the amount o f imput r e q u i r e d per u n i t o f output from a c t i v i t y j and V i i s the a v a i l a b l e supply o f i n p u t i .  Data i n p u t The necessary data f o r the s o l u t i o n o f the problem  are g i v e n f o r the f o u r stands i n the  m a t r i c e s o f the simplex format i n Table XXVI.  first The  a c t i v i t y or r e s o u r c e l e v e l column, i n Table XXVI, r e p r e s e n t s the volume o f m a t e r i a l a v a i l a b l e f o r d i s p o s a l ,  55. manufacturing or s e l l i n g a c t i v i t i e s .  For example,  i n the 145-year-old stand, there are 2158 cu. f t . o f grade 3 p e e l e r s , 1992 cu. f t . of grade 4 p e e l e r s , 44^2 and 7328 cu. f t . o f grade 2 and 3 sawlogs, r e s p e c t i v e l y , and 800 l i n e a l f e e t of p i l i n g . The net r e t u r n s shown i n Table XXVI were c a l c u l a t e d from the data of foregoing s e c t i o n s of t h i s thesis.  They represent the net worth per u n i t of  output from the v a r i o u s a c t i v i t i e s .  Thus, i n the  145-year-old stand, lumber from grade 3 p e e l e r s has a net value of $116 per M fbm and lumber from p i l i n g has a net worth of $34 per M fbm.  S i m i l a r l y , plywood  from grade 3 peelers has a net value of $75 per M. sq. f t . o f 3/8" plywood.  In the s e l l i n g a c t i v i t i e s a l l of  the values i n the net r e t u r n l i n e are d o l l a r s per M fbm of l o g s except f o r p i l i n g , which i s 28 cents per l i n e a l foot. are  Log p r i c e s used f o r the s e l l i n g  activities  shown i n Table XXVII. The numbers i n the matrix of each format  represent the requirement c o e f f i c i e n t s .  F o r example,  i n the x i column of the 145-year-old stand, the q u a n t i t y 125 i n d i c a t e s that 125 cu. f t . of grade 3 p e e l e r s are  56. r e q u i r e d to produce one thousand board f e e t o f lumber. In the X6 column the requirement i s f o r 65 cu. f t . o f grade 3 peeler to produce one thousand square f e e t o f 3/8" plywood.  Column X I 1 shows that 154 cu. f t . o f  grade 2 sawlogs are r e q u i r e d f o r one thousand fbm log  scale. In equation form, using the 145-year-old stand  as an example, the o b j e c t i v e f u n c t i o n i s : (1)  Maximum conversion r e t u r n = 116X1 + 78 X 2 + 97 X 3 + 7 0 X 4 + 3 4 X 5 + 75 X 6 + 52 X 7 + 0.28X8 +96X9 + 80 X 10 + 59 X 11 + 39 X 12 with the c o n s t r a i n t s t h a t : -  (2)  125 X 1 + 65 X 6 + 148 X 9  - 2158  (3)  149 X 2 + 72 X 7 + 167 X 10  - 1992  (4)  134 X 3 + 154 X 11  * 4482  (5)  135 X 4 + 169 X 12  ^ 7328  (6)  135 X 5 + 1 X 8  ^  800  and that (7)  XI  X12  s  0  where X i are the volumes produced i n each activity. In equation (1) there are 12 a c t i v i t i e s ,  only  f i v e of which can enter i n t o the f i n a l s o l u t i o n because  57. of the r e s t r i c t i o n s imposed by the c o n s t r a i n t equations (2) t o ( 6 ) . I n equations (2) to (6) each X i represents an a c t i v i t y which could occur up to the l e v e l o f the constraint.  Tor example, i n equation ( 2 ) , X I represents  the manufacture o f lumber from grade 3 p e e l e r s , X6 represents the manufacture of plywood from grade 3 p e e l e r s and X9 represents the s a l e o f grade 3 p e e l e r s . As w i l l be noted, equations (2) t o (6) are inequalities.  To make them e q u a l i t i e s , which i s  necessary f o r the s o l u t i o n o f the problem, d i s p o s a l a c t i v i t i e s are added to each equation.  Thus equations  (2) to (6) become:-  (6)  125X1 + 65X6 + 148X9 + 1X13 == 2158  (9)  149X2 + 72X7 + 167X10 + 1X14 = 1992  (10)  134X3 + 154X11  + 1X15 = 4482  (11)  135X4 + 169X12  + 1X16 = 7328  (12)  135X5 + 1X8  + 1X17 =  800  In the above equations, X13 to X17 represent the d i s p o s a l or non-use o f resources; p e e l e r s , sawlogs and p i l i n g .  Equations (8) t o (12) represent the f i r s t  s o l u t i o n to the problem  t h e o r e t i c a l l y , the m a t e r i a l  could be l e f t i n d i s p o s a l and the conversion r e t u r n would be zero.  58. When the primary m a t r i x has been e s t a b l i s h e d the s o l u t i o n i s o b t a i n e d by r e p e a t e d i t e r a t i o n s  until,  i n this;case, t h e c o n v e r s i o n r e t u r n i s maximized. W i t h each i t e r a t i o n t h e a c t i v i t y which c o n t r i b u t e s most to the conversion r e t u r n i s incorporated i n the plan u n t i l t h e c o n v e r s i o n r e t u r n can be i n c r e a s e d no f u r t h e r . T h i s i s the optimum s o l u t i o n .  A d e t a i l e d accounting  o f t h e procedure i s g i v e n i n many l i n e a r programming texts.  The most e f f i c i e n t method o f o b t a i n i n g t h e  s o l u t i o n i s t o e n t e r t h e m a t r i x data i n an e l e c t r o n i c computer w i t h an a p p r o p r i a t e L.P. programme, many o f which a r e a v a i l a b l e . The optimum s o l u t i o n s The  s o l u t i o n s t o t h e maximisation  problems  i n t h e f o u r stands were o b t a i n e d by use o f l i b r a r y programme 0 1 - 6 f o r l i n e a r programming on the I.B.M. 7040 a t t h e U.B.C. Computing Centre.  The maximum c o n v e r s i o n  r e t u r n s , i n t h i s case the amounts a v a i l a b l e f o r stumpage and p r o f i t , were $ 1 1 , 1 9 7 ,  $6,996,  $ 6 , 2 0 8 and  $ 2 , 6 8 5 per a c r e f o r the 1 4 5 - , 1 0 6 - , 8 6 - and 6 3 - y e a r - o l d stands, r e s p e c t i v e l y .  The d e t a i l s o f the optimum  a c t i v i t i e s p r o v i d e d by the l i n e a r programming s o l u t i o n are g i v e n i n Table XXVIII.  59.  In  each case i t was more p r o f i t a b l e to  p r o c e s s p e e l e r and saw l o g s than to s e l l them.  The  s a l e o f p i l i n g as such rendered h i g h e r r e t u r n s than the manufacture  o f lumber from p i l i n g .  a l s o i n d i c a t e d t h a t the manufacture  The  solution  o f plywood from  p e e l e r l o g s was more p r o f i t a b l e than lumber  manufacture  from p e e l e r l o g s , except f o r the 6 3 - y e a r - o l d stand. In t h i s case the p e e l e r l o g s were o f very low and the p o t e n t i a l plywood product was  quality  valued at l e s s  than the a c t u a l lumber product from these l o g s . The r e l a t i o n s h i p between the optimum c o n v e r s i o n r e t u r n and the lumber c o n v e r s i o n r e t u r n i s shown i n Figure 1 .  Transformed t o v a l u e per u n i t volume, the  lumber over age r e l a t i o n s h i p i s expressed adequately by a s t r a i g h t l i n e , whereas t h a t f o r the optimum product i s c u r v i l i n e a r i n nature.  The shape o f the optimum  conversion return regression i n F i g u r e 1 ,  and i t s manner  of dt&viiation from the lumber c o n v e r s i o n r e t u r n , can be a t t r i b u t e d t o the i n f l u e n c e o f a g r e a t e r percentage o f the stand volume i n p i l i n g i n younger stands and i n p e e l e r l o g s i n o l d e r stands.  Table XXVI.  F i r s t Matrices of Simplex Format f o r Maximizing Conversion Returns per Acre of 145-. 106-. 86- and 63-year-old Douglas 7 i r  Ret Returns  Activity of Resource L^vel 113 114 115 X16 117  2158 1992 4482 7328 800  Disposal A c t i v i t i e s 3P* 0 113 1  4P* 0 114 1  23* 0  115 1  33* 0 X16  PI* 0 117  1  1  Hot Returns  113 X14  115 116 X17  Het Returns 114 X15 X16 117 Het Returns XU  X16 117  *  98 123  414 1380 4752 5302 2200  106 Tear 65 80 55 136  76  133  2527 872 8705 2630  556 4749 2540  3P 116 XI 125  145 Tear Manufacturing A c t i v i t i e s Selling Activities Lumber Plywood PI 3P 4P PI 3S 4P 25 33 3P 4P 23 70 78 97 34 75 52 0.28 39 80 59 18 X2 X3 X12 X9 XlO X l l 14 X5 X6 X7 148 65 149 72 167 134 154 135 169 1 135  77  0 1  142  3P - Grade 3 Peeler Log; 4P - Grade 4 Peeler Log; 23 - Grade 2 Sawlog; . 33 - Grade 3 Sawlog; PI - P i l i n g x  135  137  86 Year 72 54  134  135  63 Year 50 142  43  63 52 66 72  0.30  95 154  81  55  168 163  148 39  43 0.30 74  68 166  200  41 77  0.28  49 169  175 38  34  62  184  180  24 189  23 212  61. Table XXVII.  Douglas F i r Log P r i c e s (Vancouver Market, Dec. 1965) Used f o r s e l l i n g A c t i v i t i e s o f L i n e a r Programming Problem  Stand Age (years) 63 86 - 106145 ,.. Log P r i c e s i n $/M fbm B.C. Log S c a l e d '  Log Grade  1  No. 3 P e e l e r  -  -  112.50  112.50  No. 4 P e e l e r  87-50  87.50  100.00  102.50  No. 2 Sawlog  -  70.00  75.00  77.50  No. 3 Sawlog  57.50  57.50  62.50  65.00  (1)  I t w i l l be noted t h a t t h e p r i c e s f o r t h e same l o g grade vary among the a g e - c l a s s e s . The r e a s o n i s t h a t , a l t h o u g h the l o g s were d e s i g n a t e d the same grade, some were a t the bottom o f the grade range and o t h e r s a t the top and were p r i c e d a c c o r d i n g l y .  62. Table XXVIII.  Optimum Product Y i e l d per Acre o f Four Stands o f Douglas F i r as I n d i c a t e d by Linear Programming A n a l y s i s  Stand Age (years) 86 106 145 Product  Unit  Lumber  M  Plywood  M 3/8ths  Piling  L i n e a l Feet  fbm  Optimum Conversion Return - $/Acre  Quantity 37.36  70.99  73.90  87-73  34.15  25-44  60.87  2,630  2,200  800  2,685 ' 6,208  6,996  2,540  11,197  70o-  Conversion Return Optimum. Stand Age  8/Ccf Conversion Return Lumber Optimum  63  36-49  3711  86  43-35  43-69  106 .  5006  50-70  145  62-40  67-45  Conversion Return Lumber  JL 50  60  70  80  90  100  110  Stand Age,Years  120  130  140  150  Figure I- Relationship between conversion returns ( S / C c f ) from lumber and optimum product, and stand age for Douglas fir-  64. Tree and Stand A n a l y s i s Tree  Values The c a l c u l a t e d c o n v e r s i o n r e t u r n s f o r the  t r e e s sampled are shown i n Table XXIX. r e t u r n (1)  Conversion  i s f o r the lumber product and (2)  optimum product.  f o r the  The column headed R i n d i c a t e s the  reason f o r the d i f f e r e n c e , i f any, between the conversion returns.  The a b b r e v i a t i o n s PI and P i n  Column R denote t h a t one o r more o f the t r e e s i n t h a t diameter  contained p o t e n t i a l p e e l e r o r p i l i n g m a t e r i a l . Average lumber c o n v e r s i o n r e t u r n s per acre  f o r the age c l a s s e s were 3 6 , 4 3 ,  50 and 62 c e n t s per  c u b i c f o o t , i n o r d e r o f ascending age.  In B r i t i s h  Columbia the assesment f o r stumpage on Crown timber i s u s u a l l y between 40 and 60 per cent o f the c o n v e r s i o n return.  I f 50 per cent o f the above c o n v e r s i o n r e t u r n s  are deducted  f o r stumpage the margins f o r p r o f i t and  r i s k would be 1 8 ,  2 2 , 25 and 31 cents per c u b i c f o o t ,  r e s p e c t i v e l y , f o r the 6 3 - ,  8 6 - , 106-  and 145-year age  classes. The r e g r e s s i o n r e l a t i o n s h i p s between lumber c o n v e r s i o n r e t u r n and t r e e diameter are shown f o r the  65. f o u r stands i n Tables XXX  and XXXI, w i t h the estimated  c o n v e r s i o n r e t u r n s by t r e e diameter c l a s s e s . per cent o f the average  I f 50  c o n v e r s i o n r e t u r n i s deducted  f o r stumpage i n each age group,  then  sub-marginal  t r e e s i n c l u d e the 12-inch diameter c l a s s i n the  63-year  and the 106-year; and up t o and i n c l u d i n g the 21-inch group i n the 145-year stand. The r e g r e s s i o n o f c o n v e r s i o n r e t u r n f o r lumber on t r e e diameter f o r the combined ages i s g i v e n i n Table XXXII. ages was  Average c o n v e r s i o n r e t u r n f o r a l l  42 c e n t s per c u b i c f o o t .  I f 50 per cent o f  t h i s i s deducted f o r stumpage, sub-marginal t r e e s i n c l u d e the 12-inch diameter c l a s s o f the t o t a l Low  grouping.  c o n v e r s i o n r e t u r n s f o r lumber p r o d u c t i o n  from s m a l l t r e e s are caused p r i m a r i l y by the sharp i n c r e a s e i n l o g g i n g and m i l l i n g c o s t s w i t h decreases i n l o g diameter and t r e e s i z e .  Another,  but l e s s  signif-  i c a n t cause, i s t h a t , on the average, lumber q u a l i t y decreased w i t h t r e e diameter f o r the t r e e s s t u d i e d h e r e . Stumpage a s s e s s e d at 50 per cent o f the average  c o n v e r s i o n r e t u r n (42 cents per c u b i c f o o t ) f o r  the combined ages o r 21 c e n t s per c u b i c f o o t , has the  66. e f f e c t o f making the 1 2 - i n c h dbh f o r lumber c o n v e r s i o n c o s t s d e r i v e d here.  c l a s s sub-marginal  a t the l o g g i n g and  milling  Reducing the stumpage assessment  to 40 per cent o f the average c o n v e r s i o n  return  makes t h i s dbh  c l a s s barely marginal.  Reductions i n  the p r o d u c t i o n  c o s t s s p e c i f i e d are r e q u i r e d i n order  to make t r e e s o f 12 i n c h e s and under economic f o r lumber  conversion. The  average l o g g i n g and m i l l i n g c o s t s used  here f o r the 12-inch dbh  c l a s s were approximately  $30.00 f o r C c f f o r l o g g i n g and the same f o r m i l l i n g . The  g r o s s lumber value o f t h i s dbh  y e a r - o l d stand was  $66.00 per C c f .  