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i.p "&r ...SE9UR.T Y IN FO.RIAAT^ION
SCOECYLINDER BODIES AT MACH NUMBERS SF 1.6, 1.9, AD 2.Copy l Aeoa:' tc. RM L53H21 SLangley Field, V a. p., UNIVERSITY OF FLORIDARANDUM ...;'DOCUMENTS DEPAR''" ' ,' .,,,o .i ,,, '3 ..... ., ..'....., & CONECYLINDER BODIES AT MACH NUMBERS i O1 MF 16ARON SENCE BD RA RO. BOX 11 AINESVLLE, FL 326117011 USA ii 1E.CH AM ERONAEUM T DC US 4...;. t ..,u nd .n .. 'j: *' t naaa toa n iiIubct* a g tH u t a l thm Uflttd BaieN within the menag a038: ::. : :6 u S Aa m I M M Ul lm an or MlWOC of which In W Ai I " T "LONao RYNOADVISORY COMMITTEE AEE i2 WASHtN GTON October 7, 1953 ,',,:,,,,.,~ ; ,'i ge A rn uialL brtr d ..:' ,,( ~ ~ ~ ~ ~~~' i:" "",',: ': ', .,i ,:;::: ", ",,, age.Fed a : ,: :'; ,; i :, ;. : . I NACA RM L55H21 !IATI,,IIAL ADVISORY COTIMIMTE FOR .A'E: [i...TICS FESEAF C'H MEMORANDUM IIJVESTIGATI,2If OF EYTI':LDS NUMBER EFFECTS. FOR A SEF E; OF CONECYLINDER PBODLES AT MACH [E.rlEFP OF 1.62, 1.95, AND 2.41 By Carl E. Grigsby and Edmund L. Ogburn SUMMARY An investigation of the Reynolds number for transition and the skin friction drag at zero lift of eight conecylinder bodies having various fineness ratios has been made at Mach numbers of 1.62, 1.95, and 2.41 over a Reynolds number rla'e from 0.5 x 10 to 10 x 10 The accuracy of the skinfriction data was not sufficient to permit any general con clusions to be drawn. The Reynolds number for transition was found to be dependent upon both the tunnel stagnation pressure and Mach number. INTRCDUCTIOj Considerable interest is shown currently in the aerodynamic charac teristics of bodies of revolution at supersonic speeds and special atten tion is shown to the Reynolds number for transition and to the effects of Reynolds number upon the skinfriction dra:. In references 1 and 2 results are presented of an investigation of the friction drat and boundarylayer transition on conecylinder bodies over a range of Mach number. In this investigation, variations in Reynolds number were made by lengthening the cylindrical portion of the bodies. References 5 to 6 have also presented a considerable amount of aerodynamic data on a series of bodies having nearparabolic and conical noses and cylindrical after bodies. In these tests, variations in Reynolds number were accomplished by changes in tunnel stagnation pressure. These investigations illus trate two techniques for obtaining the effect of Reynolds number upon skin friction. In reference 3 data are presented which indicate a dependence of the Reynolds number for transition upon stagnation pressure. It was suggested that changes in tunnel turbulence level were responsible for this effect. CONFIDENTIAL CONFIDENTIAL NACA RM L55H21 Additional data for bodies of revolution indicating this same phenomenon have been published in references 2 and 6 with results for several hollow cylinders presented in reference 7. Although the temperature was held nearly constant for the windtunnel tests, it was not clear that similar results could not have been obtained by variations in temperature, in which case the results would be more properly expressed as a function of Reynolds number per unit length. The need for further research on this phenomenon is apparent. The purpose of the present investigation was to determine the effects of Mach number and sti attion pressure upon the Reynolds number for tran sition, and to obtain the zerolift skinfriction drag from measurements of total drag, base drag, and forebody pressure drag for a series of eight conecylinder models of varying fineness ratio. Some objections have been raised about the use of conecylinder bodies for skinfriction investigations because of the severe adverse pressure gradient and the possibility of local separation at the juncture of the