INTRODUCTION DATA METHODS. bark at breast height (d.b.h.) and total height (H) of the tree.' volume to merchantable cubic- and board-foot volumes.

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2 NTRODUCTON Red alder s a speces of ncreasng mportance n the Pacfc Northwest. nterest n mproved volume tables for the speces resulted n publcaton' of the 1949 volume tables (Johnson et a, 1949; Sknner 1959). More recently, Browne (1962) publshed cubc-footvolume tables for red alder n Brtsh Columba, and Hoyer (1966) presented tarf access tables, based on the 1949 tables, for use wth th e general tarf tables of Turnbull et a1. (1963). Ths paper presents new volume and taper tables for red alder. These form a unfed system, permttng computaton of cubc- and board-foot volumes for alternatve assumed scalng practces and lmts of merchantablty. DATA Basc data used n constructon of these tables conssted of (1) tree measurement data from Oregon, Washngton, and Brtsh CohÚnba used n constructon of the 1949 tables; (2) addtonal tree measurement data from Washn gton and Oregon contrbuted by Weyerhaeuser Co.; and (3) tree measurement data orgnally used for the volume tables publshed by Johnson et a1. n After elmnaton of trees lackng measurements of upper stem dameters to less than 10 nches, havng low forks or other gross abnormaltes or apparent errors n recordng of data, a total of 473 trees were avalable for the analyss (table 1). METHODS A report on the method of data analyss s planned for separate publcaton. There- "- fore, only an Qutlne of the approach used s gven n ths paper. Bascally, the method conssted n dervng from the pooled tree measurement data an equaton expressng squared dameter nsde bark - (d..b.)2 -- as a functon of the relatve heght at pont of measurement, dameter outsde bark at breast heght (d.b.h.) and total heght (H) of the tree.' Cubc volumes (CV) were then estmated by ntegraton of the resultng equaton. Estmates of upper stem dameter were obtaned as the square root of the estmated (d..b.)2. Boardfoot volumes were estmated by applyng assumed merchantablty and scalng standards to the estmates of upper stem dameters. Equatons were then developed for converson of total cubc volume to merchantable cubc- and board-foot volumes. Snce the prncpal ntended use of the equaton was n estmaton of volume, usng the relatonshp cubc volume = k / (d..b.)2dh, (d..b.)2 rather than d..b. was consdered the varable of prmary nterest.

3 Î f ~ ~1 ~!.! \, CUBC-VOLUME TABLE RESULTS Table 2 gves estmates of average cubc volume of red alder trees of specfed d.b.h. and total heght. Volumes are nsde bark, from a stump of heght n feet equal to LYí + (Yí) (d.b.h./12) J/ to the ndcated nsde bark (.b.) top dameter lmts of 12.0,10.0, 8.0, 6.0, 4.0, and 0.0 nches. No trm allowance s made. These estmates were obtaned by ntegraton of the estmatng equaton for (d..b)2 from assumed stump heght to heghts correspondng to the ndcated dameter lmts. \ t TAPER TABLE Table 3 gves estmated dameters nsde bark of red alder trees of specfed d.b.h. and total heght, at ntervals of feet above stump heght. Values gven are square roots of the values of (d..b.)2 predcted by the estmatng equaton. The heght nterval used provdes trm allowance of 0.50 foot per 16 feet of bole. VOLUME TABLES N BOARD FEET f Tables 4, 5, and 6 gve estmated average tree volume n board feet Scrbner (SV) for stated assumed scalng lengths (8 and 16 feet), top dameter lmts (12.0, 10.0, 8.0, and 6.0 nches.b.), and dameter measurement practce ("nearest nch" versus roundng of fractonal dameters to next lower exact nch). V olumes were obtaned by applyng the formula Scrbner log rule (Bruce 1925) to estmated upper stem dameters (table 3), wth trm allowance of 0.50 foot per 16 feet of merchantable stem and usng, for top logs, estmated length (unrounded) to the stated top d..b. lmt. Use of formula rule rather than scale stck values elmnates the arbtrary and llogcal jumps whch result from roundng and the dagramng process. Volumes for measurement to "nearest nch" were obtaned by usng estmated top d..b. n the formula; volumes for meas~ urement "roundng down" were obtaned by usng (d..b.-yí) as the dameter n the formula. Snce volume tables represent the means of many trees, smoothed values are approprate. Table 7, whch gves estmated Scrbner volumes by d.b.h. class and number of 16. foot logs, was prepared by graphcal nterpolaton from values shown n tables 3 and 5. Table 8 gves estmated tree volumes n board feet by nternatonal ~-nch rule, wth the same assumed measurement practces used n table 4. CHOCE OF TOP DAMETER LMT n applcaton of ether board-foot or merchantable cubc-volume tables, the choce of mnmum top d..b. lmt should be based on the user's estmate of the top d..b. to whch awrage trees of the sze under consderaton can actually be utlzed. Ths lmt wll vary wth tree sze, because of excessve branchng n the tops of large trees. Thus, board-foot volume to a 6-nch top n a tree 24 nches d.b.h. s not a realstc estmate of the volume of materal actually utlzable as sawtmber, even though smaller trees may be utlzed to ths lmt. ~ 2 An arbtrary rule, whch approxmates average heght of stumps as cut. 2 l 1