63-  c l a s s i n the  Thus the amount  a v a i l a b l e f o r stumpage and p r o f i t was  $6.00 per  Ccf.  I f stumpage were charged at 50 per cent o f the average c o n v e r s i o n r e t u r n , o r $21.00 per C c f , the i n c h dbh  c l a s s would remain sub-marginal u n t i l  12-  logging  and m i l l i n g c o s t s were reduced to $45.00 per C c f  or  approximately $22.50 per Ccf each. As i n d i c a t e d e a r l i e r i n t h i s t h e s i s , t h i n n i n g c o s t s r e p o r t e d f o r s e v e r a l s t u d i e s i n Washington B.C.  and  ranged from $12.60 to $17.55 per C c f o f l o g s .  67. The  equipment used f o r these o p e r a t i o n s were e i t h e r  horse o r c a t e r p i l l a r t r a c t o r .  Thus, w i t h t h e use o f  equipment s u i t a b l e f o r s m a l l t r e e and l o g h a r v e s t i n g , it  i s p o s s i b l e t h a t c o s t s c o u l d be reduced  sufficiently  to make the h a r v e s t i n g o f s m a l l m a t e r i a l p r o f i t a b l e . No one p i e c e o f equipment i s s u i t a b l e f o r the economic l o g g i n g o f the range o f t r e e and l o g s i z e s p r e s e n t l y encountered i n most c o a s t a l stands o f timber. T h e r e f o r e , u n t i l the t r e e s i n a stand can be grown a t a uniform r a t e , a combination o f s m a l l - l o g and l a r g e - l o g h a r v e s t i n g equipment, and perhaps a two-stage o p e r a t i o n , may reduce the o v e r a l l c o s t s o f l o g g i n g .  The same  h o l d s t r u e f o r m i l l i n g whereby many companies on the coast a t the present  time stream t h e i r s m a l l m a t e r i a l  into a small-log m i l l ; t h e i r large material to a conventional  mill.  A considerable p o t e n t i a l increase i n conversion r e t u r n from s m a l l t r e e s i s a v a i l a b l e by the p r o d u c t i o n o f p i l i n g r a t h e r than the manufacture o f lumber.  A  l e s s a p p r e c i a b l e i n c r e a s e i s a v a i l a b l e from l a r g e t r e e s by the manufacture o f plywood, where p o s s i b l e , i n s t e a d o f lumber.  The average optimum c o n v e r s i o n r e t u r n f o r  a l l ages was 47 c e n t s per c u b i c f o o t .  With a stumpage  assessment o f 5 0 per cent o f the average r e t u r n , a l l o f the t r e e diameter  conversion  c l a s s e s shown i n  Table XXIX a r e economical when converted to an optimum product.  Table XXIX.  Conversion Returns - Cents per Cubic Foot - f o r Douglas F i r by D.B.H. and Stand Age  Stand Age Years 63 86 106 145 Tree Ko. of Trees and Conversion Return Cents/Cu.Ft.- (1) Lumber. (2j Optimum Product Mix No. (1) (2) R . U J DBH No. (1) (2) R. DBH No. (1) (2) R T DBH NO. (1) (2) 20 18 2 PI PI 1 22 U PI 1 23 41 PI 16 32 PI 22 PI 2 PI 26 4 7 36 PI 16 3 27 36 PI 19 3 32 PI PI 20 PI 1 23 36 2 20 43 PI 17 3 33 42 PI 23 35 PI 36 3 PI 4 20 30 PI 18 2 PI PI 21 2 25 PI 25 42 46 3 PI PI 22 27 2 27 3 47 53 35 PI PI 2 5 56 23 39 17 PI PI 18 1 PI 29 31 1 81 24 36 75 41 PI 32 1 61 23 3 25 56 64 19 3 42 42 23 2 43 43 25 1 p 20 1 1 PI 1 33 24 32 79 79 47 21 6 P 2 34 1 41 27 73 85 41 41 22 6 P 2 35 2 72 46 75 51 38 2 P 1 42 66 66 23 40 27 1 43 43 29 3 47 40 1 86 86 24 2 42 42 29 3 49 p 1 P P 63 1 1 30 68 41 81 25 43 43 2 43 43 P 31 4 54 26 46 46 1 2 3 42 32 1 78 31 78 55 59 P 1 1 50 1 47 34 33 62 75 84 30 1 50 34 1 62 62 1 35 53 61 4 63 P 1 37 54 54 38 48 3 51 P 1 39 47 47 1 41 65 65 42 1 53 53 1 43 49 1 45 58 64 P  12 13 14 15 16  (1)  3 4 2 4 4 5 3 3  14 7 20 20 21 31 42 35 41 43 40 43 5 0 50  26 26 36 43 30 35 35 35 42 39 44 43  15 16 17 18 20 21 22  1 3 3 2 4 3 2 2 1 25 3 26 3 1 3 2  23 27 33 2 8 28 36 40 40 48 43 43 41 51 43 49 43 52 57 57  41 36 42 40 40 41 40 40 48 43 43 43 51 43 50 50 43 52 57 57  3 0 30  23 2  26 28 3 0 30  33 3 36  R - Indicates the reason f o r differences between (1) and (2).  30 30  31  32 40 42 40 56 57  30  47 47 63 67 54 56 53  PI - P i l i n g ,  P » Peeler Log.  R PI PI ."'  P P P P P P P P P  T a b l e XXX.  Lumber C o n v e r s i o n R e t u r n p e r Cubic F o o t and p e r Tree by D.B.H. C l a s s e s f o r 63- and 8 6 - y e a r - o l d Douglas F i r Average Stand Age ( Y e a r s )  Tree DBH (inches)  Av. Cu.ft. Recovered  12  30 45 68 95 128 162 200  15  18 21 24 27 30 33  63 C o n v e r s i o n R e t u r n (1) Lumber P e r Tree Cents/cu. D o l l a r s f t . 14 22 29 37 45 52 60  " Av. Cu.ft. Recovered f  4.20  35  19-70 35-15 57-60 84.24 120.00  75 108 145 190 235 285  9.90  50  8 6 C o n v e r s i o n R e t u r n (2) Lumber P e r Tree cents/cu. D o l l a r s t . 24 29 33 37 42  46 51 55  8.40  14-50  24-75 39-96 60.90  87.40  119.85 156.75  (1)  Con. Ret. L b r . (63 y r . ) = - 15-92 + 2.52 D.B.H.:r=.833**:See=+6.5 c e n t s .  (2)  Con. R e t . L b r . (86 y r . j =  6.5  + 1.47 D.B.H.:r=.766**:See=+6.2 c e n t s .  ^3  o  Table XXXI.  Lumber Conversion Return Per Cubic Foot And Per Tree By D.B.H. Classes F o r 106- And 145- Year Douglas-Fir Average Stand Age (years)  Tree D.B.H. (inches)  Av. Cu. F t . Recovered  12  40  18 21 24 27 30 33 36  75 108  15  39  42 45 48  50  145  190 235 285 345  400 470 530  106 Conversion Lumber Cents/cu.ft. 22 26 30 34 38 42 46  50  54 59 63 67  Return Per Tree Dollars  Av. Cu. F t . Recovered  8.80 .13.00.  35 42 65 95 135 180 240 300 365  22.50  36.72 55.10 79.80 108.10  142.50 186.30  236.00 296.10 355.10  440 530 620 685  145 Conversion Lumber Cents/cu.ft. 8  15  23 30 37 44 52  59  66 74 81 88 95  Return Per Tree Dollars 2.80 6.30  14.95 28.50  49.95 79.20 124.80  177.00 240.90 325.60  429.30  545-60 650.75  (1) Con. Ret. Lbr. (106 y r . ) = 6.25 + 1.34 D.B.H.: r = .744** : See = + 8.8 cents (2) Con. Ret. L b r .(145 y r . ) =20.81 + 2.42 D.B.H.: r = .818** : See = +11.7 cents,  -0 I—  1  Table XXXII.  C o n v e r s i o n Return Benr Cubic Foot and per Tree by DBH C l a s s e s f o r combined ages o f S i t e C l a s s I I Douglas f i r  Tree DBH (ins.) 12 15 18 21 24 27 30 33 36 39 42 45 48  Av. c u b i c Feet Recovered 35 48 7 7 2 102 138 180 230 290 355 425 500 575 655  Con. Ret.. Lumber v D Cents/cu.ft.  1 9  24 2 9 35 40 45 50 55 60 66 71 76 8 1  Con. Ret. Per Tree Dollars 6.65 11.50 20.80 35-70 55.20 81.00 115.00 159.50 213.00 280.00 355.00 437.00 530.55  ( 1 ) Con. Ret. L b r . = - I . 5 8 + 1.73 D.B.H. : r = . 8 2 0 * * : See = +9.6 c e n t s .  -<1  ro  73. Stand n o r m a l i t y and growth The CTttbic. volumes r e c o v e r e d were from t r e e s 12-inches and over i n dbh.  The average stump h e i g h t  i n each stand was 2 f e e t and the average top diameters of u t i l i s e d stems were 8.4-,  9-7-,  11.5-  i n c h e s i n o r d e r o f i n c r e a s i n g stand age.  and  12.7-  Thus, t h e r e  was a c o n s i d e r a b l e c u b i c volume of m a t e r i a l i n stumps and unharvested t o p s which must be added to o b t a i n the t o t a l volume per acre of t r e e s 12-inches and over i n dbh.  E s t i m a t e s of a d d i t i o n a l cubic volumes were  d e r i v e d from average stand data and are shown f o r each stand i n Table XXXIII. The a d d i t i o n a l volume t o a 4 - i n c h top, shown i n Table XXXIII, i s what might be regarded as pulp material.  The c u r r e n t Vancouver m a r k e t - p r i c e f o r  Douglas f i r pulpwood l o g s i s $40.00 per M fbm on $24.00 per C c f .  Thus, f o r the m a t e r i a l t o be  utilised  p r o f i t a b l y as pulpwood, i t would have t o be yarded, loaded, bundled, t r u c k e d , boomed and towed f o r l e s s than $24.00 per C c f , which, a t the c o s t s d e r i v e d f o r t h i s study, i s not p o s s i b l e .  However, as w i t h s m a l l  diameter t r e e s , use o f a p p r o p r i a t e h a r v e s t i n g equipment  74. c o u l d c o n c e i v a b l y make the u t i l i s a t i o n o f l o g g i n g r e s i d u e an economic p r o p o s i t i o n . The t o t a l cubic volumes and number o f t r e e s per acre 12 i n c h e s and over i n dbh f o r each stand, are compared i n Table XXXIV w i t h the n o r m a l i t y v a l u e s o f McArdle, Meyer and Bruce (1949).  The  n o r m a l i t y c r i t e r i o n o f number o f t r e e s per a c r e , rendered n o r m a l i t y percentages  which ranged from 18  to 28 per cent lower than those o f the c u b i c volume criterion.  McArdle e t a l . suggested  t h a t number o f  t r e e s per u n i t area i s an u n s a t i s f a c t o r y index o f n o r m a l i t y and s t a t e d t h a t the u l t i m a t e d e f i n i t i o n s t o c k i n g should be i n c u b i c volume. percentages  The  d e r i v e d here from the two  l i t t l e r e l a t i o n s h i p to each o t h e r .  of  normality  c r i t e r i a bear .  They i n d i c a t e  t h a t a g r e a t d e a l o f c a u t i o n should be e x e r c i s e d i n e s t i m a t i n g the n o r m a l i t y by one by  c r i t e r i o n from t h a t  another. Curved estimates o f past tree-growth  on stump r i n g - c o u n t s i n the 63-  and 86-year-old  are shown by t r e e dbh i n Table XXXV.  based stands  The purpose i n  r e d u c i n g t r e e growth f o r these stands was  to compare  75. the i n d i c a t e d stand volumes w i t h e s t i m a t e s c a l c u l a t e d from t h e normal y i e l d t a b l e s o f McArdle e t a l .  This  procedure was n o t c a r r i e d out f o r t h e two o l d e r groups o f t r e e s because o f the l i m i t e d amount o f growth data o b t a i n e d from these  stands.  In order t o estimate t r e e diameter  distribution  i n p r e v i o u s p e r i o d s f o r the two younger stands, i t was necessary a l s o t o estimate bark-growth and t r e e m o r t a l i t y t o t h e present time.  Double-bark t h i c k n e s s e s (D.B.T.)  a t b r e a s t - h e i g h t were estimated u s i n g t h e r e g r e s s i o n suggested by Smith e t a l . (1961), where D.B.T. = O.64 +.  0.1021 dbh - 0.049 cum. h t . - 0.0008 t o t a l h t . r e l a t i o n s h i p i s shown i n F i g u r e 2. it  From t h i s  This graph  can be seen t h a t the estimated i n c r e a s e i n D.B.T. i s  approximately growth.  2 i n c h e s f o r every 20 i n c h e s i n diameter  Thus an i n c r e a s e o f 20 i n c h e s i n dbh i s  e q u i v a l e n t t o an i n c r e a s e o f 18 i n c h e s diameter bark  (D.I.B.).  inside  Conversely, a decrease o f 18 i n c h e s  D.I.B. i s the e q u i v a l e n t o f a decrease o f 20 i n c h e s dbh. This relationship i s i l l u s t r a t e d i n Figure 3. Stand t a b l e s f o r p e r i o d s i n the past were d e r i v e d f o r the two younger stands from t h e growth data  76. of Table XXXV and f i g u r e 3.  These are shown i n  Table XXXVI along w i t h the t r e e diameter d i s t r i b u t i o n f o r each stand as i t was before l o g g i n g . Smith et a l . (1961) pointed out t h a t m o r t a l i t y estimates made by Staebler (1955) amounted to 35 per cent of the t o t a l c u b i c - f o o t volume over a 100-year period f o r normal stands.  There are so many  v a r i a b l e s which could a f f e c t percentage m o r t a l i t y that such estimates may deviate widely from the a c t u a l occurrence of m o r t a l i t y .  However, the above  35 per cent, or .35 per cent per annum, has been used here f o r m o r t a l i t y estimates.  From the stand t a b l e  data of Table XXXVI, and the m o r t a l i t y estimates derived as above, the merchantable volumes f o r past stands were c a l c u l a t e d f o r the 63- and 86-year groups. These data were curved and extended. the merchantable  Estimates of  cubic volume f o r these stands a t  v a r i o u s age c l a s s e s are presented i n Table XXXVII. These are termed here the "growth approach estimates**, i n order to d i s t i n g u i s h them from those d e r i v e d from the normal y i e l d t a b l e s of McArdle et a l .  (1949).  The a c t u a l cubic volumes per acre u t i l i s e d i n each stand were 16,600, 13,800, 14,208 and 7,235 i n  77. order o f decreasing stand age.  The t o t a l volumes  f o r each stand were 19,221, 15,850, 16,355 and 8,524 cubic f e e t per acre, a l s o i n order o f decreasing stand age.  U t i l i s e d volumes amounted to 87 per cent o f  t o t a l volumes i n each o f the three o l d e r stands and to 85 per cent i n the youngest stand.  Thus, the  percentage o f t o t a l volume u t i l i s e d was remarkably uniform among stands.  A u t i l i s e d volume o f 87 per cent  i s used here to o b t a i n what i s termed ^normal y i e l d estimates". On the theory that sub-normal stands tend t o approach n o r m a l i t y , McArdle et a l . (1949) presented a t a b l e o f estimated decadal normality i n c r e a s e .  Using  these estimates o f normality change, w i t h present stand normality and normal volumes per acre, normal estimates of merchantable calculated.  volume per acre f o r each stand were  These are shown f o r the two younger stands  i n Table XXXVII and f o r the two o l d e r stands i n Table XXXVIII. The stand normality percentages shown i n Tables XXXVII and XXXVIII are based on the t o t a l c a l c u l a t e d cubic volumes per acre given f o r each stand i n Table XXXIV.  The two estimates of merchantable  volume f o r the 63-year stand are f a i r l y  comparable,  i n d i c a t i n g a degree o f a f f i n i t y between the approaches f o r t h i s stand.  