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. B R I T I S H C O L U M B I A F O R E S T S E R V I C E . .; i

.!j NO. 19 VICTORIA, B.C. 1951 ", :, . ,

Preliminary Site-clm Volume Tables by Logs as an Aid to Grade-cruising , , '

Douglas Fir, Western Hemlock, and Western Red Cedar

RESEARCH DIVISION R. E l Spihhry, Fbt"

PREL,IMINARY SITE-CL,ASS VOLUME TABLES BY LOGS

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Introduction

For s tumpage-appra i sa l pu rposes on t imber s a l e s , manage - ment o f f icers des i re an es t imate of the proport ions of the total volume occurring in each log grade. The requisites of the method of es t imat ion to be employed are threefold.

1. The method need only proportionate stand vo!ume among the various grades, wi thout regard to the precis ion cf the tc ta l -volume es t imate . The total volumes of stands based on 10 pe r C P ' cru ises and com- p i led by s i te -c lass vo lume tab les a re acceptab ie es t imates of t r u e vo lumes fo r p re sen t s tumpage-appra i sa l pu rposes .

2. The method should be one of mechanical application with a minimum necess i ty for judgment by seasonal ly employed c ru isers .

3 . Any necessary tables should be based on available data.

Grade-cru is ing

Grade-cruis ing has usual ly been the duty of highly experienced cruisers who are thoroughly famil iar with the fol lowing factors :

1. bark- thicknesses and tapers for var ious local condi t ions and species , o r some sound bas i s for es t imat ing log- length and top D.I.B. f o r application of the official L,og Rule:

2. problems re la ted to fa l l ing and bucking--s tump and top ut i l izat ion l imits, breakage, and local company policies re bucking for scale, g rade , o r s t anda rds of t ransportat ion faci l i t ies :

3 . defect deductions;

4. grades a s spec i f i ed by var ious local or regional Off ic ia l Rules , sup- plemented by bush, boom, or mill experience with opened t rees and logs;

5. select ion of a representat ive sample within the cruised area f rom which grade proport ions are determined for appl icat ion to the total c ru ise ; and ,

6. problems common to any vo lume c ru ise such as s t r ip -width and intensity of sampling.

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The accuracy of g rade-cru ises i s d i rec t ly re la ted to the ab i l i ty W'

of the c ru i se r t o e s t ima te t hese f ac to r s . The expe r i enced c ru i se r ap - parent ly develops this abi l i ty as an ar t , and confidence in the resul ts can not be built up by a sc ien t i f ic assessment of individual factors but only by comparison of r e su l t s , ove r a long period of t ime, with the actual bush or wate r s ca l e s of the s tands c ru ised . Such compar isons a re im- possible with the seasonal ly employed cruiser , hence the a t tempt to design an a id to grade-cruis ing based on average condi t ions.

Grade-cru is ing Tables

Essen t i a l ly t he t ab l e s a r e based on t he p remise t ha t t r ee s w i th in the range of form and d iameter c lasses found on the South Coas t of B r i - t ish Columbia (of a s ing le spec ies and of the same merchantable l ength to s imi l a r s t anda rds of utilization) have f o r prac t ica l purposes the same percentage dis t r ibut ion of total t ree volume according to log posi t ion in the t ree . These percentages, appl ied to revised total-volume es t imates for each diameter and height class listed in the site-class volume tables current ly in use, provide a mechanical basis for es t imat ing volumes in each log in each t r ee . A technical note on the de ta i l s of table construct ion and a tes t of the pract ical u t i l i ty of the above premise fol lows the tables .

Tables for Douglas f i r , wes te rn red cedar , and wes te rn hem- lock for each of the pr incipal s i tes have been compiled.

Suggested Use of Tables

1. Thoroughly memor ize the g rade requi rements spec i f ied in the Fores t Act.

2. Thoroughly memorize the minimum scales acceptable in each grade. Specif ical ly , a l l o ther requirements having been met , a 32-foot log must sca le a t l eas t the fo l lowing to be inc luded in the g rade ind ica ted :

Fir No. 1 1235 board feet No. 2 125 " I,

Hemlock No. 1 915 I f I ,

No. 2 520 " , 1

Cedar No. 1 520 " I ,

No. 2 320 " ,I

3. Determine the maximum height c lass of the s tand being cruised. The maximum height is the average height of dominant trees only; no o ther t rees need be es t imated , s ince s i te -c lass vo lume tab les au to- ma t i ca l ly t ake ca re of the lesser heights of codominant and inter- media te t rees . Se lec t the appl icable t ab le .

