ACE No. UII9 [ NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS WARTIME REPORT OtlG»4ALLy rSSUED Noveniber 19^4- as Advance Confidential Eeport L4I19 THE THEORY OF PROPET.T.ERS II - METHOD FOR CALCULATIHG THE AXIAL INTERFERENCE YELOCmf By Theodore Theodoreen Langley Memorial Aeronautical Laboratory Langley Field^ Va. UNIVERSITY OF FLORIDA WASHINGTON NACA WARTIME REPORTS are reprints of paper -Iginallv issued to provide rapid distribution of advance research results to an authorized group » / inr ° q for *he war effort. They were pre- viously held under a security status but are now uncias:- i-^-'. " -no of these reports were not tech- nlcailly edited. All have been reproduced without change in r. • ■, expedite general distribution. L - 157 ■) . NACA ACH No. L4I19 NATIONAL ADVISOPTiT CO!i!:^ITTES FOR AERONAUTICS Ai'VANCE co::pidt/tial rlpo;it THrL TmOHY 0? PROPZ^LIERS II - T^iETFCD rOR CALCULATING T?JE AXIAL INx"'I%nPER.SNCE VSLCCITY By Theodore TYeoAovzen SU^:MA"{i A technical -nethod :. s given for calcv-.latlng the axial i.-itcrf 3rence velDcity of a pr-ofeller. The -nethod involves the nse of certain v/eight functions ?, ^, and F. liumer-ical vrluos fo"' the weight function? are given for two-hlade. three-clade, and sLr-blade propelleiT . i.yinci^ciiciT It has forriierly been the practice to u?e the jlauert- Loik simplified assumption that the interference velocity is proportional to the loading at the point considered. This assvinption is obviously inadequate since the inter- ference flew depends on the slope and curvature of the loading function rather than on the local magnitude. A method is developed herein for calculating the axial interference flov; for any loading. The method is accui-ate to the first order and therefore gives the interference flow in ratio to the loading for small loadings. It can be shovm that this accuracy is adequate for all technical applications. The present paper is the second in a series on the theory of propellers. Part I deals v;ith a m.ethoc? for obtaining the circulation function for dual-rotating propellers. (lee reference 1.) sy:,ibol3 V]^ axial interference velocity at -/.j^ | V2;('x2\~l w rearward displacement velocity of helical vortex surface (at infinity) 2 COMPTDENTIAL NACA ACR !Io . L4I19 V advance velocity of propeller p nuinber of blades n order nijitiber of blar'e (o ^ n ^ p - l) CO angvxlar velocity of propeller r circulation at radiuc x K circulaticn cocfficTcnt to firrt order (7=.--^— i X nondimensional i-adiup in terms of tip radius X]_ reference point at v/hic-i jnterference velocity is calculated 6 anjular distaace of vertex element fron propeller advance ratio ( v/j-'^B. ) tip radius of pi^opeller function defined in equation (1) function defined In equation (?) P used for fiC--"") in tablet; and figures; refers to other blades (n ^ G) Q used for Qi(x) in tableo and figures; refers to blade itself (n - 0) T phase angle of nth blade \—~-i \ p / / 1 \ \ cp-j_ helix ana;le at x-|_(tan --— j \ "^l/ WEIGHT FUNCTION Pn (?:) It can be shown that the axial interference flow Is given by the expression cokpide:;:tial \ R Pi (X) Qn U) NACA ACR No. L4I19 CO^TIDZI'TIAL ^1 _ 1 \" rclK ^^1^^^^ , ¥ " dj ~ X ax ex where the sunvaatioii is over uhe nuuber of blades to p - 1. -he iraportant furctlon Pn (x) is defined as Pl(x) = d 0-- 2(1 1 u I' 4tt'-'/v. ■\ ''• :"' + Xt ^ - cxXt cos (u + 1 1 V P VLTTy' where n = 0, 1, 2, ... p - 1, the nuiuber of the par- ticular blade. The problem is thus essentially solved by TTTAL KACA ACR No. L4I]9 6 = C. This difficulty, v;hIoli ocr-ui's only for n = ( chat is, for the blade itself) , is ovsrcorne in the following manner: The expres^ilon -; c Jo Ly4A^'^ \| 4l^A.'^ '\}:' ----- + 1 -: i '^2tt ') 1 2 ]^ (2) vi?Lich is integrable and eqr^al to iO' \' T ZX. may be subtracted from F-i (>0 to yield a finite and sriooth integrand. Thus, by subtraction, a quantity C0:':FID2NTIAL NACA ACR r.^. L-1I19 CO"a;'TDE"TTAL Ql(x) = ! Var^v ^(.>%xi--.x-ci cos9).(|^f Jl .(l^J J=V(---'=-@-W 9 (5) i? obtained. Finally, for the blade it?elf (n = 0) , Pi (X) = vn (x) + F where I ^ - - -\172 lo- >'1 The integral Q-i(x) If convenient for graphical integra- tion and i"., in fact, ?,r:all in conparison v/ith the function F. coi':pidi.i:tial CONFIDENTIAL NACA ACR No. L4I19 No di scent inuities arise in the F functions for the other 'ol?.des (n ^ 0) . The t functions are there- fore used directly in the calculation for the other blades. It should be noted that the functions T, 1, and F are all syir-mstrical in x and xt_. The use of the subscript, v/h3ch has been used to indicate reference to the point x-., is ther'efore discontinued. Iri the following discussion, the functions ana refer to the blade itrelf and P refers to the other blades. .X- .dP dx' Since the v/eight function is needed in the form It. l: v'ritten as dp ■QX It is to te noted that by far the lar-erest contribu- tion comes from the logaritliiaic function F since it really represents the entire field in the neighborhood of the point considered. In developed form, X' 9=1 dx \l xx-i '^ r loc X (4) MJiERICAL EVALUATION 0? V;EIGHT FUNCTIONS Q, T? The we i frh t f unc t ions ' , and P are shown m a series of tables and figures. The first step of integrating against the anele 9 is omitted for sim- plicity. The functions £^ and ~~ have been obtained dx ci:-; by graphical differentiation of the Q, and P functions with actual calculation at the end points x = and 1 for accuracy. It should be noted that these functions and their derivatives are continuous and smooth, results are given in the follov;ing order: ^he CCIxTFIDENTIAL imCA kCL l.o. L4I19 C0K5-IDErTIAL 7 (1) Table 1 and figure 1: Q acMnr.t (o 1 x 1 1.00; 0.1564 i J^i 1 l.CO; \ = -r, 1, and 2), obtained fror: equation (2) (2) Table IT and figure 2: ^ against x (o ± X ':i 1.00; C.1564 i x^ 1 l.CO; \ =1, 1, and 2), whrre -,— !^ (0 ^ X '^ 1.00; C.1564 ^^ x^ | 1.00; ^ - \, 1, and 2), obtained from equatjon (].) (5b) Figure 4: P(x) - P(l) against x for t = eO*'^ (0 ^ X S 1.00; 0.1564 i Xt ^ l.CO; \ - ^, \, and 2\ (Ca) Table VI: carre as table V for t = 120° (6b) Figure 5: san.e a.? flg\ire 4 for t = 120'^ (7a) Table VII: .<:arr.e a? table V for t = 180° (7b) Figure 6: ?air:e a? figure 4 for t = 180° (8a) Table VTII: scT.e a? table V for t = 24C° (8b) Figure 7: sar.e as figure 4 for t = 240° (9a) Table IX: sare as table V for t = 300° (9b) Figure 8: san.e as figure 4 for t = 3C0° C0:'PID~"T'TAT. C0IIFID5NTIAL NACA AGR No. L4I19 (10) Table Xj -~ against r for X = ~ (t = 50' o^ dP 'dy. "" '" 2 120°, ISO'^, 2-^.0°, and 500^; x = and ] .00 0.15c4 ^ X2 -5 1.00), obtained analytically (11) Table XI: seme as table X for A, = 1 (12) Table XTI;- ?amc es table X for X = 2 (13) Table XJII rxd fipure 9; -x--.- against x for X = I (t = 60^, 120°, ieC°, 240°, and 200°; 0.1564 1 :: ^ 1.00; C.1564 ^ x-^ < 1.00), obtained by multlTJlying values in table X hj -x (14) Table XIV and fifui-e 10? satr.e as table XIII and figure 9 for X = 1 (15) Table XV and figure lis sane as table XIII and figure 9 for X = 2 (16) Table XVI and figure 12 ; > -x~ arair-st x for ^_ dx - . three-blade and six-blade propeller? (t - 120° and 240° for three-blade propeller; t = gO°, 120°, 180°, 240°, and 200° for six-blade propeller; 0.1564 ^ X ^ 1.00; i x.^ | l.CO; K - \, 1, and 2^; it may be noted that these- values for two-blade dp r propelle:'' are given by ~x-^— for t = loO in tables XIII to XV and in figures 9 to 11 APPLICATIOII C? :iETHOD ^1 steps to obtain the Induced velocity expressed as are as follo'-vs* o dO (1) Plot the ouantlty x-— against the circulation coefficierjt K and perform graphically the integration h ^^ CCKFIDEKTIAL NACA ACP. No. L4I10 COtrPIDENTTAL (£a) i^v.-. .:..:x^c,-ly the functions x-^ ar;aliist K r^ X-.— d/C ax Since x-?— becor.ies infinit'? at x ■= x-\ , it is necen- nx -1 J- ' , CX ] cary to exclude a "rap fron x-i - •^^ Ax t^ xt + 7^ A> and to con"ider this givp sepai-'atTly b^ use of a Taylor expansion . (tb) xhe contribv-tion i'rom tlic gap Ax bocoir.es A = -b :r^K" + /l - io lop -^jy'l A where Ax = 2 [ X - v^^ j t = — ^:r: + X ~ = sin cp-i 2 ^ c = coe'^cd. ^ " 4. V i\. + Xt and K' and K'* are the derivatives of I'v rlth respect to X . (3) Finally, there is a contribution from the other dP blades. This conti-ibutlon is obtained by plottlnr x-^ aK'^'-inst K for the other blares. Since the valur <~ dP y^ -x-rr- can be taken directly fron the tabler, this v/ork contains only ore step vith "• •^'..