two  However, the e s t i m a t e s f o r  the 86-year stand i n d i c a t e t h a t , i n t h i s case, a decrease towards n o r m a l i t y a c t u a l l y o c c u r r e d (from 133  per cent t o 115  maintenance o f 115 o f McArdle et a l .  per cent i n 30 y e a r s ) r a t h e r than per cent as suggested  (1949).  by the work  Table XXXIII.  A d d i t i o n a l Cubic Volume per Acre i n Stumps and Tops f o r Four  Stands  o f Douglas F i r  Stand Age (yrs.)  Stump Ht. (ft.)  Average U t i l i s e d Top Length Dia. (in.) (ft.)  Av. Tree Height (ft.)  Av. No. Top Trees Length per ( f t . ) Acre  A d d i t i o n a l Volumes per Acre i n cubic f e e t To 4» To 0» Total Stump Top D i a . T i p o f Tree (2) (1)+(E) (1) (3)  63  2  75  8.4  117  42  107  386  555  903  1289  86  2  96  9-7  150  54  126  605  1060  1542  2147  106  2  114  11.5  173  59  71  568  1030  1482  a05Q  145  2  110  12.7  172  62  65  675  1310  1946  2621  -0  vO  Table XXXIV.  Comparison o f Normal Stand Data  ^  with A c t u a l Stand Data f o r  Four Stands o f Douglas F i r Stand  63  Age  (Years)  86  106  145  S i t e Index  No.  160  165  17-5  165  107 139  126 132  71 102  65 91  8524 9000  16355 14250  15850 17500  19221 19200  77 95  95 115  70 91  72 100  Trees Per  Acre.12" and over  DBH Actual Normal  Cubic Volume Per Acre F o r Trees 12" -and over DBH(cu.ft.) Actual Normal Normality (percent) Trees Volume {!)  Normal Stand Data as Suggested  by McArdle Meyer and Bruce  (1949).  Table XXXV.  Past Stump-Height Diameter Growth by Tree QBE f o r Two  Stands o f  Douglas F i r Stand  Age  (Years) |6  61  Past Growth P e r i o d (Years) 10  Tree  Q3H,  11  Diameter  (in)  12 14 16  18 20 22  24  26 28 30 32 34  1  0.8 0.9 1.1 1.4 1.7 2.0 2.1 2.2 2.3 2.3  1.8 2.0 2.2 2.6 3.2 3.6 3.9 4.0 4.1 4-1  2.6 2.9 3.3 3.9 4.8 5.3 5.6 5.8 5.9 6.0  0.4 0.4 0.4 0.4 0.5 0.5 0.6 0.7 0.8 1.0 1.2 1.4  io*" Increment 0.9 0.9 0.9 0.9 1.0 1.1 1.2 1.4 1.6 1.8 2.0 2.2  15.  20  (Inches) 1.3 1.3 1.3 1.3 1.4 1.7 2.1 2.4 2.7 2.9 3.0 3.1  1.8 1.8 1.8 1.9 2.3 2.8 3.3 3.6 3.8 4.0 4.2 4.3  COH  82. Table XXXVI.  C u r r e n t and Past Stand Tables f o r 63- and 86-year-old  D m :MERCH. (ins.) cu. ft.  12 13  14 15 16 17  - 30 35 40 45 52  63 y r . Wo. o f Trees NOW 5 10 15 yr. yr. yr. ago ago ago 4 6 12 12 13  19 20 21 22 23 24 25 26 27 28  68 76 85 95 105 115 128 140 150 162 175  11 12 12 5 5 6 2 2 1 1 1 1  30 31  200  1  18  29  60  188  12 12 13 11  18  11 5 6 2 2 1 1 1 1  12 12 13 23 12 8 8 2 2 1 1 1 1  12 24 12 22 6 4 1 1 1 1 1  1  32  33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48  Total  107/103;  97 85  Douglas f i r  MERCH. cu. ft.  35 37 42 50 56 65 75 85  9$ 108  120 132 145 160 175 190 205 220 235 250 270 285 300  86 y r . No. o f Trees NOW 5 10 15 20 yr. yr. yr. yr. ago ago ago ago 10 10 7 9 7 3 4 3 7 9 7 10 10 10 1 1 1 3 4 3 3 2 2  10 10 7 9 7 3 4 3 7 9 12 10 15 1 1 1 3 4 3 3 2 2  10 7 9 7 3 4 37 9 7 10 10 10 2 1 3 4 3 3 2 2  10 7 7 9 9 7 7 3 3 4 4 3 3 16 12 7 11 10 10 15 10 6 10 1 2 1 1 3 3 4 4 3 3 3 3 2 2 2 2  126 126 116 116 106  Table XXXVII.  "Growth" and "Normal" Estimates o f Stand Merchantable Volume Cu. F t . per Acre - By Stand Age f o r Douglas F i r  63 Year Age (yrs.)  55  60  Growth Estimate o f Merch.Cubic Volume Per Acre  5700  6800  65  7800  75 80  9500 10000  70  8600  86 Year 55 60 65  70  75 80 85  S.I. 160  8700 10000 11000 12000 12800 13600 14200  Normal T o t a l Cubic Volume Per Acre  Stand Normality Per cent  6700 8200 9500 10700 11700 12600  95  7500 8800 10200 11300 12300 13200 14000  Utilised Volume Per cent  Normal Y i e l d Estimate o f Merch. Cubic Volume p e r Acre  96 97 98  87 87 87 87 87 87  5400 6700 7850 8900 9900 10700  115 115 115 115 115 115 115  87 87 87 87 87 87 87  7500  93 94  S.I. 165 8800  10200 11300 12300 13200 14000  Table XXXVIII.  "Normal" E s t i m a t e s o f Stand By Stand Age f o r Douglas F i r  106 l e a r Age (Yrs.) 55  60 65 70 75 80 85 90 95 100 105  Normal T o t a l Cubic Volume Per Acre 8400  9700 11000 12300 13400 14200 15000 15700 16300 16800 17400  145 Year 55 65 75 85 95 105 115 125 135 145  S.I. 175  7500 10200 12300 14000 15300 16400 17200 18000 18700 19200  Stand Normality Per Cent 78  80 81.5 83 84 85.5 87 88 89 90 91  Utilised Volume Per Cent 87  87 87 87 87 87 87 87 87 87 87  Normal Y i e l d Estimate o f Merch. Cubic Volume per Acre  5700 6750 7800 8900 9800 10500 11300 12000 12600 13100 13700  S.I. I65 79 82 85 88 90 92 94 96 98 100  87 87 87 87 87 87 87 87 87 87  5200  7300  9100  10700  12000 13100  14100  15000 15900 16600  Source:Smith et q|- (1961) Economics of reforestation of Douglas f ir western hemlock and western red cedar in the Vancouver Forest District-UB-C-Faculty of Forestry,Bulletin No-3f  20  30  40  50  D- BH-(Inches)  Figure 2- Relationship of double-bark thickness of Douglas fir to D B H , using the regression:  D B T = 0 - 6 4 + 0 - l 0 2 l D B H - - 0 - 0 4 9 cum- ht- - 0 0 0 0 8 total ht-  Financial  Rotations  C r i t e r i o n f o r f i n a n c i a l maturity The formula used here t o determine t h e f i n a n c i a l r o t a t i o n o f the f o u r a g e - c l a s s e s i s the s i m p l i f i c a t i o n o f the Faustmann formula e l a b o r a t e d upon by Gaffney  (1957)•  T h i s formula i s based on  the c l a s s i c economic theory t h a t optimum p r o d u c t i o n o c c u r s when m a r g i n a l revenue equals m a r g i n a l c o s t s ; o r , from the f o r e s t economist's s t a n d p o i n t , t h a t the f i n a n c i a l r o t a t i o n f o r a crop i s when:dg = G i + a where dg i s the marginal revenue o f the stand G i s the v a l u e o f the stand n e t o f a l l c o s t s i  i s a s p e c i f i e d a l t e r n a t i v e opportunity rate of interest  a i s the annual maximum s o i l r e n t or t h e maximum amortized present value o f net revenue. The  c o n v e r s i o n r e t u r n s f o r lumber and the  estimated optimum product were presented by stand age i n F i g u r e 1.  Deducting  50 p e r cent o f the c o n v e r s i o n  aa. r e t u r n s f o r stumpage, the net value per acre f o r the v a r i o u s estimates o f stand volume are as appear i n Table XXXIX.  The v a l u e s based on normal growth estimates of  cubic volume.are shown g r a p h i c a l l y i n F i g u r e 4.^"  Also  shown i n F i g u r e 4 are the graphs o f establishment c o s t s of  $20.00  $1.00  per acre and annual maintenance o f  compounded a t 3,5  and 7 per cent i n t e r e s t .  The  per acre same stand  v a l u e s are shown i n F i g u r e 5 w i t h establishment c o s t s o f  $50.00  per acre and the  $1.00  per acre annual maintenance  compounded a t the above i n t e r e s t  rates.  In F i g u r e 4 i t w i l l be noted t h a t at 5 per cent i n t e r e s t , c o s t s exceeded stand v a l u e s a t ages i n excess o f 82 y e a r s .  At 7 per cent i n t e r e s t none o f the stands  revenues i n excess of c o s t s , although the 86-year-old had v a l u e s equal to c o s t s between 45 In F i g u r e  5  i t i s apparent  ment c o s t , p l u s $1.00  that a  and 50 y e a r s o f  $50.00  had stand age.  per acre e s t a b l i s h -  per acre annual maintenance, both  compounded at 7 per cent i n t e r e s t , were c o n s i d e r a b l y i n excess of v a l u e s per acre f o r each stand. old  Only the 86-year  stand had v a l u e s per acre i n excess o f c o s t s compounded  at $ per cent i n t e r e s t . 1. The t o t a l c o n v e r s i o n r e t u r n would be a v a i l a b l e to a f u l l y v e r t i c a l l y i n t e g r a t e d f i r m owning i t s own l a n d and m i l l s . Because a 50% f a c t o r has been used the f o l l o w i n g d i s c u s s i o n s of r o t a t i o n l e n g t h apply e q u a l l y ; o n l y the p r o f i t a b i l i t y w i l l change.  89. F i g u r e s 4 and 5 s p e c i f y the upper age l i m i t s below which the f i n a n c i a l r o t a t i o n w i l l  occur.  An i n d i c a t i o n o f t h e approximate age o f f i n a n c i a l r o t a t i o n may be o b t a i n e d from the annual  s o i l rent,  which i s t h a t sum when r e c e i v e d and compounded a n n u a l l y e q u a l s the stand v a l u e n e t o f a l l c o s t s . By d e d u c t i n g the compounded c o s t s from stand vsalue, and d i s c o u n t i n g the r e s u l t i n g n e t revenue by t h e stand age concerned,  t h e maximum s o i l r e n t f o r each stand was  calculated.  Then by f u r t h e r a n a l y s i n g t h e n e t revenue  and c o s t o f c a p i t a l f o r those y e a r s around the maximum i n d i c a t e d s o i l rent the p r e c i s e f i n a n c i a l r o t a t i o n f o r each stand was o b t a i n e d . Duerr  (I960) showed a d i f f e r e n t approach t o  sustained-yield f i n a n c i a l rotation calculations.  Using  h i s method t h e y e a r o f f i n a n c i a l m a t u r i t y o c c u r s when the average m a r g i n a l value growth p e r acre o f t h e r e g u l a t e d growing stock expressed as a percentage o f the m a r g i n a l v a l u e o f the growing stock, i s equal t o the s p e c i f i e d i n t e r e s t r a t e d e s i r e d .  In short, the  Duerr c r i t e r i o n i s t h e marginal v a l u e growth o f the t o t a l s u s t a i n e d y i e l d u n i t whereas t h e Faustmann c r i t e r i o n i s the marginal value product o f the l a s t u n i t o f i n p u t (time).  90.  R o t a t i o n ages As evidenced by the c a l c u l a t i o n s shown i n T a b l e s XL and X L I , the two approaches render results.  different  Stand v a l u e s f o r the c r i t i c a l y e a r s around  the f i n a n c i a l r o t a t i o n are g i v e n i n Table XL f o r t h e 63-year-old  stand and i n Table X L I f o r the 86-year-  old  The d e t a i l s o f the f i n a n c i a l  stand.  rotation  c a l c u l a t i o n s f o r the 106- and 145- y e a r - o l d stands are not g i v e n here.  Because o f t h e i r s i m i l a r i t y i n  v a l u e t o the 63-year-old stand ( F i g . 4 ) , t h e i r estimated f i n a n c i a l r o t a t i o n s were e x a c t l y the same as for  that class.  I n Tables XL and X L I the n e t revenues  shown have been c o r r e c t e d f o r the $20.00 per a c r e establishment c o s t and the $1.00 per acre maintenance charge.  annual  The s o i l r e n t s shown under the  Faustmann r o t a t i o n are the maximum amortized  present  v a l u e o f net revenue t o conform w i t h t h e formula where dg = Oi + a .  The Faustmann r o t a t i o n s occur when the  c a p i t a l p l u s i n t e r e s t o f the stand p l u s the s o i l r e n t equals the net revenue o f the stand. to  This i s equivalent  s a y i n g m a r g i n a l revenue equals marginal c o s t s . With the normal y i e l d approach t o volume  e s t i m a t i o n the f i n a n c i a l r o t a t i o n f o r the 63-year-old  91. stand was  c a l c u l a t e d to be 68 y e a r s f o r the lumber  v a l u e and 67 y e a r s f o r the optimum v a l u e .  Using  the growth approach to volume e s t i m a t i o n the r o t a t i o n f o r stand lumber value was  financial  64 y e a r s .  In the  63-year-old stand the Duerr estimate o f f i n a n c i a l r o t a t i o n was  approximately  64 y e a r s .  For the 86-year-  o l d stand (Table XLI) Faustmann r o t a t i o n s o c c u r r e d a t 63 y e a r s f o r lumber v a l u e s and 62 y e a r s f o r optimum v a l u e s u s i n g the normal y i e l d approach to volume estimates.  With the growth approach to volume  estimates the r o t a t i o n f o r lumber v a l u e s o c c u r r e d at 59 y e a r s . age was  Here a l s o the Duerr estimate o f r o t a t i o n  lower than Faustmann*s f o r the same stand  v a l u e s and was  about 60 y e a r s f o r lumber v a l u e s o f the  normal y i e l d volume e s t i m a t e s . under s i m i l a r circumstances,  Thus i n b o t h  stands,  the Duerr e s t i m a t e s were  3 to 4 y e a r s l e s s than Faustmann*s. At an i n t e r e s t r a t e o f 5 per cent and $20.00 per acre establishment c o s t , the r o t a t i o n f o r the 63-year-old stand was  financial  reduced  and f o r the 86-year-old stand to 52 y e a r s . h i g h e r i n t e r e s t r a t e was  (Table XLII)  to 58  Thus the  i n s t r u m e n t a l i n r e d u c i n g the  years  92. r o t a t i o n by about 10 y e a r s f o r both c l a s s e s .  Shown  a l s o i n Table X L I I a r e t h e r o t a t i o n c a l c u l a t i o n s based on an e s t a b l i s h m e n t c o s t o f  $50.00 p e r a c r e and $1.00  p e r a c r e a n n u a l maintenance.  The r e s u l t i n g  rotations,  a t 3 p e r cent i n t e r e s t , were 68 y e a r s f o r t h e 63-year c l a s s and 62 y e a r s f o r t h e 86-year c l a s s .  At 5 per  c e n t i n t e r e s t t h e 86-year-old s t a n d had a r o t a t i o n o f 50 y e a r s .  Thus a l l o f t h e r o t a t i o n s c a l c u l a t e d f o r  $50.00 p e r a c r e e s t a b l i s h m e n t c o s t s were w i t h i n one y e a r o f those c a l c u l a t e d f o r a  $20.00 p e r a c r e  establishment cost. The i n f e r e n c e i s t h a t e s t a b l i s h m e n t c o s t s do n o t s i g n i f i c a n t l y a f f e c t t h e f i n a n c i a l r o t a t i o n . U s i n g t h e t o t a l s t a n d v a l u e o f t h e 63-year-old s t a n d u n c o r r e c t e d f o r compounded c o s t s , t h e c a l c u l a t e d r o t a t i o n a t 3 p e r cent i n t e r e s t on t h e s t a n d c a p i t a l was 68 y e a r s .  