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4. Measure the d . b . h . and record the d . b . h. and total volume of each t ree .

5. Determine f rom the t ab le the po ten t ia l g rades of t he l ogs i n t he t r ee with respect to minimum s izes only. These a re the bes t g rades t he logs may have. Degrade each log in the t r e e wi th r e spec t t o o the r r equ i r emen t s .

6. Using the table , record the volumes in No. 1 and No. 2 logs.

7. Summar ize s tand vo lumes , express ing the vo lumes in Grade 1 and Grade 2 a s a percentage of the total volume. The balance of 100 p e r c e n t is ungraded volume.

Discussion of Tab le s

Volume-table methods of es t imat ing s tand vo lumes , as opposed to direct f ie ld es t imat ions of log volumes in each individual t ree , neces - sa r i ly dea l wi th average t rees under average condi t ions . Wi th re fe rence to t he f ac to r s l i s t ed a s a f f ec t ing t he r e su l t s of grade-cruises--volume tables dispense with the need f o r a sound knowledge of bark-thickness and tapers , necessary for es t imat ing the top D. I .B. for var ious log lengths and species , in favour of easi ly measured factors of d.b.h., 0. b., and total height; and they dispense with problems related to fall- ing and bucking by sett ing a s tandard average log-length and f ixed l imits of uti l ization. Such a p r o c e d u r e c a u s e s g r o s s d i f f e r e n c e s i n t h e e s t i m a - t ion of volumes and grades in individual trees. For example , an ave rage - s i zed t r ee bucked into 16-foot lengths will scale about 15 per cen t more t han t he same tree bucked into 32-foot lengths . Whether or not there will be a s many longer logs of the r igh t sizes to compensate f o r shor te r logs during actual utilization is usually unknown. Further , a 29-inch, 40-foot log scales 1, 400 board feet. The top diameter is insufficient f o r a No. 1 and, i f o t h e r r e q u i r e m e n t s a r e m e t , its bes t poss ib le g rade is No. 2 . By bucking at 3 2 f ee t , however, the d iameter would be 30 inches and a potential Grade 1 log scaling 1, 235 board feet is avai lable , p lus an 8-foot chunk which would account f o r approximately 330 board feet of the next 24-foot potential Grade 2 log. In this single log, bucking policy changes our estimate from 100 per cent No. 2 to 79 pe r cen t No. 1 and 21 per cen t No. 2 and i nc reases s ca l e by 9 pe r cen t . Again, proof of whether o r no t such var ia t ions a re compensa t ing , when c r u i s e s to f ixed s tandards of u t i l i za t ion a r e compared t o s ca l e s of logs a s ut i l ized, is beyond the scope of this s tudy. I t is known, however, tha t to a l low for inherent var ia t ion of individual t rees in es t imat ing board- foot volumes of s tands, volume tables should be used only on tall ies of no t l ess than 50 t r e e s i f a tal ly-volume estimate within 6 p e r c e n t

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(19 t imes out of 2 0 ) is to be expected. (This precis ion is dependent on carefu l f ie ld work and se lec t ion of the cor rec t vo lume tab le ; it should not be confused with the precision of to ta l - s tand es t imates due to a rea- sampl ing in tens i ty . ) I t i s be l ieved such a tally will contain enough individual logs to provide compensatory effects in the log-length and grade-proportion variations noted above.

Nothing can be added to the tables to supplement the individual's knowledge of the grade rules or to aid him in estimating hidden grade fac tors in s tanding t rees , except in so f a r a s s t a t ing min imum-s ized logs in a grade. Hence, while the tables will provide a re la t ive es t imate , entirely compatible with the total-volume estimate, of the volumes in any run-of-log posit ions, the correct assignment of the logs to grade is dependent on the ability of the c ru iser a lone .

Based on experience f rom a 10 per cen t c ru i se of approximately 7, 000 a c r e s on which every tree was graded, the f ield staff reports that no substant ia l gain in t ime would resul t f rom at tempting selected sampling of the g rade fac tor .

