The drying rate of sugar maple as affected by relative humidity and air velocity

Material Information

The drying rate of sugar maple as affected by relative humidity and air velocity
Series Title:
Report ;
Torgeson, O. W
Forest Products Laboratory (U.S.)
University of Wisconsin
Place of Publication:
Madison, Wis
U.S. Dept. of Agriculture, Forest Service, Forest Products Laboratory
Publication Date:
Physical Description:
8, [5] p. : ill. ; 26 cm.


Subjects / Keywords:
Sugar maple ( lcsh )
Lumber -- Drying ( lcsh )
federal government publication ( marcgt )
non-fiction ( marcgt )


General Note:
Caption title.
General Note:
"April 1951"--Cover.
General Note:
"Information reviewed and reaffirmed"--Cover.
General Note:
"In cooperation with the University of Wisconsin."--Cover.
Statement of Responsibility:
by O.W. Torgeson.

Record Information

Source Institution:
University of Florida
Rights Management:
This item is a work of the U.S. federal government and not subject to copyright pursuant to 17 U.S.C. §105.
Resource Identifier:
029511294 ( ALEPH )
757552107 ( OCLC )

Full Text

Informdtion rcvkitucd and IPcaffirmcd
April 1951


No. 1?12C4

Madison 5, Wisconsin
In Cooperation with the University of Wisconsin


0. X T=.C- SSO S.._...cer

I:.t product ion

Ler .dry kilns o'. ir. use vary fro:.m natural circulation k:ilns
'ith hand control to tre latest type of far. kilns w7ith,- automatic control
cf .ot te..pers'iire d h'idity. In between are re...odeled kilns equipped
at v'rios t0" .es anc sizes of fans, and various types of control.

Some slo circ';.lation kilns ire se.d for ri green stock t here
Ci rulato n are used
rapid circulation ',ovli be beect, and soie raid circulation kilns are sed
for ( ryin: air-dri'd stock heree a .;uc- slower ratc; would be satisfactory.

Circulation is needed to replace het loses'.!< ''alls and
around leers and were these losses are largo a brisk rate is helpful in
Lai n tai in,; .ifor. dryiug co nditio s. A, other r important consideration,
o'.VC ver, I s tne supp 2'in.-] of heat for evaporation, and, the-refore, more
efficient cdesilnin and drying could 'e acco..plishcd if ...Lre specific
info.r:.. tion vas availalle conccrnirin the air needs for various species and

HoW lon :'-osc it take to kiln d'.,y sumar n;aple? This sec;s like a
Gi- lo Qao, btt it ca. be a rd stisfactorily only after :.ay
fajcrr"" ac taken into con.idLra.tion. h:se factorss rc: s'1) ori
a::i finel :,it-.; i air, () si of ( rlative hu.,iity of kiln air,
(6) ...ociy- of kil ...r, ad (7 length. f air travel. ro correlate
v'riolus co.01 n. tions oIf t -.. f .ctor r .d dr-in tine rec uires considerable
k owi0-/.,: Of t: iffcct of eicn.
Oe-f' 4"- --f( .. 4- C "I Cn.

:c ntl7 e- Cors Products Labrn story completed a snrits of kiln
r .ns on : *1r;.ood n.. tyood of 1- o 3-nch sugar iaplc primarily
ffor o of t:..i t ff"ct of air velocity on dr-ing time.
.-:i r un er: rade in o ,.rird tre.'l t,-c of dryi.-.,; unit v,'ithin which the
ten.perature, reltive hu..idity, ,.'Id air velocity were i.aintained constant
duri.'i; each. of t4-he '.. r-, ias, ..- 1oard s 'r'ere piled on 1-inch stickers
o a '.idt of 4 feet i. trie 'irection of air travel. .he original green
Lcistu co. .t avcr- d, appr )xi;.atey, 70 percen-t a;nd the dryiing period


p(*Tr t Io. i' -"--

was from this 3ond.ition down to) a .-oisture content of 20 to 30 percent.
Only one te...oe ratui-e, 130 T. v'as used for eli rains, b.t the relative
hu..idity, b-ec,:use of surface c.ecini tendencies, ..:_ from 20 to 76
percent for the sa wood boar ds and froi 76 to 91 percent for the hecart-
,ood o rd-s. -e air velocity raned, from 155 to 1,640 feet per minute.
The data: obt-,;C :i in tiese '-il runs at arc. peted hcre in adiscussing
the sovc'n factors cnumerated in he precede .. paragraph.