T h i s i s w i t h i n two y e a r s o f the o t h e r  r o t a t i o n c a l c u l a t i o n s f o r t h e same s t a n d and a l t h o u g h i t i s apparent t h a t t h e c o s t s do n o t a f f e c t t h e r o t a t i o n t o a g r e a t e x t e n t , t h e y have an i m p o r t a n t e f f e c t on t h e s t a n d n e t revenues. F o r t h e 63-year-old s t a n d , t h e n e t revenue a t  3 p e r cent i n t e r e s t and $50.00 p e r a c r e e s t a b l i s h m e n t  93. c o s t s was $1,002 p e r acre a t r o t a t i o n age o f 68 y e a r s . At $20.00 per acre establishment and 3 per cent i n t e r e s t the n e t v a l u e was i n c r e a s e d to $1,266 a t r o t a t i o n o f 68 y e a r s .  At establishment  costs of  zero the net revenue f o r the stand i n c r e a s e d t o $1,500 per acre a t a r o t a t i o n age o f 66 y e a r s . To summarize b r i e f l y , the f i n a n c i a l r o t a t i o n o f the 63-, 106-, and 145-year-old  stands was 68 y e a r s  f o r lumber v a l u e s based on 3 p e r cent i n t e r e s t on the normal y i e l d e s t i m a t e s o f stand volume.  F o r the 86-  y e a r - o l d stand t h e r o t a t i o n under the above c o n d i t i o n s was 63 y e a r s .  The e f f e c t o f u s i n g the estimated  optimum v a l u e s was t o reduce the r o t a t i o n by one y e a r f o r a l l o f the stands.  The e f f e c t o f u s i n g the growth  approach t o volume e s t i m a t i o n was t o reduce the r o t a t i o n s by f o u r y e a r s f o r a l l stands.  I n c r e a s i n g the i n t e r e s t  r a t e from 3 t o 5 p e r cent has the e f f e c t o f r e d u c i n g the r o t a t i o n s by about 10 y e a r s . establishment  Different levels of  c o s t s d i d not s i g n i f i c a n t l y a f f e c t the  r o t a t i o n age but net revenues i n c r e a s e d as e s t a b l i s h m e n t c o s t s decreased.  The Duerr approach to r o t a t i o n  c a l c u l a t i o n s rendered lower e s t i m a t e s o f r o t a t i o n than those o f Faustmann by a few y e a r s .  I t i s of  ages  94. i n t e r e s t t o note t h a t a t t h e r o t a t i o n ages c a l c u l a t e d at a 3 p e r cent i n t e r e s t r a t e u s i n g t h e Duerr method, the p a r t i c u l a r acre o f the s u s t a i n e d - y i e l d u n i t a t t h a t age was e a r n i n g 4 . 2 p e r cent i n t e r e s t i n t h e case o f the 63-year-old stand and 4 . 1 p e r cent i n t h e 86-year-old  stand.  The 86 y e a r - o l d - s t a n d had the h i g h e s t volume and v a l u e p e r acre and the lowest r o t a t i o n age. S i t e index f o r t h i s stand was 165, which was the mode f o r the f o u r stands.  Thus stand d e n s i t y would  appear to have more i n f l u e n c e on r o t a t i o n age than stand s i t e index w i t h i n t h i s broad s i t e grouping.  As  l o n g as i n c r e a s i n g d e n s i t y i s c o n s i s t e n t w i t h i n c r e a s i n g value p e r acre then f i n a n c i a l decrease w i t h d e n s i t y i n c r e a s e . Smith and Haley  Haley  rotations  (1964), and  (1964), i n d i c a t e d t h a t c o n t r o l o f  stand d e n s i t y from i n i t i a l l y open t o normal a t r o t a t i o n age was an important f a c t o r i n r e d u c i n g the age o f financial  rotation.  Table XXXIX.  Margin f o r P r o f i t and Risk - $/Acre  F o r Lumber and Optimum Product -  Based on Growth and Normal Y i e l d Volume Estimates o f Four Stands o f Douglas F i r Stand Age (Years) 55 60 65 70 75 SO  55 60 65 70 75 80 85 90 95 100 105  36-year-old Stand - S.I. 165 Margin f o r P r o f i t and Risk 'acre (Years) Growth Normal Y i e l d Estimate Estimate Lumber Optimum Lumber Optimum 140O 1260 1320 1530 55 1760 1820 1600 60 1550 2010 2060 1860 1910 65 2320 2180 2190 2310 70 2560 2580 2460 2480 75 80 2840 2740 2760 2820 3050 3080 3010 3O3O 85  63-Year-old Stand - S . I . 160 Margin f o r , P r o f i t and R i s k Stand Growth Normal Y i e l d Estimate Estimate Lumber optimum Lumber Optimum y6u 1UUU yiu 9i>0 1200 1240 1180 1220 1420 1460 1430 1470 1660 1670 1710 1720 1900 1910 1980 1990 2220 2240 2075 2090 Stand -S.I.175 1000 960 1190 1230 1420 1460 1710 1720 I960 1970 2180 2200 2430 2450 2690 2710 2920 2960 3200 3140 3390 3460  55 65 75 85 95 105 115 125 135 145  145-year-old Stand •-S.I. 16! 880 . 910 1330 1370 1820 1830 2300 2320 2780 2820 3240 3220 3720 3840 4200 4400 4700 5000 5180 5600  vO  F i n a n c i a l Rotation Calculations f o r 63-year-old Douglas F i r at a 3 Per Cent Interest Rate;  Table XL  Establishment Cost of $20.00 per Acre and Annual Maintenance of $1.00 per Acre 1. (a)  (years) Het Rev. $/Ac  1096 1140 1182 1224 1266*  (b)  63 64 65  i  Hormal Y i e l d Approach to Volume Estimation  Stand Age  64 65 66 67 68 69  Duerr Rotation  Faustmann Rotation  Lumber Value Annual Soil Rent $/Ac  5.87  Capital Plus Xnt. $/AC  1084 1129 1174 1217 1261  Growth Approach to Volume Estimation  1054 1092*  5.81  1046 1086 1125  Net Rev. $/Ac  Optimum Value Annual Capital Soil Plus Rent Int. $/Ac g/Ac  1136 1180 6.07 1224 1264* 1500 1332  1125 1170 1215 1261  Stand Age (years)  Net Rev. $/Ac  Normal Y i e l d Approach to Volume Estimation  Lumber Value Total Average Net Value Value of of growing Growing Stock Stock Dollars $/Ac  Regulated Av. Value M.R. Growth of Gr. Stock $/Ac $/Ac  60  920  9810  163.50  15-35  61  964  10774  176.62  15.80  62  1008  11782  190.03  16.26  63  1052  12834  203.71  16.70  64  1096  13930  217-66  17.12  65  1140  15070  231.85  17.54  Marginal Value Growth of Stand $/Ac 36  13.12  .47 3.6  13.a  .46  3.4  13.68  .44  3.2  13.95  .42 3.0*  14.19  .42 2.9  * Indicated Rotation Age. ON  Table XLI.  F i n a n c i a l Rotation Calculations f o r 86-year-old Douglas F i r at a 3 per cent Interest Rate; Establishment Cost of $20.00 per acre and Annual Maintenance of $1.00  (a) Stand Age (years)  58 61 62 63 64 65 55 56 57 58 59 60 61  1. Faustmann Rotation Normal T i e l d Approach to . Volume Estimation  Lumber Value Net Annual Rev. Soil Rent $/Ac VAC  1188 1239 1290 1340 1390 1440* U90 1540  7.92  7.92  Capital Plus Int. S/Ac  1276 1329 1380 1432 1483  2. Duerr Rotation  Optimum Value Annual Net Soil Rev. Rent $/Ac  1248 1299 1350 1400 1450* 1500 1550 1600  per Acre.  8.28  Capital plus Int.  a/Ac 1338 1390 1442 1493  $Ac  Normal T i e l d Approach to Volume Estimation Lumber Value Total Average Regulated Av. Net Value value of Value H.R. of Growth growing Growth of GR Stock stock Stock Dollars $/Ac $/Ac . S/Ac  14058  242.?5  20.48  59  1239  15256  258.58  21.00  60  1290  16495  274.92  21.50  61  1340  17835  292.38  21.97  Net Stand Age Rev. (years)  58  il£d  Marginal Value Growth of Stand $/Ac JS  16.03  .52  3.2  16.34  .50  3.0*  17-46  .47  2.7  Growth Approach to Volume Estimation (b) 1235 1302 1272 1361 1341 1402 1414 1456 1461* 9.20 l5<XJ 1538  * Indicated Rotation Age.  NO  Table TT.TI.  F i n a n c i a l Rotation Calculations f o r 63-and 86-year o l d Douglas F i r at 5 per cent interest with $20.CO per AcreEstablishment Cost and at 3 and 5 per cent Interest with $50.00 per Acre Establishment Cost: Annual Maintenance Cost o f $1.00 per Acre Based on Normal T i e l d Approach to Volumes Per Acre and on Lumber Values  (a)  (b)  $20.00 per Acre Establishment Cost 3 1.00 per acre Annual Maintenance S per cent i n t e r e s t  Stand Age (years)  50 51 52 53 54 55 56 57 58 59 60  63-year-old Net Annual Rev. S o i l Rent $/Ac &/Ac 230 260 290 320 350 380 405 430 M0* 475 490  Capital Plus Int. $/Ac  241 273  304 1.39  336  86-year-old Net Annual Rev. S o i l Rent $/Ac S/AC 560 590* 625 650  2.67  50.00 per Acre Establishment Cost 1.00 per Acre Annual Maintenance 3 per cent Interest  Capital Plus Int. S/Ac  551 588  367 399 425 451  Stand Age 63-year-old (years) Net Annual Capital Rev. S o i l Plus Rent Int. $/Ac $/Ac $/Ac 60 61  62 63 64  A 66  e  67 68 69 70  1.39 * Indicated Rotation Age  730 764 798 832 866 900 934 968  1002*  T035 1070  752 787  822  857 892 927 962 997 1032  86-year-old Net Annual Rev. S o i l Rent $/Ac s/Ac 1110 1152 1194*  T236  6.81  Capital Plus Int. $/Ac 1100 1143 1187 1230  1278  5 Per Cent Interest Age 49 50 51  180 168 190*.91 189 197 200  Stand Age at Harvest (Years) 63 86 106 145  |4  Margin for Stumpage and/or Profit and Risk (8/Acre) 1300 3050 3450 5150  Co-5%  Va-86yrVa-63yrVal06yrVal45yr-  o  > o  >  c o b O < / > o O  Co-3%  0  30  40  50  60 70 80 90 100 . Stand Age,Years Figure 4- Stand values and costs (S/Acre) by stand age (years) for Douglas fir- Establishment cost of S 2 0 0 0 , a n d annual maintenance cost of % 100, per acre.cornpounded at 3,5 and 7 per cent interest- Stand values based on normal growth estimates of volume-  ,*Co-5% Stand Age at Harvest (Years) 63 86 106 145  4)  - kO  ond  Margin for Stumpage /or Profitand Risk (8 /Acre) 1300 3050 3450 5150  pCo-7%  Va- 86yr-  ca o  > 3 o>  Va- 63 yrVal06yrVa-145 yr-  3 O > TO C  o  6  2  w o  o  60 70 80 100 90 Stand Age,Years Figure 5- Stand values and costs (8 /Acre) by stand age (years) for Douglas fir- Establishment cost of 8 50-00 and annual maintenance cost of 8 100, per acre,compounded at 3,5 and 7 per cent interestStand values based on normal growth estimates of volume-  BIOLOGICAL RELATIONSHIPS Regression  analysis Although the r e a l v a l u e o f a t r e e as  lumber or some o t h e r product cannot u n t i l the t r e e has been converted,  be  determined  certain  b i o l o g i c a l c h a r a c t e r i s t i c s o f the t r e e may u s e f u l f o r estimating value.  I t may  be  be found,  from  a sample o f the p o p u l a t i o n , t h a t v a r i a b l e s such  as  diameter, h e i g h t , crown c l a s s , age and o t h e r s have s i g n i f i c a n t r e l a t i o n s h i p s with t r e e value. A c c o r d i n g l y , by the f o r m u l a t i o n o f a  mathematical  model, i n c o r p o r a t i n g chosen v a r i a b l e s , e s t i m a t e s o f the expected value o f other t r e e s of the p o p u l a t i o n can be made. An e x p r e s s i o n d e r i v e d from the c h a r a c t e r i s t i c s o f one p o p u l a t i o n may  unique  or may  not g i v e  v a l i d estimates i n another p o p u l a t i o n with i t s own unique  characteristics.  General e x p r e s s i o n s are  sometimes u s e f u l i n the absence of l o c a l e x p r e s s i o n s ; u s u a l l y more p r e c i s e e s t i m a t e s can be o b t a i n e d from a l o c a l l y d e r i v e d model.  Mathematical  expressions of  the r e l a t i o n s h i p between t r e e v a l u e and  biological  102. variables were formulated f o r the tree samples discussed  in this thesis.  Those incorporating a l l  of the age-classes might be regarded as general and those f o r each i n d i v i d u a l age-class as l o c a l . Regression analysis, which may as the estimation  be  defined  of the value of one variable from  observed values of other variables, was determine the most appropriate  used to  models i n each case.  Regression analysis enables the e f f e c t s of  various  independent factors on a dependent f a c t o r to be evaluated from the observed data without the necessity of having a designed experiment f o r the control of certain variables. When s i g n i f i c a n t relationships have been established, by appropriate  t e s t s of significance  on the c o r r e l a t i o n c o e f f i c i e n t s or variance r a t i o s , for example, i t remains to decide which variables to include i n the regression model and which to omit. From a p r a c t i c a l point of view those s i g n i f i c a n t variables which are e a s i l y and cheaply measurable i n the f i e l d would merit close attention.  There i s no  p r a c t i c a l advantage i n using a r e l a t i o n s h i p which involves variables d i f f i c u l t to measure when equally  V  103. e f f i c i e n t e s t i m a t e s can be o b t a i n e d from e a s i l y measured f a c t o r s . Also,  there i s l i t t l e  i n the r e g r e s s i o n  point  i n including  a number o f independent  variables  which a r e h i g h l y c o r r e l a t e d w i t h each o t h e r .  I f they  are  s i g n i f i c a n t l y r e l a t e d t o the dependent v a r i a b l e  and  to each o t h e r then they u s u a l l y account f o r more  o r l e s s the same p o r t i o n o f the v a r i a n c e dependent v a r i a b l e .  o f the  In such cases the estimate o b t a i n e d  from one o f the independent v a r i a b l e s u s u a l l y i s not s i g n i f i c a n t l y improved by the i n c l u s i o n o f the o t h e r i n the r e g r e s s i o n i n regression describes  relationship.  "Account f o r " as used  a n a l y s i s does not imply cause but merely  t h e r e l a t i o n s h i p between dependent and  independent  variables.  One o f the problems i n u s i n g  regression  a n a l y s i s on t r e e s i s t o f i n d b i o l o g i c a l v a r i a b l e s which are not c o r r e l a t e d w i t h each o t h e r .  