cone and the cyl inder. These objections are based on the belief that this local separa tion or the adverse pressure gradient or both would make the results of questionable value in assessing theoretical predictions. Although there is some justification for objections on this basis, there is also suffi cient reason to investigate these bodies in that they are employed in several current and proposed missiles and have the advantage of simplified construction. The tests were conducted at Mach numbers of 1.62, 1.95, and 2.41 over a Reynolds number range from about 0.3 x 106 to 10 x 10 for the condition of zero heat transfer. SYMBOLS Amax maximum crosssectional area of body (equal to AB) Aw wetted area of body (surface area forward of base) AB base area Total drag CDT totaldrag coefficient, qAmax AB CDB basedrag coefficient, PB PB CmTlax CONFIDENTIAL Ci FID DiTIAL ,L NACA RM L55H21 pL \ I d /r \ CDp foreb:L, pressuredrag coefficient, j P d dx O dx\rmax Cf skinfriction coefficient. AB CDT Dp + CDB L body length r local body radius rmax maximum body radius P2 Ps P pressure coefficient, P q PB base pressure coefficient PO stagnation pressure Ps freestream static pressure PZ local static pressure q freestream dynamic pressure M freestream Mach number R Reynolds number RL freestream Reynolds number based on model length RT transition Reynolds number based on axial length to transition point Tn stagnation temperature CONFIDENTIAL CONFIDENTIAL NACA RM L55H21 APPARATUS AND TE'S'T Wind Tunnel The Langley 9inch supersonic tunnel is a continuousoperation, closedcircuit type of wind tunnel in which the pressure, temperature, and humidity of the enclosed air can be re _lated. Different test Mach numbers are provided by interchangeable nozzle blocks which form test sections approximately 9 inches square. Eleven finemesh turbulence damping screens are installed in the relatively largearea settling chamber ahead of the supersonic nozzle. The turbulence level of the tun nel is considered low, based on the turbulencelevel measurements pre sented in reference 8. A schlieren optical system is provided for qualitativeflow observations. Models A sketch illustration, the models and sting support and giving the pertinent dimensions is shown in figure 1, and a photograph of the models is shown in figure 2. The eight models varied in fineness ratio in incre ments of 1.0 from 2.0 to 9.0. All models for the force tests were made of magnesium and were available from the investi.tion of reference 9. The surface roughness of these models was about 14 rms microinches. At the beginning of each run the model was polished with a metal polish and carefully wiped with chamois to preserve a uniformity of surface condi tions during the tests. The hollow sting which served as a conduit for the straingage wires was sealed at the support end and vented to the chamber within the model. The pressure in the hollow sting was measured and was assumed to be the average pressure in the chamber within the model. A special model constructed of steel having a surface roughness of 8 rms microinches, and otherwise identical with model 8, was employed for the detailed schlieren observations of transition and for the pressure distribution tests. Pressure orifices were located in the conical nose on the 00, 900, 1800, and 2700 meridian planes. As in the other models, the hollow sting served as a conduit for the pressure tubes and was sealed at the suppJrt end. The tests were conducted at Mach numbers of 1.62, 1.93, and 2.41 and over a Reynolds number rarLce from about 0.5 x 10 to 10 x 106. The starna tion temperature was 1000 l 50F and data were obtained only for equilib rium temperature conditions. Throughout the tests the dewpoint was kept sufficiently low to insure negligible effects of condensation. A condi