-igle graphical integration cc::?iD-:i:,T?iAL 10 COi^'FIDSNTIAL KACa ACR No. L4I19 Ey addition of the results of steps (l) to (3) , the total interference velocity v-j_ in the axial direction is obtained. The relationship betvtfcen the axial inter- ference velocity v-^ at the radius x-^ to the axial displacement velocity w of the vortex sheet nay be seen from the sketch in figure 13, The relation is 1 2 v-j_ = -^-w cos '-r-^ or, conversely, the dj splaceT.ent velocity w of the vortex sheet may be obtained from the calculated axial interference velocit;r V]_ by the relation 1 ^ _ _Ji_ _ Vn^ which gives the axial displacement velocity at the pro- peller disk. For the case of the Ideal loading this axial displacement velocity must corne out as a constant, thus per.nittlng a check on the v/eight functions. Cases of nonideal loading are evidentl3r of ir.ore practical con- cern. It is the purpose of this paper to give a Tnethod for calculation of the axial Interference and displace- n^ent velocity for any (light) loading. Langley Memorial Aeronautical Laboratory National Advisory Coiir-r.ittee for Aeronautics Langley Field, Va. 1. Thecdorsen, Theoaoi'e: The Theor" of Propellers. I - Determination of the Circulation Function and the Mass Coefficient for Dual-Rotating Propellers. NACA AGH No, L4H05, 1944. CONFIDSKTIAL NACA ACR No. L4I19 CCrPID~''TIAL 11 e-- OT l-i «»: c < o rnlCVJ II o x; »-l f-H a as h ' — - El. o 5- NO NO 3 o to> f\j r— l-H LTi 00 o K? K? o o o o l-H f-l l-H Oj OJ • • • • t • • % • • • o 1 1 ITN 1-1 K-N 1 1 1 1 1 • S 1 LA I. A o ^ r«^ o KN ?i C1 rr\ l-H ITN >• o «-H OJ KN Ov O o o l-H l-H l-H CJ OJ OJ CVJ o o 1 I 1 1 I 1 1 1 1 ■ t-:" vO ri LA o- NN C-- OJ -:d % r— * ^ > 0~ LTN O NN LTN ^ O s (-1 VU fvl l-H UN ^ ■ rN r-- C- OJ o ViJ l-H OJ NO a>. c\ -I- nD t^ lO CO o o o o o l-H l-H l-H l-H rH c o 1 I 1 1 1 1 i 1 1-t r-l rj -h' l-H r^TN CO c> rT% o «-< \s\ u^ t~- ■n tc. rr^ LfN OJ K\ r~ p 00 o mJ o LTN CJ Q o ^ r r^ o 1^ c^ ON CvJ -d- in \S\ C-- o O o o o o l-H rH r-K <-i cr o 1 1 1 1 1 1 1 1 -4- 3N xO s> -3 l-H CO LTN IT. L-N 00 N^ Ir. CVJ ON OJ I-H rH UN t-- KN ^ ON l-H l-H UN N-^. K^ t- co o CvJ o rCN nO CD c •-\ <~^ li^ o O o o O o o r^ 1-^ o o 1 1 1 1 1 1 1 CO vO l-H vO Ou r- KN o UN ^ o 0^ CO o CJ t^ IXN t^ UN i?i> CO O I-H KT o o l\l ^ P l-H o o o o o o o c o o O 1 1 ~^~^ 1 1 r~ o vO On l-H ON -+ C3 c^ ^ (~1 T-\ CO ^ LTN IXN t^ € o cr> CO ITi OJ CO vO IM c^ C-- c? t-\ O CO vO KS T-i o rH OJ rrs r-f l-H o O O o o CN o o O O 1 1 1 1 cff ^ l-H C-) — t iH in l-H U-N a t^ m g; CJ U"N M^ ro CO hA f^ c C3 a- CvJ ir- o3 l-H o 0- o ^i co O o ON UN CD o / t-' fON -:1- ITv t^ CO CD ON 0^ o • O ■ • • • • • • • • CO o >H < o « l-H fH E-H Eh 6 TIDZ^TIAL NACA ACR No. L1I19 COIJr'IDS'ITTAL 12 •a o 3 U 4-> « O O I 09 CI cv ,_^ CJ g o o o o O r- o o f-> c ~. CM SO On C .-h' S 'Vl 3 3 I I I I ^._. OJ NO r~ t-i CVi o _-■ r- vO c^ CJ Li c— -:.t NO 1-1 UN o 1 r- C5 r<-^ p CO 00 s UJ 1^ ^ &( r < rr\ o ^^ c-~ ON ^ ^ o O o i-t ,-t r-l r-l rl o o i 1 1 1 • 1 1 1 1 1 xO o< r-i lr^ c- o o a 2? o r-l f<\ UN -rt KN cn Li» CM (1N (-1 r-i o iB o o OJ «s> rH CO S^ ^ ON o O o r-H 1-1 r-> rH 1-1 r-t i-l o o 1 1 1 ITN 1 1 1 I 1 o 1 cu CO Pj ^JD o rvj fOi U\ IfS o LfN CM L-\ tVJ l-l r~ ?J' o- O t- t^ Lr\ ^ CO r ON 1-4 u% '"N l-t M ■ lT. t- JO Ci o O C^ O r-H rH r-l r-* >- <— o o 1 K. 1 o 1 1 CO 1 1 1 lO i-l ON OJ o o i-i o S t«"\ _7t IT, LP* rH ON o ?(? le o o ^ OJ s 1—1 NO CO o o o o r-4 .-4 rH rH rA rH o o ! 1 1 1 1 i 1 1 1 o di CO CO • o • • o • • 1 • 1 * 1 • 1 • • 1 1 ^ -1 K- CM -»■ ■JN rfN NN '£) t-\ NO r-l o r-^ r-i ^<^ Lf> -cf r- o -d" _^ _^ OJ t;^ Cn S- t'"^. _;r ^i _tr OJ O 1—1 fO, -:t ir> r- r- • o o • « o • • o • r ■ • • o • o • o / LTN ON OJ o CvJ O O KN rH rH NO OJ I^ UN LT, o o CO O o -d UN O c c^ C- 1-H CO o CO o^ KN (^ I nO O UN o rH O I "On I r-. K\ C' o I r-l NO r- o I Ll> o KN irN K^i CM o CD CN O O IJN I-l f7N C CO OJ o l_ --t -zt -cr Lr\ OJ Q CM r-- C O CO NO CO o o o KN I NO KN <£'- O.' o I I ON o K> o CM L> u^ OJ K-\ -^ KN K"N o o -rf o CO LT. O rH ON o KN lA CM i<-\ KN nO C C I 'Id-' UN o CO KN CJ O I CM c~- I o I OJ o I o O'- •'& c 8. 8=- 8. o cr o K-\ O O Q O On 0> Ch On ^ ^^ ^ N^ ^ o o o o o in r-l o O 00 L^v CO -a- IT. C> rH CO c;> UN CO O O'- o o O CI n Ch >- '< fc o C/J t-H tl fs- <: C") «J s ^ tl. (-H E-< -* 1-H CJ g:^i •'J c o t5 F- o < C n o g u. rj o i-i ;^ l-< ^ Kl 0^ o 1-H oo ON ro, f-* ^ rH CO r-l -:t r^N r- t-- o O C^J -3 NO r^ c^ o rH r-» r-l ,^ 1—1 o o O o o r-l rH i-t I-I r-l r-i 1 1 1 1 1 1 1 1 1 Lr» OJ o rH 1^ CD _:t rH CsJ CO r^ o t^ i-H ro •-I O t-t CO o o ^ 14 S f^ o c^ CM CI I-I ir\ r : rH iJtN o o o o o o rH f H f— t •-' o o « 1 1 1 1 1 1 1 1 l-H p s t— r- r-- ON o r-l TD »-< o C-- (Jv (-. QO r-\ C-- 1—1 r-l f— < K'> UN 3 CO -t C~- O CJN OJ rCN to o l-H LT* r- oo O o rH r1 cr o o n. O o o rH r-i rH r-l • • • • • • • • m • • o o t 1 1 • 1 1 1 1 • I-" L-^ CVJ CN L-N vO r- CN ^ r- n C\J s r-l CvJ i-H -' t^ r-l CD KN i-i lOv -o K> ^ oJ OJ CD CM -3 'TV < ■> 1-1 fr\ L> 00 o O c:. o CD o o O O o o o I-i I-I 1-1 o o • 1 I 1 1 1 1 1 1 OJ CTi i-H vO _r+ _^ •o rH C' ON Q o CVJ ^ ro vj r-l le CJ _rt ON 0> r- I-f ^ L.-> CN pr\ r- ^ rH O CT (-H --r U\ C^ CO co 0-- CO O o o o c o o o o o • • • • • • • • • • • o o 1 • 1 1 1 • 1 1 1 r-< CM ■c€ •o 00 ^ in t^ o. r-l :?■ r- r-l vO c\ r- o cr 53 -J- f~ X) o t-* c M K> L•^ LTS r- t>- r- • (■"; • o • o • o • 1 o 1 O 1 1 • 1 • 1 • i_ 51= CI CVJ o "^ I-t oo f>- -^ s -J- t- r- ir» tr-. CO 5 1—1 lO f-H r-( CvJ M-N -ct ■S\ iPi nO LTN o O o O c> o o o o o o o 1 1 1 1 1 1 t 1 1 ^: L*" CVJ OJ vO r— OJ s c 1-H Q _^^ ^' iO t<~. _v -f r-\ rH u-, -^ r- .-t -t CM R,- NO o 5f c\ lA r-! o o rH CM KN -J -^ O c o o O o O o o o C o 1 1 1 1 1 1 1 1 CD o t^ _-r cq OD LPv o CM ^ Q o r- ^- CO CM ^ r- t^ O o rTN Q v<-i r-l o ^ o o CM r— ' o O O l-t r-\ 1-H CM K-. O o o o O o o o o O O c- 1 1 1 1 1 1 1 ?1 cr- no vO OJ CM r-* rH u> o ^ o -cf OJ o C^ (M O c 1—1 UN ^i t~- ^ t-\ t-- ir\ h^ r a- C" r - t>- ?^ f^J t>- r- (^ r- fi- '7^ CM ou CJ CM CM CJ CM CM c o o o o O O o O O o / c5 §. 3 00 l-< 8. O i-H I-H r-< r- r- / L^ o ■4^ cn o c (r- \s\ co O t / 1 t-A tc- J- L\ t-- CO co O o- o / o •- I-H t- ul ^^ ^.. C-1 O U I-I f- ^ r4 CD o COITT'IDS-TriAL :"ACA ACR T'o. L4I19 CONFIDENTIAL 14 Pi ■a kvi o Hi •a: Eh ^ -:t -:t CM cv Qi ON o o ON ^^' CO CVJ 5)^ r-l Cv o ■— 1 s un Kj ITS ?^ 'P r-l K> N^ o l-H CVJ CvJ CVJ OJ K^ M^ K^ K> f— » O 1 ' ' 1 1 1 1 1 • ' S a ?i o o « s c\3 I ir\ OJ LTi r- lO Rj o r-l c- r-» OJ CJ CJ CVJ fON ^<^^ K-> tr\ o o 1 ' 1 1 ' ' 1 • ' -J- CC 3 Si o CO OJ a o o ^ ^ L^N r-l LTN t-- CO R? o r-l r-l CVJ en i-l C\j C\J C\J CO rrs K\ ro K-\ o O 1 1 1 1 ' 1 ' 1 1 1 o c -X) OA o lA CO r, lA Q r- K-. ir\ c o 1 1 1 1 ' • 1 1 1 1 r o Xi •'S CM IJN i:^ O a l-^ r-- r-l ^~ ■ r- CTn o r-l r-l ir\ r-< i-" Al CJ C^ CVJ CVJ NA K> hA n 1 1 1 1 1 1 1 ' ' 1 o vO CO o vO o ^ Q -3- o o cr> (\j o r- o o ^ >.\J CO re. J^ KN [S\ r- o r-l CJ KN -3- o r-" i-i CJ OJ CVJ K> hTN KN KN c» o 1 1 1 ' 1 1 1 1 1 ' o LfN <^ o 00 ^ Q ir\ \S\ ^ t^ C\J :^ LPv -cr -:+ c- CVJ ^ O r-l Lr\ r-- i-i 1^ lA U> K^v o r-( r-l CJ CVJ OJ tr\ ^> K ••"■. r c. 1 ' 1 ' 1 1 1 1 1 ' o o 6 o s fXJ LTV -i o -CI iS r-l ^o hO. a Lr> CO to\ r~- c- r-4 CM o c 1—1 CJ CVI K> K-. _^ ^ O o 1 1 1 ' ' 1 1 1 ' L'N c li^ Li"i cf- IXn O r" o o t - I—I CVJ rj CO ^ CVJ o o OJ CI r-l ce •-: c- o o i-i CV NA -d- --r ur. irv o o 1 1 1 1 1 1 1 1 1 r, c .■<^- C - CC 'Tj CD Cn -—1 -> o ITS o r-H £^ CO in ^'b^ urv o o o 1— ♦ cr. CJ ^' k> r-l 1—, 1 1 I 1 1 1 1 1 >^/ •:^ 9 Ci I- r-l a o l-l <— I r • / i/\ c^ iC? 0) o o J> m co o — < K> _;+ H"< t- CO CO O^ C o 1 / .-: " • k • • • • • • ^^ ^ "^ f-i o o i-i 5 o M -1! COKFIDEIITIAL ■J.^A ;.CR No. L4I19 COin^IDSNTIAL 15 •a o 3 -P c o o I X w l-H r-« O c^ Q K? o CO r-l K? O ir> ^ ^ t^ r- CO r-i KN t<> t-t CM OJ CM CM t^ N> ^^ K-\ o o 1 1 1 1 1 ' 1 1 1 1 ^ U-N O u> LPv LO ITS o o o hTN LA ?. C^ P CO r-< I-I ^ CO OJ '. ^ t-H CvJ OJ Ol CM ^f^ hr\ hTS f-< K-. -d^ in KN m CM O ir» co i>^ c^ t^ ir< t-- CO J?^ O r-l rH UN .—1 I-I CM OJ CM CJ o> ro r<> h^ c- O 1 1 1 1 1 ' 1 1 1 o __ Cj LT-. r-^ .^> o o ir. r-l o -+ LTN NO c • 1 ^ p S^ CO o c^ • O « 1 • (^J • OJ • CvJ • 1 • 1 1 1 • t c 1— 1 >-.1 u^ o c ir\ ^. o LTN S O- (~ ^U ^ c>- _d- fC' Lr\ On o tJ^ c r-t y^ r-l rr-. -^ ir\ K\ o r-< r-> CM CM OJ ro K> K\ KN ^^ 1 1 • ' 1 1 1 1 1 ' ^ c 1— 1 ^ iS^ c o CO o I-I L.-N ^ ^ LTN ir\ c li^ l-H C UA o u^ Q. -; . LTN t-H o o .—1 f— ' OJ KN ro _:t o o 1 ' 1 ' 1 1 1 1 1 o r-. K^ c,- cc' CJ ^' C rH ON o Ll-\ f; —J hfN CO ITi ^•' L"N o CM rH OD • 1 00 lA t^ o Lr\ O vO vO 00 MA K> ON r-l c • c o • O • 1 i-< • Oi • 1 • • 1 • • 1 ^/ ^ 'H 3 CO .-1 B. r" r-l r-l 1 — t r^ t— / LT. o LO CO c o O ir\ CO o /^ f-< rf> J- lr> c^ CO CO C> c^ o / ^ r 1 . — 1 CO o r— I < e w Ed E-i CJ g CO COIIFIDZ'JTIAL liACA ACR No. L4I19 CONFIDENTIAL 36 0) 3 a -p p o CI a Er ^o K> 00 OJ r-l c o o o to CVJ rn _;j l-> CN ^.