Many o f the t r e e  c h a r a c t e r i s t i c s , f o r a given population all  of trees, are  s i g n i f i c a n t l y c o r r e l a t e d one w i t h t h e o t h e r .  W i t h i n a stand o f timber the t a l l e s t t r e e s u s u a l l y have the l a r g e s t diameters and the l o n g e s t  crowns.  Crown  104. w i d t h i s u s u a l l y s i g n i f i c a n t l y c o r r e l a t e d w i t h dbh and  crown dominance.  This  m i u i i t - i c o l i n e a r i t y has t h e  e f f e c t o f r e d u c i n g the number o f v a r i a b l e s  required  f o r s i g n i f i c a n t e s t i m a t e s to a manageable few, which i s b e n e f i c i a l both f o r measuring and computing purposes. Test o f b i o l o g i c a l v a r i a b l e s The  data o b t a i n e d from the f o u r samples o f  timber were subjected  t o computer a n a l y s i s on t h e  I.B.M. 7040 a t the U n i v e r s i t y o f B r i t i s h Columbia. The  v a r i a b l e s measured and d e r i v e d  a r e presented i n  T a b l e s XL-IT I and XLIV w i t h t h e p e r t i n e n t The  statistics.  simple c o r r e l a t i o n c o e f f i c i e n t s shown a r e f o r the  regressions  o f the lumber c o n v e r s i o n r e t u r n and the  optimum c o n v e r s i o n r e t u r n on the independent v a r i a b l e . As i n d i c a t e d i n T a b l e s X L I I I and ZLIV a great  many o f t h e independent v a r i a b l e s t e s t e d were  h i g h l y s i g n i f i c a n t l y c o r r e l a t e d w i t h the dependent variables.  Many o f these independent v a r i a b l e s a r e  d i f f i c u l t t o measure, p a r t i c u l a r l y on the coast  where  the topography i s broken and the underbrush i s dense. Measurements o f t r e e crowns a r e d i f f i c u l t t o make and  105. subject to considerable error when intervening trees and interlocking branches obscure the line of vision. Similarly with measurements of total height and height to first live and dead limbs. Data on tree ages and tree site index can only be obtained by boring the standing tree which is a time-consuming process. The retention of a variable in regression models is justified when its ability as an estimator is deemed to outweigh the difficulties of measurement. Also i t may be possible that estimates by classes, such as height or crown-width classes, will render results similar to those obtained from specific measurements and at the same time be much more easily obtained.  Crown width, for example, showed itself to  be consistently highly, positively correlated with value for each analysis. 1/hen the crown width-^data were sorted into 5- and 10-foot groups the resultant estimates of value were of the same significance level as for the actual width measurements. The inference is that class groupings can be useful when specific dimensions are difficult to measure. 1. Although this study showed an.increase of value with crown width, tree improvement should be directed towards finding trees with small crowns but fast growth to provide maximum yields per acre and high technical wood quality.  Important v a r i a b l e s f o r value p r e d i c t i o n From the v a r i a b l e s l i s t e d i n T a b l e s X L I I I and XLIV, e i g h t which were c o n s i s t e n t l y s i g n i f i c a n t among the a g e - c l a s s e s and measured i n the analysis.  which could be  objectively  f i e l d , were s e l e c t e d f o r f u r t h e r  These were s u b j e c t e d  reduction  routine  described  by Kozak and  to the  automatic  o f the programme used, which Smith (1965).  By  was  successive  eliminations  the programme d i s c a r d s t h a t v a r i a b l e w i t h  the  variance  smallest  r a t i o o f each  combination and  re-computes the  remainder.  elimination  The  successive  statistics for  can be  the  stopped when a  s i g n i f i c a n t set o f independent v a r i a b l e s i s o b t a i n e d o r can be c o n t i n u e d u n t i l o n l y one  variable i s l e f t .  In a d d i t i o n to the above o p e r a t i o n ,  the t h r e e  w i t h the h i g h e s t s e l e c t e d and  variables  simple c o r r e l a t i o n c o e f f i c i e n t were  t e s t e d i n combination.  Because o f the problem o f m u l t i c o l i n e a r i t y p r e v i o u s l y mentioned, the v a r i a b l e s with the simple c o r r e l a t i o n c o e f f i c i e n t s were not  necessarily  those which appeared i n the best r e g r e s s i o n For  highest  combination.  the grouping o f a l l ages the t h r e e independent  v a r i a b l e s , o f the  e i g h t s e l e c t e d , which c o n t r i b u t e d  most  t o the r e g r e s s i o n ( R and crown c l a s s .  2  = .729)  were age, crown width  The t h r e e v a r i a b l e s w i t h the  h i g h e s t simple c o r r e l a t i o n c o e f f i c i e n t s were dbh, h e i g h t and crown l e n g t h which, i n combination, removed 67.4  per cent ( R  the dependent v a r i a b l e .  2  = .674) Simple  o f the v a r i a n c e i n correlation  coefficients  between crown width and crown c l a s s , crown width and age, and crown c l a s s and age were  -.616,  .009 and -.008,  r e s p e c t i v e l y , o n l y one o f which i s s i g n i f i c a n t .  The  simple c o r r e l a t i o n c o e f f i c i e n t s between dbh and h e i g h t , dbh and crown l e n g t h , and h e i g h t and crown l e n g t h were highly  .846, .814  and . 845> r e s p e c t i v e l y , a l l  significant. The s t a t i s t i c s i n v o l v i n g the s e l e c t e d  independent  v a r i a b l e s a r e presented i n Tables XLV,  XLVI and XLVII.  I t w i l l be noted i n these t a b l e s t h a t ,  i n a l l cases, the t h r e e v a r i a b l e s which c o n t r i b u t e d most t o the r e g r e s s i o n i n c l u d e d a t the most o n l y two w i t h the h i g h e s t simple c o r r e l a t i o n c o e f f i c i e n t s . independent  Ideally,  v a r i a b l e s used i n a r e g r e s s i o n model should  be h i g h l y c o r r e l a t e d w i t h the dependent v a r i a b l e and not c o r r e l a t e d w i t h each o t h e r . such requirements  As p r e v i o u s l y noted,  are d i f f i c u l t t o f u l f i l l  with  108. v a r i a b l e s f o r e s t i m a t i n g the volume o r value o f standing t r e e s . TablesXLV, XLVI and XLVII show t h a t the d i f f e r e n c e between the v a r i a t i o n a t t r i b u t a b l e t o the e i g h t s e l e c t e d independent v a r i a b l e s and to the best combination  o f f o u r , was  i n s t a n c e 3 per cent i n another i n the remaining  4 per cent i n one and 2 per cent o r l e s s  eight analyses.  w i t h the best combination  A s i m i l a r comparison  o f t h r e e independent  v a r i a b l e s showed t h a t they accounted  f o r 5.6  per cent  o r l e s s o f the v a r i a t i o n i n Y than d i d the e i g h t selected.  Thus f o r most p r a c t i c a l purposes the use  of  t h r e e or f o u r v a r i a b l e s would be adequate f o r a c c e p t a b l e e s t i m a t e s of t r e e v a l u e i n the stands d i s c u s s e d here. I n each o f the a n a l y s e s , R r - squared f o r the best combination  o f t h r e e independent v a r i a b l e s was  higher  than t h a t f o r the t h r e e v a r i a b l e s w i t h the h i g h e s t simple c o r r e l a t i o n c o e f f i c i e n t s , accounting f o r from  one  to 15 per cent more o f the v a r i a t i o n i n Y. C e r t a i n independent v a r i a b l e s c o n s i s t e n t l y appeared i n the best combinations  o f f o u r and t h r e e  o t h e r s i n the s e l e c t i o n o f the t h r e e h i g h e s t correlation coefficients.  The frequency o f  and  simple occurrence  109. of  the e i g h t s e l e c t e d v a r i a b l e s i n t h e above  c a t e g o r i e s i s shown i n Table X&V.. Butt l o g grade  (X6),  t r e e age ( X 7 ) ,  (X12)  crown c l a s s (115)  had an occurrence percentage  o f 9 0 , 90,  r e s p e c t i v e l y , i n the best f o u r . v a r i a b l e s had percentage 50,respectively,in of  and crown width 80 and 60,  The same f o u r  o c c u r r e n c e s o f 80,  the best t h r e e .  6 0 , 7 0 and  I n the a n a l y s e s  the t h r e e v a r i a b l e s with t h e h i g h e s t simple  c o r r e l a t i o n c o e f f i c i e n t s , dbh (XI) o c c u r r e d 1 0 times, crown c l a s s ( X 1 3 ) all  8 times and crown width  (X12)  5 times,  out o f a p o s s i b l e 1 0 .  S e l e c t e d r e g r e s s i o n models The s t a t i s t i c s f o r some p r e d i c t i o n o f v a l u e e q u a t i o n s f o r the combined a g e - c l a s s e s a r e p r e s e n t e d i n Table XLLX and Table L. combinations  Most o f t h e r e g r e s s i o n  i n c l u d e dbh as an independent  variable  because i t i s the most f r e q u e n t l y used v a r i a b l e i n t r e e and stand a n a l y s i s and i s a l s o one o f t h e e a s i e s t f i e l d measurements t o take.  I n TablesXLIX  be noted t h a t dbh alone accounted  and L i t w i l l  f o r almost as much o f  the v a r i a n c e i n the dependent v a r i a b l e as d i d most o f the combinations variables.  Thus,  o f two, t h r e e and f o u r  independent  i n these i n s t a n c e s , i t i s s u f f i c i e n t ,  110. i n the s t a t i s t i c a l l y s i g n i f i c a n t sense, to use alone as an e s t i m a t o r of v a l u e .  The best  combinations  o f two and t h r e e v a r i a b l e s i n Tables XLIX and u s i n g Rgrade  dbh  L,  squared as the c r i t e r i o n , i n v o l v e d b u t t -  (X6)  and crown c l a s s (X15) w i t h dbh ( X I ) . A summary o f the s t a t i s t i c s f o r p r e d i c t i o n  o f value equations i s shown f o r the t o t a l  age  grouping and f o r each i n d i v i d u a l a g e - c l a s s i n Table L I . Again u s i n g R-squared as the c r i t e r i o n , the b e s t p a i r o f v a r i a b l e s f o r p r e d i c t i o n of the lumber c o n v e r s i o n r e t u r n i n the combined and i n each i n d i v i d u a l stand, was  dbh and crown c l a s s .  F o r the p r e d i c t i o n o f the  optimum c o n v e r s i o n r e t u r n the best p a i r , f o r i n d i v i d u a l and c o l l e c t i v e stands, was  dbh and b u t t - g r a d e .  Although  the above p a i r s were c o n s i s t e n t l y best f o r t h e i r r e s p e c t i v e f u n c t i o n s i n each and i n a l l ages, i t i s p o i n t e d out t h a t a l l of the combinations shown i n Table L I have the same l e v e l o f s i g n i f i c a n c e .  Merchantable  volume equations  Some merchantable  volume equations f o r the  combined a g e - c l a s s e s are p r e s e n t e d i n Table L I I . dbh was  Tree  the most important simple v a r i a b l e a c c o u n t i n g  111. f o r 87 per cent and 90 per cent o f the r e s p e c t i v e v a r i a n c e i n merchantable board-foot  and c u b i c - f o o t  o  volumes.  The compound v a r i a b l e D H, accounted f o r  92 and 93 per cent r e s p e c t i v e l y o f the v a r i a n c e s i n merchantable board-and c u b i c - f o o t volumes. Smith and Breadon (1964) volume equations t a b u l a r data.  presented  d e r i v e d from B.C. F o r e s t  Service  They used D H as the independent 2  v a r i a b l e f o r e s t i m a t i n g t o t a l c u b i c - f o o t volumes o f trees.  Two o f t h e i r e x p r e s s i o n s which c o u l d be used  to estimate  the cubic volumes o f the t r e e s o f t h i s  study a r e : -  (1)  V = 11.8 + 0.166 D H/100 and  (2)  V =  2  4.3 + 0.164 D H/100. 2  A p p l i e d t o the data o f t h i s study,  estimates  o f average t o t a l c u b i c f o o t volume p e r t r e e a r e 193 and  202 f o r equations  (1)  and (2)  respectively.  The  average merchantable volume p e r t r e e o f the combined stands was 173  c u b i c f e e t which was estimated  to be 87 per cent o f the t o t a l c u b i c volume. seven p e r cent o f the volumes estimated (1)  and (2) above i s 168 and 176  by  previously Eighty-  equations  cubic f e e t r e s p e c t i v e l y ,  which compare f a v o u r a b l y with t h e 173  cubic f e e t a c t u a l l y  112. r e c o v e r e d on the average.  The e q u a t i o n shown i n  Table L I I f o r e s t i m a t e s o f merchantable c u b i c volume f o r the data used here i s (3)V The average  = 16.148 + .0014  estimate by t h i s e q u a t i o n i s 177  D H. 2  cubic feet  o f merchantable volume which would be the e q u i v a l e n t o f 203  c u b i c f e e t t o t a l volume. Thus, u s i n g equations (2)  o f average merchantable volume (176 r e s p e c t i v e l y ) and average  (3),  estimates  and 177  cubic f e e t  and  t o t a l volume (202  203  and  c u b i c f e e t r e s p e c t i v e l y ) are almost i d e n t i c a l .  Estimates  u s i n g equation (1)  than  are about 4.5 (3)  per cent lower  those o f (2)  and  e q u a t i o n (2)  i s more a p p r o p r i a t e than  indicating that, i n t h i s (1).  case,  The c l o s e  agreement i n the e s t i m a t e s p r o v i d e d by the above equations i n d i c a t e a l s o t h a t 0.87  i s a useful reduction  f a c t o r f o r e s t i m a t i n g merchantable cubic from  total  c u b i c volume. Two  additional relationships of i n t e r e s t  o b t a i n e d from the a n a l y s e s o f the data were the  average  l i n e a l f e e t o f t r e e r e q u i r e d per M fbm lumber and per Ccf logs.  