The suggested use and l imitations of the tables supplied should be kept in mind by the es t imator and by those using the f inal resul ts .

PRELIMINARY SITE-CLASS VOLUME TABLES--MATURE DOUGLAS FIR GROSS BOARD F E E T , B . C. RULE -

Tot. Merchantable DBH Ht. Length

Ft. 32 .6 ' Total Volume in Log Posi t ion

Top Volume 1 L 3 4 5 6 7 Logs Log

Site 80 (Max. Ht. 116)

16 85 0 0 0 0

28 112 2 2 725 465 250 10 34 115 2 15 1130 640 410 80 40 116 2 23 1560 850 590 120

22 102 1 11 355 295 60 - -

Footnote: Volumes scaled in 32-foot logs, 2-foot stump to 12-inch top D . I .B . In the above table, any log scaling 1, 235 board feet o r o v e r is a potential No. 1; any log scaling 125 board feet o r over is a potential No. 2; underlined volumes are for odd length top logs.

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PRELIMINARY SITE-CLASS VOLUME TABLES--MATURE DOUGLAS FIR GROSS BOARD F E E T , B. C. RULE

Tot. Merchantable

Ft. 32.6' Top Volume 1 2 3 4 5 6 7 DBH Ht. Length Total Volume in Log Posit ion

Logs Log

16 22 28 34 40 46 52 58

16 22 28 34 40 46 52 58 64 70

99 121 131 142 144 144 144 144

112 139 158 170 174 174 174 174 174 174

0 1 2 3 3 3 3 3

0 2 3 3 4 4 4 4 4 4

16 26 16

3 11 18 21 24

24 3 3

24 3

10 14 18 21 22

Site 100 (Max. Ht. 144)

8 5 8 5 - 465 330 135 925 515 325 85

-

1525 715 520 275 15 2100 930 695 415 60 2720 1175 880 570 95 3400 1455 1100 735 110 4090 1740 1320 905 125

- -

-

Site 120 (Max. Ht. 174)

125 125 585 370 200 15 -

1180 550 400 215 15 1875 770 580 400 125 2600 1020 775 545 245 15 3380 1290 985 700 355 50 4260 1610 1220 885 470 75 5230 1960 1480 1090 605 95 6230 2310 1770 1290 750 110 7270 2710 2040 1520 885 115

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-

Footnote: Volumes scaled in 32-foot logs, 2-foot stump to 12-inch top D.I .B. In the above table , any log scal ing 1 , 235 board feet o r o v e r is a potential No. 1; any log scal ing 125 board feet o r o v e r is a potential No. 2; unde r l ined vo lumes a r e fo r odd length top logs.

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PRELIMINARY SITE-CLASS VOLUME TABLES--MATURE DOUGLAS FIR GROSS BOARD FEET, B C . RULE

v Tot. Merchantable

DBH Ht. Length Total Volume in Log Posit ion Ft. 32.6' Top Volume 1 2 3 4 5 6 7

Logs Log ft. -

Site 140 (Max. Ht. 206)

16 22 28 34 40 46 52 58 64 70 76

16 22 28 34 40 46 52 58 64 70 76 82

126 157 181 197 205 206 206 206 206 206 206

140 176 204 224 236 241 241 241 241 241 241 241

1 0 2 18 3 21 4 13 4 26 5 5 5 8 5 1 3 5 18 5 21 5 23

1 10 2 31 4 5 5 0 5 20 6 2 6 8 6 11 6 1 6 6 20 6 21 6 23

170 170 730 380 255 95 -

1420 580 440 290 110 2220 830 630 455 235 70 3130 1130 860 630 375 135 4110 1410 1090 820 525 240 25 5150 1760 1340 1025 670 315 40 6370 2120 1655 1260 840 425 70 7680 2500 1960 1510 1050 565 95' 9030 2910 2300 1790 1240 680 1 1 0

10460 3340 2650 2070 1465 815 T O

- - - - -

-

Site 160 (Max. Ht. 241)

285 235 50 860 410 285 165

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1650 640 485 340 160 25 2470 850 665 485 300 170 3680 1180 925 715 495 260 105 4890 1490 1190 940 685 405 170 10 6180 1850 1495 1185 865 525 220 40 7670 2290 1845 1460 1070 655 290 60 9140 2700 2200 1735 1270 785 365 85

10750 3160 2595 2040 1485 935 430 105 12450 3650 3010 2370 1710 1090 510 110 142.60 4210 3450 2700 1940 1240 600 E

-

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Footnote: Volumes scaled in 32-foot logs, 2-foot stump to 12-inch top D.I .B. In the above table , any log scal ing 1 ,235 board fee t or over is a potential No 1; any log scaling 125 board feet or over is a potent ia l No 2; underlined volumes a r e f o r odd length top logs.