tion of zero pitch and yaw was maintained as closely as possible. C'OIFIDETITIAL (CF I DEPiTIAL NACA RM L55H21 The first phase of the investigation consisted of detailed schlieren observations of the boundary layer for the visual determination of transi tion Reynolds numbers of model 8 (steel). This model was later used to measure the pressure distribution over the conical portion of the body. The effect of the tunnel staticpressure distribution upon the forebody pressure drs, was found to be negligible. The second phase of the investigation comprised the measurements of total drse and base drag over the Reynolds number ra .e at each test Mach number. The magTLeslium models were used for these tests. It will be noted from figure 1 that the strainrave balance protruded from the rear of models 1 and 2 and caused an interference in the basepressure measure ments. Additional basepressure measurements were made without the bal ance, and the total dra, measurements were corrected by the difference in the two basepressure measurements. Additional unknown tare forces may still exist on models 1 and 2; however, these forces are believed to be small, especially for mrdel 2. Precision of Data All models were maintained within +0.150 of zero pitch and yaw with respect to the tunnel sidewalls and center line, respectively. Previous measurements of the flow an :ularity in the tunnel test section have shown negligible deviations. The estimated accuracies of the test variables and measured coefficients are given in the subsequent table. Values are given for a tunnel stagnation pressure of 30 in. Hi. The accuracies of the coefficients are functions of the stavnatin pressure and increase with decreasing sta,nati n pressure. Mach number, M . . ... ..... + 0.01 Reynolds number, R, per in. . ... .0.004 x 106 Totaldrag coefficient, CDT . . .. 0.005 Forebody pressuredrag coefficient, CDp . .. .0.002 Basedrag coefficient, CDB . ... 0.0[ RESUzLTS AND DISCUSSI:IJ Total and Base Dra; The totaldrag coefficients for all models are shown for varying Reynolds number at M = 2.41 in figure 5. These data are typical of the results obtained at the other test Mach numbers. The coriresp.nding basedrag coefficients are shown in figure 4. For model 8, the reflected CONFIDENTIAL CONFIDENTIAL NACA RM L53H21 nose shock entered the wake at a position such that the base drag was affected (see ref. 10). r:'e variation of both the base and totaldra,, coefficients with Reynolds number is typical of the variation shown in previous results for this type of confi irati:n. The effects of both model fineness ratio and Mach number upon base pressure for these con figurations have been discussed in reference 9. Forebody Pressure Drag Typical pressure distributions over the conical portion of model 8 at M = 2.41 are shown in figure 5. These distributions at each Reynolds number were integrated to obtain the forebody pressuredrag coefficients shown in figure 6. It can be seen that the forebody pressure dra., is rela tively independent of Reynolds number at the Mach numbers tested. The experimental results are also compared with the values from the tables of solutions to the theory of Taylor and Maccoll given in reference 11. The experimental results are about 6 percent higher than theoretical results at M = 1.62, in good agreement at M = 1.;3 and about 4 percent lower at M = 2.41. SkinFriction C efficient The skinfriction data results left much to be desired with regard to accuracy and scatter of the results; consequently, only typical results at M = 2.41 will be presented. The skinfriction coefficients were obtained in the following manner: Cf = CD CD + CDB (1) The results at M = 2.41 are shown in figure 7. Also shown in figure 7 are the following theoretical results for laminar flow: the flatplate