4 :ed ual 0.0,.b)2 t- t COMPARSON OF "ACTUAL" AND ESTMATED VOLUMES "Actual" cubc volume of sample trees was calculated by Smalan's formula (except wth butt secton treated as a nelod) and the dfferences L CV estmate -CV actual J, where estmated volume was CVT as shown n table 2, were expressed as percentages of estmated volume. The mean percentage dfference, excludng 131 trees for whch stump dameter had not been recorded, was -1 percent wth standard devaton of 9 percent. For a porton (139) of the sample trees, dfferences between estmated Scrbner volume (SV8 n table 6) and "actual" Scrbner volume were calculated. These, when expressed as percentages of estmated volume, had a mean of -0.8 percent and standard devaton of 15 percent. and +1 the rm \ for 6.0 :mal :rbí nce \ :un- ~cal Lt to easula. 16..Y th TARF ACCESS CURVES Those wshng to use the tarf system for volume computaton (Turnbull et a ) can readly use table 2 as the bass for a tarf access table by means of the relatonshp (CV4) tarf number = (basal area ) gven by Turnbull and Hoyer (1965). Fgure 1 s such an access table n graphcal form. COMPUTNC EQUATONS The equatons gven below may be used for calculatons on automatc data processng equpment. 1. Dameters nsde bark may be estmated by the followng equaton, whch s the bass of table 3. where ßd..b.)2 J d..b. = (d.b.h.) est L( d.b.h.) 2J est ~(d..b.)2 J L( d. b.h.) 2 est = (x) (x1.5-x3) (d.b.h.) (10.-2) (x1.5_x3) (H) (10-3) (x1.5_x32) (H) (d.b.h.) (10-5) (x1.5_x32) (H)o.5(10-3) (x1.5_x40) (H)2(10-6) e of ver-.\'th me 'ral ~ ~ n whch H = total heght of tree, and d.b.h. dameter outsde bark at breast heght, x = (dstance (H-4.5) from tp to estmated d..b.) The rato (d..b.)2/(d.b.h.)2 has a standard error of estmate of approxmately 0.07., 3 ""\'::-.

5 ~ / y,"'-..v. 50.1, '9"Y o~..".. '9'Y u / / / O-- O~ ",., / / / A....rö. ~'9"Y ~. 40. ~ Zr. o: 35.. tõ'ç '9"Y.. O. O~ "l ~ '9~' 45.1 L / / / Lj / / / //////././.// t: / //4////"1 0 ~.N '9"Y tz".'ç "l /1 / /Y///y////Y/ß TOTAL HEGHT (FEET) 100 no 120..,,, Fgure 1. -Graph - for estmatng ~ tarf number of red aldetfrom #;' d.b.h. and total heght...~ :.. /