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SITE-CLASS VOLUME TABLES--MATURE WESTERN HEMLOCK. GROSS BOARD F E E T , B. C. RULE

Tot. Merchantable Volume DBH Ht . Length Tot . in Log Posi t ion Stump Top

Ft. 32.6’ Top Vol. 1 2 3 4 5 Ht. DIB Logs Log Ft. In.

10 16 22 28 34 40

10 16 22 28 34 40 46 52

10 16 22 28 34 40 46 52 58

67 1 9 2 1

106 2 110 2 110 2 110 2

72 1 102 2 123 2 136 3 140 3 140 3 140 3 140 2

74 1 1 0 7 2 134 3 154 3 167 3 174 3 175 3 175 3 175 3

Site 80 (Max. Ht. 110)

1 45 45 0 28 215 160 55 11 500 330 140 30

- -

16 810 530 220 60 16 1140 745 320 75 16 1490 980 415 95

~~ - - - -

Site 100 (Max. Ht. 140)

4 50 45 5 2 250 180 65 5

24 620 425 130 65 2 1095 605 345 140 5 6 1610 855 515 210 30 4 2120 1120 700 275 25 0 2600 1460 820 320

27 2990 1900 855 235

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- Site 120 (Max. Ht. 175)

5 50 45 5 6 270 190 70 10 0 690 385 220 85

-

15 1285 625 400 205 55 26 2025 930 630 345 lx 29 2825 1300 875 480 170 25 3505 1655 1085 585 180 17 4100 2050 1290 610 150 8 4555 2400 1460 615 80

-

2.0 6.5 2.0 7.8 2.0 9.0 2.5 10.2 3.0 11.4 3.5 12.6

2.0 6.5 2.0 7.8 2.0 9.0 2.5 10.2 3.0 11.4 3.5 12. 6 4.0 13.8 4.2 15.0

2.0 6.5 2.0 7.8 2.0 9 .0 2.5 10.2 3.0 11.4 3.5 12.6 4.0 13.8 4 .2 15.0 4.5 16.2

Footnote: In the above table, any log scaling 915 bd. ft . o r over is a potent ia l number 1; any log scal ing 520 bd. ft. o r o v e r is a potent ia l number 2; under l ined vo lumes are for odd length top logs.

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SITE-CLASS VOLUME TABLES--MATURE WESTERN HEMLOCK. GROSS BOARD F E E T , B. C. RULE

” Tot. Merchantable Volume

DBH Ht. Length Tot. in Log Position Stump Top Ft. 32.6‘ Top Vol. 1 2 3 4 5 Ht. DIB

L o g s L o g Ft. In. ft.

10 72 1 16 106 2 22 135 3 28 159 3 34 180 4 40 194 4 46 204 4 52 ’ 209 4 58 210 3 64 210 3

4 5 0

19 3

12 13

7 29 17

Site 140 (Max. Ht. 210)

50 45 5 - 2.0 6.5 265 185 70 10 2.0 7.8 695 390 220 85 2.0 9.0

1340 630 415 225 70 2220 940 685 400 180 15

2.5 10.2

3245 1290 960 615 310 5 3.0 11.4

4280 1710 1260 820 395 3.5 12.6

5165 2170 1600 930 405 a 4.0 13.8 4.2 15.0

5780 2730 1790 960 300 4.4 16.2 6360 3255 1990 910 205 4.5 17.4

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-

-

Footnote: In the above table, any log scaling 915 bd. ft. o r o v e r is a potent ia l number 1; any log scal ing 520 bd. ft. o r o v e r is a potent ia l number 2; underl ined volumes a re for odd length top logs.