incompressible result of Blasius, the compressible result of Chapman and Rubesin, and the flatplate values corrected to the conecylinder by the formula given in reference 2. Cf = Cf f2 ( + a)(s + a (2) flat plate s + 2a CONFIDENTIAL CONFIDENTIAL NACA RM L53H21 where s is the slant height of the cone and a is the length of the cylindrical afterbody. This formula follows from the transformation by Mangler and does not consider changes in pressure along the body. The incompressible, turbulent, skinfriction coefficient is also presented together with the extended Frankl and Voishel theory. These theoretical predictions for turbulent flow are presented only as a matter of refer ence since there are no comparable experimental results. The experimental results can be seen to exhibit considerable scatter, particularly in the transition range where the values of skinfriction coefficient are smallest. No general conclusion can be drawn from the results about the effects of varying model fineness ratio upon skin friction. Reynolds Number for Transition From theoretical considerations, it is well known that, for airfoils at subsonic speeds, the Reynolds number for transition is a function of wing Reynolds number. This dependency upon wing Reynolds number is a consequence of the favorable pressure gradient existing over the forward position of the airfoil. Configurations having zero pressure gradient, such as flat plates, have transition Reynolds numbers which are invariant with wing Reynolds numbers. Thus, it is surprising when the results in reference 7 for hollow cylinders at supersonic speeds show transition Reynolds numbers which increase with increasing stagnation pressure (increasing stream Reynolds number). Since, for a given Mach number, Reynolds number is a function of temperature and pressure, it was not clear that similar results could not have been obtained by variations in stagnation temperature in which case the transition Reynolds numbers would have been shown as a function of Reynolds number per unit length. However, unpublished data of the transition Reynolds number on a 100 cone from the Langley 9inch supersonic tunnel have indicated that decreasing the stagnation temperature (increasing stream Reynolds number) gave slightly lower transition Reynolds numbers, whereas increasing the stag nation pressure (increasing stream Reynolds number) gave higher transi tion Reynolds numbers. Thus, it appears that the effect cannot be iso lated as a function of Reynolds nurLber per unit length, but is a function of some parameter which is influenced by changes in stagnation pressure. Schlieren photographs of model 8 (steel) were obtained for several stagnation pressures at each Mach number; typical results at M = 1.62 are presented in figure 8. Points of transition were measured at each stagnation pressure from the photographs and the ccrrespndinr transition Reynolds numbers were determined. These transition Reynolds numbers are shown in figure 9 t:ether with a compilation of data from other sources which include results for several bodies of revolution, a cone and two hollow cylinders refss. 2, 3, 6, 7, and unpublished results). The COrJFIDENrTIAL CUITFIDEiTLAL 8 C':i~I IEEIITIAL NACA RM L35H21 ballisticrsar, results of reference 2 are plotted with ambient pressure as the abscissa. The windtunnel results shown in figure 9 represent equilibrium temperature conditions. The relative turbulence levels of the various tunnels are not known, and the possible effects of stagnation pressure upon these turbulence levels and upon other tunnel conditions such as Mach number and stream angularities and disturbances, cannot be determined. In the pressurized ballisticrange tests (ref. 2), any effects of tunnel turbulence are presumably excluded, although it is possible