^ o LfN o UN C) o o UN f-i § CV CV ^ "c^ l-l 61 1-1 o 1 ' 1 1 1 ' ' 1 1 1 1 Cj o o o vO o u> o o LN a o o o L'N i-l o o t-i CJ Si c 3 o o 1 1 1 ! 1 1 1 1 1 o o 4^ o. ■>o o o •o o O 5 in o F- ^ CO J3 r-l cvl 03 o l-H r-l 1-1 1-1 i\l CVJ CJ CJ ► ^ o o 1 • 1 1 1 1 1 1 ' ' 1 1 L!^ -4 v^' C\' o c:> LTN O o CO p-*- OJ #—■ ^ r> OJ LfN K fo >H UN o c- « CJ t^, ^ ■ --t H ^^ o r-l ^ : t—* ,— ; CJ CVJ r\ CJ • • • • m • • • • • CO o <-l 1 t 1 1 1 1 1 1 1 n i > o l~. O LTv o ro f ' sO r> U"N '^, u^ . •■> c IPX O 05 t-t CO O o o 7-i f— 1 r^ OJ CJ ce -^ UN CJ ^ C' 1 1 1 1 1 1 1 1 1 1 O t-i F-i < o Ll^ Ll> LT. Q O, o CO LTN o hO- u^ t- c^ vr) _M- cu c C— c? ^^ Lf V o l<~- <•■ JN r-l ^ \ LP* UN o '-'"' C o r** rH 1— ' CJ CJ CVJ CJ CJ c c ' 1 I 1 ' 1 1 1 ' a o o o ^0 o J?. o o o LTN K~^ vU Cv rH -•t vO r- -3- c o ■— 1 «-H l^-f rj CJ CVJ Oj CJ o C 1 1 1 ' 1 1 1 1 1 O O ^ li^ o KN (6 s CVJ CVJ KN IT* o K\ o CM Lr\ f- CO CJ N- C o r-l CVJ ^^J OJ CVJ CJ OJ r^ G 1 1 1 1 ' ' • 1 1 ' O OJ Q K> o vj OJ ^ - ■ *\ CO c OJ t^ 1—1 -' 1 , — w o :> r-TN ^- r-l K? c— CT o o CM o o r-H r-l CVJ CJ CJ hT t^. c o 1 1 1 1 1 1 1 1 1 1 o R o o ••s ^J co ^ CJ CVJ ^_^ i»> CO OJ vO F; CVJ h> r-i c. o (— ( .-^ CM OJ K^ t>r f-N o 1 1 1 1 1 ' 1 1 ' 1 5 CO -t- ■Jj) >o L' V r-' r-l c- f-l s ^ r-l CVJ C c s. Q c — "''■ 'O -cr Cn W'. O -:3- C-- c^v o o — 1 r— « 0.' K> fo K-- KN K- c 1 1 1 1 1 ' 1 1 ' y ^ s^ 3 CT) r-* 5^ c> r-l r^ c^ / Lf\ o •-^i cu o o CN ir\ ^ O / r~' .■'^ J- L^ l"^ CO o c- o /«" • • • • • C0!TTD3-TTIAL r NACA kC3. To. L4I19 CO»TFIDZfITTAL 17 R; -^ OD r-l C\J rH o o 9. o o 8. c— r«> ON LTv crt 1 t:- CO g O r-l I-I r-l CJ Ki -■! 3 rH O 1 1 1 ' 1 1 1 1 1 1 ^ r— giv, o o (-1 OJ CJ lA P 1 o o O l-t r-l OJ S CQ s o O 1 1 ' 1 1 1 1 1 1 1 r-< o N^ OJ r- u'^ r— ON rS CM -::J of w O o rH 1—1 rJ r-l CO OJ C\J c o 1 1 1 1 1 1 1 1 1 n 13 1 t-J O a o m Lr\ CO ^^ NO CO r^ ^^ vM on g c —1 o CO CN K^ ON CM >-< 0, Cv O a- o r-l 1-1 r-l ON rH ?. OJ CO K? -^ tw d • • • • • • • a • • • ^ o o c 1 1 1 1 1 1 1 1 1 o 1 w •-> o o r-l o r-f r-l NO ON o CO o CJ CM O ON o t-< p 5 c. -§ • o • • • 1 • • • 1 • 1 • 1 • ^ to ,-H 1 o M c r-* ir» o o CO o CO tX\ Lr\ 00 NO tH <: o r- r- rj ''_!^ r-l -t CO OJ <-\ K^ Eh c- o »— • UA o -rt t^ VJN o CO Cf^ ■^ <; < t^ o f— ) i-i r-l •-K C\J OJ CO OJ a c C' 1 1 1 1 1 1 1 1 1 O" X .- 1 T3 -O II tn o ro ^ r^. r~> o L!> Cf.' u^ CD t^ LPv C- o\ * tr. rH CL> OJ Qi rH S5 ^ cc U> o K> ■7n rH CJ ■sx c? L'N C "^ j^ o o r— 1 r-< r-" '"J CJ OJ CJ fc^ .^ o o 1 1 1 1 1 1 1 1 1 K -^ 1 £ - ^ ^iv c — f^ o C\J 3 UN ■s ITN L.N fr. _^ CVJ _;i o- rr- r^ rx •^ e U"". 1^ a- ho vO a rH CfN tf> NO ' O o r-< r-' <-H CM OJ OJ OJ rj t-H o r^ 1 1 1 1 1 1 1 1 1 l-H 1 U o Lf'. OJ r-l CC' c~- OJ (~. OJ o C'l ^. CO ON ^ 00 LfN tc 9P. CM 9? '^* N> C! o r-< 1— ( CO OJ OJ OJ OJ E-t • c • • • 1 • 1 • 1 • 1 • 1 • • 1 • 1 ;H c 8. S °9. o ^ o o CM K? LfN u*- -«■ I^ T^ rH ^ 5R o ,-^ w-l r-l o o r-l r-l OJ CJ K•^ K\ KN o o 1 1 ' ' 1 1 I 1 1 1 1 5 00 J OO vO L■^ rH T-K ON r-l cn KN LP\ 0-- ^ /—• 3 rH c Cv o g • r c • 1 • 1 r-< 1 • 1 r CO o O ON UN co o /^ 1—1 IV- J LN C-- CO CO CJN o ."7 /^ ' I—* COMPIDENTIAL V.hCk kCr. No. L4I19 CON^aOErTIAL 18 a •H -P a o o CO C5 cvlx Eh I ►J CO OJ u ■ — i-^ O o o c a t>~ o C\J o r^ ^ a a fo OJ -:r r- ON o rH , • ■ -d- o o .-) f> r- .— < >-( r-t rH '-' r-t r-t o ' 1 t 1 1 1 ' ' 1 o (M ii> ON CO r- ^N ?> vO o K: CO rH OJ 1^ vj N4J 3 IH -:t r** Cn o r-t OJ r<> o o o o o r-H t-i rH r-, rH rH o 1 1 ' 1 1 I ' I 1 1 vO i-i u^ o CO o o vO P 03 ^- Qi CVJ ^^ l"- t^ c- O OJ £4 OJ -1 t- c- o -H OJ NN ,jf]* CO o o o o rH r-H r-i r-i rH r-t -^^ o CO 1 1 1 1 1 1 1 ' o rH -^ (^ f:. (3i '0 g^ c~-- r-i CT CJ r-t _-t S -I r- c o o f "' r-t r-i rH r-t rH o o ' 1 ' 1 1 1 ' 1 ' -•• o o v-* CO CO f) o vO S a:; o p ^^ c- uD o K> '-f> c; o^ c ■ o rH ^^ -J- _j -:t --0 o o o o rH rH rH rH r-t r-t ^ 1 1 1 1 1 1 ' 1 ' ' a) o o c^ O o t^ -f 00 vO ^,i lO 5^0 CO n pj CM ^ !? S ij-\ o O o C' r-" ■-^ ,-i r-J r—t r-^ o o 1 1 1 1 1 1 1 ' 1 1 f^. o u - o ^J o rH o o f^ a^ OJ UN CQ o rt CJ a> ON o OJ N> _-t UN ITN -c' c o o o i-H r-< rH rH rJ t— * o c. 1 1 ' 1 ' ' ' 1 1 t t-< o Lr> r> o ^C' r- a> o CO ^ o C\J ^^ o ^ CO a ^f^ K\ ir> c^ Cn o i-> ir\ ITN l;-N r<~ o c o o f' r-4 i-t ■-^ i-i rH C 1 ' 1 1 1 1 1 ' 1 1 J- S^ a o o ^ o CJ ^ rH I— c>- O- r-1 'AJ _:j U-A ir> U^ C^ c o o c- ( — ' ^-^ rH rH r-l rH o c 1 ' ' 1 1 1 1 1 ' ' u. C\J CVJ Cn ■■ o o o sO f: S-( 1— 1 OJ l-H rH R? LTN s 5 r—' r- ./- r-. rH r-t r~* r-> r-^ .—1 • • • • • • • • • r: ' ' 1 1 1 1 t ' ' o C-- v'S s< •^.N tr> CO _-t _:t t^ VjJ U"v O IT. -rt f- Lr\ in c ^^ 'H O .— 1 C\) rH -::t QJ ib^ S CI o o o ,—4 rH r-t rH r-t 1 , o 1 1 1 ' 1 1 1 1 ' K / ^ o Q o rH Ss o t—' t- / c- -::t- t^ t^ rH t-t C-- / liA o m ^, O O c^ LTv co o /, r-« to, -d- f- CD ro o> o o 1/'^ < "■.' r-l to o fH M a 10 o t-t f-t CO^IFIDZ'JTJAL r 1 'A^A ACR No. L4I19 CONFIDENTIAL 19 C c o I CO < 'vis o O H ^ •a 0) T3 D u o o I H M, vTVJ OD CJ o o UN _:t Q 85 f— 4 in C-- o o o rn __" ■ t^ o OJ CO r~- t^ O o KN o CI -:J C-- CN o i-< CD -:f -i o o o o o r-^ i-< i-i r-< »-l l-H '- o I t t 1 1 I 1 1 1 t~- CM OJ o r- o o O o CM 1 ij Fl 01 CO o r-t ?^ 3 i^ c o o o f-< r-< r-l 1-1 1-1 o o 1 • 1 1 1 1 1 t 1 ' l-H c> CO .-1 CO o S CO N> ON _-i r-4 ^o t^ l-l CM 00 NO :^ o 15^ OJ -d- t- On o 1—1 OJ ro c- o o O •-i i-H 1-H 1— i 1-1 1-t e o 1 1 1 1 ' ' 1 ' 1 1 o o N-N CO ?^ CO t:- vO C-i nO o <-4 c— CO <-l t^ vO NO a-> 1— 1 CJ ^ OJ -cl r- Gn c l-< o; KA -(• -4 CO o o o o r-< r-H i-< I-' 1—1 I-I o o 1 1 1 1 1 ' 1 1 1 R K\ o N-\ c CO •^ ^^ nD o CO r- a- CO l«l^ r^ o On % OJ o C\J c— Cn o r— f CO fo. -J- CO c o o o r-' (-( 1-" 1-1 r-* r-^ o o 1 ' 1 1 1 1 1 1 1 1 1— • c ^ o l-< CO c— o 0. N- ON p E^ C-- t^ CO c rn K^ o CO -ct o 1—1 CJ J- — ^ -^ c-^ o o o o l-H •-• t-* r-1 I-I 1-1 o 1 1 ' 1 1 • ' 1 1 1 OD Lr\ o o r- OD ON -4- CJ ON '•^ f- CO o ro, Ki C^ CO o rn IT, o OJ ir> r~ CN o «-l KN 7? -^ lOi c o o o 1—' 1—1 i-i i-< 1-1 o o 1 ' ' 1 1 1 1 1 1 3 c o o c , o r^ c c~ R^ o p ^N CO o ^ to, :h QI 5 c- o o O t-" l-> I-I 1— • 1-" I-I c c 1 1 1 1 1 1 1 ' 1 1 (~ f-^ o <> o &.. 1-1 -i- u . ■x> _-t -^ 8; c AJ — J "c\ CO o OJ ro, o in f~ C^^ o r^i ir\ in m r<^ o o o O r-i 1—1 1-1 •-" I-I 1-1 o 1 ' 1 1 1 ' ' ' 1 1 •s5 U"% c^ CO r<" 00 7n CM Nf oo ON c^ '^^ r-< 5^ o ?^ fi^! -zr c~- CO LPs CJ C^ r-< -ct L;■^ in tn r-* c o O o rH i-< I-I 1— t 1— ' 1-1 o c 1 1 1 t 1 1 1 ' ' 1 s ^•^ 8^ iB IT. in 3 ■fi In ITN c- CO o rH CVJ i-< c^ 00 iS' r>- o Ol l-^ O hr. -cj- liN vO r e • o • 1 O • 1 • 1 r-H 1 I-I • • 1 1—1 1 1— 1 1 V ^J 8. o -3" 8> s 1—! 1-1 / in o '-'> co - 00 CO 0^ ON o c- 1-H to I- 1 w M E-< I-) £a o o >-l e CO H I t» o M r-i COI;?IDErTIAL I I MAC A ACh ::o. T4T19 COin^IDRl'TIAL E- C/J -o l-d o • N -^ E- I -:r ■^ -fr Ol CvJ CT. C\ o o O (.M CM ^ i-< ^1 o r-4 «s IT. c; lTN ^ rH hTN rr o /-H Ol KN K^ r-l o CJ S "cm" __ CM r > CM O L^ o t-4 l-l % 'R^ LTN «0 IV ^ :> 1-1 r-t K? OJ CvJ CI CM CM w k: o o ^3 CM Oj LTn s o s O '3 KI 5 e-t fC\ i^^ o VU 1-4 3 Oj Kx r- CO cu 1-1 r— « 5?. .— I CM K? fj^ ^ Lr\ CJ o o ii> o 5 en o CD 00 LA X) 'K, Ox l-l .-- r-1 1— t~- l-l a .^ l-l CM l-l CJ c CI c -) . ^ — O fM CO o C.I O (.) o O^ o 0> o l-l — J o r-t CM 1-4 v3 ^ lO l-l LTv r- r- CO CJ OD vO r> i-H 1—* .—1 J— 1 1— t r— l-l l-l •-" o o Li^ o ^ .".-. c o il\ o o o o ^> ■t CVJ CJ i-\ U \ iX\ L'N u . .-> r- CD 1-" KN C-- cc CM t~ o .-> co o OJ hO ^'^ -:j' U> u'^ LfA LP, o o l-< I-* i-» 1— 1 l-l l-l i-< Q o o — ^ CI o -4 o Vi> o o O a to l-l o C3 ^ o CC CM to\ LPs C-- 0^ o O CM KN MA -*- o O o o I-H r^ r-1 •— > l-l l-l c o o L. \ -5 o ^ 8 a CM LiA r, -d^ o c> :2( CM ^~^ 1— t LPi t-- 1-H K> -h f- CJ CN o O o fC-. ^> o o o o o o l-l r-l r-l O Q o o c Q 8 o o 5 o CO CD O CD ccj N~- 1 ^ O o r-l l- c^ -:a CJ CJ o l-l C] -^ ITN (--x sO c^ '."> C^i OJ c t"^' o c o c o o f"> o c c •J^ p. ir> ir% O} L'-\ o 83 o C' r— CM ^ LPl o o 7i 1-1 s- CO C^J o vO rH o ^ 1-^ CM rr\ -a a> L-A r-H o o o o O O o o o O O c o o o C-' o O o o o o a >- / ^ ;^ ^-^ ^ r-t ^ r-l r-i l-l / ITx o \S\ CL' o o C^ ir\ 'H. o / I-( ^<^ -J- LTN r- CO cr> Ov L> o / '^ c r-t b E-" E-" 1—1 ^' e 6' u CO l-l ■AL r I L4I19 COMFIDINTTAL TJ O 3 C •H -P o c> X x» a> E-< ■3 CO 3 s r-H »-« O < e- o << o ry\x 1 X 1 u ^ o 1— 1 ^-^ p-1 a) u *fc.^ B 1^ 1 • i-i !-l l-« Cd 1-:! OJ «; F- •^ -1 -^ ^ o OJ ON o o o r— LTN oo --r r^ c o o <3^ CVJ in S KN en rH o r^ o <-< CJ OJ OJ OJ CVJ KN KN tf\ N-. r-< O r.