EIIIIIIIIIIIu- -EllllEllEEEEE EE//EEE/IEI/I ///li/eli/il

Transcription

1 lilllll 7A-A VORTEX ASYMIETRY DEVELOPMENT ON A TANGENT OGIVE(U) NAVAL SURFACE WEAPONS CENTER SILVER SPRING NO UNCASSIFIED YANTA ET AL. OCT 82 NSWC/TR S9-1A-F F/0 O 20/4 119 NL EIIIIIIIIIIIu- -EllllEllEEEEE EE//EEE/IEI/I ///li/eli/il

2 Nis Q8111L f. MICROCOPY RESOLUTION TEST CHART NATIONAL BUREAU Of STANDARDS-1963-A

3 44 e m UUW Jo YATAr ANQREW L. WANDAW JR. ~MY~ 1I LAWL MNSEARCW AND TECHMX013Y WEARTMINT OCTOBER US9PT' 1"VAA La S..s

4 UNCLASSIFIED SECURITY CLASSIFICATION OF THIS PAGE (UWuen Dat Entered) REPORT DOCUMENTATION PAGE BEFOR CMPTING ORM 1. REPORT NUMBER 2. GOVT ACCESSION NO. S. RECIPIENT'S CATALOG NUMBER NSWC TR / kl)-t 4. TITLE (and Subtitle) S. TYPE OF REPORT& PEIOD COVERED VORTEX ASYMMETRY OGIVE DEVELOPMENT ON A TANGENT el T s. PERFORMING ORG. REPORT NUMBER 7. AUTHOR(*) William J. Yanta S. CONTRACT OR GRANT NUMBER(&) Andrew B. Wardlaw, Jr. Daniel Sternklar 9. PERFORMING ORGANIZATION NAME AND ADDRESS 10. PROGRAM ELEMENT. PROJECT. TASK Naval Surface Weapons Center (Code K24) AREA N WORK UNIT NUMBERS Whit Oak61153N; WR02302; WR02302; White OakR4A Silver Spring, MD R44AA I I. CONTROLLING OFFICE NAME AND ADDRESS 12. REPORT DATE October NUMBER OF PAGES MONITORING AGENCY NAME & ADDRESS(t different from Controlling Office) is. SECURITY CLASS. (of this repot) 16. DISTRIBUTION STATEMENT (of this Report) UNCLASSIFIED ISa. DECLASSIFICATION/DOWNGRAOING SCHEDULE Approved for public release, distribution unlimited. 17. DISTRIBUTION STATEMENT (of the ebstract entered in Block 20, if different Irom Report) 18. SUPPLEMENTARY NOTES 19. KEY WORDS (Continue on reverse aide it necessary aid identify by block numbar) High Angle of Attack Vortex Shedding Side Force Separated Flow 20. ABSTRACT (Continue on reveree aide if neceesary and Identify by block nunber) A rigidly supported tangent ogive model has been tested in low turbulent, incompressible flow at an Incidence of 450. A constant streamwise Reynolds number of 1.5 (105) was maintained which produced laminar boundary layer separation. The sharp nose tip was replaced in some tests with a 10% spherically blunted one. In the sharp nose experiments it was found necessary to stabilize the flow field by adding a small trip. Both unsteady surface pressures and flow field velocities in the crossflow plane were DD IoJN EDITION OF INOV 65 IS OBSOLETE UNCLASSIFIED SECURITY CLASSIFICATION OF THIS PAGE (Uheni Date eere )

5 UNCLASSIFIED.LLURiTY CLASSIFICATION OF THIS PAGE(fWhU Dota Entered) measured, the latter with a two component Laser Doppler Velocimeter. The flow field in the vicinity of the leeside of the model surface, including the primary separation region was examined in detail. Results indicate that the flow field generally features two secondary structures on each side of the model which contain vorticity of opposite sign. Asymmetry starts with the windward crossflow plane streamline from the primary saddle point, which detaches from the body. It appears to be completed when the crossflow plane focus of the shed vortex combines with the primary saddle point. The introduction of nose bluntness is not found to fundamentally change the leeward flow field, although it does significantly reduce the level of asymmetry and the side force magnitude. UNCLASSIFIED SECURITY CLASSIFICATION OF THIS PAGE(Wen Date Entered)