6 ., tn '0).. 'ë..., 0 "' : co ' S Q) "' 'ë "'Q).. 0 ;: Q) ~ S :: 11 :.., : co., bl.5.. co.s 1; Q) : co.. ø., Q).. :: t 2. The basc equaton for total cubc volume above stump (CVT), derved from (1), s: where3 CVT = (d.b.h.)2(h-4.5) (F) n whch F = (Z) (Z)2.5(d.b.h.) (10-3) (Z)2.5(H) (10-3) (Z)2.5(H) (d.b.h.) (10-5) (Z)2.5(H)2(10-6) (Z)2.5(H)o.5(10-3) (Z)4(d.b.h.) (10-3) (Z)4(H) (10-3) (Z)33(H) (d.b.h.) (10-6) (Z)33(H)o.5(10-4) (Z)41(H)2(10-7) Z- (H-l1-(d.b.h.)/24) _ (total heght above stump n feet) - (H-4.5) - (total heght above b.h. n feet) The estmates of total cubc volume (CYT) for trees of specfed d.b.h. and heght (H) gven by equaton 2 above may be converted to merchantable cubc volumes to top dameters of 4, 6, 8,.10, and 12 nches.b. (CV4, CV6, CV8, CV10, CV12) by multplyng estmated total cubc volume by the followng converson factors: CV4 _ _ _ (H) CVT -. (d.b.h.)3 (d.b.h.)4 (d.b.h.)3 (d.b.h.)3(h),cv6 _ _ (H) _ (105) CVT -. (d.b.h.)4 (d.b.h.)4 (H)3 (d.b.h.) (H) (d.b.h.)5(h) CV8 _ _ O (H) CVT -. (d.b.h.) (d.b.h.)4 (d.b.h.)2 (d.b.h.)3(h) CV10 = _ (H) _ CVT. (d.b.h.)2 (d.b.h.)4 (d.b.h.)4 (d.b.h.)6(h) + CV12 = _'C (H) _ (H) _ CVT. (d.b.h.) (H) (d.b.h.)3 (d.b.h.) (d.b.h.)4(h) (d.b.h.)2(h) A smlar set of converson factors, some what less accurate but based on d.b.h. only, s gven by the curves shown n fgure 2. These cubc-volume converson factors, and the board-foot volume converson factors of followng sectons, should of course not be appled to trees of dmensons too small to contan merchantable volume to the specfed top dameter lmt. 3 "F" s Led.b.h-:)J dx, whch s a form factor based on a cylnder of dameter equal to d.b.h. and c rz fed..b.)l2. heght equal to (H-4.5). 5 ".,_'Ò' -.~'."3. _-. ~

7 ,. --~--'.:---- -_..--=~~--=:~-- ~~~~ -l_7~"'~~_""~"","! '..~ ~en 1.0 o E- 0.9 ~ :E :E :::: O. 8.. o E- t :: r, "" ::' ~ 0.7 :: 0 u 0.6 ~ ~.. :E :: E- 0 ~:: 0.4 : u 8 ø::: 0.3 ~ u :E.. ~ ~ E- E- 0.1 ~ o CV~/ / CVT / 1\ ~.../ /.r ~ ~ ~ ~ /' ~ ~ /' ~ -- / /, /" V / / / m CVT 1/ / CV8 / /1/ CVT / / / CV0 CVT J 1/ / CV12 1/ ff / ' 1/ DAMETER AT BREAST HEGHT (NCHES) Fgure 2.-Relatonshp of ratos of (merchantable cubc volume) /CVT to tree d.b.h.

8 L l ~ 4. Total cubc-volume estmates (CVT) for saw-log-sze trees of specfed d.b.h. and H may be converted to board feet, Scrbner, by ml1ltplyng by the converson factors gven below. 'Ratos are for board-foot volumes to tops of 6, 8, 10, and 12 nches.b. (SV6, SV8, SV10, and SV12). Scalng s assumed to be n 16-foot logs, wth fractonal dameters rounded down to next lower exact nch, snce ths most nearly approxmates current commercal practce.. SV6 = _ _ CVT' D H D2 D4 DH CVT' D2 H H3 D D2H D6H SV10 = _ _ _ ;105) _ (1~B) CV8 = _ _ _ (H) _ (107) CVT' (d.b.h.) (H) (d.b.h.) (d.b.h.) (H) (d.b.h.) CVT' (H) (d.b.h.)6 (H)2 (d.b.h.) (H) (d.b.h.)4(h) SV12 = _ _ (H) (105) _ (106) Total cubc-volume estmates (CVT) for saw-log-sze trees of specfed d.b.h. and H may be converted to board feet, nternaton l 1)-nch rule, by multplyng by the converson factors gven below. Ratos are for board-foot volumes to tops of 6,8, 10, and 12 nches.b. (V6, V8, V10, and V12). Scalng s assumed to be n 16-footlogs, wth fractonal dameters rounded to the nearest nch. V6 CVT V8 CVT V10 CVT V12 CVT. D2 D4 H D2H D5 = _ _ _ (H). D2 D4. H. H4 D2H = _ _ _ 1.211(106) D3 DB H D3H. D2H D3H D6 H 7.299(106) H4 = _ _ (10B) _ (105) = _ (105) (H) _ bl':(~a tj.o ~ J Yl ~'(u_ 8 8- U.:; \( ; E:: :y~:,~ : J ~ -, '-.'. ~-.3 J J,l.t ~ \ 1 7