-N ir» L^ ^ CO CO r- OJ -t CO t-- O r- KN nZj L> cJ vO UA 5 CC' t~- CO o N^ vQ ^ r- ON o §> in CVJ L'^ *0 t— CO o r^ CJ H\ 1-1 CM C\J OJ OJ OJ toi t<-\ r<> K\ O o o li-N r-t K-\ ON L> c^ UN vO rH P-* l^ O 0^ r-t ir\ CJ t^ ^Q' C> 1—1 f-4 o S o ITN o rH r-< C- l-t C\J OJ co OJ KN t^ ^^^ o O o — ' 1— ) CO CD o LfN iB' rH rH S OJ l-H CT r~- F; IT. r- «^ CVJ r-i CO Cs' ON hfN o ^ LfN i^ CO CO R? 03 r-" t~> OJ OJ C\J CVi CVJ OJ O O > CD (D t-- s: c-- CVJ c^ c~-- rH o LP". ON «^ nO co r- r— NO K^ ON ce r- rH CM (> -3 oi o f- rH o c^ O CM tf> KN LTV LPv nO Oj rH i-f cu OJ OJ CJ CVI CJ CVJ o o o r^ 4> OJ K^ OJ r^ rH o c-^ vO \0 -+ ^ s ^ o ^' s c O irN r- 00 o O I-I r-i CJ c- i-( f-< 1-1 r-1 (M OJ Oi t\J OJ CVJ c o o r-t nC 5 -3 L"N o OJ CJ NO CO rrv CJ 5- t<^ liN OJ ^-: r- t^ LA c- 1—1 ^ fc r- OJ U'N» co t>- 1-1 hTN J o t-- CO CO Lr\ O i-H 1-1 1—1 rH •-< rH r-i r-i r o J ON L'> 5 o H- u> •WD ^<^ o r^ Q LA C- -i ON c-~ O CC rH Tr\ -5 OJ On o c> K^ UN s t-; -cf O o O I-i rH t-l r-* r-i r-i 1— t o o CC LT-. LTN IT-. rh. r-l f~\ r-l O o c J- t-- 73 O -^ \S\ ^ LfN o o o m Cvl c- CO -3- hTN CO o o i-i rA la \ vO t^ CJ ON C o rH K--. o o o o o o o rH rH r-i O o so K", a Cn iT. CO r-i c> r<-\ <£> _:;+ r-< 1-1 OJ r— > KN o C^ rH rH C^ IT. O o CO o i-< o 3 -^ ^ ^ o »— t o o o O o o o o o o r.- e O c o o O o o o o o o X / ^ o Q CO rH o o rH r- J O" -:t f~- C^ OS r-i rH r- / IT. o "_J oo o o c^ LTN ^ o / r-l ^r -t ir\ t^ CO CO c^ o / ^ c rH c n f ^ 13 [:i o o CO Q H o t-i Eh COlfr^IDENTIAL A.CR No. 14 119 COJn^IDENTIAL 22 3 -P g E- CO HH <: !-• e < D o-lx ^ ■o!-3 ,o E- Si r~- -o K> o CVJ 1-1 o c> o o (M CO r-l CN r- o UN o in o o r— • g g 73 CJ CVJ 1 t^ ^ cc T\J »— * o n o o o _M- o io o o u> r~- l-« o rTN c\ ^ CVJ rn 00 rH >o ?i^ in O _^ ' o >rN t~- c^ ir» K\ ITv r-- CO ^ l-H 1-1 r-t o o o r-t 1-1 i-i 1-1 CVJ CJ CVJ c c- c o o O CD o o C3 1—1 O o CD a CVJ CJ H € 5 ^ CO CVJ -3- CD t-l ^^ irv vO r- 00 i C- CO CO CO ^ c-~ "IJ -? c:> O s^ Cn in in -;f s o -d- r- 1-1 KN -d- in NU r^ r~ o o O r-l 1-1 r-l 1-1 I-I • f-* • • c o o o o o o CO o NO o o r. OD o 1-1 o ^ ^ CJN CO rCN r^ CU _:t l-< r~ -:. CO O KN ir\ CO o 1-1 CVJ t<>. -^ in o o o o 1-1 1-1 1—1 1-1 1-1 rH rH o r: (^; L'^ IXx LT. o c o o Lr> o L'^ c^ c— r- o o o ^ r^ o vO c^ s t<^ CO r~ CJN in co o CI -t o ON o 1-1 CVJ ai KN u-\ o c o o o 1— 1 1-1 1-1 i-i l-t r^ o c P; o 1— - c -f o o ^ o CO CO CO CN.I CO o °1 o ^, ^ p oo 9i -a- o o o -f o o o o o o o 1-1 l-H rH c C' o o s o IT i^ IS ^ rH rH ?^ 3 o S S CVJ CO oo IT* iO 1^ o o o o o o o o o o o r S R 1-1 CM o 8 CVJ 1 in o -+ CO a s o in 5 CVJ o c o O O o o o o o r- o o O O CO CvJ o NO cr. CO 1-1 g CVJ CVI re- o o l-H r-l CJ CVJ CVJ r-^ N^ KN l-H o o o O O o o o o O o o o o o o O O o o o o O ' / 8 o -3 CO 1-1 8. o 1-1 (-1 l-H / LPs o IT co o o CJN in ?^ o i-H K-> ^ ir\ c— CO oo c-v c J - 00 o f5 w w 6-1 fH O to > o (-H <; C0NPID5.NTIAL ACR No. L4I19 COKTIDU'TIAL T3 O Vj r •1-1 4' c c o 1 « Tl e- CO CVJ r-> o a o o CVJ C) -Cf t-< CK >- o LfS o ir» r- b\ rox Q^ ITV -3- CO cv CV t^ °3. o vO r-l \S\ p~ CV 1-1 CM o3 o o T-K I-' l-t i-i OJ CVJ CM r— 1 o .o 'Js CM o o CU O CM t^r « 1^ 3 1-1 r-l s CO IVI L'A O ^ 8^ ^ i-< e— 1 On r^ r-l CVJ CM CM K? rv O vO -t •j^* rH r-l CO o 3- s CO ^4J r^ O -if rH CM CO CM eg VJN O f-H »— t l-f 1—1 (J OJ CM o o ^ r~ ^' vO O ^^ t~- CVJ rH ^A o vO CM IfN ki o C>- •S f> 1—1 ITS vO KN ^- IVJ a) O -rt Vi) o i^ c^. rcA UTv C^ to c- rH rH rH o o o rH <-* i-i r-l rH CM C^J CO o o J r^ VJ •< ^ t~ OQ CO UN t^ o u-% o C— 0- f\J On 0^ NA Q^ 0^ ^ CO CD o -3 L.-N ^ ID ?^ -^ CO o C) i-< •-I T-* rH r-* l-H i-i i-i o o 1—1 :S n i-t ^ ^J CO ^ UA OJ t- o f\J r-I rH t^ t— v'£' o CVI 1^ — ^ r~ o CVJ N^ -d- \J.\ r- f- l- o o (-• i-< 1—1 rH 1— l—t r-l r-l c o rr\ CA c~- N-, ;j K-v r~'- Ai ^ rH ;0 r<~^ -t f— 1 CJN vO o N^ — ! o t-- 5\1 c- CVJ -cr -c^ <^ Si ^ co M> LA cu Q^' 1— < rrv _:1 -:t LTN o o o O r-< r-l r-* rH rH t-f O o CO fA K^ CVJ fO K^ CD O CM r~ 00 S 03 s § CO ON CO ^ rH r-H o o _:f o o o c o o r-> 1—* rH •-' /-^ o ^ r-l irv cc r-< ^'S' ^ PJ o CD CO f3 S f- o I— i OJ --i Lfv VO t-- 03 CO cr» ^<^ o o C' O o O o O o o o o vO CO o -• _:J- r-l r*~ !^ _d h'N ^ _-!■ r; r<^ Cf> £^ CO CM rO o t— -ct l-f ?;>■ N^ CD h < C-- Cii Cn ur\ o r-l CJ rcN S". -3 -d- -•t i-t o O o c O o C~> O o o c o o o O o o o O o o o o v^ ^ n cc r-l 8. r-l rH c — / ir> O ITv CD o o C-- LfN CO o /.i r-l hr\ -d- lr^ t~~ to Cl 0> ON n / '^ r r-> 1-1 o (X, a Hi .J o o O CO t-i > O HH E- cc:;fid3-^tt;.l !:ACA ACR No. L4119 CCllKTDSN'TIAL 24 I g bJ U u I o r.5 3 (M cu O O o m -CJ o R i-t ir% C-- o o o t<- i~ c> C\- C3 r- 5:^ Q CV '•jj vM .-r t- ON O rH CVJ -:f _^ 7? o O I > o o r-« 1-1 .-t rH I-H C/) • • 1 • • • • • • • • fl 1^ O o "5 CO r > r-i o P,^ ■e{ O r-t -;■ o n ^ :^ ;r< 00 r- <> o Ki- rvj o o o o o o o r-l r-" iH rl »H [.1 o o '.] -o "^ r o o on 5i ^ 3 «3 0.; -\ u> r- 'O C" o f-1 rH r-< -J -". •"^ • o 1—4 f— • • • • o o r-« f-< -S • ) C.J i — ^o o ^■ c lO O tH CO f-i i-t ^ C3 VlJ C-- fO, CI S o iB- 1J^ OO •§. O o c. c^ o O O c o O o o «-l •"■ CJ o o >-• to o O o o CO ^ o CVJ o CO vS^ C^ o '•> vO :3 I—I 00 u> t*- M rH K». _-t Li . r~- C-- 00 CO CJ t-- •-0 o O o O o o o C' o o i^ c c ^ o o o L . o o L \ o S r~ H- o L.N GN c .-> K-s C-- -> i^: ( ^ _3- u> vO >i s vj OJ N-s -J- o rJ fVJ K\ u> o e'- c- t-- n Ll-^ o f^ O C o '"^ o er^ o o O c 5 o T- ^ -*■ c:> s i-H a r- "li 3 Ln &^■ ^ 5 — o o O o O C' o o o o o o p o o ^i ^ Ki" :o CJ o a- -4 r— * CO LP. rH OO (\J r- r-H m:5 ^ vO o i-H rj C\J to N~, -3- _:+ J l<^ e o o o O O o e o o c c Oj 5 o «• o 00 o CJ iX.' CJ on K s ••o -t v^J OJ _^ u> >\ OO IT* s?. O iH -H o 6 I-H rH C\J CVJ CVJ r«\ r<^ K-. C\J o o o c c- /—J o c- c o o LTv a (VJ p.- • r-t o s O nC C"v /-•^ I-H 1-t n L> s rH fl -d- l^ r. 1—1 cV ^ U\ vO o o o o (— T 1— ' l-i r-l rH r-< .-1 o o o o r c o O o o c f o ! - c. D o o o c o o o 1 ^/ y^ 5t f- 8 o I-l «-l rM u>> o ir\ f^j o o U^ CD o /^ 1— • • • c~- • CO • a • • / ■< r~ •— rll^-'^I/X 1 i rACA ACR No. L4I19 CCNPILENTTAL 25 o c G O • CO I :3 o l-H O T1 ~ o o o K-. CVJ ^ r^ o CJ 03 r>- t~- s (V to o OJ -:i c- g^ o iH CVJ _; ' -:r o c o o fH 1-4 >-i 1-1 l-H t-\ r-l *^, CO 3 R ir, § NO ITN CO i5 o 73 r-< "P OJ J- m5 c- o i-< CVJ ro» -cr -J- 0> o o o o r-* rH «-< t-K 1-1 1-1 o o rH c ^ NO CVJ OJ ON O S s NO iS rH LTv IT. r-- CO OJ i-t ?^ ^ LTV a\ CVJ ^ vO 00 o 1-1 ro ro. KN ON O O O o l-H 1-1 rH 1-1 .-< 1— t o O xO -d- r- t-- LT. CO O Lfv t^ OJ o CVJ CO C> r-. ro O OJ 1-1 (.O KN CVJ 1— ( NO OJ OJ CO c o o o o 1—1 (-1 1-1 1-1 l-< (-^ f~ o I ^ s? c^ I-" 'VJ ^ C3N 00 1> a- CO IT. l^ -f CVJ OJ J UN o CVJ lO ir\ t^- 92 CIN o r-t »—* l-H CO o o o O o o l-l '-' (—1 1—4 o e rH CJ ^ ^ S ro> CJ 1— 1 Lfv ^ ro. r- a- li> f-i i& r^N O M^ 1-1 i-< ( • 1-1 KN L\ t-- to C?N o^ C5 o c- o o O o o o O o r-l 1— t -.> o LTv o r-" OD vO ,"^ Lr> c^ vO o CO I— ro 1-1 ON £4 to, at 1—1 CO r— lA CO CO m O o C; c o o c o o o O c § o s o § ON o^' ^ ^ NO ON r- ' 8i CVJ --i s c« nO ^ J- • o • o • O • o • o • CT • o • c • o • o • ^ N-N - + LfN 3 CO CJ o CVJ r O o 1— < CJ CVJ ro. r.> -cr ^ -J --t • o • 1.1 • o • • O • o • o • o • o • i-« .-^ to a^ rr o C; X l li^ V? -J- K OJ .-1 Lf^ l^ o o Ol y u~> o o l-H r-" i-< CVJ CVJ CVJ r-t c o o o o CI o c o o o c o o n o o o o o Q o o ■ /' ^ g 5t ie 1-4 ^ o l-H 1-1 / u^ o LN CO o o ON ir. % o / r<^ -rt \S\ C"^ CO CO C> c / X • • • • • * • • • • l-H CO C-N s o 6 g M O o F-I coi;fid3i.tial I KACA ACR i:o. L'1119 COMPTDEl'TIAL 26 I CO M < <; K n O '< t-i E-' .-^ I t3 s r-l ^ vO "cO o R ON CO S; 8 O o sO o Jj* -o ir\ 01 ^^ KN 3 C/N 1 • 1 »• ■* •- ' 1* f—l ^< r-i 0* Ji cA t^ ! 1 • ' ' 1 1 1 1 1 s 1 1 r~- K> K^ o ID -J- \S\ ir\ ^^ 1 - CO o lO l< o o On K -o^ rH O K? ON o g • • • « « ■ • • • • • C' ,--. 1 t-H 1-H r-» CM KN UN CO u^ &H ' 1 1 ' 1 1 1 r-l 1 MN M CJ -~Zj NJ r-l ^i C^ F- rH vO ^- « r^ H % K-, E-i .-< CJ ON G> r-l -«j QP fc-; On r o o S? ^ RI +1 r-* c^ K • • » • • • • • • O r-< 1 .-( rH »-* rj hfN CO r-\ CO o ' 1 t 1 1 ' 1 rH S)-. Zr' f^- t-\ "•"err' 13- 0^ C\J i- ir. g o r-i ON CI o t— C\ OJ r-l nO t<^ ai LfN LOi r** UN r-l to 03 o o IT, .-1 :4 a ?^ 8 +1 ^ ^' g • • • • • • • • • • • o 1 r-: 1 1-4 1 r-< O.I LTN 1 NO r^ r<^ l-H r-l ^- ^^ NO CJ OJ C>~ o ^ vS Ml 3 u. & g. o CJ C' O <.\J -•« UD ■i-i iS\ -:* CO r- E-i C' r ; 1 1 I r' 1 Cv'l 1 1 -J- oJ r^ r-l t - 0,1 (^ .4 f-< 8 C3 NO LTN CJN CD y-N U^, r-l o O o "•ij ri K-, CO OJ ^ u^ o r- c 1—' -:J r 1 o M N^ c- o o • • » • • ■ • • ■ • • o 1 r-- 1 I-" 1 ^-f r."". r-l rH r-i r-l o vO l-A - * \S\ rH OJ t^ _::r CO K o -I- ^*-» vO ON nO <-^ r- .-J o> vj e C\J N^ CV) -:J O O cn o vO o r-l rH t^ o h"% 5 u■^ o CV ro _::?• 41 vO CO CD t~- N_> • • • • • • ■ • • • • o »— 1 f— : 1 1 1 CM r-l CO ^ t-'. p<\ L'N "S" rH UN CJ o IXJ X>- rr t- Q t- C\J 3 ^ rO\ iT 1—4 t~- Kn 5n U>i R^ b\ o CO On KN <-* CO r-< LJ _-+ o — ^' t- +1 C; (?^ MJ -»■ ^ N^ H: r~. »— * 1 1^ 1 1 '- K r-t r - f— t t^ «~*. 