(l) Oriinal and ( inal oi stut ,C ont nt

-he 1ryin; rate of a -iven pie-ce of ,rood is proportional to the
moistene gr ;-iet. radi3nt is r cant tr-o rate of increase in moisture
content f'rox the srface fibers tow :ard t;.c ceter. :his 'rodiecnt is
great. t tt t c beginning ad, under ay iven relative humi,,,diIty, is a
maxi:-... only '*,in Tohe air velocity is s-Tfficiently I-ah to bring, t s-
face fibers to a moisture con-,n in ewilibriu;:. with te surrondins
air. A.s the interior dries, tnh -_adintc- docrcase.s causing corroscondin,
..-. :es in the dry-in- rate.

Io illustrate the iorf ... n "oist"r- content, t .. .ve.a.
drying rate cf sugar ia.aple under a te..pcraturc of 130 F, .z nd a rltivc
humidity of 76 percent is given in tble 1 for 10 percent moi tv rc con-
tent TThe highest air v:locity run l,640 f t per .inuto) is
used to eliminate as I:ruch as possible the v-elocity effect.

The dring rate at any o-peci-fic moisture aliue is influenced by the
original green moisturee contentw. 'or that reason a slig-ht error is intro-
Cduced in comparing the rate. of te s ood wic hss an averge
o. iinal .oisture content of 70' percent ,itl. t:nat of the ne',rt',ood which
had an avera-. original i.oisture con ent of 65 perce nt. At 55 percent
moisture content, this error .aountz.- to rpro'-irrtelb 15 percent, but at
20 percent moister content error is nIniiAble. In other .,ords, if
the average original oistu content of the near :wood had beer 70
instead of 6, p-oerc cnt, the averag.4e rate b, t'-etcn GO and 50 percent
moisture content would have ben approxiNatey 15 percent less than that
sIo, n.

nor tes constant drying conditions, mor t>.li. was ecded to
dry from 'C to 20 percent .oistur contient than from 70 to 50 percenIt.
This illust.ate.s th. necessity_ of spcifyin,_, quite d.fiitcly th- icstur-
cotentn limits in. estimating trying time.


Re ort 1,o. Sl"C

Table I.--Dry-ing time of 4/4 sugar maple under a temperature of 130 F.,
a relative humidity of 76 percent, and an air velocity of
1,640 feet per 2.inute

Sapwood Heartwood
:oist'lre content ----------------------------------------------------
-------------Dryi: :..- verag-e moisture: -ryi,-. Average moisture
ror To : time :content loss per: time :content loss per
hour hour

percent r percent : Hours : percent : Hours percent

70 60 : 3. 2 3.1 ............
60 50 4.4 : 2.3 : 6.3 : 1.6
50 : 40 6.1 1.6 : 10.0 1.0
40 30 : 10.9 .9 20.0 : .5
30 : 20 34.9 : .3 47.0 .2

60 : 20 : 56.3 : 83.3

(2) Sap:wood Versus Heartwood

In general, heartwood dries slower than sapwood, and in the case of
the sugar maple the ratio of dryi:. rates was approximately two-thirds.
This is illustrated by the data given in table 1. Under the conditions
given, the drying time from: 60 to 20 percent moisture content was 30.0
hours for heartwood and 56.0 for sapwood.

('") T. ;r.-.p- rc of :"iln Air one tc.pc4rature (130 ) was used but some data on oak have
indicated that betwreen 130 oa:-id 160 F. drying rate increases approxi-
r.ately 2 percent for each 1 decree increase in temperature. On this basis,
the sugar a,[le.e sapwood at 160 F. would idry fro:i 60 to 20 percent mois-
ture content iln 6. or 35 hours. This co;mputed dr':ing tie is only an
approximra'ti)n and is given merely as an illustration that tc.,icr,-ture .iust
bc consiicr.d in estimn.ain, drying time.