that heattransfer effects and effects of slight oscillations in angle of attack are present. The results for the bodies of revolution contain effects of varying pressure gradient over the cylindrical afterbody, and it also appears that consideration must be given to the length of the adverse pres sure gradient as well as to the value of the pressure gradient. However, in spite of the variety of the test conditions and tech niques represented in the summary of data, a definite increase in Reynolds number for transition with increasing sta.nati.rn pressure is evident. The present results showed an increase with increasing stagnation pressure ranging from about 3 x 106 at 30 in. Hg to about 5 x 106 at 120 in. Hg. It is also interesting to note that the results shown for the cone and for the hollow cylinders which have essentially zero pressure gradient are in substantial r 'er:nt with the results for the bodies of revolution. Up to the present time, no satisfactory explanati n has been found for this phenomenon, but it is evident that comparisons of windtunneltransition results or attempts to apply these results to free flight must take into consideration this phenomenon. The variation in Reynolds number for transition at the base with Mach number as determined from schlieren photographs is presented in figure 10 together with a summary of results for conecylinder bodies of revolution refss. 1, 2, 5, 6, 10, and 12 to 15). The average surface roughness for these configurations ranges from about 8 to 20 rms microinches. Each point represents a single value of stagnation pressure; some effect of stagnation pressure as discussed previously may be seen in the present results where the lowfinenessratio bodies have the largest values of transition Reynolds number. In view of the number of factors which may influence transition and which may occur as variables in the present com pilation, it is not surprising that the results show considerable scatter. However, it may be seen that, in general, the variation of Reynolds number for transition with Mach number is to increase with increasing Mach number and, then, reach a peak in a range of Mach number from about 2.0 to 2.5 and, thereafter, decrease with further increases in Mach number. This decrease in transition Reynolds number with Mach number is consistent with theoretical results for the stability of the laminar boundary layer in com pressible flow (see, for example, ref. 16). It might be noted that higher Reynolds numbers for transition have been obtained at the higher Mach num bers where boundarylayer c. lln;, was present. For example, a transition CONFIDENTIAL NACA RM L53H21 Reynolds number of about 8.5 x 106 has been obtained on a hollow cylinder in the Langley 11inch hypersonic tunnel at a Mach number of 6.9. CONCLUDING REMARKS An investigation of the Reynolds number for transition and the skin friction drag at zero lift of eight conecylinder bodies having varying fineness ratios has been made at Mach numbers of 1.62, 1.95, and 2.41 over a Reynolds number range from 0.5 x 10 to 10 x 10 The accuracy of the skinfriction data was not sufficient to permit any general conclu sions to be drawn. The Reynolds number for transition was indicated to be a function of some parameter which is influenced by changes in stagnation pressure. For the present results, the transition Reynolds number increased with increasing stagnation pressure r,ing from about 3 x 106 at 0 in. Hg to about 5 x 10 at 120 in. Hg. Up to the present time, no satisfactory explanation has been found for this phenomenon. Analysis of the present tests results together with the results of other conecylinder bodies of revolution having zeroheat transfer showed that the Reynolds number for transition at the base increased with increasing Mach number and reached a peak at a Mach number from about 2.0 to 2.5, and, thereafter, decreased with further increases in Mach number. Langley Aeronautical Laboratory, National Advisory Committee for Aeronautics, Langley Field, Va., August 18, 1955. CONFIDENTIAL COirF IDElITIAL NACA RM L55H21 REFERENCES 1. Potter, J. L.: Friction Drag and Transition Reynolds Number on Bodies of Revolution at Supersonic Speeds. NAVORD Rep. 2150, U. S. Naval Ord. Lab., White Oak, Md., Aug. 20, 1951. 