The averages of each o f the above v a r i a b l e s f o r  the combined and i n d i v i d u a l ages are presented i n Table L I U  w i t h r e g r e s s i o n r e l a t i o n s h i p s based on  dbh,  height,  age and s i t e index.  dbh was  the best s i n g l e v a r i a b l e f o r e s t i m a t i n g  l i n e a l f e e t requirements  As might be  the  per u n i t volume o f lumber and  l o g s and f o r most p r a c t i c a l purposes alone.  expected,  could be  used  The p r e d i c t i o n equation f o r the combined ages  u s i n g dbh alone as the independent  variable i s  p r e s e n t e d a l s o i n Table L I I I . Formulation of tree  grades  A c o r o l l a r y o f the d e t e r m i n a t i o n o f important and s i g n i f i c a n t b i o l o g i c a l v a r i a b l e s i s the formulation  o f t r e e grades.  The b a s i s f o r t r e e  can be v a l u e or volume or some o t h e r depending on the area o f i n t e r e s t .  grades  criterion, Net v a l u e per  cubic  f o o t of t r e e i s used here as a q u a l i t y c r i t e r i o n f o r the assignment o f t r e e I t was  grades.  shown p r e v i o u s l y  s i g n i f i c a n t combination  that a highly  o f v a r i a b l e s f o r the p r e d i c t i o n  o f value per cubic f o o t o f t r e e was and crown c l a s s .  b u t t - l o g grade  The r e l a t i o n s h i p f o r the  o f the combined a g e - c l a s s e s I =  dbh,  34-95 + 1.114  dbh  lumber-value  was:-  -3.698  b u t t - l o g grade  -4.874  crown c l a s s where I i s net value i n cents per cubic f o o t o f t r e e .  114. T h i s combination  o f independent v a r i a b l e s removed  74 p e r cent o f t h e v a r i a n c e i n the dependent v a r i a b l e and had a standard e r r o r of estimate +8.6  of  cents. The number of t r e e grades used i s a g a i n a  m a t t e r of choice and t h e d i v i s i o n s made may be a r b i t r a r y o r based on the c h a r a c t e r i s t i c s o f t h e t r e e population.  Three d i v i s i o n s were used i n t h i s i n s t a n c e  and the grouping was based on the assumption t h a t t r e e value f o l l o w e d a normal d i s t r i b u t i o n . the middle grade was g i v e n a range o f +.5  Accordingly o f a standard  d e v i a t i o n around t h e mean and the o t h e r two grades were a s s i g n e d above and below t h i s range.  F o r a normal  p o p u l a t i o n 38 per cent o f the v a l u e s l i e w i t h i n + .5 o f a standard d e v i a t i o n o f the mean and 31 per cent each on e i t h e r s i d e o f t h i s range. The average net v a l u e p e r c u b i c o f t r e e f o r the combined stands was 42 c e n t s w i t h a standard d e v i a t i o n o f + 17 c e n t s .  T h e r e f o r e the middle  o r grade 2  t r e e s had a v a l u e o f from 34 t o 50 cents p e r c u b i c f o o t w i t h grade 3 being 33 cents and under and grade 1 v a l u e d a t 51 cents and over.  The r e s u l t a n t d i s t r i b u t i o n o f t r e e  grades by dbh, b u t t - l o g grade and crown c l a s s a r e shown i n Table LIV.  115. Using the a c t u a l t r e e value t o a s s i g n a grade from one o f the above t h r e e c a t e g o r i e s an " a c t u a l " grade was o b t a i n e d f o r each t r e e .  Checking  this  a g a i n s t the grades as estimated by the r e g r e s s i o n f u n c t i o n i t was found t h a t t h e estimated grade was i n e r r o r i n 33 t r e e s from a t o t a l o f 162.  Thus t h e grades  d e r i v e d from the r e g r e s s i o n f u n c t i o n had an accuracy o f 80 per cent.  Many o f the estimated grades were i n  e r r o r by o n l y a few cents and the a c t u a l and estimated average (42  net v a l u e s o f a l l t r e e s were e x a c t l y the same  cents p e r c u b i c f o o t ) . Many o t h e r combinations  o f the above o r  a l t e r n a t i v e b i o l o g i c a l v a r i a b l e s c o u l d be used t o d e r i v e t r e e grades.  The s e l e c t i o n depends on p e r s o n a l  p r e f e r e n c e but i t should, i f p o s s i b l e , combine s i g n i f i c a n c e w i t h ease o f measurement.  Table XLIII. Mean Values. Standard Deviations and Correlation C o e f f i c i e n t s of Independent and Dependent Tree Variables f o r Combined Ages and f o r 63-vear-old Douglas F i r A l l Ages  Age Class  SD r Independent 1 2 Variables DVB".E7~(in.) ~55T2" "7T7 ~T8T7** 7755*"* TL X2 Total Height (ft.) 150.4 29.2 .723** .687** X3 Height of Clear Bole (ft.) 7-3 10.1 .510** .615** 14 Height to f i r s t dead limb (ft.) 22.2 17.9 .327** .435** X5 Height to f i r s t live limb (ft.) 75.5 16.6 .040 -.014 X6 Butt Grade (1-3P,2-4P,3-2S,4-3S) 3-0 1.0 -.624** -.707** X7 Tree Age (yr.) 96.9 29-9 .542** .597** X8 Site Index (ft. at 100 yr.) , " 156.6 18.1 .653** .548** X10 Merch. Bole surface area(sq.ft./10) 44-7 20.7 .809** .757** X l l Crown length (ft.) . 61.7 22.2 .711** .672** X12 Crown width (ft.) 27-2 9-2 .558** .439** X13 Crown width (5 f t . classes) 27-3 9-3 .544** .416** H 4 Crown width (10 f t . classes) 27-6 9-4 .503** .410** X15 Crown class (1-D,2-CD,3-I,4-S) 2.0 0.9- -.629** -.522** X16 Crown density (per cent) 71-6 13-2 . .399** .343** X20 D.B.H.2. 696.1 434-7 -779** .756** 121 D.H./100 39-8 19.1 .796** .769** X22 D.2;ff./1000 114-9 89-3 .764** .755** X23 Crown length per cent Total Height 40.1 9-1 -549** .489** X24 C.W./D 1.1 0.3 -.200* -.252** X25 H./C.W. 6.1 2.5 -.203* -.131 X26 Lineal feet tree /K fbm lumber 117.3 68.4 -.858** -.700** X27 Lineal feet tree / Ccf logs 80.4 42.1 -.818** -.688** X28 Crown volume (cu.ft./lOO) 14-9 13-1 .588** .505** Dependent Variables TI Conversion Return Lbr.(cts./cu.ft.) 42.0 16.6 Y2 Conversion Return Optimum(cts./cu.ftj 46.8 14.8 Observations 162 11) r - simple correlation coefficient; 1 on T l , 2 on 12.  X  63 Year SD  18.8 57J~ 117-1 11.1 1.0 0.0 13-3 8.2 68.8 9.8 3-7 0.7 63.4 2.5 145-9 13-5 26.6 8.6 43'.3" 12.9 23-4 6.7 23-5 7-0 23-4 7.5 1.9 0.9 70.2 12.7 372.7 170.3 22.4 6.7 44-9 23-2 36.5 8.6 1.2 0.2 5-3 1.4 172.7 77.1 115-2 44.9 7-4 5.4 31.4 37.8  13-7 9.6 50  .833** .720** .000 -.020 -.265 -.382** .307* .693** .789** .688** .702** •721** .593** -.756** .594** .799** .839** .805** .614** .059 -.591** -.914** •.846** .680**  -535** .425** .000  .141 -.130 -.405** .333* .367** .446**  .451**  -475**  .488**  .463** -.475** .467** -532** .543** -543**  .401**  -099 -.452** -.559** -.523** .469**  ON  Table XLIV.  Mean Values. Standard Deviations and Correlation Coefficients of Independent and Dependent Tree Variables f o r 86-, 106-, and 145-year Douglas F i r Age Class 86 year 106 year X SD r X SD  Independent Variables(l) XI 22.4 X2 150.0 X3 1.0 X4 11.5 X5 81.3 X6 3-4 17 86.5 X8 159.1 39.9 no 57.5 Xll 33-4 H2 33.7 X13 34.0 .XU 1.8 X15 75.4 X16 545-9 X20 34.8 X21 84.7 122 37.9 X23 1.4 X24 4.8 X25 116.3 X26 84.4 X27 20.3 X28 Dependent Variables(1) 40.2 n 43.8 12 Observations (1)  5.0 15.2 0.0 10.7 15-6 0.9 4-3 14.6 11.3 17-5 9.7 9.6 9.1 0.9 9.8 238.8 10.7 43.7 9.2 0.2 1.3 45-8 31.0 15-7  1 .768** .740** .000 -.098 .350* -.517** .610** .690** .759** .514** .627** .595** .568** -.762** .465** •743** •774** .744** .360* .121 -.474** -.879** -.820** .564**  9.7 6.8 35  2 •572** .570** .000 .112 .318 -.605** .450** .548** .397* .325 - .430** .389* .386* -.652** • 397* .575** .590** .583** .179 .032 -.284 -.635** -.608** .391*  30.2 171.7 5.5 26.7 88.7 2.7 106.2 168.0 58.7 72.6 30.1 30.2 30.4 2.1 72.6 962.7 52.9 171.6 41.9 1.0 6.0 81.6 56.9 19.9  "7^4 18.1 4.2 21.5 15.9 0.6 3.0 17.2 18.2 19.0 7.7 7.9 7.9 1.0 11.8 450.2 17.1 91.8 8.8 0.1 1.1 43.6 26.5 U.l  46.7 49.6  Variable Designations are the same as i n Table XLIII  13.3 11.6 43  .744** .655** .253 .197 .221 .431** .179 .666** .731** .503** .737** .730** .635** .775** .410** .690** .725** .671** .316* .047 .694** .863** .827** .621**  2 .725** .662** .217 • 309* .192 ••597** .248 .656** .689** .541** •733** .716** .649** -.750** .466** .675** .711** .658** .373* .074 -.670** -.8116* -.788** .635**  X  145 year SD  3oT7 6.9 22.4 173.1 6.2 25.3 ll.l 40.8 62.7 11.5 2.1 0.9 144.7 7.5 155.5 19-5 21.6 58.4 79.2 19.7 22.8 9.0 8.6 22.5 23.5 9.5 2.0 1.0 68.5 17.4 989.2 445-6 54.1 17.3 177.3 94.1 7-2 45.3 0.2 0.7 8.8 3.8 82.0 42.8 54.7 23.1 13.8 11.7 53.4 59.6  20.4 20.0 34  1 .818** .664** .689** .032 -.136 -.583** .611** .636** .840** .691** .819** .818** .700** -.794** .456** .789** .823** .800** .567** .641** -.661** -.894** -.840** .779**  r  2 .848** .687** .788** .086 -.121 -.726** .647** .663** .817** .682** .836** .827** .724** —795** ,471** .811** .845** .815** .556** .652** -.672** -.901** -.880** .757**  Table XLV. R- Squared** Values for Regression of Conversion Return Lumber (Yl) and Conversion Return Optimum (Y2) on Selected Biological Variables for combined ages and 63-year-old Douglas F i r  TL  R2  R2  ( 1 ) R2  . 717  (a)  Total^ )  .760  (b)  Best Combinations 6,7,12,15 7,12,15 7,15  .748 .729 .684  (c)  Variables with Highest simple correlations 1,2,11 .674 1,11 .673 1,2 .671 2,11 .558  1  Age Class (Years) 12  YT  Independent Variables (I)  A l l Ages  63 years  -  Y2 R2  .742  . 403  1,6,7,15 1,6,15 1,6  .709 .694 . 671  1,7,12,15 1,7,15 1,15  .741 -741 .730  6,7,12,15 6,7,12 6,12  .370 .353 . 312  1,2,6 1,6 2,6 1,2  .671 .671 .601 .592  1,2,15 1,15 1,2 2,18  .731 -730 .718 .590  1,12,15 1,15 1,12 12,15  -300 .298 .289 .276  I D X I D.B.H. (inches) X2 Total Height (feet) X6 Butt Log Grade (butt 34« of tree) X7 Tree Age (Years) X8 Tree Site Index (feet at 100 years) X l l Crown Length (feet) X12 Crown Width (feet) XI3 Crown Class  \  ** A l l of the R- Squared values shown i n the table indicate that the R values are significant at the 99 per cent level.  P »  Table XLVI. R.- Squared**  v a l u e s f o r Regression o f Conversion Return Lumber ( Y l )  and C o n v e r s i o n R e t u r n Optimum (Y2) on S e l e c t e d B i o l o g i c a l V a r i a b l e s f o r 86- and 106- y e a r - o l d Douglas F i r Age C l a s s (Years)  Independent V a r i a b l e s (X) (a)  Total* )  (b)  Best  (c)  Variables with h i g h e s t simple correlations  1  Combinations  1,6,7,8 6,7,8 7,8  1,2,15 1,15 1,2 2,15  86-year Yl  Y2  R2  R2  106-year (X)  Yl  Y2  R2  R2 .775  .745  .623  .724  .731 2,6,7,8 .714 6,7,8 .631 6,8  .603 6,7,11,15 .567 6,7,15 .515 6,15  .686 6,11,12,15 -770 .673 6,12,15 -763 .656 6,15 .734  .643 .637 .627 .604  .541 1,12,15 .541 12,15 .476 1,15 .427 1,12  .634 .633 .624 .571  1,6,15 6,15 1,6 1,15  1,12,15 12,15 1,15 1,12  .607 .607 .588 .554  JT)  V a r i a b l e D e s i g n a t i o n s same as i n Table XLV.  **  A l l o f the R-Squared v a l u e s shown i n the Table i n d i c a t e s i g n i f i c a n c e o f the R v a l u e s a t the 99 p e r cent l e v e l .  Table XLVII.  R-Squared** Values f o r Regression o f Conversion Return Lumber (YI) and c o n v e r s i o n r e t u r n optimum (Y2) on s e l e c t e d B i o l o g i c a l f o r 145-year-old  Douglas F i r YI  Independent V a r i a b l e s (a)  T o t a l CD  (b)  Best  (c)  (1)  (X)  Variables  R  Y2 (X)  2  .822  R  2  .917  Combinations 6, 7, 1 2 , 15 6, 1 2 , 15 1 2 , 15  .819 .809 .788  6,7,12,15 6,12,15 6,12  .913 .900 .828  V a r i a b l e s w i t h Highest Simple C o r r e l a t i o n s 1, 1 2 , 15 1 2 , 15 1, 15 1, 12  .792 .788 .754 .712  1,12,15 12,15 1,15 1,12  .820 .808 .789 .755  V a r i a b l e D e s i g n a t i o n s same as i n Table  XLV.  ** a l l o f the R-squared v a l u e s shown i n the t a b l e i n d i c a t e s i g n i f i c a n c e of the R v a l u e s a t the 9 9 per cent l e v e l . H JO  o  Table X L V I I I .  Frequency o f o c c u r r e n c e o f e i g h t s e l e c t e d independent v a r i a b l e s i n r e g r e s s i o n s o f lumber and optimum c o n v e r s i o n r e t u r n s on b e s t c o m b i n a t i o n s o f 4 and 3 v a r i a b l e s and on t h e t h r e e h i g h e s t r f o r 10 a n a l y s e s o f Douglas  Independent V a r i a b l e XI X2 X6 X7  X8 Xll X12 XI5  D.B.H. T o t a l Height B u t t Log Grade Tree Age Tree S i t e Index Crown Length Crown Width Crown C l a s s  Frequency i n Best 4 3  1 9 9  2 2 6  8  of  fir Occurrence (Maximum 10) I n Best 3 2 8  6 2 5 7  10 4  2  1 5 8  ro  Table XLLX. Equations f o r Regression o f Lumber Conversion Return i n Cents per Cubic 86-, 106-. and 145-year-old Douglas F i r Independent Variables(l) (X)  Intercept  1 2 6 7 12 15  -1.509 -20.060 74.271 12.790 14.558 64.110  1.727 0.413 ±10.626 0.301 1.008 -11.021  1,2 . 1,6 1,7 1,12 1,15  -6.101 14.154 -2.047 -3.072 14.987  1.526 1.483 1.690 1.606 1.429  0.064 -3.131 0.015 0.169 -4.476  1,2,6 1,2,15 1,6,15 1,12,15 7,8,15  11.070 9.367 34.950 16.022 10.750  1.390 1.144 1.114 I.449 0.276  0.033 O.O87 -3.698 -0.044 O.I44  -2.987 -4.643 -4.874 -4.647 -8.996  1,2,7,8  -52.922  1.313  -0.440  0.303  (1)  a  Regression bl  b2  Coefficients b3  Variable Designations same as i n Table XLV.  b4  0.630  Standard Error of Estimate (cents) ± 9.63 11.53 13.04 14.02 13.85 12.98  R2*#  (Cents) .667 .523 .390 2294 .311 .395  9.61 9.36 9.65 9.58 8.98  .671 .687 .667 .673 .712  9.37 9.37 8.61 9.00 9.29  .688 .719 .741 .713 .694  9.34  .692  1  Mean YI 42TD  '  A l l R-Squared values i n d i c a t e s i g n i f i c a n c e o f r o r R a t the 99 per cent l e v e l .  