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1

SITE-CLASS VOLUME TABLES--MATURE WESTERN RED CEDAR, GROSS BOARD FEET, B . C . RULE

Tot. Merchantable Volume DBH Ht. Length Tot . i n Log Pos i t i on Stump C l a s s Ft. 32.6' Top Vol. 1 2 3 4 5 6 Ht.

Logs Log Ft. ft.

16 22 28 34 40 46 52 58 64

16 22 28 34 40 46 52 58 64 70

67 83 95

104 108 110 110 110 110

80 100 117 129 136 140 140 140 140 140

- 1 1 2 2 2 2 2 2

- 1 2 2 3 3 3 3 3 3

16 0

20 2 9

14 14 14 14

25 18 5

21 2

10 10 10 10 10

Max. Ht. C l a s s 110

85 170 595 9 70

1440 2030 2850 3620 4600

85 170 490 105 640 320 10 915 475 50

1285 670 75 1825 950 75 2335 1210 75 3000 1525 75

-

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Max. Ht. Class 140

130 130 395 300 95 710 450 235 25

- - -

1170 690 370 110 1780 965 545 260 10 2560 1360 780 370 50 3500 1870 1070 510 50 4650 2510 1430 660 50 6000 3250 1850 850 50 7600 4120 2340 1090 50

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Footnote: Maximum Ht. Classes 110 and 200 based on insufficient data. Volumes scaled in 32-foot logs, var iable s tump to 12-inch top D.I.B. In the above table, any log scaling 520 bd. ft . o r o v e r is a potential No. 1; any log scal ing 320 bd. f t . o r o v e r is a potential No. 2; underlined volumes are for odd length tops.

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SITE-CLASS VOLUME TABLES--MATURE WESTERN RED CEDAR, GROSS BOARD F E E T , B. C. RULE

Tot. Merchantable Volume DBH Ht. Length Tol. in Log Posit ion C l a s s Ft. 32.6'

Stump Top Vol. 1 2 3 4 5 6 Ht.

Logs Log Ft. ft.

16 22 28 34 40 46 52 58 64 70

16 22 28 34 40 46 52 58 64 70

93 117 137 152 163 168 170 170 170 170

105 133 157 175 189 197 200 200 200 200

1 1 2 3 4 4 4 4 4 4

1 2 2 3 4 - 5 5 5 5 5

5 28 21 14 0 8

10 10 10 10

Max. Ht. C l a s s 170

180 435 830

1380 2100 3000 4150 5500 7150 9 100

180 290 145 465 255 110 645 430 230 75 925 630 375 170

- - -

1280 900 550 230 40 1770 1240 770 320 50 2360 1640 1010 440 50 3080 2130 1315 575 50 3910 2710 1670 760 50

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Max. Ht . Class ZOO

12 210 5 500

30 950 26 1580 21 2420

2 3500 8 4800 8 6400 8 8300 8 10600

145 65 315 160 25 505 290 155 685 475 285 135 915 675 470 250 110

- - - -

1310 990 650 395 145 10 1800 1330 890 540 200 40 2400 1780 1190 720 270 3110 2320 1540 930 360 % 3980 2980 1970 1200 430 % -

2.4 3. 0 3.4 3.9 4.4 4.9 5 . 4 5.8 6. 3 6.8

Footnote: Maximum Ht. Classes 110 and 200 based on insufficient da ta . Volumes sca led in 32- foot logs , var iab le s tump to 12-inch top D.I.B. In the above table, any log scaling 520 bd. ft. o r o v e r is a potential No. 1; any log scaling 320 bd. ft. o r o v e r is a potential No. 2; underl ined volumes are for odd length tops.

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- 11 - Technical Note on Table Construct ion

1. Douglas Fir

(a ) Tree Volume-Si te Class Tables . The to ta l he ight -d . b. h. re la t ionships by s i te c lasses had previously be es tabl ished in connection with Provincial inventory tables. ffi Tota l t r ee volumes were read f rom a base total-height volume table.(2) Total height-merchantable length re la t ionships were extracted from work-sheets used in construct ing base- log length and total-height tables. (3 ) Tota l -volume es t imates c ross -check in the two base tables.