2. Potter, J. L.: New Experimental Investigations of Friction Drag and Boundary Layer Transition on Bodies of Revolution at Supersonic Speeds. NAVORD Rep. 2571, U. S. Naval Ord. Lab. (White Oak, Md.), Apr. 24, 1952. 5. Jack, John R., and Burgess, Warren C.: Aerodynamics of Slender Bodies at Mach Number of 5.12 and Reynolds Numbers From 2 x 106 to 15 x 106. I Body of Revolution With NearParabolic Forebody and Cylindrical Afterbody. NACA FM E51H15, 1951. 4. Jack, John R., and Gould, Lawrence I.: Aerodynamics of Slender Bodies at Mach Number of 5.12 and Reynolds Numbers From 2 x 10 to 15 x 106. II. Aerodynamic Load Distributions of Series of Five Bodies Having Conical Nose and Cylindrical Afterbodies. NACA RM E52C10, 1952. 5. Jack, John R.: Aerodynamic Characteristics of a Slender ConeCylinder Body of Revolution at a Mach Number of 3.85. NACA RM E51H17, 1951. 0. Jack, John R.: Aerodynamics of Slender Bodies at Mach Number of 5.12 and Reynolds Numbers From 2 x 106 to 15 x 106. III Boundary Layer and Force Measurements on a Slender ConeCylinder Body of Revolution. NACA RM E53B05, 1953. 7. Brinich, Paul F., and Diaconis, Nick S.: BoundaryLayer Development and Skin Friction at Mach Number 3.05. NACA TN 2742, 1952. 8. Love, Euierne S., Coletti, Donald E., and Bromm, August F., Jr.: Inves tigation of the Variation With Reynolds Number of the Base, Wave, and SkinFriction Drs of a Parabolic Body of Revolution (NACA RM10) at Mach Numbers of 1.62, 1.93, and 2.41 in the Langley 9Inch Super sonic Tunnel. NACA RM L52H21, 1952. 9. Love, Eiene S.: The Base Pressure at Supersonic Speeds on Two Dimensional Airfoils and Bodies of Revolution (With and Without Fins) Having Turbulent Boundary Layers. NACA RM L55C02, 1955. 10. Love, Eugene S., and O'Donnell, Robert M.: Investigations at Super sonic Speeds of the Base Pressure on Bodies of Revolution With and Without Sweptback Stabilizing Fins. NACA RM L52J21a, 1952. CONFIDENTIAL CONFIDENTIAL NACA RM L553H21 11. Staff of the Computing Section, Center of Analysis (Under Direction of Zdenek Kopal): Tables of Supersonic Flow Around Cones. Tech. Rep. No. 1, M.I.T., 1947. 12. Chapman, Dean R.: An Analysis of Base Pressure at Supersonic Veloc ities and Comparison With Experiment. NACA Rep. 1051, 1951. (Supersedes NACA TN 2157.) 13. Bogdonoff, Seymour M.: A Preliminary Study of Reynolds Number Effects on Base Pressure at M = 2.95. Jour. Aero. Sci., vol. 19, no. 5, Mar. 1952, pp. 201206. 14. Kurzweg, H. H.: Interrelationship Between Boundary Layer and Base Pressure. Jour. Aero. Sci., vol. 18, no. 11, Nov. 1951, PP. 743748. 15. Eber, G. R.: Recent Investigation of Temperature Recovery and Heat Transmission on Cones and Cylinders in Axial Flow in the N.0.L. Aeroballistics Wind Tunnel. Jour. Aero. Sci., vol. 19, no. 1, Jan. 1952, pp. 16 and 14. 16. Anon.: BiMonthly Survey of the Project Hermes. No. 47, Gen. Elec. Co., Nov.Dec. 1949. C01iIFIDEIDTIAL CONFIDENTIAL NACA RM L55H21 (n m Li) cr tc '00 I 1 ci) f z  (1J , co) o a CONFIDENTIAL C(.l!iFIDEnlT. IAL NACA RM L53H21 N CONFIDENTIAL CONFIDENTIAL 14 COTFIDEiTIL NACA RM L55H21 36 i,  .. .. i "" 0 2 3 0 I 2 3 0 2 3 4 Model 1 Model 2 Model 3 36 32  32' .' _. S241 i  2 2 3 4 5 0 I 2 3 4 5 6 Mo 3el 4 Model ,r ^ jrI , .. S236       t . 4. ^24 CDT 28  .24 Model 6 24    .. 16   Molel 7 248 .  