(4) Size of Stoc'"

Alhough only one size was dried in these particular pcri..Cnts,
it might be w11 to cxplai. how the data can be used to estimate the drying
time of other sizes. trying ti.:e is not directly proportional to thickness,

Report -o. R"4


but, for an in, finite _widtn, is ;..ore nearly proportional to tIne square of
the thickness. "'7"ith is a factor also because as th.e w-idtn decreases the
0d-:e dr-i, relatively r..ore important as co-.pared to the a.ount of
-:" -L front the faces. A athe:.atical method of co.utin this has been
used at the aorator ad hras Yeen found to check i-,ell with empirical
met1ho10'.C Soze of t-ere cocmputed r-tios are shown in table 2.

Table 2.-- o _-oet-icoal dryin< ti:e of various si7es 5 sed on tnat of
l-iCch stoc of infinite widt n as purity

: W'.id"th
Thic- :----------------------------------- -----------
ness : 1 : 2 : 3 4 : 6 : 8 : I:finitc

Inches" ;e 1 : iv r ti me

1 O. O C 80 0 p G.94 0. 9(7 9 1
..w /,O /^/ U.t. >. . : 0 U .. .7 1
2 : '.70 : ,. : : 3.77 4.0C
3 : : : 4.50 : 5.76 : 7.20 : 7.39 : .00
4 : : : b.O0 : 1.03 :12.0 16. 60

vo l show th r t'ivc *ii: tiL- as compared to t.,;?t of
1-inch Ztock of in.'-;itc wid1th. -Eti_.atcs can co :..a.-c for -arrow widths
only when te; air circu.latcs frel-y arc -n& all si.Cs. Whro. tic stock is
piled ucdCI to edgc in a ,.ide soi lay;r, a:n infinite widtnh ray be acssu;cd.

(b) Rclative Hu:.idit of l.-1 Air

Frevio.sly, it '.,as stateI t:hnt to cr,1 dri rate is proportional to
in o i t d c; ua c tor lili.ting i i. ; ,- .i ie the c ii briu
ooistJurc conltnt at the surface of "'.ood and t 'is, in turn, is a
function of tc lativ hui of L of- tlo ir. Cne confusing ticin;, ho', vur,
is t tat the relative >'aciditics at t., s-'.rfacos a.nd at the leavi.. -air side
are :ot tie 7a::ic as that of t.o co:ndi'nio:d air. As eat pr sss iro.. ti:C
air stac. >, to t.e '...d. s'urface :nd is *a sed for cvw. oration, a tco.p-r,'t-rc
dro- occurs *-rhicn, to ther *'ic: thc .,,ti on of tne evaporate -oItro
reslS in o:i !icrease in rlvtiv< :iiA;idity7 nt t 'oa surfae Tn ;i
cir st=.n i2 t sC affected a. da. c- t'he ti:.e it r'ac .-K tre len'vin:" nir
sidC, it hs a o-dr :;.pxrat-r :and roT tivc .:nir it- thai ''ahe it
entrad tne lo'-.. -.' :,:nitudc of the difference tet-.een ti. air streak,
and tne surface is "-overned ..ainly -'b tne air iie that 'et'-een
the entering and leavin_-air sies of the loo" is -overned iby t.-e volume of
air suppl.ied am"d tce length of air t:avei. 2ot iffere:ces (one
-.pendicular a..d one parallel ro the board s."rfraces) are affected b( the
rate at '.ich. te .oisture is :iven off.

- -, .~-~r1- r'-v 2I~6K~
- -~ -"S.


his i ilustrate.d ;:;"'.. icl!y in figure i. The dryiw data were
collected fro:: a s Ories of cartwood runs gere tne relative humidity" and
air velocity of the individual riums were as follows: 76, 0, ', and 91
--rcnt at 35 fo t per ..inuite, a:nd 76, 30, and 36 p-rcent at 450 and 930
feet per .0inu. On the charts, the lines drawn through thie data points
wer exeded to thne zero dryinL; rate line at 100 percent rel-a.tive humidity.

it :-iLi:t be well to .:etion here that the moisture content values
rntifi" tne curves if figures 1 to 4 are av-erae *aluec and- ht in each
case a .oistc;ie radient existed from tne intCerior of the ',ood. to the sur-
fae a nd firo:-.. the e.terin,. t) ti- leaving J-air iics of the load. At the
... 7;, 0C r:o.strre contest, differ c.ces in the slope of theIsc jradie ts
a ccu d. for t:he dif .er. .s in dcryin rate.