'AJ t<: -* R o l-J 0^ r-t -T -1- rH rx "F- K\ ^ r- cc O Cvi 4:i -^ o c> o 5: +! fN V4^ --* r-" ^ ^ K? . « ■ • • • • • • • • o r-' 1 "Y r-l f>^ f:: Viy o IXN CL. JN r- :" o P. Kn |x^ r-' to i3 C! CVJ o CJ ON r^ o i*^ r'^ CJ r-*- r-l rH rH r^ f-l • • +1 • • • • • • • • O 1 o 1 o O o o CN o O o (•: / 1 ^ T' :^ r-l 8. s r- in o lr^ CD o o c ITN cp Ci / r-" •r. ■♦- ir- r- CO CO C '^\ w^ c / f-\ • « • « • • • • • • / ^ 1 o CONFID£i;~IA: I '■'A^A ACR NT. I4T-19 CC^yFTDE^'TIAL a C C o I K -1, -c l-o X o l-l u ss I Eh n OJ o o UN l-l OO r-t r.> (~i l-( O o ur\ o vO lA I^ 8 o o ^ N^ in o CO r-l O r-l r -^ 1 r-^ r-l 1 oJ oj 1 -4 1 lA r-l 1 OD ITN 1 .-1 ON o vO "O a> ^ KN Kn t-- P -::f -rt -d- CO o (VJ K^ t- ^■^ oo O r-l LTv 3 OD f'^ r-l ?^ o o ^ ^ s ir\ C^ 8 00 rH • • • • • • • • • • • o i-H 1 1 «-t OJ 1 OJ 1 1 1 CN r-l vO LTi C\J ^"H IT. o ITN ^ i-i c O rH ITN o o ^^ LTN NO ^ r-l O ^ r=^ tvJ fO o t^ -::t h"^ o ^'^ -i- S "^ fQ ir\ l-l 8 CD .7x o l-H N^ CG fOi rH O KN • • • • • • • • • • ■ o .—4 1 1 1 1 C\J 1 KN 1 LTN 1 OJ r-< 1 CO K^. r-l Q^ oo i-H CO rTN CD r- O ^ c • c> p o t>- CJ -J- (T) r-i I-H K\ r-1 vO r-l OJ CJ r^ ■-^ o n Lr^ c; OJ J LTN S 8 ^2> OJ CJ o cH _-t CO UA O -•t K^ \S\ c> i— < 1 r-< 1-" 1 1 oj 1 -4 1 CD o r-l vO LTN ri 3 CTn ff LTN LTN 8^ r-l 0^^ o 8. o ^ o l-l KN l-l OJ "^ 8 p 00 o r-l ir\ o CM 8 l-l o o CD • • • • • • • • o 1 1 i-H 1 OJ 1 ro 1 1 C-- r.A KN OJ o o r-l CV) t-- OJ OJ J- sO r-' "t^ CN OJ ^ o ro ITi rH O r- vO ro> I-H hTN LTN r~* KN K% ^ o a OJ S OJ o ITi 8 a LTN CVJ o P i& • • • • • • • • • • • c I—* 1 t-l 1 1 0.1 I 1 LTN OJ CJ rH •"" c^ ^-^ r— 1 vO cq CO Cn n£) CN iX. c- CO K t— -^ to K^ CJ -:t t-- t~- C- C-H o t- -^ o ITN r-t QJ o M> OJ O t^ ^ o LTi KN o IT. o ro» o o 8 CO -J- rH O o • • • • • • • • • • • r 1 — I 1 r ^ 1 1 -J- K^ r-< r-H r-l r-" r-l f^J -J- r-l r-l -f hr\ CD vO K~. 5} k; r? LTN 5 r-< LTN S OJ r-l UN r-l l-H 8 OJ r-l t>- r- c^r ^ r-l _-;J- 6 b^ O CO J- 9^ r- vO NO c -^ r-l t 1 oJ r-l -^1 o CO a> r^ c ^ Lr\ C\) Q r ■< -a C\J IN r^ -»• CD r~ C^ O ^ 00 5^ a> CD C3 OJ O o C\J cB' ^ r-\ c-~ ITN u^. N \ o o 8 OD o -Ci -* KN K\ KN • • • • • • • • • • • o 1 CO 1 I"-* Q o CO r-{ CJ o -J- S r-l _-+ o t<\ CJ t^ i^ t- o o 8 CO UN r-l r-l tO\ 00 r-l r-4 r-t r-l NO r-l o i-H 1 o o a o c o o c o O O V •4 o r-' 'O 1— 1 e. o t-l C^ ^■\j c^ _^ r~- r~- r-< r-t r- u^ o m CO o o O ITN CO o /„ r-l to -^ IT, r- OJ tc l> c^ o A' ^^ -- o g b1 H n o o 9 t-i fH CONFIDE-N'TIAL r ■^ACA ACS Ho. L4T19 COIIPIDEIITIAL 28 o O a o •4; o I > (xl CJ II C\J 3 CO CO 9P CM ^ 7^ a 0. UN rCN l-H § .3 a"> l-H S 5: 1-K 8 • • • • • • • • - --I 1 1 1 1 1 CM 1 .>fN < 1 CO 1 1 i\; r-< N . NO LTN CD ^ ^ t-- C\J « fZi ^N Q. ON r- ' {^ -rf r.i -J en t;: •-H CO V.' i-t N*J KN r~ KN nO CM L,^ C_> r-' .H »^^ ^^ fO* rH -t ir\ 8 JN c > _, r— 1 ._, r-H CJ ro LTN ON -;f l-H 1 1 1 1 ' 1 OJ 1 I— On cc Lr\ KN nO rr- NO r- ^ r-H r-' ii -^ r> -3- nO m CO r^ ON P r-* l-H (r\ C irN r-l On fM (,N r-< lO IfN r- CM L'N t l-H OJ 1 1 1 f-H l-H 1 C) N . 1 nO fC C'J v^ u> r- f-* (-( aN rr\ t^ r-t r - C— •T. CO t^ f^ f-1 ON CJN c« cr> C-- rj f-l c^ i^^ CO <■:! l-H ■*N CO nO 1-4 8 00 l-H CvJ • • • # • « • • « • • ° 1 1 1 r-i OJ 1 "T" 1 •-- CO r-- ,-, b^^ r; ^^ r-t CN ^ Ki ^' ^J ON <\J KN ON U-N a- a' •r\ 8 CJ 00 LfN •-•vJ rvj KN 8 g ^ • • • • • • • • • • m . — t r" r-' 1 'M 1 1 u^ -3- K- r- > ^; fO V * V.1 CO CO i-H .— ( ?. f^ _-+ ^ ^ p ^ 3 r-- *_i ■. K- f^ 8 LT. ^o CO tf" t- CJ ^• i'**- l^ K> -J- LN CM !-• • • ■ • « • • • • • • 7 1 1 OJ LfN ■0 N-> CJ OJ CJ a> U-- .-4 C\! ^ ^ fO LTN Cn i-H ?o ^ c 3 01 CO P ICN CO C3 U> tO *-^ 8 rr, ITS l^ l-H ^^'-— ia-> K> N> ir\ -d- t- hT- CJ • • • • • • * • • • • T 1 CM 1 1 — i Ot •- '-' •-' •— •0 CN p -+ OJ CO CJ f NO r-- _1 rj Cn -^ NO cy r (.\j r- CO ^ r'~\ t-- lT- -S c. L^ K C>J l-< CO C^ t— 1 1 1.-- i-i -■ KN t^ L'> G^ v^ ^ -i rH CO •~i ON ^ L'^ c^ fO NO r K? 8 ^ OJ R: NO o- CM X) r-' ^'^^ c l:^ -J t 1 CJ 8 U ^ ir- CJ CJ 1— • l-H 1— ' • • * 9 • ■ • • • • r-* rj V ^ R Q CO ?. i-i iTv U\ CO ON u> ^ c r-t KN -=l ir r- to CC c^ c> ' r-J • • • • • • * « • • / ^ .#--^ CO 1-4 to Fh o o CO '.3 tP ~ "T;- ■•^. L-1T19 CONPILENTIAL eg TABT.E v.- FJ-'CTTON P AGAPIST x FCR j ° 60 i^>x 1 1 !o.l561ii 0.3090 0.5978 0.9090 0.0511 l.CO 1 '-> ^ ' - 1 0.15a 2.2!i78 1.9613 l.Ii950 0.8830 0.5696 0.U113 0.^600 .3000 1.5673 1 .1+980 I.2U15 .iQ-iG .a^65 .3580 .30U6 .5676 .9.259 .0830 .76i;6 .5li;6 .5280 .2250 .1866 ,80c« .6oeiJ .5696 .i;9ce .3260 .10U6 .IUU6 .0826 .9511 .Ui82 .UII3 .3580 .2230 .l'U46 .oUi.6 .0213 1.00 1 .3986 .3600 .30^6 .1866 .0b26 .0215 1 (t) X = 1 1 o.l5<'i; 2. 21^12.0200 1.500c O.883U 0. 5700*0. i+200 o.373i; .^300 1.5655 1.5000 1.31^1 .8267 .5300 .3800 .5500 .5^76 .9^23! .r£3'i ,£267 .606? .3^001 .2567 .213ii .80<^0 .6C39 .5700 .5500 .3900 .2UO0| .1367 .1000 .9511 ..'4/-25 .12*30 .3800 .2567 .13671 .0567 .0267 1 .ro T. 01.! V77l. .'3 ?0 .21.^U .i--^:' .^267 t (c) r = 2 0.1S£ii ~^.\121 2.2335 1.5200 0.8667 0.5^33 0.^667 0.31^3 .3OQO i.iicoal 1.5200 1.2667 .7700 .I;900 .3367 .2867 .5876 .3U£3 .6667 .7700 .5^67 .3667 .2500 .2067 .8090 .5^95 .535^ .U9OO .3667 .2U3^ .1^67 .1067 .9511 .3678 .3667 .3567 .2500 .ii;67 .o6:;o .0267 1.0. 1 .3177 .3153 .2867 .2jt7 .1067 .0267 1 i • NATIC"^'^, ADTTSORY caa-'ir'^E3 fcr aeromautics COi:?IDF.KTIAL 'AC A AC . L-i 1 i ^ COIIFIDS^ITIAL 50 TABLE VI.- FUTICTICN P AGAINST x FCR T "123 — T 1 0.156; • 0.3090 1 0.5378 JO.JO9O t 0.0511 _. — . .. . 1.00 1 o.i5Ch j 2. 2r 2511. 669^- 1 . 2393 0.8000 0.5377 o.'.96o 0.35U7 .5090 1.6:20 1.2393 -QS'i") .646O .4360 .^i£o .2313 .5'376 .0606 .8000 .6U6O .1+260 .2777 . ■'.8-?^ .16;0 .80GC .■^:3i .5377 .ii360 .2777 .1693 .0977 .0777 .9511 .laC29 .^^60 .3160 .1693 .0^77 .0360 .0167 l.OD .i4:'53 .^5a7 .2313 .I6ii0 .0777 .0167 (I) \ - 1 1 1 1 o.i56h 1 2.'+:63|l.323^ 1 .5900 0.9067 0.6500 O.^;100 0-i;6lC • 3090 1.73 55; 1.393:. 1.1100 .75<'7 0?^^ ./iiv.^ .le^i .5376 1.09231 .9067 .7507 .!;9t7i .3l'3.^ .6090 .7739 .6500 .530c .3:^3 U .2:0? % ^^ J ' ^Ov3a .9511 .6125 .5100 .u^u .23:/j a^O') .0700 1.00 .562U .i;600 .•36$a .2067 .093'^ .0300 1 (c) \ ^ 2 1 0.15ci; 2.U79U 1.C93U 1.51^3 1.02^7 0.7267 0.^600 0.5067 • 3090 1.7^65 l.=;i3^ 1.2300 .8800 .6067 .^^-'^ .liOOO .5376 1.1=^55 1.0267 .C&OO .6000 .3934 . y. -:7 .2200 .80^ .3^621 .7267 .0)67 '393U .233 '4 .l'3^ .1000 .9511 .67U5 .5600 .U53li .26(:7 .133U .-^53i; .0267 1.00 .62L'h .5067 .iiOOO .2200 .loco .0267 NATIONAL ADVISOI^Y CCi'J.-:iTTEE ^02 AEROiJAUTICS CC::i'^IDS::TIAL NACA ACR No. L4T19 COMFTDSNTIAL TAI?LE VII.- FACTION P A'}Ar:ST x FOR r - 180° 31 _ N. X X^ \^ 0.156U 0.5090 0.5878 0.8090 0.9511 1.00 (a) K . ^ 0.156a 2.1518 1.5666 1.1586 0.7106 0. 1+653 0.^220 0.2786 .-^090 1..U713 1.1586 .9320 .5973 .3920 .2753 .2320 .5876 .3299 .7106 .5973 .3986 .2575 .1756 .1386 .8000 .512U .U655 .3920 .2573 .1600 .3986 .0600 .9511 .3^22 .3220 .2753 .1736 .0986 .0^470 .0220 1.00 .3026 .2786 .2320 .1366 .0660 .0220 (b) \ = 1 0.156ii 2.^063 1.6e.67 1.2667 0.8100 0.5600 o.Uioo D.36^U .3090 1.6255 1 . 2667 .9931 .653U .U531+ .3300 .2931+ .5878 • 9828 .8109 .6531+ .^367 .295U .2031+ .1767 .8090 .6'':59 .5600 .i.53ii .293U .I63U .1100 .0831+ .9511 .5025 .I'lOO •3500 .203U . 1100 .01+55 .0200 1.00 .U52U .363U .293U .1767 .083 It .0200 fc'l >.. = 2 0.156i; 2..U06D l.7ii35 1.3000 o.euoo 0.5953 0.U633 0.1+200 .3090 1.7251 1.3000 • 9933 .6533 .i+600 .31+66 .3066 .5378 1.0821 .81+00 .6533 .1+200 .273^ .1966 .165^ .80Q0 .7623 .593^ .U600 .2733 .1600 . 100 J .0733 .9511 .6011 .Ue33 .3U66 .1966 .1000 .01+00 .0200 1.00 .5511 .t;200 .3066 .1653 .0733 .0200 J 1 , . NATIOIIAL ADVISORY CamiTTEE FCR AERONAUTICS COIIPTDSl-rriAL VkCk ACR Ko. L4I19 COIJFIDET^TIAL 32 TAHi.E VI IT.- FUnCriCN P A'^xAL.i;? x FOR T - Sv"^ 0.155i^ 0.3390 0.5673 0.8C90 3.9511 1.00 (a) X4 0.156U 1. 878-3 l,U720 1.1153 •3 -5693 0.2C0O 0,1220 0.0680 .30<^o 1.1930 l.il5^ ,93^0 .5^53 .2e5^ .1267 .5876 .5"^ 66 .:69' .5U53 . 14066 .2U13 .1233 .0773 .8093 .2391 .2800 .2353 .2i|13 .1573 .0707 .01+53 • 9511 .073Q .1220 .12c7 .1220 .0787 .0^20 .0120 1.00 .0293 ,0680 .0720 .3/73 .•j1;53 .0120 (b) \ = 1 0.1S£ii 2.02-96 I.5S67 1.1833 0.6767 0.3967 0.21+00 0.1853 .3090 l.^L8? 1.18-^3 .Q653 .5933 .$600 .223li .1767 .5878 .7071 .6767 .5933 .'4C67 .2567 .1653 .1267 .5390 .3672 .3967 .3600 .2567 .1567 .0900 .06:3 .9511 .2253 .PJiOO .22'U -1^53 .0930 .01+33 .0230 1.00 .1757 .:'833 .1767 .1267 .0633 .0230 fc) \ = 2 1 0.156!+ 2.1927 1.703^ i.33'3 C.8167 0.5500 0.5730 0.3167 .3090 1.51W 1.33^3 1.0Q67 .7300 .1x767 .3330 .2767 .5^78 .863^ .8167 .7^00 .5200 .3li33 .2200 . 18'^ .6090 • 51^95 .5300 .U767 .3ii33 .2167 .1267 .0933 .9511 • 3878 .3700 .3300 .2200 . 1 267 .0567 .0267 1.00 .3377 .3167 .2767 .1800 .0933 ,0267 1 1 - ... .... NATIONAL ADVISCI-Y CQf.l'ITTEE FCR ALRONAUTICS COIJFIDZirriAL ,..,: .v3R Mo. 14 119 C0MPID2NTTAL 33 TAIXS IX.- TTJNCTION P AGAINST x FOR T - 50O ^ D ^.l^jO, 1 0.509010.5676 1 0.8090 0.9511 1.00 o.