9 TABLE. --DSTRBUTON OF SAMPLE TREES BY DAMETER AND HEGHT CLASSES. DßH TOT Al FOR DBH CLASS CJ q TOT AL TO TAL NO. FOR H r CLASS

10 SES~ FOR LASS 7 o 6 5 o j ) ~ )... NO. - (CV), FROM STUMP TO SPECFED MNMUM TOP DAMETER NSDE BARK (DB). STUMP HEGHT = 0;5 FOOT x DBH. MERCHANTABLE VOLUMES OMTTED FOR TREES LESS THAN 6 NCHES DBH OR HAVNG LESS THAN 8 LNEAL FEET OF MERCHANTABLE BOLE. TABLE 2. --VOLUME OF RED ALDER TREES N CUBC FEET NSDE BARK MNMUM TOP DB - NCHE S DBH TOT AL HT CV 12 CV 10 ev8 ev6 CV4 evt ~ ~o ~ !t q " '-\~=;'-"lv.-r;~~~~~~'?1

11 10,... "Í

12 TABLE 2 (cont nued) L, MNMUM TOP D8 - ;~CHE S OBH TOT AL C 0.0 HT C V 12 cv 10 (V8 C \16 CV4 CVT ) 1 1 B 2 3 l l l a oa a ') a oa a a a a. a S, oa a q !j q :' a ' a ,...-..,.C"'.,''''',

13 1 TABLE 2 (cont nued) MNMUM TOP 01 B - L'-CHES DßH TOTAL C.O C 0.0 HT CV 12 CV 10 CVB CV6 CV4 C V T

14 - t r TABLE 2 (contnued) M N 1 MU M TOP 01 B -,K H E S OOH TOT AL 12. J 10.0 e.o C ).O HT CV 12 CV 10 ev8 CV6 CV4 C VT e 'J B ' l L, 1 13."""~"~""-,~

15 TABLE 3. --TAPER TABLE FOR RED ALDER, BASED ON DAMETER OUTSDE BARK AT BREAST HEGHT (DBH) AND TOTAL HEGHT. VALUES ARE DAMETERS NSDE BARK N NCHES, AT NDCATED HEGHT ABOVE STUMP. STUMP HEGHT = 0.5 foot x DBH. VALUES LESS THAN 4.0 OMTTED.. DBH HEGHr ABDVE S rump ') , b.oo ó.1 6. ' ) , L q L d ') :; ') ') d

16 n TABLE 3 (cont nued) 5 rump,$ HE GHT :0.. 08H ABOVE SlUMP E " 'l Ü L " q q q q CJ q ' ') q C) q q ö.OO q q ~ q '9.4 ').5 q. ') 9.? CJ CJ.O ') ) 10 2ö ') '). q CJ 10 41~ ') ' 1 () ü CJ ~~""""'''~f'

17 TABLE 3 (contnued) ()ßH HL GHT ABCVE STUf,P 4C l t R L ó.o u.oo " LO Y ? b.. R , ')0 ')

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19 "'1 TABLE 3 (contnued) ObH H,EGHr ABOVE SlUMP ~ q q ~ ~ el 1, ~ s q ) ') lj B ') l) q ) 'j ' ') ' ) ' '

20 .! TABLE 3 (contnued) 120 OBH HEGHT AOVE STUMP 4J ') ; ,.0. ' ~ ~ , l l l Z l l l l l2.3 l '1 6.4 l ' L 1. 5 l ll.2 LO L '15.9 LO r ' ? ') l ö ') ".d'~'...'~ --'" '~." -". '.