~~A com r of th.e three charts of figure 1 shows that at 60 percent
o ...... t re la.. t4 ef-fect on dryin2 rate under an air
v locit ocf 230 feet per uin':te '.'as quite different fro.. that at 235 feet
per .i.:tc. .At a ..ois0ure content of 30 percent, however, tho difference
was v2ry c;Ci lcSs.

At a ..oisture cnt ..nt of 60 percent, a constant dr-,,ing rate of 0.48
percent content loss per ho 1- was obt:_in.d under each of the
fol..i.. dn i nI conditions, 73 percent r1eati-Je umcidity arnd 235 feet per
nit air vlocit, 35 pCrcant and 450 feet per ainuite, and 91 percent a-.
C0 feet per -..iute. Each of the so three conditions, then, produced the
same avc rae t ffcctive equilibriu:. ;:oi stvrc content on the surface of the
wood at that ,rticular oitur nent of stck.

Figure 2 showvs the dryin-g ata for sapwood boards when dri' d u-nder
relatie nuar.iditis from 75 dc',,n to 20 percent. Tha eir velocity ,,as 1,-4
foet per minute, which was sficently -igh to prevent any appreciable
.u-izity rise nex t to the wood surface o cially at the low moisture con-
tent v-'l'ca. curves, t rprct th r:l>tive humidity effect on
dryin, rate o'-d show' how ..uc ore i:.:'ortant it was at the hieLer no.sture

h. c rv. s also show that h- i..-port"r.nce of chanres in relative
hu:vi:.ity becnue vncrcurinly ,reator as the huxiidity increased ,above 60 or
70 ;rccnt. eow 60 percnt_-, the. humidity effect bccaxe rc!-,tivcly
uni-..por t .t.

(6) 7clocit, of Kiln Air

YTo kiln-dryi-- time records ar, co'pletc without show-in- the air
Slci ri ad volu.e ca wmll s th. t,..pcrture and re:lativw. humidity, -,c
i..port. otnc of ic fho':an by t constant Jryin rat- curves of figure 3.
ach cuvet rp pri'. nt_ s so:,e a fii.ite. drrinri' ate of a 4-foot piie of 1- by
s-inch ;;u,:". r :;p'lc sap,,ood boards when at 60 percent moisture content and

Rcoort 1'o. R1?64

het subj ictcd to v''rious cobi aio.s of air velocity and .. ty. e
chart ,c'' ta 'a. e.o a t.:i aigh .oi e c, conLtent n t eur
face ',s.s sciojecttc to t e re tive :ia:.idity of tE.0e conditioned 'r onlly
w11en the ai r veeoir I reD higw. elow this ..x ... air locity, a
constant -ry.: ate J. only by lo'erin. t.e r 2lative idt
of the coCitioned air.

Tor, 'qen tne stock' was at K60 percent ..oict'.e content an
air veloc-ity of 1, 6C0 feet per .' .. and a relative humidity of 'z4 :ri .ied
in a moisture i.os of 2 per>:t per -r. C'xe t air velocity 'a to 400 "U0 pr c:c, rcl.ati -....,.1.i-ty :-ad to be rd'ic:c.-d to 43
percent to 7.aina tca sa;.. average c.r-. ... I. t cas; t.e efc-
tive 7 O, :r..idity ;at th1 v'A sear:Y2o ..:^s; h ivc bo tn aproit cly 4
perceat, .... i the cos' of tn:` lo"'er %vlocity tl ,.;.;id i.y variei fro ,0 the0
43 peorce..t of t: d conditioned ar to r.o vcrage of 4 percent n.xt to t:.o
wood ; For t;niS re e.asoa, the rt'- lts in vo t "
...... o's tyjcs of {:iL s
appear ntiy 1, i tU same da, ryia, SC 0L-O .aoy vary ,,idely boca, of a
differ r'.'e i.i ai r--

l:h cffe'ct of air vel oity- oa -r;-a - rate a definite "oi -;ruc- o';-ont
vahlcs is sao'-:n b, t, c':rvc f f. obvios conclu i....s *at
air velocity is nost :. hi "-';. ..o.s. 7"-co'ntCt values, a, boc :::s
relativcl., 1 ni.-- porta-nt b, !o-. ,0 ....c..nt , cont.,nt For thorou-hl_
air-dried stock very little e ty. is n:Ceded except to cst blizs unifrm
dirin condCiltions in all partY of the "i_.