\5Ch l.lil98 l.i.953 o.giioo 0.3100 -O.OcOO -0.275ii -0.5U00 .":o9o .739? .9^00 1.0566 .ii566 .0766 -.1531 -.?J..~U .5673 .0979 .510c .h'^CS • UlOO .2233 .0235 -.065U .0090 -.2i;6 -.o6no .0766 .2233 .2100 .0866 .0155 .9511 -.579e -.26^.h -.153U .0253 .0866 .0U66 .0066 1.00 -.1.^91 -.31^00 -.2U3U -.063U .0155 .0066 (b) X = 1 0.1'= 6U 1.1296 1.3U67 0.9567 0.2I4.35 -0.0967 -0.2700 -0.5200 .5090 .7ii86 .9567 .9067 .1+100 .0553 -.1600 -.2155 .5578 .1061 .2U35 .Uoo .U533 .1333 .0167 -.0367 .0.001 -.2126 -.0967 .0533 .1833 .1900 .0900 .0567 .9511 -.5742 -.2700 -.1600 .0167 .09:^0 .0567 .0200 1.00 -.U2U3 -.5200 -.2153 -.0367 .0367 .0200 (r) \ = 2 0.156U 1 . GlQh 1.96JO 1.3000 0.553!+ 0.173U -0.0100 -o.o6:o .3090 .9985 1.30X 1.1200 .c53u. .2331+ .0867 .o.^3ii .5878 .3555 .5551 .653U .5234 .3000 .iU5l .oeoo .8090 .0362 .175U .28314 .3000 .lUZh .0967 .055U .9511 -.125'=^ -.0100 .0867 .1U3U .0967 .0U67 .0200 1.00 -.1756 -.0600 .0231+ .0800 .053ii .0200 yATia:aL ADVISCfti COJ.?.'ITTEE FOR AERONAUTICS CCNPIDENTIAL ;^Ck ACR Ko. LUlO CO':FTD»i:!'TIAL 34 TAFLS X.- FT'i0'!'I0!J ^ AGAINST T F?^ ^ = 1 ux 60 120 180 2140 '00 1 (a) r = 0.1 56J.., .3090 .^673 .7071 .EO'X) .6910 .9511 .9877 l.r^O 2.2667 - . .4 : . ■' -.2'-'C0 -3 ■^335 -1.86t^7 -.7:35 -.5';T5 -.5) 'CO -6.0000 -2.2o67 .l.Q-,7J; 1 _ ; „•: __.:.:.._ i._ -.Ur.o 1 .5T.t -.3000 .3017 -.26:0 j .2600 1 1 7 177-^ ^..^,267 .'.'53;> • SiiOO (0) ~ = 1.00 o.l56f+ .3090 .U5I4O .5878 .7071 .8090 .6910 .9511 .0P77 l.OC -0.9:67 -.8767 -.7500 -.5350 -.5r-3 -.U7<:7 -0.8 ':a3 -.7';67 -.5300 -.^700 -.Uicc -.3967 -0.9333 -.7T*3 -.6lf3 -.r-67 -.1,000 -1.0153 -.9967 -.8533 -.6630 -.17^3 -1.100 -1.U133 -1.1567 -.6700 -..U333 NATIOJfAL ADVIECRY COWirTSS FOR AER0?'AiJTICS c-- KACA ACR No. L4I19 COi.VIDE'n'TAL TAFLE XI.- FUNCTION ^ AGAINST T FOR \ = 1 35 60 120 180 240 ?00 (a) X - 0.1564 .50Q0 ..'Mo .5879 .7071 .3090 .8010 .ni .9377 1.00 5.0667 .7667 .213' -. :^'.^ -.liiOO -.1667 -8. 6667 -I •7333 -.Q667 -.6?53 -.^'iOJ -.6200 -10.3333 -5-1^667 -1.1000 -.7500 -.5200 -.4800 -5.0667 -.7667 -.21^3 .~333 .1400 .1667 8. 6667 1.9535 .96c7 .6^?53 .6/400 .6200 (b) X = 1.00 0.1S64 .3090 .U5iiO .5879 .7071 .5090 .6^10 .Q5II .9877 1.00 -0.9567 -.9733 -.S135 -.6633 -.^^67 -.553^ -0.8533 -.7933 -.6267 -.^100 -.U635 -.41.67 -o.e4oo -.7600 -.5767 -.46:0 _. -.4100 -.3800 -0.9535 -.8667 -.6600 -.U333 -.4033 -.36^3 -I.03CO -1.0755 -.95^3 -.6467 -.5^33 -.2900 NATIOIIAL AD7ISCBY Ca-7.riTTEE FCR iiZRONAUTICS ""ID5.niAL NACA AC- L4119 COiFIDS^JTJAL 36 TABLE XII.- P'l.CTIC: ^- AGVIKS: T KOI \ - 2 CO — 1 1 ^iiO ! 7G0 1 (a) X - o.i^:.!. .3 39C .lj5li.O .5378 .70^1 .6090 .6910 .9511 •9877 l.CO 11.3333 .66-->3 .?030 .1600 -3.63^ -2.Ipo -.9',"3 -.6667 -.5U-7 '-lt).3'^3 I -^.6667 -.7667 -.^-53 -.5'367 1 -n.33',3 -2.6 DOO -.6533 -.253^. -.2000 -.1600 1 8.^35 2J.,?0 .9333 .6667 .^667 .r.i;67 1 0.156U .3090 .L5U0 .5878 .7071 .C090 .0910 .9511 .-677 1.00 -0.Q733 -1.0533 -.9U67 -.720D -.6200 -0.9067 -.760c -.6600 -.f667 -.5000 -.W67 -0.77:3 -.6+00 -.5000 -.i4367 -.i;??0 -.39.0 -0 . 7L67 -.7200 -.i+800 -.U067 -.'.too -.3irOO -C.KOO -.EUOO -.7200 -.5I67 -.U267 -.2^33 ':ATion;i advisctcY '^ar.ITTE^ FOR .\L~"^ -TCS GC IT?' IDH^'T I AL !:ACA ACR No. L4I19 COTTFIDS^ITIAL TAKE XITT.- FWCTTON -x— AIAPIST x FCR \ - i- ex 2 •^ 3.15'^ j.^ogo 0.5373 j.j-^'"': :).9511 1.0: (a) T = 60° 0.1^ :'i O.J 99 0.803 l.oi44 !o.964 0.955 0.9367 .'^^0 .19U .570 .877 • 787 .810 .8767 .5'^73 .135 .261 .526 .623 .695 .7300 .8390 .37.'; .159 .375 .460 .532 .5653 .9511 .055 .124 .309 .379 .4'i8 .5033 -( '- ~y .053 .111 .280 .347 .417 .K767 (b) T = 123° 0.156!4 3.1^26 0.662 0.705 O.C34 0.859 0.863^ .30C^3 .516 .457 .609 .690 .751 .7467 .5273 .162 .2^9 .Uii .503 .562 .5800 .8CO0 .117 .203 .321 .406 .453 .4703 .9511 .085 .I'^k .266 .^42 .391 .4100 1 .'^0 rv7C .142 .2h'^ .^28 .3967 (c) T = 130'" o.i56'4 3.^37 0.679 0.736 0.K23 n.90C 0.9353 .3090 .26U .465 .611 .663 .752 .7953 .5673 .118 .2^8 .3^U .462 .579 .6135 .8093 .064 .149 .273' .377 .45li .4867 .9511 .oUh .106 .236 .285 • 553 .4000 1.0? .^Ll ( •) .134 T - 2'.' .260 -0 .354 .3693 0.1564 0.397 0.6^99 0.924 0.987 1 .0090 1.0135 .30^3 .11^7 .ii3l .771 .905 .973 .9967 .5578 .038 .091 .381 .663 .616 .6533 .3390 -.023 .325 .159 .Uoo .598 .6650 .9511 -.318 .302 .059 .223 • 4315 .4753 1.00 -.01,:. -.>06 .042 7 - T "• .194 - .36' .1.3 '3 o.i5£U 0.6230 0.^^-'70 1.15^0 1.216 1.239 1.1900 .5090 -.2330 .3383 1.0630 1.3222 1.550 1.5400 .5378 -.2374 -.1591 .3590 1.021 1.360 1.413^ 1 .8393 -.1372 -.2565 -.1734 .402 .970 1.1567 .9511 -.117'=; -.2143 -.2933 -.025 .46^ .6733 1.00 -.0040 -.2042 -.32/i5 -.067 .284 .4353 NATIONAL ADVISORY C0l'?>TTTEE ^OR AERONAUTICS CC:il''IDS:TTIAL- NACA AC A To. L4I19 coi.tid3:tial 33 T.VbLS XTV.- FUNCTION -x~ AGAIMCT x FCR X = 1 X 0.15^ 0.3000 0.5378 ! 0.8390 1 0.0511 1.03 1 (^0 > T r, £00 o.i;: 6ii 0.1+50 0.01+5 1 . 020 0.990 0.9^ 0.9567 .^c^o .130 .Li5 .970 .913 .9iiO .97:'^3 .^^G7'3 .050 .163 .5-3 .770 .oil .81^3 .8090 .038 .117 .3Ue .C02 .660 ' ' .9511 .035 .103 .2^^0 .IS6 .570 • >-o7 1.00 .029 .09"^ .270 .U27 .528 .5533 'X, 1 T = 120^ c.i5^i+ 0.515 o.;ii O.6I7 0.8+9 0.553 • 0.6533 .^C90 .3ie .1,30 .6iD .7295 • 778 .7933 .5E75 .167 .^00 .'406 .55? .610 .6267 .20Q0 .12L .22c .575 .LO, .501 .5100 .9511 .106 .191 .3^6 ,bj26 .1+60 ,U653 1.00 .0V5 .179 .318 'IPk .IdP .U'467 1 (c) T = ICO^ c.i56J^ . 518 0.668 C.7''0 ! O.SlU 0.631+ 0.81+0 .■^C90 .307 .L70 .622 .7015 .7/:8 .760 ."^■67? .162 .2C3 .U19 .510 .560 .577 .6090 .110 .191 .319 .103 .iJL96 .1+63 •9511 .037 .153 .2705 .350 .395 ./+10 1.00 .OGO .1U7 .2505 .326 .^69 .3 So :o T = 2!0° 0.156^ 0.UU2 0.733 0.800 0.93 V 0.9505 0.9533 .^COO .205 .160 .688 .791^ .S500 .8667 .5C7e .OcG .;o8 ..'4I5 .S6- .CiiOO .6cO0 .8090 .022 .095 .256 .379 .456 .1+333 .9511 .002 .052 .163 .27.'. • bOi .U033 1.00 1 .0006 .0^9 .13U .o5 .'21+ • 3^33 1 (e) T = 3cc° 0.1R64 0.2!^1 0.967 1.1580 1.1:33 1.053^; 1.03:0 .3090 -.051 .293 1.1266 I.222I+ 1.1500 1.07:3 .5873 -.175 -.259 .516 .995 1.0330 .9533 .8090 -.128 '■ 1 1 -.205 .311; .6367 .£^67 .-^511 -.10: -.230 -.330 .215 .33^5 1.00 -.109 -.21'+ -.508 -.030 .185 .29C0 ' :Aiiot:;iL aoviscry coi.:}>"ivtee for aero^'autics c-' ■-.■.ITIAL :ACA ACR No. L4I19 COWPIDENTIAL dP TABIE XV.- FTTKCTIO^' -X;^^ AGAINST x FOR ^ = 2 39 ^1^<^ 0.156^ 0.3093 3.5378 O.8O9O 0.9511 1.00 (a) T = 60° o.i:^£iA O.ctO I.JI9 1.061 l.Oi+O 3.9965 0.9753 .5090 .GQ? .725 .85:. .959 1.02^ 1.0555 .5578 .055 .202 .UhB .a-2 .861 .9ii6'7 .eoQo .027 .110 .305 .509 .6615 .7200 .9511 .021 .081 .255 .U22 .568 .6203 l.OJ .017 .067 .210 .^6U .51U .5600 (b^ T = 120*^ J.156J, 0.1i7'' 0.6^5 0.656 0.Q22 0.910 0.9067 .^ )90 .260 .UPO .731 .852 .8195 .7600 .5873 .IU2 .501 .565 .750 .730 .6600 .8090 .117 .259 .hk2 .560 .5775 .^667 .9511 .10^5 .221 .579 .U62 .U95 ."^000 • .^"'.2 .210 .558 .Uhi .U7- .!;S67 '") T = 130° 0.156U 0.551 0.707 3.752 C.7l0 0.7550 0.7735 .^093 .575 .5^6 .531 .612 .651 .6i;00 .5e.78 .220 .527 .1+19 .U65 .1;91 .5OOU .3093 .15^ .256 .552 .579 .1+51 .11667 .9511 .12'; .200 .281 .527 .59i'. .i!530 1.00 .122 .197 .262 .301 .551 .-^60^ (^) T = 2h:>° o.i^at O.U39 0.6S9 0.695 O.91U 3.632 C.7L67 .5oqo .aD8 .ii06 .708 .81U .738 .7i;67 .sc-'e .077 .200 .160 .6^.6 .585 .U800 .5000 .oU3 .119 .522 .U69 .152 .U067 .9511 .055 .ICO .278 .5996 .591 .5603 1.00 .:2p .091 .262 .361 .'76 .5LOJ (e) T = 300° 0.1561+ o.eui 1.367 1.202 1.121 0.9U5 0.0003 .50^0 .0^6 .I4S2 l.COO l.llS 1.059 .blOO .5979 -.liiQ -.o!iO .1.81 .362 .657 .7200 .e-^so -.127 -.161 .162 .ii^e .5585 .'^i;67 .9511 -.107 -.160 .0U5 .281 .U12 .L26'7 1.00 -.100 -.iLo -.008 .166 .250 .2^,3^ NAPICN/vL ADVISORY OOMyiTTEE FCR AERONAUTICS CCTPIDK^TIAL 1^ ACR !:o . L4I19 COITPIDEOT lAL TABT.E ::VI.- "ALUES OF > --^jrj- AlAIVST x r^ rraSE-BT.ADE A^'D SlX-ULJd>E rROIELLSR. fl-'cr three-blaee -^rcoeller, T = 120° and 2i{.0°; 1 rj;- b ' ;■ - "nac'e propeller, T « 60°, i.20°, 160°, 2^0°, an i 300"] :).i3Ci^ o.-';c9o 0.5.878 o.f?oq3 ! o.Q^ii 1 1.00 >, ^a) T.^re«-tlade p'-opoll'^r; ^ " -y 1 ! .l^6h . -x^ AGAINST x FCR TI31EE- PLAOE A'lD SIX-BT.ADI; "T^OPEILERS - Concluded [_For three-blade Dropell<=r, T = 120° and 2ii0°; for six- blade oropeller, t = 60°, 120°, 1Q0°, 2l40°, and 300°] 41 -N^ X O-l^^^^ij ' O.3OQO 0.'^.876 0.8090 1 0.9511 1.00 ( (d) Six-blade propeller; X. ■ 1 n d iO .I5cli 2.U:90 3.837 i+.622 [t.32U 14.918 i;.9366 .i^on .713 2.261 3.9i^3 U.367 U.616 a.753U .•^376 .IE56 .6999 2.071 3.297 U.012 ia.l9l;9 .6000 .^978 .29i;5 .95^6 2.O4S 3.007 3.363a .9511 .0l;85 .1712 .5U87 1.209 2.0^? 2.1+566 1.00 .0?S0 .11+18 .ii305 1.062 1.773 2.1093 (e) Six-blade oropeller; X. = = 1 .15^ 2.166 ^+.022 U.655 U.6933 h'&^h^ U.6335 .30QO .909 2.171 ii.oU66 .u.3651^ h.lh6 I.U666 .5378 .272 .677 2.3&U 3.1+07 3. ^'4 3.650^ .boo .166 .387 1.093 2.162 2.6733 2.7t?3 .9511 .122 .276 .7295 l.i;31 2.00it 2.2066 1.00 .0956 .250 .66U5 1.312 _ J i.eU6 2.0333 (f) Six-blade propeller; X. = = 2 .156ii '.100 U.157 h.76h h.1^1 ii.Ui65 1+.200 .