21 ', TABLE 3 (cont nued) OßH HEGHT ABúV E SlUMP 4 () " l ' q , 1S 16.S ' q 14. ') , a _~ t t ls ').1 18 '

22 ~ SlUMP TABLE 3 DSH (cont nued) HEGHT ABOV E q q q Q q la " q ll a 'o ) 'j ll q a ' ) ) ò R Y " v q "",..y,~ -~: "-'11

23 'J ' TABLE 3 (contnued) D8H HE 1 GHT ABOVE SlUMP ö ~ !; "; : ~ b l, ') l 1

24 TABLE 3 (cont nued) 08H HE GHT ABOvE 120 SlUMP ) ~ B ' ' ') '~

25 TABLE 3 (contnued) DBH Hl: 1 GHT ABOVE S rump ' ' q '

26 TABLE 4.--ESTMATED TREE VOLUMES N BOARD FEET SCRBNER (SV), BY FORMULA RULE. BASED ON 16-FOOT SCALNG LENGTH (EXCEPT TOP LOGS) AND ESTMATED LOG TOP DAMETERS NSDE BARK (CORRESPONDNG TO MEASUREMENT OF SCALNG DAMETERS TO "NEAREST NCH"). 6- NCH TR 1M ALLOWANCE PER 16- FOOT LOG. VALUES OMTTED FOR TREES 120 HAVNG LESS THAN 8 FEET OF MERCHANTABLE BOLE. LMT- ~. 9 TREE TREE ~. 2 DBH T UT Al OßH TOT Al 12.0 HE GHT SV 12 ~. 6 SV6 HEGHT SV 12 l l.l ) ~ ~ r ) ) t ) ~ ) J.9 q J J ~ ~ ~ ' r.6 10 qo r ) s ) ) O t ~ ) J ~. 9 r. 9 )e 9.8 ~. 6 l 25 1 ","""'91,

27 TABLE 4 (contnued) TREE THE DBH TOTAL DBH TyT AL C HEGHT SV12 SV6 HE GHT SV 12 SV ~ ') ' c)q

28 TABLE 5. --ESTMATED TREE VOLUMES N BOARD FEET SCRBNER (SV), BY FORMULA RULE. BASED ON 16-FOOT SCALNG LENGTH (EXCEPT TOP LOGS), AND ESTMATED LOG TOP DAMETER NSDE BARK MNUS 1/2 NCH (CORRE- SPONDNG TO "ROUNDNG DOWN" FRACTONAL SCALNG DAMETERS TO. G NEXT LOWER EXACT NCH). 6-NCH TRM ALLOWANCE PER 16-FOOT LOG. V6 VALUES OMTTED FOR TREES HAVNG LESS THAN 8 FEET OF MERCHANT- ABLE BOLE. t 73 ) 39 TOP DAMETER )98 TREE TREE DBH TOTAL DKH TOTAL HE GHT SV 12 SV6 HEGHT SV 12 SV ) ) ) 'l ~ t ) ) r t )41 q ) r r t t ) B ) r ~ : U S oa ló , '7.....'v"...'''''''~~

29 ",J,..~ TREE TABLE 5 (contnued) LMT- TREE OflH TOTAL Q DßH TOTAL HE GHT SV 12 SV6 HE GHT SV 12 SV lo 221 n lo 44~ ') 'j lo 50': lo ' L q 'l n 18 oa q b U n j J C \28 1 l 1

30 VALUES ~ "6.1 ' TABLE 6.--ESTMATED TREE VOLUMES N BOARD FEET SCRBNER (SV), BY FORMULA RULE. BASED ON 8-FOOT SCALNG LENGTH AND ESTMATED LOG TOP! DAMETERS NSDE BARK (CORRESPONDNG TO MEASUREMENT OF SCALNG DAMETERS TO "NEAREST NCH"). 3-NCH TRM PER 8-FOOT LOG. OMTTED FOR TREES HAVNG LESS THAN 8 LNEAL FEET OF MERCHANTABLE BOLE TR E: TKEE 93 DBH TUT AL DßH TeT AL 2. a b. ù 48 HE GHT SV 12 SV6 HE GHT SV 12 SV6 n B oa Y YO ': U q 'l 'l J ' ': ClO L 'l b 90 14? :: ': \, 1 29 ';,"'l; ---:~'rl