Table L. E q u a t i o n s f o r Regression o f Optimum Conversion Return i n Cents per Cubic Foot (Y2) on S e l e c t e d Independent V a r i a b l e s f o r Combined Stands o f 63-,86-,106-, and 145-year-old Douglas F i r Independent I n t e r c e p t Variables(1) a (X)  Regression C o e f f i c i e n t s bl  b2  b3  1 2 6 7 12 15  10.532 -5.645 79.259 18.204 27.582 63.074  1.434 0.348 -10.695 0.295 0.705 -8.123  »? 1,6 1,7 1,12 1,15  5.499 38.796 7.456 11.211 18.659  1.218 0.998 1.224 1.491 1.292  0.070 -5.651 0.088 -0.074 -2.205  1,2,6 1,2,15 1,6,15 1,12,15 7,8,15  37,682 13.369 50.952 23.680 27.010  O.965 1.024 O.782 1.389 0.286  0.012 0.082 -5.982 -0.213 0.045  -5.599 -2.362 -2.849 -3.035 -7.441  1,2,7,8  -26.374  1.060  -0.364  0.311  1  "(1)  b4  0.453  R *# 2  Standard Error of Estimate (cents) ± 9.53 10.77 IO.48 11.89 13.32 12.65  .473  9.50 8.53 9.35 9.55 9.40  .592 .671 .605 .589 .600  8.55 9.34 8;25 9.32 9.14  .671 .608 .694 .610 .625  9.24  .619  Mean Y2 (cents)  .586  4oT§  .500 .357 .193 .272  V a r i a b l e D e s i g n a t i o n s same a s i n Table XLV. A l l R-Squared v a l u e s i n d i c a t e s i g n i f i c a n c e o f r o r R a t the 99 per cent l e v e l , ro VO  Table L I .  S t a t i s t i c s o f P r e d i c t i o n o f Value Equations f o r Regression o f Lumber Conversion Return  (YI) and Optimum Conversion Return  (Y2), i n Cents  per Cubic F o o t , on S e l e c t e d Independent V a r i a b l e s f o r A l l Ages and I n d i v i d u a l Stands o f Douglas F i r Independent Variables(l) (X)  A l l Ages See " R2** -  1,2 1,6 i;i2  +9.61 9.36 9.58 8.98  1,6,15  8.61  1,2,7,8  9.34 .692 42.0  1,15  Mean Y l ( c e n t s )  Age C l a s s (Years) 63 Year §0" Year See R2 See R 1.  .673 .712  7.66 7.71 7.24  .718 .698 .694 .730  +6.10 6.12 6.35 6.03  .627 .625 .596 .637  .741  7.31  .731  5.92  .660  .687  9.50  1,15  9.40  .592 .671 .589 .600  1,6,15  8.25  .694  8.53 9.55  1,2,7,8 .619 9.24 Mean Y2(cents) .8 46,  2  145 Year See R  2  P r e d i c t i o n o f Lumber Conversion Return (YI)  ±7.41  .671  7.52 .721 31. 5 2.  1,6 1,12  106 Year See R  2  5.73 .692 40 .2  +9.01  .564 8.39 .622 8.930 .571 8.36 .624 7.84  .678  9.18 .570 46.7  +11.56 11.71 11.30 10.44  .699 .691 .712 .754  10.24  .771  11.78 .707 53 .4  P r e d i c t i o n o f Optimum Conversion Return (Y2)  8.26  .288  8.00 8.25 8.20  .289 .298  8.06  .336  .332  .326 8.21 37. 8  5.44 4.92  8.07  5.15  .359 .476 .345 .427  6.33 7.95 7.64  4.68  .541  5.95  5.32 .426 43 .8  8.28  $.50  .541 .717 .588  10.30 8.99 10.22 9.48  .751 .810 .754 .789  .756  7.57  .870  .554  .541 49 .6  .759 10.47 59 .6  (1) V a r i a b l e D e s i g n a t i o n s same as i n Table ZLV. #*. A l l R-squared v a l u e s i n above t a b l e i n d i c a t e s i g n i f i c a n c e o f R a t 99 per cent L e v e l .  ro f"  Table LIT.  Equations f o r Regression o f Merchantable Board Foot (10~±) and Cubic Foot Volume f o r Combined 63-, 86-, 106-, and 145-year-old Douglas F i r 1.  Independent Intercept Variables(l) U) a 1 -150.665 2 -245.182 12 - 33.535 22(D2H) - 3.862 1,12 -149.010 -154.101 1,15 1,2,7,8  -121.567  Merchantable Board-Foot Volume (10~i)  Regression  Coefficients  b2  bl 9.936 2.292 5.074 0.0009 10.064 9,998  -0.179 0.932  9,825  0.414 2.  b4  -0.171  -0.459  R2##  30.0 30.1^  .873 .873  30.2  .873  Mean Merch.  ,  Vol.dO-f)  .872 .638 .311 .924  99.6 fbm  Merchantable Cubic-Foot Volume  1 2 12 22  -209.394 -353.748 - 42.829 16.148  15.181 3.501 7.926 0.0014  1,12 1,15  -209.432 -209.312  15.178 15.179  0.0041 -0.022  1,2,7,8  -147.388  15.119  0.993  (1)  b3  Standard Error of Estimate (Volume) + 30.0 50.5 69.7 23.2  -0.575  -0.984  40.5 74.2 103.1 32.2  .898 .656 .335 .935  40.6 40.6  .898 .898  40.6  .899  173 cu. f t  V a r i a b l e Designations same as i n Table XLV. A l l R-Squared values i n d i c a t e s i g n i f i c a n c e of R a t 99 percent l e v e l .  1—• ro  Table LIII.  Equations f o r the Regression o f Lineal Feet of Trees Required per Mfbm Lumber and per Ccf Logs on DBH, Height, Age and Site Index f o r Combined and Individual Age-Classes of Douglas F i r  Dependent Variable(1)  an Value  ME  Independent Variables(2)  ill  Constant All  3 4 3 4  117.293 80.372 117-293 80.372  1,2,7,8 1,2,7,8 1 1  475-587 305-796 307.564 199.899  3 4  172.688 115.157  1,2,7,8 1,2,7,8  371.539 188.042  3 4  116.297 1,2,7,8 84.410 1,2,7,8  538.902 409.916  3 4  81.592 56.903  3 k. (1)  82.005 ^•745  1,2,7,8 1,2,7,8  Mil  Regression bl Ages  -5.694 -3.550 -7-553 -4.745  Coefficients  b2 0.850 0.636  63 year age-class  -14.095 -3.129 -8.171 -1.927  86 year age-class  -6.546 -4.759  0.805 1.662  106 year age-class  86.725 291.941  -4.341 -3.521 -2.713 0.870  , 145 year age-class  437.269 241.583  H.33™ -2.567  0.992 1.207  Standard Error of Estimate  R2**  b3  b4  -0.615 -0.508  -1.808 -1.165  + 32.48 18.73 34.06 19.57  .780 .807 •752 •785  3.594 2.793  1.404 0.887  29.99 18.34  .861 .847  -2.314 -2.030  212 820  17.56  11.29  .870 .883  2.144 -0.951  2.993 -1.200  16.28 9-31  .874 .888  -1.296 -0.646  -1.327 -1.437  18.89 9.62  .829 .847  (2)  13 - L i n e a l Feet of tree per Mfbm Lumber XL - D.B.H. 12 - Height X7 - Age  **  A l l R-Squared values indicate significance of R at 99 per cent l e v e l .  14 - Lineal Feet of tree per Ccf Logs. X8 - Site Index.  JO ON  Table L I Y .  D i s t r i b u t i o n o f Tree Grades by Crown C l a s s , B u t t - L o g Grade and QRH. f o r Combined S t a n d s o f Douglas F i r  1.  Tree  Dm  1  (in)  12  Dominant 2  2  2  «  tt  16 IS  20 22 24  2  25  30 32 34 36  38  40 42 44 46 48 50  3  2  2  « 1  6  -  «  1  »  4  3  n  Crown C l a s s 3. I n t e r m e d i a t e 2. Co-Dominant B u t t - Log Grade 1 2 3 4 1 2 3 4 Tree Grades  2  11  2 «  1 _ " 1 " ,  3  3  "  _ ^ 2 «  tt  _ 1 «  3  " " 2 " 2  1 » •  2 »  1 »  .  3  it  3  it  .  3  it  2  l n  3  it  3  3  n  3  4  3  it  2 «  2  » _ 1 "  _ 1 «  3  tt  4. Suppressed  _ 2  »  _ 1  .«  -  _ 1 »  2 » -  _ 2 »  2  »  2  _  _ 1• "  1 " .  1 »  1  »  1  ro  i2a. "  IMPLICATIONS FOR  STAND MANAGEMENT  U s i n g the h i g h - l e a d l o g g i n g c o s t s and  the  b a n d - m i l l sawing c o s t s d e r i v e d f o r t h i s s t u d y i t was shown t h a t t r e e s o f t h e 1 2 - i n c h dbh c l a s s and under were s u b - m a r g i n a l f o r lumber c o n v e r s i o n .  I t was  i n d i c a t e d t h a t t h e c o s t o f h a r v e s t i n g and  processing  s m a l l t r e e s might be r e d u c e d by t h e use o f l o g g i n g and m i l l i n g equipment.  also  appropriate  The problem o f h a n d l i n g  heterogenous t r e e s i z e s i n a f i n a l h a r v e s t  operation  c o u l d be o b v i a t e d t o a g r e a t e x t e n t by t h i n n i n g i n t h e e a r l i e r s t a g e s o f the s t a n d  life.  H e i b e r g and Haddock (1955) p o i n t e d out t h a t a managed s t a n d w i t h p e r i o d i c t h i n n i n g s c o u l d  be  e x p e c t e d t o y i e l d about 39 p e r cent more i n t o t a l board f o o t volume and about 54 per cent more i n v a l u e t h a n an unmanaged s t a n d d u r i n g an 85 y e a r r o t a t i o n . (1959), i n a study o f t h i n n i n g i n two Cowichan Lake, B.C. 21.4  stands  Warrack  at  i n d i c a t e d t h a t , at a saving of  per cent i n r o t a t i o n l e n g t h , a pruned and  s t a n d c o u l d y i e l d a l m o s t 2.25  t i m e s t h e net  thinned  dollar  r e t u r n per acre of a n a t u r a l l y regenerated  stand,  unpruned and not t h i n n e d u n t i l 29 y e a r s o f  age.  T h i n n i n g r e g i m e s c o u l d be d i r e c t e d t o t h e procurement o f  129. u n i f o r m t r e e s i z e s a t f i n a l h a r v e s t w i t h a consequent more e f f i c i e n t use o f l o g g i n g equipment.  Thinning  f o r p i l i n g , when the t r e e s are o f a s u i t a b l e  size,  a l s o r e s u l t s i n a c o n s i d e r a b l e i n c r e a s e i n the c o n v e r s i o n r e t u r n from s m a l l t r e e s . An a l t e r n a t i v e t o stand management by t h i n n i n g i s the open i n i t i a l l y  to normal a t r o t a t i o n  age approach d e s c r i b e d by Smith e t  5  al. (1961).  The need f o r t h i n n i n g t o promote the growth o f the r e s i d u a l stand i s dispensed w i t h by wide s p a c i n g o f t r e e s a t stand e s t a b l i s h m e n t .  Smith e t * a l .  (1961)  e s t i m a t e d t h a t the open-to-normal approach should produce stands o f Douglas f i r w i t h a v a l u e two o r t h r e e times those o f normal stands.  They a l s o  h y p o t h e s i s e d i t s advantage f i n a n c i a l l y  over a stand  where s u r p l u s t r e e s had been removed by two t h i n n i n g s before f i n a l h a r v e s t . Grah (I960) initial  i n a study o f the e f f e c t s o f  s t o c k i n g on the product y i e l d and v a l u e  from  young-growth Douglas f i r concluded t h a t , over a r o t a t i o n o f 50 t o 70 y e a r s , the t o t a l volume o f stands initially  understocked  was o n l y s l i g h t l y l e s s  than  130. t h a t o f f u l l y - s t o c k e d stands.  He a l s o  concluded  t h a t q u a l i t y , w i t h r e s p e c t t o sawmill and p e e l e r l o g s , i s much lower i n stands i n i t i a l l y  understocked,  p r i m a r i l y because o f e x c e s s i v e amounts o f f a s t - g r o w t h wood and l a r g e knots.  He i n d i c a t e d , however, t h a t  p r u n i n g c o u l d be i n t r o d u c e d t o overcome t h e q u a l i t y d i f f e r e n c e s due t o low i n i t i a l s t o c k i n g . *Where t h e r e i s , o r i s l i k e l y t o be, a c o n s i s t e n t demand f o r s m a l l i n t e r m e d i a t e c u t t i n g s i t may be t h a t the d e s i r a b l e s i l v i c u l t u r a l  practice  would be t o take advantage o f the n a t u r a l pruning c h a r a c t e r i s t i c o f i n i t i a l normal d e n s i t y and t h i n f o r the d e s i r e d spacing and number o f f i n a l crop t r e e s . Otherwise,  the concept o f i n i t i a l l y  open s p a c i n g t o  induce f a s t e r growth i n fewer t r e e s p e r a c r e f o r approximately the same t o t a l wood p r o d u c t i o n as i n denser stands appears t o have a good d e a l o f m e r i t . C o n t r o l l e d spacing should be such t h a t wood q u a l i t y i s not a d v e r s e l y a f f e c t e d by t o o - f a s t growth o r t o o large knots.  As p r e v i o u s l y mentioned, Grah  (I960)  p o i n t e d out t h a t pruning c o u l d be i n t r o d u c e d i n such a stand model t o improve wood q u a l i t y .  131. R e s u l t s o f the discussed  study o f the f o u r stands  i n t h i s t h e s i s i n d i c a t e the  o f having the h a r v e s t e d  desirability  volume i n a s m a l l e r number  o f l a r g e r t r e e s r a t h e r than i n a l a r g e r number o f smaller trees.  In the two  o l d e r stands t h e r e  was  a very d e f i n i t e i n c r e a s e i n wood q u a l i t y , w i t h r e s p e c t t o lumber grades, w i t h i n c r e a s e s i n t r e e T h i s t r e n d was  apparent a l s o i n the two  but to a l e s s e r degree. value  younger stands  In other words the  gross  per cubic f o o t o f t r e e as w e l l as the net  i n c r e a s e d w i t h t r e e s i z e and w i t h such v a r i a b l e s as dbh,  increased  value  significantly  crown width and  When i t i s considered  size.  crown c l a s s .  t h a t not o n l y  are  l a r g e r t r e e s cheaper to l o g per u n i t volume, but  also  t h a t , i n v a r i a b l y , more lumber per cubic f o o t o f t r e e i s obtained evident  from l a r g e than from small t r e e s , i t becomes that a harvest  composed o f l a r g e t r e e s i s h i g h l y  desirable. The  f o u r stands d i s c u s s e d  in this thesis  had  l e s s than what i s g e n e r a l l y r e g a r d e d as the normal number o f t r e e s per acre f o r t h e i r r e s p e c t i v e ages (McArdle e t . a l . , 1949).  Spacing o f t r e e s w i t h i n  the  132. stand was age  f a i r l y uniform  class.  The  o n l y i n the  63-year-old  other three stands were c h a r a c t e r i s e d  by groups o f t r e e s growing i n f a i r l y  close  a s s o c i a t i o n , the o c c a s i o n a l open-grown t r e e , openings i n the crown canopy, some o f them in  the two  o l d e r age  classes.  and  considerable  A l s o t h e r e was  little  evidence o f m o r t a l i t y on the f o r e s t f l o o r o f each stand. The is  i m p l i c a t i o n o f the above  t h a t these n a t u r a l stands d i d not r e f l e c t  true productive The  observations  capacity of t h e i r respective  the sites.  a r e a s were u n d e r - u t i l i z e d w i t h r e s p e c t to number  o f t r e e s and, had been.  as f a r as c o u l d be determined, always  Despite  the f a c t t h a t the stands were sub-  normal on a t r e e count b a s i s , t h e i r percentage n o r m a l i t y based on cubic volume per acre  increased  c o n s i d e r a b l y and approached or exceeded t h a t expected for  normal stands.  This i n d i c a t e s that, with  stand management and f u l l  u t i l i s a t i o n o f the  proper site,  these  a r e a s c o u l d be made to produce volumes o f timber c o n s i d e r a b l y i n excess o f those c o n s i d e r e d  normal.  