^09:: .9€l4 2.607 3.901I I..365 U.5005 U.oac .5^=76 .3C5 1.070 2.391 3.365 3.u7i; 3 .3067 .&090 .213 .563 1.565 2.ii35 2.700S 2.7268 .0511 .17l;5 .Uh2 1.218 1.8916 2.263 2.3567 1.00 1 ■ .1622 .125 i.oei; 1.673 i 1.9i;8 2.000 jATIO!:AL adviscsy COIT'TTTEE FOR AERONAUTICS G0I.-?IL2NTIAL NACA ACR No. L4I19 CONFIDENTIAL Pig. la (a) '■h Figure 1.- Function Q against x. CONFIDENTIAL NACA ACR NO. L4I19 CONFIDENTIAL Fig. lb (b) ^ = 1. Flgiire 1,- Continued. NACA ACR No. 1. 4119 CONFIDENTIAL Fig. Ic CONFIDENTIAL NACA ACR No. L4I19 Fig. 2a -T 1 r 3 < z Ex] Q • I e 6 y|^ NACA ACR No. L4I19 Fig. 2b r' 1 ! ! 1 i ! 1 ■ ' i i , ... _ ■ ■ - ■ ]■ . .r ^ : ^ : ! f 2 i 1 & ^ " -g - ll- j- ? i , it ^WJ ri ; i L..J--T ^,,.^.^...':^:| i ^ .:. i r iB ^ i ' I if i 3 u" .ittT: r"i:i::±: ■ ^iii'tiT i 1 J i ^ . i 1 (_. ._...,_,._,..._|^ . . __!__ j- - . ^ 1 < r i M H -^ 1 1 : \l ** "£ _ .._n: Ij" ""t: ! tIjz ■ :Lt: ^__ ^ w J ! ! i L 11 ^ " i i 1 \ U i Q ^ ''1 ! \ \i r ■ S 1 I k li o ! \ W \ vi V V v\ 1 i \ \\ 1 I w \ ; \ i \ \ \ 111 \ \l \ \\ 1 \ \ V ^ V t ■ r^inii t: ' Jil: .i^j rrTi^i-i- " -+- 4. . itjirrii^,.^^ -\-Sw^ - - ' L 1 L \. ^^^\ - r-^-\ -r^ ^. "s v*. „ __ T„ L. __^ „ \ ^i^^J: ! 1 - . • ■ ■ . . M I 3W NACA ACR No. L4I19 Fig. 2c 1 M 1 1 ■ . ' 1 ' 1 1 i' ' ; ri j" i ii ail it ,^.:!:;; ~ 1 i M 1 1 • ' "1 1 1 . 1 1 1 ^ i-: "T 1 1 il E- E-< ' ■ ' 1 ■■■j '11' i Z M 1 II 11. II A Ji . Jib ^ ° 1 \i gI! On. I i 1 1 ^ 2 . ■ \' U ' ^ 1 1 11 I \l ■ J ■ i Ik 1 1 1 11 i • 1 \ ' In n I i 111! I I in ' 1 I \u \ \ I ft 1 \ 1 H 1 \ 1 u \ i I jL i i 1 t \ \l 1 1 \ I v\ n \ \ \\ I '!.( i 1 I llu. . 1 o • g ^i NACA ACR No. L4I19 CONFIDENTIAL Fig. 3a .36 .30 .25 .20 dx .15 .10 .05 ^1 i .0 ) .9 (11 1 1 j n — 1 • ^A / t ^ t9 )9C • - •,- . / /^ ■.;: ■ "^ A .b B7E| 1 A / y Aa \ A ^ 1 ■ // // - / / ' / ^// ^1 ^VC / 7} A Y y y V/ A // /!/ / V . / ■ J Vi / !/ ^i.^ 1 1" / '/ // y • &A^ 1 1 'A y / // . / Y »\ »M // / / /!/ / . ! {/\/ // y t 1 / // ^/ / y / 1 , / i \0^ // / / / t 1 i / /i/1 // 7~ / 1 1 // ^ // A / 1 /V / , / I , ^ //f / / / 1 / ;"" i — r 7^ ^ / / / 1 // / \ / / / 1 i / ' / / / \ / '^ \ / / / / / -SL -d / / y : /: , /! \ 1 ATK NAl. OSoitY / AX / \/ c OMMIHE E fO ROHAUrp ' /y" y\ y / 1 ^^^P^^j---^ _ _i ' 1 • 1 i i ' 1 ' i ■ 1 i 1 ; 1 1 1 ' .4 .6 X (a) X-1 2 .8 1.0 CONFIDENTIAL Figure 3.- Function -x^ against x. dx NACA ACR No. L4I19 CONFIDENTIAL Fig. 3b .25 .20 .15 dx .10 .05 1 ^.g A r / ^/ 1 // A ^ / .d( >90 A V / J / / 1 // r / i 178 ^/ / / .a ^ / / r ', / ^ / y ^ / / .4^ 4Q /^ / y ?^ / / ^ / / / '• y / ! • 1 1 ^ /^ y / / / y i t /^ / y / / y / y .3< >90 i^ ' / r / / • ,/ r / /, y Y / ' t / ^i^ / f / /* y / / '/^ y / 1 / ^ // .^^ y 'r^ |.H «4 lA /.'^ r ' ^^ ^ // '/^ X ^ ^ y^ ^ --' ^/ yx\ >- X i.-^ i 1 ATKiNAl AOUSO !V P yyA.^x___^ ^^^-^ :^ cxmin ITTBE f( RAtROf HUTCS /^ ^ ^^ 1 ^ ^ . 1 1 1 .4 .6 (b) ^ - 1. Flg'jr© 3.- Continued. .8 1.0 CONFIDENTIAL NACA ACR No. L4I19 CONFIDENTIAL Fig. 3c 1 ' i •2U i - X .15 1 / 1.(0 i j ^' P^ »\ 61 }. i i 1 ;^ y 1 1 1 ,^ ^ / j .£090 1 ^ <^ ,^ X 1 .10 1 /i ^ y y -^_ 1 i ■ .r^ ^ . ,^ 1 ■ L -^ ^ A ^ ^ y ^ ^-^ 1 ^ n ii >\ : X ly A -^ ^^ --'^ •« 04 P ■ 1 , y ^ J-" "" .Ub 1 1 'j^ ^/^ y^ .'^ ■^ i . J , --■— 1 •« 09 } i t yyx "^ -^^ -^ __U-^ 1 ! /X^.^ ! — JTATir 55* ' A ^:::^>::^ i — — "^ i c )MMin{ ' FOR A£R0NAUT1 ^ i ^ ^ ^ ■::^ — ■ — ' ^\ \ ■ 1 i ' 1 1 .4 .6 (c) X - 2. Plguro 3.- Concluded. .3 1.0 CONFIDENTIAL NACA ACR No. L4I19 CONFIDENTIAL Fig. 4a 2.0 1.6 ^ 1.2 Ou I X p^ .8 .4 . 1 \. J ^ 1 ^ 1.1^ *< \ zzr. __; "s r."- -:; -T;j- - ,;-■- - \ :V:' \\ \ ■*" :-.:■ --T^ .3< )fK V ^ >u i N > \ -_-- ,_-. 1 \ \ ; k \ \ "^ V \ ;- .^.- ■ V s \ - ,te!n — ^ \« \ " ~~ ' -. "^ \ \s -■ *aH£ ^ s^: •: \J k N AT1C NAL ADl ISOfi Y ! ^*fti5^ --, "> ^ N V c )MMinfc ■ FOP AWUNAUFIi I.S • Si ill 1 Os. 1 ^^■_: T ■\ ::::; ;_: ^ N^ >^ nJ - ■ ~r~ J 1 \n J -.-■ =^ -"■^^ 1 ~"^^ ^vk c>^ .u. . " n- -.--^■: ^^fc::^ ^^^ - 1 :;::. ---" _: _ ' — t ^^^> "^ ' 5s^ 1 ^ •2 •4 .6 .8 1^ CONFIDENTIAL (a) \ » I. 2 Figure 4.- P(x) - P(l) against x for t « 60°. NACA ACR No. L4I19 CONFIDENTIAL Fig. 4a Cone. .25 ,20 ^ .15 I H a. .10 .05 1 ■ — 1 . .... .... .... 1 i i ■ : — : •• c^ 1 1 < K . !.J ^ 1 N| s. \ \ V ■- \ .N v. N ^ ^ ■ s i^ — 1 ( . Sff ^ < \ ^s -" Xj Sw ^J "s \ H ^ ■ ■ i £: V v^ L— is N i N 1 — 1 — 1 1 1 i 1 1 ^ \j V S| V t — ' 1 ... . .., ■•.^ \. :^ -N N N Sk DO ^ "^ >v^ S. >, % ■ — 1 — 1. ■^ S| Vi "^ '-«^ %^ t ■s. N \ \v ; '—- ...^ x^ V| k. > ^. '^ X. k "^ ~v ^Sv N V 1 — --- - "!^ M^ ^i L \ 1 .. i K f\T!0 HAl m i50F 1^ ■^ ~""^ - _c6mw n£tFO| M f» ■N s^^ ^1 - — .... 1 — ^ n^j .8 .9 X (a) ^ « i - Concluded. 2 Figure 4.- Continued, 1.0 CONFIDENTIAL NACA ACR No. L4I19 CONFIDENTIAL Fig. 4b r^ ^ Ttr: -" T^. '■''V n# H^ ■™.'! ', .'■*■ "i 2.0 ■ ' rrrr r — r i \ ^— j ' \ \ ' ^ 1 ■ lift ^ ft — 1 >.j — '^ ^:^ 5^ ^ il-U ± ■ i 1 . J. : 1 1.6 :i± , , \ . _^._ W ■^ Ti". ' * I \ ; ! 1 ■ ., 1 '. ' ~> k" ■ : \ ,j.. , . ^ 1.2 H ', t 1 . ^ [^ - \ 1 1 "■: OU 3:- .rl V ^1 N^ \. ... 1 1 " 1 ._■" \ \ 1 ! i _ X p, .8 N N. t t .. . ^ OCTI ■ "V"-' .^ \ 1 1 :h ''■~~ CT/< u N ^ 1 _.., iMv "^ ^ "^ \ 1 MTII^ INAI An' n^ ff ;■;■ ^*^ "S. ^ 1 « C ^ v' OMFIlllbi: l-d iHW AUIiUS ' .4 C f ^ ^ ..:■ - • lTc i«jj. ^ ==i=i X >s i .1 *-<^^ "T^N L I - ■*.«_ t*'"'^'"**' ■.>>d _ 1 : ' r -."-■ ■ is: : r^"**" ^ - *55b ^*>. ; , .. . __ L- ^ n L— ■J': z. .-- - ^ ^^ : u .4 .6 .8 1.0 CONFIDENTIAL (b) \ - 1. Figure 4.- Continued, NACA ACR No. L4I19 CONFIDENTIAL Fig. 4c r isi \ — 1 — — , ■ — — __ -"^ -r 2.0 I [' V A . , i V i 1.6 V. 4^ LL— •_ f 1 t ptoi ti4 1 1 t - 1 ■ z \ ) » - i '- ^* )^ N 1 ■ 4 ' . :, V < H 1*2 N \ 1 ) I a< "T ——^ '- - " \ — ^ \, 1 1 i 1 'i" 1 k \ s. I i '■ ;_L -^ s: .8 - — \ -N s '•:: 1 1 k \ HI ITIW AL WWfeOR^ i — :iS?Z; i J i I X \ COlifMI IK FOF AERONA 1 JTTCS ; 7""^ H. "NJ ^^ i — — .iSjO^ ) j ^ ,^^^ "v <^ s • 4 — i — uam u_^ j h^ ^L I ' l.QO^ ■ r^ =i=:= -^w ^N i 1 i t ^ ^^^"^ 1 1 u ^^ /-». "" r i ^^«4i ^k^f .2 .4 .6 .8 1.0 CONFIDENTIAL (c) \ - 2. Figure 4.- Continued, NACA ACR No. L4I19 CONFIDENTIAL Fig. 4c Cone. H I H 04 ,25 .20 .16 .10 .05 ..- . --i -_ . ' ~*T ■■ ' • ••^•~- — — — '•**' T* ' ' - fn "1 O.lfi •■a}' \ ( f .'30 JO V \ N \ \\ 'k • • ■■: ' 'J.' '■ - \ \ RV 7ft 1 ^ \ . ■ 1 \, ■ ^J k s V V 1 — ■ ;: -T-- — ■^ N -\ —^ .:• 1 &0 .... >oL^ v . N ^( N ^ \ ■ — ■ -* QB 11 "N \ N \ ^ ■ ' ■ • t ■ ■ - x; 00 L.L V ^ ^ "x N ^ \ ^ \ \— — 1 1 -: — I 1 -O =-^ ^ Cx "^ s '■r ■■:-. — >> fv\ . -_\ r--:' i Nv^ '\ K ^ N \ ^ ^c — ■- i . \ N =Vr- \ N ^N \j < ^ k \ ^■^ V r .11-'- -r. : ! S N Ss k^ •»■ xS. ■" - - ^ 4^ .-;• -r * " --'"_' :^ 1 N iTini HAt ADV snfl r ^ kX^ s " ::: ro'iM nu ro! :AE ^ONJ >i \ uTiqs kN^ -'I - t- :i i 1 1 ■ 1 "^ ^ O^^ \ "^1 - ■ ! i i t • i ■ t 1 - J i ^^ I .8 .9 X (c) \ ■ 2 - Concludsd. Figure 4,- Concluded. 1.0 CONFIDENTIAL NACA ACR No. L4I19 CONFIDENTIAL Fig. 5a 04 I ■;Jill. ' .1 J!LI ;.l ' { ' {-l.; !' -.. l I I f I I I I ■ If I ' I rrr- AW1S0?Y AUTICJ' .8 1.0 CONFIDENTIAL (a) X = ^. Plgur© 5.- P(x) - P(l) agalnat x for t - 1200. NACA ACR NO. L4I19 CONFIDENTIAL Fig. 5a Cone. I a, (a) \ • i - Concluded, 2 Figure 5.- Continued, CONFIDENTIAL NACA ACR No. L4I19 CONFIDENTIAL Fig. 5b I H .8 1.0 CONFIDENTIAL NACA ACR No. L4I19 CONFIDENTIAL Fig. 5b Cone, I .20 .16 I I X ,10 .06 ^ 1 1 ■■ 1664 , ^ \ ' i ^ttv\r\ \- :. 4 30^ .N . • ■-' X ^ :., 1 j „.^ ! V s. ■ t C-5500 ! \. \ - . . ( 1 1 -^ K ^ \ -- T >^ > ^ X— i 1 ' -- r:- i 1 1 t 95.11 "^ -N ■^ ^ ^ 1 I i J-; V, ^ V 1 00 ■^ \ \ ■\. - NS ■ ;; ; ' ~^ '^ k f^ ^ ■ :: ( ■ ■ 1 ^ X ^ i i -:•. .- ■ ■ I ^ •^ . -v^ ^ ! " t i i : ^ ^ s%, iHATiOfW . A£)VIS< CT "Q ^ V •-- ; COM MiTTEEfi OR AERO 4Airncs . :"^ ^\ ! : ^ ^ ^ - '::: 1 ] .._.:. ■-.: ■lb -- .^•^ .■;-n: .."^ ', -t 1- i i ^ .8 .9 X (b) X ■ 1,- Concluded. Figure 5,- Continued. 1.0 CONFIDENTIAL NACA ACR No. L4I19 CONFIDENTIAL Fig. 5c I X (c) \ - 2. Plgxire 5.- Continued. CONFIDENTIAL NACA ACR NO. L4I19 CONFIDENTIAL Fi g. 5c Cone . .25 I '^ H a. .05 ,8 (c) \= 2 - Conoluded. Figure 5,- Concluded, .9 1.0 X CONFIDENTIAL NACA ACR No. L4I19 CONFIDENTIAL Fig. 6a 2.0 1.6 ^ 1.2 I .4 .6 X .8 1.0 CONFIDENTIAL Pigtu?e 6.- P(x) - P(l) against x for t = 180°. (a) >. . 1, 2 I NACA ACR No. L4I19 CONFIDENTIAL Fig. 6a Cone I X (a) \ ■ i - Concluded. 2 Figure 6,- Continued, NACA ACR No. L4I19 CONFIDENTIAL Fig. 6b 0* I K 0. 2.0 1 — V ■•;. \ \ I 1.6 \ »3 . !>, '64 ■ \l ■ V \ s. - : ::'\. ... ^:, 1.2 \ \ ' ■ \ ,3^90 \ Tr ■ 5:- ■ ■- r " -_.-, 'U. r- 1 \ \ '■ ■ k, ; \ \ V " .: .8 \ \ N ^ .6i r^ k \ \ " :,. ■ \ ,..