Aotr in.por'tant co.c-.'io. cane '.e.e froo the data as prese'nted
in fi ure 5. >is ,raph shows tne average ryi-y ti:.e in hours of a
4-foot vide cile of 1- by 3-inch *sa--, ..n are sapwood boa-rds ".t.n cried fro"
70 to 25 percent .'.cistture c tt nde r ... ost'it t;:.,Tpcratura. of 130 0 .
and nider th e Jndicatedc,. relative o...::iidios ;n ,ir 'elocities. Th' 'a.a
irdic't. tha.t ..oca --: ;her ai'i velocitie sorc needed for t" "el r o0
c-- "e a s .. e rr~ io it t ,at
relative hu::-dix'.,y sche dules. ..e reason fo :t.:is is ...,';
hluaiditie-, changes in. TL 2uiiibriuj., in, creasily :reactr '.nit> ". it i casess in hu;ii".:ltj, ane as a result the
date i affected by b-y ca.,cs ir. ihmdity lro....t 0ot 'b. an
addition of m:oist-re fro. te. '',2.'. an t.c dop in t across tnea

Definin.. opti.u:; air ve ocity as bein.; so:c v c'city beyo d c tich
the effect on0 :. i.t.. b.:0co.:0s relatively. ,i...port ant, t.e ci.tiXuj;.
valucs :or reliv ....ic.i-i. s of 0, .. .i 76 ercent :..i be selected
0:.2_ cin 0, 4 0, aOL '&0 fe t o:r 2.,.it c
ri-sp ctiv.el,. O"' .... 'or slo r-d. r,'in; sp-c.ies s'c-': as o. ...':, th. .c
vaJue's vS ; be lo'.'cr.a

?e;)ort 7o. ."l''^. -6-

(7) Length of .-ir Travel

As conditioned air passes t]rou-' a loai and heat is used for evapo-
ration, the pro-ressivC. c.... ;os in t ratr and idity rsult in
change in dying rate, an_, therefore, in a drying lag across the load in
the direction of air direction. Undr othrise fixd co tions, the
amount of this l g is governed by te lcngta of air travel, but is not
directly proportional. To illustrate; data 4rc given in t.bcl 3 to show
the time to dry from 70 to 40 percent moisture content at even intervals
across a 4-foot pile of 4/4 sugar maple sarwood. As tne air velocity
effect on tne e iter-e ;-air side is q ite different fro.-. that on t _e 1eavin -
air side, th'e data ,iven are fro:.. three se-oarate air-velocity runs.

ab 1 0o.--Dr--in< ti.e of j/4 ,uar ::.aple sapvwood from 70 to 40 percent
moisture coCnte'nt at definite intervals across a 4-foot wide
pile under an ent- rin.. -air te,.:perature of 1300 a-. a
relative >umidit t of 76 percent

Lent:n of air travel
Air : ----------------------------- --------------- Aver -e
velocity : 0 feet : I foot : 2 feet : 3 feet : 4 feet :

SEn-tering : : Leaving:
ai r air

-0, t pr o rs ,ors : Hours : ours : oOurs rou'rs
minute : : :::

256 : 15 : 40 : 54 : 63 : 69 : 49
54 : 12 24 : 2 : 0 : 31 : 27
c2 10 : 16 : 19 : 21 22
"- "IP *| -; v atp ??r

The dry:n ti..e lag i clach run is considecrbly ru than that
c : bc, .r't d fr; t av- ra .cpar.t droo across the lo0'..
The air, as it tnters the load, is ;. foray in temperature and hmidity,
and -2, cns enutly, te- veloci t-y afft. on te dri.:. rate of the cntcring-
air edg is r elatively svc ali. 'Thc directional force of tne air, howevcr,
pr a nhor. triton of te a.oratcd moisture and heat loss,
and, as a rcault, t air at te lc iavi.g;-air C' o varies :-'catly in
tempPrtk -d, fro:; t %o ,ood surface to thI center of t-li air
str'*,. Tihe velocity of th-c air i.flucaces this nonunifori.ity and conso-
q-. ntl hr's its criato t cffct on t S l vii-air side.