The average deviat ion of individual values in the base tables i s 15 per cent . Correct ly appl ied to ta l l ies of a t l e a s t 50 t r e e s , the total-volume es t imate should be within approximately 6 p e r cent (19 t imes out of 20). When, however, the base-table values a re used in s i te -c lass vo lume tab les , there i s the fur ther poss ib i l i ty that an individual stand may vary by half a c l a s s f rom the nea res t average s i te- table and a cons is ten t under - o r over -es t imate of up to 10 per cent on individual tal l ies is thus possible . This l a t t e r non- sampl ing o r me thod e r ro r is accepted by management fo r p re sen t pu rposes . ( I t shou ld be r emembered t ha t t h i s e r ro r may be included in, though it is d is t inc t f rom, the 30 to 60 p e r cent coefficient of var ia t ion used for intensi ty of sampling determinat ions for old-growth Douglas Fir types . )

(b) Log Volume-Si te Class Tables . The method employed in deter- mining the proportion of the total cruised volume occurr ing in any run of logs, say, grouped by grade, wi thin the t rees must be compat ib le wi th the above e r rors . For example , i f a particular total volume of a g roup o f t r ee s c ru i sed i s unde r - es t imated by 10 per cen t , then the volume occurring in any group of logs within the t rees must a lso be underes t imated by 10 p e r cent. The absolute volume in the group of logs is only of im- portance re la t ive to the total volume es t imate .

The t ree-measurement da ta used in cons t ruc t ing the base-volume table were reviewed and 273, or all those t rees showing f ie ld measu remen t s up t o a 12-inch or less top, were selected. Within each t ree the percentage of the total tree volume, 2-foot stump to 12-inch top, occurring in each 32.6-foot log and the odd-length top

(1) P. 12, Report of t h e F o r e s t S e r v i c e , 1948, King ' s P r in t e r , V ic to r i a . (2) Table 7, Volume, Yield, and Stand Tables, B.C.F.S., 1936, Victor ia

( 3 ) T a b l e s 5 and 7, ibid. (out of print) .

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was ca lcu la ted . The da ta were sor ted by ha l f - log c lasses and averaged. Fig. 1 shows the plot ted averages and the resul t ing, ve ry we l l de f ined mrves . Tab le 1 shows the curved percentages fo r each l og o r ha l f - log i n t r ee s up t o 7 logs.

TABLE 1

Average Percentage Dis t r ibu t ion of Total Volume by

Logs fo r Var ious Merchan tab le Leng th T rees .

Douglas Fir , B. C. Rule 32.6' Logs, 2 'Stump, 12" Top.

Number of Log Pos i t ion in Tree Logs 1 2 3 4 5 6 7

in T r e e P e r c e n t a g e of Total Volume

1 100.0

2 66.0

72 2

55.0

3 48.1

2 42.5 2

4 40.0

4L 37.2 2

5 35.0

32. 7 2

6 30.7 + 29.5

7 29.0

34.0

35.0

34.3

32. 1

30.0

28.3

27.0

25.6

24.6

23.9

23.5

10.0

17.6

20.2

21.0

20.3

20.0

-

19. 7

19 .4

19.0

18.9

5 .2

9 . 0

-

11.0 3. 2

12.6 5.4

-

13.4 6.9 1.7

13.9 8.2 3.2

-

14. 0 8 . 6 4.0 1.0 - 14.0 9 . 0 4.1 1.5

Y

Underlined values are fo r half logs.

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* t- I

,-I-.

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1

“””, a ““I

l lstLog

3 z?!Log

3 3 ‘ d 4 ”“

q 4+Log

I 5 t ” L o g ””” i

71hLOg

7 Merchantable L e n g t h of Tree - 32.6’Logs

Basis: 1410 logs in 2 7 3 trees. Weights on first log curve apply to a l l points vertically below.

Broken l i nes a r e p lo t t ed a t p lus and minus one S t anda rd E r ro r of Es t imate and enc lose approximate ly two th i rds of the individual observat ions.