^ \ s. \ s. 1 ^-^ «^ .Sped \, ^ ^ \ s N ( iati6nal ADi/lSO n .4 ^^:::^;~4.9^ ^ "S-^ '•v k^ ij braiTrEEFc RACRON AUTCS ^ rdip^ -«-. ^^ ■-^ K LJX ■ ^:^>;:>Os^ ! " 1 ^^T*'"T^r'7"--fr^^^ ^ ^ ^ • A 1 ' ! ^4^ i .2 .4 .6 X (b) \ = 1, Flg-ur© 6,- Continued. .8 1.0 CONFIDENTIAL NACA ACR NO. L4I19 CONFIDENTIAL Fig. 6c a. I X : * ^ i ■ I 1 1 j • 2.0 : ... : i 1 1 1 1 1 , ! ; : . ; . - \ .... i \ 1 \ H 1 ! 1 1.6 .1664 ! i 1 — _ ^ . \i i \ \ \ \ k .\ . 1.2 ; ^ .369c \, ■• ::: ^- \ \ s 1 1 k i\ N ■ 1 N s I ^ \ \ 1 1 I 1 .8 N, ^/H k s ; 1 i N --^ \ s \ - 1 s^ ^S^i-^^**w '^ S N.^ Sv lATK )NAl mso JY ..,^__^ "V ^^^ ^v^ N CK f^m irret H i ^moh AU7IX .4 1 1 .9, 511 ^'^^s fc>Il"^ ^>^ ^ . ^^vN 1 1 - f X • m ) ^^ =:^ ,^S^ ^. t ^ ^ ^^i^ ^ i?>. /-v i 1 1 ^^'^s^ c^ ^ Ifc^ .2 .4 .6 .8 1.0 I (c) \ • 2. Figure 6,- Continued. CONFIDENTIAL I NACA ACR No. L4I19 CONFIDENTIAL Fig. 6c Cone. a. I X .10 (c) X = 2 - Concluded. Figure 6,- Concluded. CONFIDENTIAL I NACA ACR No. L4I19 CONFIDENTIAL Fig. 7a a* I X 2.0 1 ■■ ■ I -■ . ' ■;- - - 1.6 ■ 1 ' 1 1 1 \ 1 ' \i ' 1 \^ 56^ i t Ek ■\ 1 I i k: 1*2 ,|___^ : \, 1 * ;_ • t , j '^ O90 ' . : ... J — t I t ^ >>. — 1 N<^ \ j J_. ; I .8 _ — t t IN k\ 1 : 1 z \^ 1 • 1 X K \ < i87B 1 ^ NA HON \l ADV15 ORY 1 — 1 — i ^ i IMITitt FOR jAERi TICS -'" .4 1 1 '*'^^' SsJ t -^ p9b 1 ^ < ' — 1 — j — ^ — 1 i ' !'.:■■ ; 1 ~~~^i:^^ n -1.4)6 ' j i— I !'■ ^ s^ .2 .4 .6 (a) \ - I. 2 .8 1.0 CONFIDENTIAL Figure 7.- P(x) - P(l) against x for t = 240°. NACA ACR No. L4I19 CONFIDENTIAL Fig. 7a Cone ,26 ,20 .16 0. I a. .10 ,05 t : 1 , ^ "■ N 3 > •1 ■ 1 1 •' ^ 09^ > ;lt *\ — '. — i . i .:-- 1 — V '^ 1 - .Sf 78 \ S ^ - X N. ^ ^. ^^ . -/-:, :-■- > \ ^'> ^. "^ ■ \ h. . \ k V N. ( i ( N ^ \ s 1 N ^\1 X \ \ ! V - ^ v.. , LRf W) rS^ "~--H -«-, <., - . > \ ' ^ -.-:- - ;7 >> ^ t - \ N \q ..HIK NAL AD ^ISOJ^Y ^d \ "\X V L tlK Al itUNAUTl ^1 ,9( US .^^ 1 1 i fx •k. N' N\ 1 i ^'^ ■ .... — ^ K i^ i: /v -*^ I ■v^^^^ 1 ) V li.OCj 1 i._^ ! j _ ^ "»;;;i^ — ■^ 1 ^>\ ^^1 — ■ ^1 k V^ ' ! ' J : _ _,;: ' 1 "trri^ ! - - - — - ^ ^ — C;2>CS X r ' ... .. r ^ .8 .9 X (a) \ ■ i - Concluded. 2 PlS'oro 7,- Continued, 1.0 CONFIDENTIAL NACA ACR No. L4I19 CONFIDENTIAL Fig. 7b PL. I X U4 1 2.0 1 \ A •:. 1 \ X 4 : , 1.6 f* »j |. loM 1 \ I ■ 1.2 \ i . ' ::-■: ■ \ 1 :.• .-■ \.^^ •a nor \ "- * ^V \ L '-'-- --'^ ..j'T" t 1 N S, \ T . ■ -'-: V-:' -.:^ X. N \ - - -; ;-,■ • 8 N^ V s ~ .4 ---' , — — - S N. N V 1 ■ 1 -i^ B78 "-— .^^ L-- ,' ;X \ N NAtiON ftL| ^ovi; lORY _...:. . n --> .^ X ^.^ AMiiiti FOR AtK JMfftC 1 1 .8P9C 1 1 \ : 1 \ V \ ; ■-■- ^ X' , — 1 — - 1 N X \ i\., M- •• i . . t , .1 . . ! 1 ■- -fs ^^ V. — — 1 ■- - - - 1 v\ , _ ' ■■ :-" ; \\ Vr — '. ' ' -.-• - -- - - i^ \\N —^ ■ '< -^ — .9^3 1 — -^ .,1^ — ^ \s\ - f' i ^ t 1 W ' — 1 — i zL' : • ^ ■ "^ 11, ^ " i t 1 N N, i [ : ! ■ NA >mU. i ijvdOftV s N : 1 l-CWI ftwr f££ fW 1 flOB — X V_ i ^V ; >s. \ ..:^309<; \ 1 .P I / r > K \ ■4H 1 I \ 1 :■:. \ sN \ k .IK. TOT 1 .8 ; \\ '"-£ 1 i \ ^ k . — ■- _;" J e wi^ — ^ \ .4 ^ [^ 1 1 t ^^ V , ■-'".. X . I <] X ^' A .8D9i V"^^ ^.^.^ ^ ^ ^ i ______^ ■■••^^ '--- ^ ^ • ' ^ ^ .^BIJ :::-^ ' — '. — 1 1 '1 t ^ \ \ ^^ ::6b . i ^ i N^ TIONAL ^OVlloR^ -U ~. w ;tMI Terftjf? AtaONA ! JTIC^ ; . ^- - . ',. ::._ -.4 . i ' 1 " „"- -'-"-^.. : -'■ ) .2 .4 .6 X CONFIDENTIAL (c) \ - 2, Figure 8,- Concluded, .8 1.0 NACA ACR No. L4I19 CONFIDENTIAL Fig. 9a - X dP dx ?lgv£re 9,- Pxmctloii -xS— agalnat x for ^ ■ ^i dx 2 CONFIDENTIAL NACA ACR No. L4I19 CONFIDENTIAL Fig. 9b - X dP dx (b) T - 120°. Plgure 9,- Continued, CONFIDENTIAL NACA ACR No. L4I19 CONFIDENTIAL Fig. 9c - X dx CONFIDENTIAL NACA ACR No. L4I19 CONFIDENTIAL Fig. 9d dx • "~ T O 1*^ , 1 - I ■ -i 1 1 ! "L- 1 A 1 :, 1 \ 1 -^^ t ^••^'■' i.«0 :•• 1 1 ^ -^ 5-^ IV ■ . > --0 ^ r-r I ^ ^ ^ X k i 1 ^_ :<16^ i / V ^ X "1 *:: • O - ■■ (/ 'A >•' ' - y ■. Th / / V / / ■ / J / / i > Jtoeb / / r : / / • D / y / :.- / \J ? 1 •-: '■- / ^ .... /- -■: / r ^ / ; i :/ / - ' y / ' / / '^ «l|l I t ■ 1 ;/ =■ i 1 / " / \/> » r' -Oi ■ .4 1 J— ■" / 1 / . - ,/ : . 4 r~ / p 1 1 / / / . / / / / •,t / y / , — / / / 7. :2 .2 ) r ! y / / Y\ / ?^ / -^ ; / 1 -"i // J ;- "" u z' ^ I 1 ^ i A 'A ::' ^ /'■ [y J ; ^.-^ ■^n <^ \ n i >^ ?^I^ir:^ p::^ . i ■ V ^^=- II iQ l'^ " i 1 'NAT ONA L A jvisif^ ! > MMMtn iu OHj £RC ' mi ICS 1 ■ - <-> '. ' ! I • '" .2 CONFIDENTIAL .4 .t X (d) T = 240°. Figure 9,- O'ontlnued, 1.0 I NACA ACR No. L4I19 CONFIDENTIAL Fig. 9e - X (e) T - 300°. Figure 9.- Concluded. CONFIDENTIAL NACA ACR No. L4I19 CONFIDENTIAL Fig. 10a - X r Plgur© 10,- F\mctlon -x^ against x for X ■ 1, CONFIDENTIAL NACA ACR No. L4I19 CONFIDENTIAL FiR. 10b 1.0 .8 .6 - X dx .4 CONFIDENTIAL NACA ACR No. L4I19 CONFIDENTIAL Fig. 10c - X dP 33E (c) T - 180°. Figure 10,- Gontlnxied, CONFIDENTIAL NACA ACR NO. L4I19 CONFIDENTIAL Fig. lOd (d) T = 240°. Plgupo 10.- Continued. CONFIDENTIAL NACA ACR No. L4I19 CONFIDENTIAL Fig. lOe - X dx i >-^ 1 1.2 1 t 1 — — , -+^ ^ p>— 1 "^ ~~^ ^ :-;" y / y ■:^-Am / i / r Z' J ">ii) .ssis .8 / t / / 1 / / / 1 / / f- / .^ > .Buyu 1 t / .■ / i n f > / - ( } / / / .4 P J / 1 — — ^' > ). ^,^^ i / ^ J l/^ 4. 00^^ / --- /! [ - / p^ ^ 1 ^-^ / ■r: -i / / J/ ^ ^ • / / / :-- N / /^ >^ %-A\{ NAL' A[^ 1/lSO RY ' j -; -r - ^^ u y^ .^^ ^ jjJ^ \ Oinlfim E FOR A J^^ vT 1 A T^- ■ • r ^'S > ''-li m ft / pr / — i .. ■^ ^ X' ,< / o / *" ^o / • o / 1 1 1 1 / 1 i /' y \) ) TsIjbc 1 / j i / y j i i i ■ / > / i r 1.9' 51^ .6 / /I / rV > 1 -n^ > / /; y '^ i / ^ / ' / i / / /^ y / ft V, / - 1 / 1

^ o 1 1 II / ^ .^ z' 1 1 1 «^ y >':^ 'C' 1 )Mn^^i4/\i, K,^ if ; /UJTCS / ii^ ::^ C Ml M. tK KAI 1 ^ j^ ^ 1 t^ ^ ! -'" .2 .4 .6 .8 1.0 (a) T - 60°. Plgura 11.- Function -x~ against x for \ - 2, dx CONFIDENTIAL NACA ACR No. L4I19 CONFIDENTIAL Fig. lib - X dP dx (b) T - 120°. Figure 11.- Continued, CONFIDENTIAL NACA ACR No. L4I19 CONFIDENTIAL Fig. lie dx (c) T - 180°. Figure 11.- Continued. CONFIDENTIAL NACA ACR No. L4I19 CONFIDENTIAL Fig. lid 1.0 .8 .6 - X dF da .4 .2 i i ; 1 i i i — 1 ^ ^ ^ V 1 ! 1 / y >- 1 Xt 1 I i y / ^ ^ - ^ O.lt.64 / n .^ S ' .3090 / i y y i '~ 1 i / ■ - '■■ - ' y /^ X T' "^-^ \ / > / / / \ \ J / y / \ 1 ' 1 ' \ . A n / A ^ >^ ■^" "N ! ) j.5^8 f y X y / / / 1 \ A \ /^ b^ r^ r • "T- - & .9Bia 5 1.00 , / f f \ : -. '^ yi r ' 1 T / / >) ^ ^y 1 / ^ -'J A / /j^ \ 1 / \/ ' > Va r i t / / r / t^ 1 1 NAT ION/ L ADVIS DRY IKS i /^. iTT^ K^ .6$7a i .6 .4 .2 / f / / / / / 1 ■ j 1 — 1 U— flV-^ - Qi m_n . 1 1 - ^ ^ r I, 1^ rrOyyvj - - - - r ' / / Sr- ; J / ( / .^ \ :-s^ su ""7 7 / -' / / / / / -;_- / / / / / 1 t 1 r J ^-:.- / / / d / -] J / / ( A ■ ^ > 1 .01 ^ 1 1 z / d r J / , A j 1 t 1 .. , ^ ^ /n v\ .... / 1 1 r ■ ■ t 1 f / / - /d y , / \ 1 i /"" / / A i 1 1 i 1 ^ 1 — -1 - / -/ ki •m ONAL hi [EROItttf \^^tec / > {/> y »M Min i ES, 1 f K^ b^-2^ 1 1 -.? 1: — ; 1 '. t ' 1 i .4 .6 1.0 (e) T - 300°. Figure 11.- Concluded, CCNFICEMIAL NACA ACR No. L4I19 CONFIDENTIAL Fig. 12a r-^ dx (a) Thr««-blade propellar; X = i. Plgur© 12.- Values of Y. -x^ against x for dx three-blade and six-blade propellers. CONFIDENTIAL NACA ACR No. L4I19 CONFIDENTIAL Fig. 12b I-^ (b) Three-blade propeller; X." 1. Figure 12.- Continued. CONFIDEMTIAL NACA ACR No. L4I19 CONFIDENTIAL Fig. 12c » 2.0 1.6 1.2 >:- dP .8 >-^-^ ^ ^ -^ 1 ^ ' ^1 r^ ^ ^ ->■ !^^ ■^ ■^ > D"^ 66tt d V ^ i\ 1 ,; onft / y 1 ^ — 1 r t / / A / ^ w ^ ^** \, / t y \.^ r T\ 1 / / / r \ > .e 87B / f / ^^° r ^ \r^ — ^"^ ! ' : ' • i A / . y y P- ' y ? .3090 / / i / / <^ ^ ^ |v .9511 p l.CK) / / / / J. A .^ ^ i 1 1 j ' : / / y r^ir« A 1 / / / y y' ^ , / / / A _ ! /: ^ A ¥^ r / n , ^ NA IDMiil LiiUi'\iiHI 1 1/ ^ ^ r WJMMII Itc f OR MLKunflljiM i ^ ^^ m * - .2 .4 .6 .8 1.0 I. I (c) Three-blade propeller; X. ■ 2 , Figure 12.- Continued. CONFIDENTIAL A NACA ACR No. L4I19 CONFIDENTIAL Fig. 12d ^-i (d) Slx-blado propeller; X Plgtire 12,- Continued. 1 CONFIDENTIAL NACA ACR No. L4I19 CONFIDENTIAL Fig. 12e I I ^-i (e) Six-blade propeller; X Figure 12.- Continued. 1. CONFIDENTIAL NACA ACR No. L4I19 CONFIDENTIAL Fig. 12f I-«i n — — - — ^ .^ >-H 1 >= N, ! . :- • y /- ^ ir- — < ?^ 1 _ 1 i 1564 ^090 / :^1 ^<^ ^ 1 u. y / . V ^ 1 1 J / / r ^'' . v_ / / r- / y^ . '^ ) ifl- R / b ,A y / _ / / / l/ r ! i/\ 1 ■/ / ^^ ■*i ) • 3Ui| / / ■ / /^ y1 / y^ ) « }6: 1 / / / f /" ^ A 7 3fi / 7 / y /' / ?^ ^ H 1 r / / .0 \^^ k / \ J [/ ,/i / -^ ^i J r 7 / y f^o ^j 1 ! i J Y i ^i^ 1 NATIOI lAl ADvlsOfiY : 1 - A X^ j~cq WMlTTEb TOTTAErtCfMAUTTCS / J ^, ^ ^ ^ ^ ^ ^^ i 1 1 .4 .6 .8 1.0 (f) Six-blade propeller; \ Figure 12,- Concluded, 2. CONFIDENTIAL NACA ACR NO. L4I19 Fig. 13 I < E-" •z. Cd O O o p-l < l-\ >— 1 / §• ■p OS CM CQ Z b3 a 1-4 z o o r-K O • (U O s O, CO o .HICVJ ^ a '- ' oJ ■H +j Xl CO ^ >> » •H ♦3 r-ijC\J O ^ O •H O r-\ O > <" >> Q) > rH (D ^ 3 :^ (U O > 1 o c !-! • H a> K) a> f^ tn rH > a> 3 8- ^'i 262 08106 549 1 ONIVERSITYOFFLOWA ii