I n d i c a t e d f i n a n c i a l r o t a t i o n s f o r these stands was  between 6 0 and 70 y e a r s .  T h i s agrees c l o s e l y  w i t h t h e e s t i m a t e s o f Haley Haley  (1964)  (1964) and Smith and  f o r t h i s broad s i t e g r o u p i n g .  However  i t was found h e r e t h a t t h e f i n a n c i a l r o t a t i o n was more a f u n c t i o n o f s t o c k i n g t h a n i n d i v i d u a l s t a n d index.  site  A l t h o u g h none o f t h e s t a n d s had n o r m a l  s t o c k i n g w i t h r e g a r d t o number o f t r e e s , t h e 86-yearo l d s t a n d most c l o s e l y approached t h i s n o r m a l i t y concept.  A t a common age t h i s s t a n d had a h i g h e r  volume p e r a c r e t h a n t h e o t h e r s t a n d s and a subsequent h i g h e r v a l u e p e r a c r e .  The n e t e f f e c t o f  t h e same compounded e s t a b l i s h m e n t c o s t s and t h e same i n t e r e s t r a t e on t h e s t a n d v a l u e was a r o t a t i o n age f o r t h e 8 6 - y e a r - o l d s t a n d w h i c h was 5 t o 7 y e a r s l e s s than f o r t h e other stands. The s t a n d d a t a i n d i c a t e t h a t t r e e s grown t o an age o f about 65 y e a r s on s i t e 160 w i l l have an average dbh o f I S o r 19 i n c h e s .  The maximum dbh i n  the 6 3 - y e a r - o l d s t a n d was 30 i n c h e s f o r a 6 8 - y e a r - o l d tree.  A l t h o u g h n o t much c l e a r lumber n o r l o g s s u i t a b l e  f o r p e e l i n g c o u l d be a n t i c i p a t e d a t a r o t a t i o n o f 65 y e a r s , p r u n i n g o f t h e t r e e s a t an e a r l y age would improve t h e i r p o t e n t i a l f o r t h e above p r o d u c t s . I n b r i e f , i t i s p r o b a b l e t h a t a much g r e a t e r  134. volume o f timber c o u l d be grown on s i t e s such as those d i s c u s s e d ,  than i s i n d i c a t e d by the volume  i n n a t u r a l stands c u r r e n t l y occupying these  sites.  A r e d u c t i o n i n c u r r e n t l y accepted r o t a t i o n ages i s i n d i c a t e d f o r these h i g h s i t e s .  Silvicultural  treatments such as t h i n n i n g o r c o n t r o l l e d  spacing  from i n i t i a l l y open t o normal a t r o t a t i o n , perhaps accompanied; by a r t i f i c i a l p r u n i n g i n both  cases,  would i n c r e a s e the t o t a l net r e t u r n s a t r o t a t i o n age from good s i t e f o r e s t l a n d .  CONCLUSION  Processing for  times per u n i t volume o f l o g s  many o f the phases o f l o g g i n g and f o r m i l l i n g , a r e  adequately estimated by a logarithmic-' f u n c t i o n w i t h a s t r a i g h t l i n e form o f I = a + b l o g (X).  The n e t value  per c u b i c f o o t o f t r e e i n c r e a s e d w i t h t r e e s i z e because o f reduced l o g g i n g and m i l l i n g c o s t s i n l a r g e r t r e e s and  a l s o because the q u a l i t y y i e l d from the l a r g e r t r e e s  o f t h i s study was b e t t e r than t h a t from the s m a l l e r  trees.  U t i l i s a t i o n p r a c t i c e s were remarkably s i m i l a r i n a l l f o u r stands. About 64 p e r cent o f t h e t o t a l t r e e  h e i g h t and 87 per cent o f the t o t a l stand volume were u t i l i s e d i n each o f the a g e - c l a s s e s . The lumber c o n v e r s i o n r e t u r n per C c f o f l o g s i n the stands d i s c u s s e d i n c r e a s e d l i n e a r l y w i t h stand age.  The optimum c o n v e r s i o n r e t u r n averaged 5 cents  per c u b i c f o o t o f t r e e i n excess o f the lumber c o n v e r s i o n r e t u r n f o r a l l stands. was  This difference  g r e a t e s t a t the extremes o f the stand ages  because o f the i n f l u e n c e o f p i l i n g i n young  stands  and p e e l e r l o g s i n o l d e r stands. The a p p l i c a t i o n o f l i n e a r programming a n a l y s i s t o the stand data o f the study- i n d i c a t e d the optimum j o i n t - p r o d u c t y i e l d from the m a t e r i a l available.  I t was  shown t h a t p e e l e r l o g s ,  although  o f low q u a l i t y , y i e l d e d a h i g h e r net v a l u e when converted to plywood r a t h e r than t o lumber.  A l s o , p i l i n g s o l d as  such, as i n d i c a t e d above, y i e l d e d h i g h e r net r e t u r n s than the p r o d u c t i o n o f lumber from p i l i n g m a t e r i a l . Analyses o f the f i n a n c i a l r o t a t i o n s of these stands i n d i c a t e d a r o t a t i o n age o f between 60 and  70  y e a r s i f 3 per cent i n t e r e s t can be assumed.  level  The  136. o f e s t a b l i s h m e n t c o s t s d i d not s i g n i f i c a n t l y change the r o t a t i o n age but d i d a f f e c t the n e t v a l u e o f t h e growing stock a t r o t a t i o n age.  The e f f e c t o f  i n c r e a s i n g the i n t e r e s t r a t e charged on e s t a b l i s h m e n t c o s t s , and on the growing stock, was t o reduce the r o t a t i o n and the n e t value o f the stand a t r o t a t i o n . A n a l y s i s o f b i o l o g i c a l r e l a t i o n s h i p s showed t h a t many measureable v a r i a b l e s were s i g n i f i c a n t l y c o r r e l a t e d w i t h n e t value p e r c u b i c f o o t o f t r e e . P r e d i c t i o n v a l u e equations i n v o l v i n g o n l y two o r three s e l e c t e d v a r i a b l e s accounted f o r almost as much o f t h e v a r i a t i o n i n the dependent v a r i a b l e as d i d eight  s e l e c t e d independent v a r i a b l e s .  From t h e  c r i t e r i o n o f Rr- squared r a t i o s , the best  combinations  o f two and three v a r i a b l e s f o r p r e d i c t i n g v a l u e involved  dbh, b u t t - l o g grade and crown c l a s s .  c l a s s and dbh was t h e best p a i r o f those t e s t e d  Crown for  p r e d i c t i n g the lumber c o n v e r s i o n r e t u r n and dbh and b u t t - l o g grade was t h e best p a i r f o r e s t i m a t e s o f t h e optimum c o n v e r s i o n r e t u r n .  Analysis  o f volume  r e l a t i o n s h i p s showed t h a t dbh alone accounted f o r 90 per cent o f the v a r i a n c e  i n board - and cubic  - f o o t volumes  whereas D H accounted f o r only an a d d i t i o n a l 2 o r 3 p e r 2  cent.  137. Stand management should be d i r e c t e d a t maximum u t i l i s a t i o n  o f the p r o d u c t i v e c a p a c i t y o f  the s i t e s c o n s i s t e n t w i t h approved economic and silvicultural  practices.  None o f these n a t u r a l  stands  was stocked with what i s g e n e r a l l y regarded a s a normal number o f t r e e s per a c r e .  I n d i c a t i o n s were t h a t the  areas c o u l d support a much h i g h e r volume o f timber than was present and t h a t the volume and v a l u e o f the product from these s i t e s c o u l d be i n c r e a s e d c o n s i d e r a b l y by i n t e n s i v e f o r e s t management.  138. LITERATURE CITED ADAMS, Thomas C. 1965. High-lead l o g g i n g c o s t s a s r e l a t e d to l o g s i z e and o t h e r v a r i a b l e s . U.S. F o r e s t S e r v i c e Research ^aper P.N.W.23, 38 p. BUREAU OF LAND MANAGEMENT, I 9 6 4 . Logging c o s t s . U n i t e d S t a t e s Department o f the I n t e r i o r . Schedule 14. n.p. BUTLER, W.E., 1965. C h i p markets - p o t e n t i a l s and problems f o r sawmill and plywood p l a n t s . F o r e s t Products J o u r n a l . 15(4): 167-169. BYRNE, J . J . , R.J. NELSON and P.H. GOOGINS, I 9 6 0 . . Logging Road Handbook. U.S. F o r e s t S e r v i c e . A g r i c u l t u r a l Handbook No. 183, 65 p. CLARKE, E.H. and A.C. KNAUSS, 1957. Veneer r e c o v e r y from D o u g l a s - f i r l o g s . U.S. F o r e s t S e r v i c e , P.N.W. F o r e s t and Range Experiment S t a t i o n , P o r t l a n d , Oregon. Res. pap. no. 23, 13 p. DOBIE, J . , 1966. L i n e a r programming to maximimize . c o n v e r s i o n r e t u r n per acre from young-growth, s i t e c l a s s I I Douglas f i r . U.B.C. F a c u l t y o f F o r e s t r y . F o r . 575 Rep. 83 p. and H.W. PARRY, 1965. Pulp c h i p s from sawmill r e s i d u e . F o r e s t Products Laboratory, Vancouver, B.C. Unpub. ms. n.p. DUERR, W i l l i a m A., i960. Fundamentals o f f o r e s t r y economics. McGraw-Hill, New York. 579 p. GAFFNEY, M. Mason, 1957. Concepts o f f i n a n c i a l m a t u r i t y o f timber. North C a r o l i n a State C o l l e g e . Dept. o f A g r i c u l t u r a l Economics. A.E. Information S e r i e s No. 62, 105 p. GRAH, R.F., I 9 6 0 . E f f e c t s o f i n i t i a l s t o c k i n g on - f i n a n c i a l r e t u r n from young-growth Douglas f i r . H i l g a r d i a . 29(14): 613-679.  139. HALEY, D., 1964. F a c t o r s i n f l u e n c i n g t h e f i n a n c i a l , r o t a t i o n o f Douglas f i r i n c o a s t a l B r i t i s h Columbia. U.B.C. F a c u l t y o f F o r e s t r y . F o r . 581 Rep. 47 p. HEIBERG, S.O. and P.G. HADDOCK, 1955- A method o f t h i n n i n g and f o r e c a s t o f y i e l d i n Douglas fir. J o u r n a l o f F o r e s t r y . 53(1): 10-18. HERSTROM, C.A., I 9 6 0 . Economics o f a u t o m a t i o n i n plywood manufacture. F o r e s t P r o d u c t s J o u r n a l .  10(8): 396-398.  JOERGENSEN, C , 1952. A commercial t h i n n i n g experiment i n Douglas f i r . B.C. F o r e s t S e r v i c e , R e s e a r c h D i v . , V i c t o r i a , B.C. R e s e a r c h Note No. 22. 22 p. KOZAK, A. and J.H.G. SMITH, 1965- A comprehensive and f l e x i b l e m u l t i p l e r e g r e s s i o n program f o r e l e c t r o n i c computing. F o r e s t r y C h r o n i c l e .  41(4):  438-443.  LODEWICK, J.E., 1941. West c o a s t l o g v a l u e s . 1. Douglas f i r f r o m t h e Oregon Cascades. U.S. F o r e s t S e r v i c e . P.N.W. F o r e s t and Range E x p e r i m e n t S t a t i o n . P r o d u c t s pap. no.3. 40 p. McARDLE, R.E., W.H. MEYER and D. BRUCE, 1949. The y i e l d . o f Douglas f i r i n t h e P a c i f i c North-West. U.S.D.A. T e c h n i c a l B u l l e t i n No. 201. 74 p. McINTOSH, J.A.M., i960. How l o g l o a d i n g a f f e c t s u t i l i z a t i o n . Canada Lumberman. 80(1)  28-31.  MATSON, E.E., 1952. Lumber grade r e c o v e r y from Oregon c o a s t - t y p e Douglas f i r . U.S. F o r e s t S e r v i c e . P.N.W. F o r e s t and Range E x p e r i m e n t S t a t i o n . Res. pap. no. 3. 10 p. MAYHEW, W.E., 1958. A new and r e v o l u t i o n a r y method o f . .. a l l o c a t i n g c o s t s t o veneer by g r a d e s . F o r e s t P r o d u c t s J o u r n a l . 8(4): 27A-31A. NIXON, G.R.W. and D.C. GUNN, 1957- F e l l i n g and b u c k i n g t i m e s t u d i e s . B.C. Lumberman. 41(4): 24-32.  140. RANKIN, A.G., 1963. C o s t - p r i c e r e l a t i o n s h i p s i n the forest industry, f o r e s t r y Chronicle.  3 9 ( 1 ) : 69-77.  SMITH, J.H.G. and J.P. TESSIER, 1961. Growth, Y i e l d and Value o f Douglas f i r t r e e s f o r p i l i n g . U.B.C. F a c u l t y o f F o r e s t r y , Research pap. No. 43. 11 p. , J.W. KER, and J . CSIZMAZIA, 1961. Economics o f r e f o r e s t a t i o n o f Douglas f i r , western hemlock and western r e d cedar i n the Vancouver F o r e s t D i s t r i c t , U.B.C. F a c u l t y o f F o r e s t r y , F o r e s t r y B u l l e t i n No. 3.-144 p. _ ,  and D. HALEY, 1964. A l l o w a b l e c u t s can be i n c r e a s e d s a f e l y by use o f f i n a n c i a l r o t a t i o n . B.C. Lumberman. 48 ( 7 ) : 26-28. , and R.E. BREADON, 1964. Combined v a r i a b l e equations and volume-basal area r a t i o s f o r t o t a l cubic f o o t volumes o f the commercial t r e e s of B.C. The F o r e s t r y C h r o n i c l e . 4 0 ( 2 ) :  258-261.  -  STAEBLER, G.R., 1955. Gross Y i e l d and m o r t a l i t y t a b l e s f o r f u l l y stocked stands o f Douglas f i r . U.S. Forest Service. P.N.W. F o r e s t and Range Experiment S t a t i o n . Res. pap. No. 14. 20 p. TENNAS, M . S . , RUTH, R.H. and C M . BERNSTEN, 1955. An a n a l y s i s o f p r o d u c t i o n and c o s t s i n h i g h - l e a d yarding. U.S. F o r e s t S e r v i c e . P.N.W. F o r e s t and Range Experiment S t a t i o n . Res. pap. No. 11. 37 p. VALG, L., 1962. Determination o f economically m a r g i n a l t r e e s i z e through the a p p l i c a t i o n o f c o n v e n t i o n a l and l i n e a r programming techniques. Faculty of F o r e s t r y , U.B.C, M.F. T h e s i s . 147 p. WARRACK, G . C , 1959. F o r e c a s t of y i e l d i n r e l a t i o n to t h i n n i n g regimes i n Douglas f i r . B.C. F o r e s t S e r v i c e , Research Div., V i c t o r i a , B.C. T e c h n i c a l P u b l i c a t i o n T.51. -56 p.  141. WORTHINGTON, N.P., 1957. Some economic c o n s i d e r a t i o n s i n t h i n n i n g Douglas f i r . U.S. F o r e s t S e r v i c e . P.N.W. F o r e s t and Range Experiment S t a t i o n . Res. note No. 137- 8 p. , 1961. Commercial t h i n n i n g o f Douglas f i r i n the P a c i f i c Northwest. U.S. F o r e s t S e r v i c e . P.N.W. F o r e s t and Range Experiment S t a t i o n . Tech. b u l l . no. 1230. 124 p. , and E.W. SHAW 1952. Cost o f t h i n n i n g young Douglas f i r . The Timberman. 53(10): 136 - 138. - , ;  

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