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The curved percentage values were next appl ied to the total t ree volumes as determined in (a) above. The expected cross-check is that the calculated volume of the top log equals the scale of a 12- inch log of the top-log length. For example, a 40-inch tree on si te 100 , on the average , has a total volume of 2, 100 board feet in three 32. 6-foot logs and an 11-foot top log to a 12-inchtop. The curved percentage in this log is 4 pe r cen t ( F i g . 1) equal to 84 board feet; the actual scale of a 12-inch 11-foot log is only 58 boa rd f ee t o r 2.8 per cent of the total tree volume. Near and beyond the l imits of the basic data (Table 2) such d i screpancies were of p rac t i ca l importance and are bel ieved due to ignoring form.

In keeping with the requisites of the presented tables, a s imple prac t ica l ad jus tment was sought . The bas ic da ta were resummar ized by 6- inch diameter and half- log c lasses and plot ted. Except for the par t s o f the curves in F ig . 1 which represent top logs (see top logs of 3- , 4 - , and 5- log t rees , F ig . l ) , separa te curves were too weak to use. In a l l cases , wi th in the range of bas ic da ta , the 6 - inch-c lass curved percentages agree wi th the ac tua l percentages in top logs . The res idual , o r difference between the average curve and the ad- justed top-log curve, could not be ignored. I t was arbi t rar i ly dis- t r ibuted over the remaining logs in the t ree . For example, in a 40-inch, site 100 t ree , averaging three 32.6-foot logs and in 11-foot top log, the curve percentages of the total volumes by l o g s a r e 44.0, 32.6, 19.4, and 4.0. The adjusted top-log percentage is 2.8 per cen t . v The res idua l 1. 2 pe r cen t ( 2 6 board feet) is added in 3 equal par t s to the first 3 logs, resul t ing in adjusted percentages of 44. 4, 33.0, 19.8, and 2.8. While theoretical objections to this procedure are ent i re ly just i f iable , the adjustments improve the answer sought for pract ical appl icat ion. The tables must be considered prel iminary and weak in the classes beyond the range of basic data (Table 2).

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TABLE 2

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Distribution of Basic Data by Site Classes --Douglas Fir

DBH Si te Class C l a s s 80 100 120 140 160 Total

Number of T r e e s

16 2 2 28 34 40 46 52 58 64 70 76 82

Total

1 1 2 8 12 3 2

1 6 11 17 6 16 17 8

22 14 21 21

13 1 3 10

3 8

5 35 64 89 80

Solid block indicates extensions in application of bas ic da ta . The t ree vo lumes a re sa t i s fac tory but the log-volume breakdowns must be considered pre l iminary in ex tended c lasses .

2 27 41 41 53 51 26 14 11 4 2 1

273

Table 3 shows the s tandard e r rors of es t imate of the basic data by half- log c lasses and log-posit ion in tree. Since all top logs were ad jus ted to ac tua l percentages , they show no e r rors . The s tandard e r r o r s of e s t i m a t e a r e h e r e a m e a s u r e of the var ia t ion of individual values about the adjusted curve values . These absolute var ia t ions a re d i f f icu l t to in te rpre t in v iew of the var iable base values which will actually fall into groups in the f ield. Deviations of individual l o g s w e r e , t h e r e f o r e , e x p r e s s e d a s a pe r cen t of the curve values , i n t h i s ca se pe r cen t o f pe rcen tages , and t he s t anda rd e r ro r of es t imate in per cen t ca lcu la ted . The s tandard e r ror of e s t ima te e x p r e s s e d as a p e r c e n t is a d i r e c t m e a s u r e of the var ia t ion in board-foot volumes of the var ious logs.

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The actual precis ion of the es t imate of the total volume occurr ing in any group of logs or grade can only be determined af ter the run of merchantable l engths o f t rees in the t a l ly and the pos i t ions of logs fal l ing in the var ious grades are known. However , it is possible to ind ica te in advance the maximum e r rors (poores t p rec is ions) to expec t i f ce r ta in conserva t ive assumpt ions a re made:

A minimum of 150 to 250 logs wil l occur in each ta l ly in the type of stands for which grade proportions would be estimated. These numbers a re based on recommended prac t ice of including a t least 50 t r ee s i n a ta l ly for des i rab le to ta l -volume es t imates .

A group of less than 10 logs would not be important enough to consider separately.

Logs will be grouped by grades--Nos. 1 , 2, and 3, as laid down in the Fores t Act .