2  . . NACA 200 2 3 4 5 6 7 8 9 10 I 12 RL x 0 Figure 5. Variation of totaldrag coefficient with Reynolds number at M = 2.41. C 2'IFIT IE TTI AL NACA RM L55H21 l2 Molel 1 !'obel 2 M, el 4 .16 08 .04 0 I 2 3 4 5 )Moel 6 30 I 2 3 4 I : 3 4 5 eolel 3 'odel 5  . _ ^^ J^^ 0 2 3 "o lel 7 5 6 RL x 06 "odel 8 Figure 4. Variation of basedrag coefficient with Reynolds number at M = 2.41. CONFIDENTIAL ' ' I CONFIDENTIAL NACA RM L55H21 R= I 66x 10" 3 4 5 ( rx 2 rmax II ACA I I I 7 8 9 Viewed from rear of model o 0 o 90 O 180 A 270  Theory, 0 ref II 0 Figure 5. Typical pressure distributions over conical portion of cone cylinder body. M = 2.41. 0 O _ 95 IJi TIL i 0 1.2 14 16 18 Exp. SM= 1.62  D M=1.93 SM = 241 ACA, Theory, 0. ref. II 20 2.2 24x 106 Reynolds number based on length of conical portion of body Figure 6. Variation of forebody pressuredrag coefficient with Reynolds number. CONFIDENTIAL o.  , 8 Q, .I =E I I 0 I CDp Az I I I i i CONFIDENTIAL 24 r _ l __l" '1~ [P~ P ~q~ i I I NACA RM L53H21 C'?I FFIDEI TiAL , io 0) a r* Cd tJ o r1 c) I ' to *H t4 0I T' 1H CONFIDENTIAL NACA RM L55H21 It 4 *i I 'L. # CONFIDENTIAL MR t C I ' A7 4cC II ri rl 0 O II 43 4 cO CO ri di S I I .. cr A CONFIDENTIAL NACA RM L55H21 'uo!HsuDi jol jaqwunu spiouAea CONFIDENTIAL 901 x l :0I[FIDEIITIAL CONFIDENTIAL NACA RM L55H21 I ',e  'o  III1 (n c ^ 0 C C , (n 0)0 0 0 aa oa) 0 ") o3 C'J 0 >V (> A D Iz iC __ __  c OJ 0 t 4'  0 o 1 SC A c> _ ()c I___ m H 0 ca 00) S(U .0 c ad *Il a *i *0 0) , *O C (H 4 0 P 0 ) CH" 0  9_01 x ly 'uoi!suDJl jo jaqwunu splou/ae CONFIDENTIAL NACALangley 10753 325 O O 8.=C S <8 0 0 0 00 0 ":O S C.  so  I jo P cd0 . w,1n L o C a. 0 0 0 0 ~ 1 C, .l a)sg o U b ., 11 S a, o 0q 0 Z, r r W00Z 0 Ed : r 0 C L ) 0 w 0 c.1 00 C ,'0 0 0) g. m w4 0 Z > E Z: V o Z 00 ,g i, ,= ,E = .5 1 ) o I 1 l0 0 = c' r.K w 0 OO z C C. 4. b. Ct . = !0 2 E o zC lriw Cd H '.2 W U O a fccx~bflgg H .co o 2 CdJIs' a 00 mr 00 z CM CO m 'd Ca CM C')OM t C'13  2w 4[ o ,4 ., 2 s " 5 i i H ta ,3 C Uuo 2 2 oo.< w m ooz ' CM O 1  CT Cd zo 2^ ^' u ; v c.^ lI3' w S~ g ^ I9 g t. < :3 i 11 I g .a h j 03 CQUUOZ zto z~e 1 0 < 60 : 05 PL : 0 o t a 0 m m mu ': I^S S g^ 3^ ^ oi' Ea a a H s '. i c^ .2 'S _2 o ^e^~~ a gxsda5's^ ^a^^.l Sb,m g~ 00o m w O S E" o ;. :> Z^ g Lo u5 19 i N 0 ll wj U3 .i ;; 5 ^ig~t ^IJ~gs w H U bp 0.0 0 u P, u z ,~~*2~o POoE 0w 0P 0 0 6 >,6 0 0 .0 o0b >, c a 0 w0 W 'a w a pd r w ' a) cd cP:O >1 cd W zE r rn 0;9 rz (D > w Ua m md ri E U bb r : 1z0 CCR1C 0 m.r r~ Q V 9 36 u IUb. 3CCUI.0 ~o~g ~ C a ~ X.~ 3 ~.~ ~~0 *U0 \  z 0 u z~ 0 ; ra wT u^ f z4 .  1' F.( z g >4y 0 \2 4 P4 U~2 .2 .2 Z: ',c . Q m U 0 C OZ ^g= MC i w^m ^ i us  .2s m 2 2  s a .0 w '.. 0 04t 04n~ 05rtbL 'aIs l^ w 9) 0 W' c C .4. 0 zg g 0 Q) Pm :03, 2d o , 4. 0 o, 0 ^ s gg _C s.. o 0 0 = 10 ; c Q0 a z> ') r C', En a wA Z c a 4 M o *' 0C' >,, 0 'O .'j'D 2 0 '0 0 C4. . ,~2 I~ 5 0 n < z cdC4 4Ci .,.' 10. rdu0 0 00 UOOZ U.2 .2 0 00 ro U O < C') c 04C~  c.~ C')O~ ') S o o c^o ; oz 0 .. 'oo a ^ s~~~ig. uf 0o 0e 0 = lOOO 0 0C ;. W< 4 ~ m ooz r) W L 0 0 n ~ ,0oz % .) s'oa i= 0m 0 o 0 . > E_ ^ S < ws3 <^ s' ZI E M x >1 >j< 0 S z z 5& 0 p o 4 2 *.4.C 4ca no. .0) 0 C oii  ml 0. C",io 00 r o a iu 44 W WO W 2w.. ; h '0. 4;) rn> r w 2 3 3 0 a) 0 r F.0. ; 4 c.) A a C4 So c, 4"S ">c '; a .o'? g 2 C; ' C)< cXN.=< C') 3ao 0. CO c C 0 ' z C" C COCO C R r~ ooo oJ g 1oC .... u.2; .2 2 4 or CM) * CM c) ;m ,; ui~U co (I' z =mm"Mo5 0m 4C 0 St2 iiin 0 0 *0 Oc rI 0 E gzo s 2 = >f 0 Ot 2 M )CR 0 r a I= O Cl nii >,0 11 Cj3 >,g 0 04 a. C 0 a ~ " Co @ oT'0 CI a.S "o a a It 04 4 = ,o 36 >~ L..) ~ ac 0 E c 0 1. < = 0 u c a' 0... a. z z Pk z 0 u izi <2 z 0 u I' SECURITY INFORMATION CONFIDENTIAL UNIVERSITY OF FLORIDA 3 1262 08106 531 9 UNIVERSITY OF FLORIDA DOCUMENTS DEPARTMENT 120 MARSTON SCIENCE LIBRARY P.O. BOX 117011 GAINESVILLE, FL 326117011 USA CONFIDENTIAL T'"i jl S.ii i I ,ii r .,ig 