a ,rt !.1264 -7-

The latest difference i. drying ti;:.e occurred within t.he f first 2
feet of the 4-foot nir travel and in each of th.e three r-un txe aw--e_' :e
drying time of the f-'.ll load was represented by, tne drying tie. of t:e wood
located app on:i.I tel 1. 6 feet (or 0.4 of ne total .width) in fro:. te
enterin-air side. At the high velocity, t.nic decreasing effect, of length'
of air travel on dryig time a ,waa such as to indicate tnat t. .e widtn of load
could have been cosiderably greater ,it- onlj a. s..all .:. in average
drying tir..o or i- that of th ioaving-air edge. he effect at th. low,
veloc it Iay ltive ih a.d .iht be akn as s .stin th ir
ability of introd:cin. severAl entcring-air od es withinr the load b- i.eoans
of vertical .fl. s. In other *'ords, it sug est- that two 4-foot loads of
s&-ar .aple s7apwood placed side by side with a space between -ht hav; a
lesser averaC dvi tim one 8-foot load.

Aside fro.-:: the velocity .: hasc it in --. t be well to po-int' out "ere
that *-ap''ooCd boards driedX '-ithout check:ing evn under a relative
amiity of 20 percent and an air velocity of 1,600 feet per .:inute,
whereas the ea rtw:ood boards c:-ched somc at a humidity as hih as 80
pcrce-t. For this reason, if, in sawing and kiln drying 4/4 maple, the all-
sap.ood boards could be sorted from the heartw-ood boards and dried
separately umder a low relative schedIol then tneir drying time
wIould be ,:rc.atl reduced fro,. tnat ordinarily allo-eod for lo run u.aple.

In general, ir needs arc prop rtional to dryin: ra.tcs. For t-at
reason, ,-ir .eds are least for the lo.,wer ; content stock rna for
the slOe'r-dr-ing species and itcc,.s. An exception to this rule occurs whpcn
r.lativo 'u.midities are increased above, approxim.. tely 70 percent. Su,.Ch a
procedue rCeduces drying rate, but requires a higher air velocity to
prevent eoxcessive; increases in the S oisture content of txe wood surface
and, cons'i,.7cntly, excessive loss of ryin time ) y infer.,ncc, tnCn, t-c
most efficient kiln from a dry-ing time standpoint would bc, one equipped to
furnish a .grea.t deal of air at the begi. ":ll and then lesser amounts s
thc moist:ue content of stock and as reductions are madc in
relative hu i"i ty.

.. :-rt R1264

Digitized by the Internet Archive
in 2013

1 2

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o.6 \ \

S0.4 z ,
.'0 \ \^V \\

. 'o.\ \ \ '\ \ \
0.4 \\--\------ ,\-- -\
.'. x^ o "" .. ,,, ,

70 60 90 /00 80 90 /00 80 90 /00
U 37826 r
Figure l.--Effect of relative humidity on the drying rate of sugar
maple heartwood at a temperature of 130 deg. F. and air
velocities of 235, 450, and 980 feet per minute.

| 4 ..... . .

c 3

K 2

4o, '.
S ______3 0 % ______"_____.^ \_

0! _.....

20 30 40 50 60 70 80 90 /00
37oc7 F

Fi-ure 2.--Effect of relative humidity on the dry*,i-r rate of s'!.''
maple sapwood at a temperature of 130 deg. F. and an air
velocity of 1,640 feet per minute.


80 7


40 --- -------------------------
-4 _____
60 Z


0 ZOO 400 600 800 /000 1200 1400 /600 1800

376&b F

Figure 3.--Effect of air velocity and relative humidity on the mois-
ture content loss per hour of sugar maple sapwood when at
a moisture content of 60 percent and a temperature of
130 deg. F.


-- t4 ------------------------------- ---------

"L--.! ................
-- I I

0 /

C- _____ ____ _________ 40 _______________

<-, 0
S 200z 400 600 800 /000 1200 1400 1600

3 31 4 F

FiF-u'e 4.--Ef'f'ecW of' air veloci ty on the dryi7n rae of sujar maple
sapwood at a temperature of 130 deg. F. and a relative
humidity of 76 percent.

400 600 800



1400 1600

Figure 5.--Effect of air velocity on the drying time of sugar maple
sapwood in drying from 70 to 25 percent moisture content
at a temperature of 130 deg. F. and relative humidities
of 20, 50, and 76 percent.




-, 60





4 37~'1 F

0 .....---
_ \__..._... ''"-"


II3 1262 08866 6242I 11 1 111111
3 1262 08866 6242

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