Potent ia l No. 1 logs only occur in the first or second log of . 3 - -

log o r l a rger t rees and occas iona l ly in the th i rd log of 5-log o r l a r g e r t r e e s . T h e g r e a t e s t s t a n d a r d e r r o r of e s t ima te assoc ia ted wi th these c lasses is 7. 1 pe r cen t (Tab le 3) .

Potent ia l No. 2 log’s can occur in any log posit ion except short tops. I t is doubtful if they could be recognized above the fourth log ( 1 3 2 feet) in a s t and ing t r ee . The l a rges t s t anda rd e r ro r of e s t ima te a s soc ia t ed w i th t hese c l a s ses is 16. 1 pe r cen t (Tab le 2).

No. 3 or ungraded logs make up the remainder of the total volume.

1 2

The p rec i s ion of the grade breakdown of a stand will depend on the number of logs and the percentage of the total volume in the grade. F o r e x a m p l e , if 10 logs fall in grade 1 the maximum e r ror in the board-foot-volume determinat ion of g rade 1 is t x - SE - - 2. 2 x I = 4.9% 7 1

(19 t imes ou t of 20). If these 10 logs r ep resen t 10 p e r c e n t of the total-s tand volume, then the s ta tement of precision would be: 10% 2 (4 .9% of 10%) o r 10% ? .49% (19 t imes ou t o f 20) of the est imated total volume is in Grade 1. If these 10 logs r ep resen t 30 per cent of the total-s tand volume, then the s ta tement of prec is ion would be: 30% ? (4.9% of 30%) or 30% ? 1.47% of the total volume is in Grade 1. In practice it is doubtful that all the No. 1’s wil l come f rom the c lass wi th the g rea tes t var ia t ion (first logs of

4- - to 5- - l og t r ee s ) and more p rec i se e s t ima tes shou ld p reva i l .

IJn 4 1 0

1 1 2 2

Y‘

- 18 -

Table 4 shows t he expec ted max imum e r ro r s i n p ropor t ions of stand for var ious numbers of logs l ike ly to occur in Grades 1 and 2. T h e m a x i m u m e r r o r s i n G r a d e 3 or ungraded percentages cannot exceed the sum or be less than the difference of the maximum e r r o r s i n G r a d e s 1 and 2 since the total volume equals 100 per cent and t he t o t a l e r ro r equa l s 0.

TABLE 4

Ind ica t ed Max imum Er ro r s i n P rouor t ions of Stand for

Var ious Numbers of Logs L ike ly t o Occur i n Grades

1 and 2. Douglas Fir.

P e r c e n t of

M a x i m u m E r r o r (. 05 Level Probabi l i ty) In Grade 10 20 30 40 50 50 100 150 200 Total Volume Number of Grade 1 L o g s u m b e r of Grade 2 L o g s

10 20 30 40 50 60 70

.49 . 3 3 . 2 6 . 22 .20

. 98 . 6 7 .52 . 4 4 .40 1.47 1 .00 . 78 . 6 6 .60

1.04 .88 .80

.91 .64 1.36 . 9 7 . 7 9 . 6 7 1.82 1.29 1.05 .91

1.61 1.31 1. 14 1.58 1 .37

1.60

Based on grea tes t var ia t ions assoc ia ted wi th grades and min imum ta l ly of 50 t r e e s (150 - 250 logs).

Two points should be kept in mind when using Table 4 as a guide to expected precision: (a) The t ab l e s a r e based on the largest var ia t ion associated with

the po ten t ia l g rades and the smal les t recommended ta l l ies . In prac t ice the maximum e r rors should be smal le r than those shown in the tables.

(b) T h e e r r o r s a r e f o r l o g s a s g r o u p e d a n d d o n o t i n c l u d e t h e h u m a n e r r o r of incorrect ly c lass i fying logs by grade.

2. Western Red Cedar and Western Hemlock

A s imi la r p rocedure was fo l lowed in cons t ruc t ing the t ab les for these species . The percentage of the total volume occurring in

- 19 - various logs for var ious merchantable lengths differed f rom that of Douglas f ir (Fig: 1). The reasons, probably associated with bark- th icknesses , form, and s l igh t ly d i f fe ren t s tandards of utilization, were not invest igated. The maximum spreads of the individual observations did not exceed those for fir and were accepted without s ta t is t ical tes t . The tables are considered prel iminary, though suitable for the recommended use.