31 t,r TABLE 6 (contnued) TREE LlMT- TRE: DBH TOTAL CBH TOTAL 12. a b.o HEG-T SV 12 SV6 H: GHT sv 12 SV6 t' % ~ ! r ó S 559, lco ') 3(H n 'O ö q Z' a ' ~ ~ 30

32 TABLE 7. --ESTMATED TREE VOLUMES N BOARD FEET SCRBNER (SV) BY FORMULA - RULE, BY TREE DBH AND MERCHANTABLE HEGHT N 16-FOOT LOGS. BASED ON 16-FOOT SCALNG LENGTH AND ESTMATED LOG TOP DAMETER NSDE BARK MNUS 1/2 NCH (CORRESPONDNG TO "ROUNDNG DOWN",.0 FRACTONAL SCALNG DAMETERS TO NEXT LOWER EXACT NCH). 6-,V6 NCH TRM PER 16-FOOT LOG. TABLE DERVED BY GRAPHCAL METHODS from TABLES 3 AND NO. NG. 650 l DBH DBH FOOT 6.0 FOOT LOGS SV6 LOGS SV U ' U q ' ' 'l ') ') q lq lj ') ,59 1 'j j E ') ' lö ~ ' ~ a 16 ') (! l 31., '. ' -":'-'1"~l1

33 TABLE 7 (contnued) ~U.. LMT - NO. FOOT 6. C FOOT 6.0 LeGS SV6 LOGS SV6 O OBH ') ') Î HO ~ ; H a ~, Z q C Ó 16 54') Z ') ' T r \!! 32

34 - (T SV6 TABLE 8.--ESTMATED TREE VOLUMES N BOARD FEET NTERNATONAL 1/4-NCH RULE (V), BASED ON 16-FOOT SCALNG LENGTH (EXCEPT TOP LOGS) AND ESTMATED LOG TOP DAMETERS NSDE BARK (CORRESPONDNG TO MEASUREMENT OF SCALNG DAMETERS TO "NEAREST NCH"). 6- NCH TRM ALLOWANCE PER 16-FOOT LOG. VALUES OMTTED FOR TREES HAV- NG LESS THAN 8 LNEAL FEET OF MERCHANTABLE BOLE )09 )86 '59 ~l,ìí TREE TOTAL Dt3H HEr GHT 8 40 t a q 'l qo ; J V , TREE TOl AL DHrl HE GHT ' LL L , ' oa C V ' LL , 1 33 ",". ~''''''"''~~'' "'-. ", --? ~

35 TABLE 8 (contnued) TREE TOT AL TREE TOT AL DHH HE! GH r 6.0 DSH HE GHT 6.0 V6 1 V , ç:o 'l : 'j cN BOZ ( BO 5ld oa B27 (

36 6.0 V r~ ~ v LTERATURE CTED Browne, J. E Standard cubc-foot volume tables for the commercal tree speces of Brtsh Columba. Brt. Columba Forest Servo Forest Surveys and nventory Dv. 107 pp. Bruce, Donald A formula for the Scrbner rule. J. Forest. 23: Hoyer, Gerald E Tarf access tables for the Pacfc Northwest - a complaton. Wash. Dep. Natur. Resources. (Unnumbered.) Johnson, Herman M., Hanzlk, Edward J., and Gbbons, Wlam H Red alder of the Pacfc Northwest: ts utlzaton, wth notes on growth and management. U.S. Dep. Agr. Dep. Bull. 1437,46 pp., llus. Johnson, Floyd A., Kallander, R. M., and Lauterbach, Paul G Volume tables for red alder. U. S. Forest Servo Pacfc Northwest Forest & Range Exp. Sta. Res. Note 55, 10 pp. Sknner, Edgel C Cubc volume tables for red alder and Stka spruce. U.S. Forest Servo Pacfc Northwest Forest & Range Exp. Sta. Res. Note 170, 4 pp. Turnbull, K. J., Lttle, Gene Roy, and Hoyer, Gerald E Comprehensve tree-volume tarf tables. State Wash. Dep. Natur. Resources. 23 pp. plus tables. and Hoyer, G. E Constructon and analyss of comprehensve tree-volume tarf tables. Wash. Dep. Natur. Resources, Resource Manage. Rep. 8, 64 pp rl