6 FOREWORD A rigidly supported tangent ogive model has been tested in low turbulent, incompressible flow at an incidence of 450. A constant streamwise Reynolds number of 1.5(105) was maintained which produced laminar boundary layer separation. The sharp nose tip was replaced in some tests with a 10% spherically blunted one. In the sharp nose experiments it was found necessary to stabilize the flow field by adding a small trip. Both unsteady surface pressures and flow field velocities in the crossflow plane were measured, the latter with a two component Laser Doppler Velocimeter. The flow field in the vicinity of the leeside of the model surface, including the primary separation region was examined in detail. Results indicate that the flow field generally features two secondary structures on each side of the model which contain vorticity of opposite sign. Asymmetry starts with the windward crossflow plane streamline from the primary saddle point, which detaches from the body. It appears to be completed when the crossflow plane focus of the shed vortex combines with the primary saddle point. The introduction of nose bluntness is not found to fundamentally change the leeward flow field, although it does significantly reduce the level of asymmetry and the side force magnitude. IRA M. BLATSTEIN By direction Accession For G RA&I ic -I2

7 CONTENTS Chapter Page 1 INTRODUCTION NOMENCLATURE DESCRIPTION OF THE MODEL INSTRUMENTATION AND EXPERIMENT. 9 4 INFLUENCE OF THE NOSE TRIP PRESSURE AND FLOW FIELD MEASUREMENTS DISCUSSION OF RESULTS TOPOLOGICAL NOTIONS FLOW FIELD DEVELOPMENT ON THE SHARP TRIPPED MODEL FLOW FIELD DT.ZELOPMENT ON THE SHARP UNTRIPPED MODEL FLOW FIELD DEVELOPMENT ON THE BLUNTED MODEL ASYMMETRY FORMATION SUMMARY AND CONCLUSIONS REFERENCES Appendix A VELOCITY MEASUREMENTS A-i Appendix B SURFACE PRESSURE MEASUREMENTS B-i 3/

8 ILLUSTRATIONS Figure Page 1 TANGENT OGIVE PRESSURE MODEL AND SUPPORT SCHEMATIC OF THE LASER DOPPLER VELOCIMETER PRESSURE MODEL MOUNTED IN THE WIND TUNNEL NOSE TRIP MADE FROM.45mm GRIT C Ypeak AS A FUNCTION OF MODEL ROLL ANGLE AXIAL LOCATION OF C AND C = 0 AS A FUNCTION OF C Ypeak Y Ypeak 7 CIRCUMFERENTIAL PRESSURE DISTRIBUTIONS ON THE SHARP, TRIPPED MODEL CIRCUMFERENTIAL PRESSURE DISTRIBUTIONS ON THE BLUNT MODEL CIRCUMFERENTIAL PRESSURE DISTRIBUTION ON THE SHARP, UNTRIPPED MODEL MEASURED CROSSFLOW PLANE VELOCITY VECTORS ON THE SHARP, TRIPPED MODEL MEASURED CROSSFLOW PLANE VELOCITY VECTORS ON THE SHARP, UNTRIPPED MODEL MEASURED CROSSFLOW PLANE VELOCITY VECTORS ON THE BLUNT MODEL ISOVORTICITY CONTOURS AND AREAS OF HIGH VELOCITY FLUCTUATIONS ON THE SHARP TRIPPED MODEL ISOVORTICITY CONTOURS AND AREAS OF HIGH VELOCITY FLUCTUATIONS ON THE SHARP, UNTRIPPED MODEL ISOVORTICITY CONTOURS AND AREAS OF HIGH VELOCITY FLUCTUATIONS ON THE SHARP, UNTRIPPED MODEL STREAMLINES ON THE TRIPPED MODEL STREAMLINES ON THE SHARP UNTRIPPED MODEL STREAMLINES ON THE BLUNT MODEL TOPOLOGICAL SKETCH OF ASYMMETRIC FLOW DEVELOPMENT TABLES Table Page I WIND TUNNEL TESTS IN WHICH LDV DATA WAS TAKEN CIRCULATION CONTAINED IN REGIONS P, Sl AND S SIDE FORCE VARIATION /6

9 CHAPTER 1 INTRODUCTION At incidences greater than a few degrees, the flow on the leeside of a slender configuration separates and rolls up to form a pair of symmetric vortices. With increasing angle of attack, the pattern becomes asymmetric, even on axisymmetric bodies. In subsonic and transonic flow these vortices have a dominant and nonlinear influence on vehicle aerodynamics. The asymmetric vortex pattern which develops on a circular body at high angles of attack has been extensively studied In the subsonic flow regime this flow produces a large side force which has been found difficult to repeat experimentally. Even on axisymmetric bodies, the side force varies with changes in the model roll orientation. 1 3, 14 The non-repeatability appears to be primarily due to the occurence of a multiplicity of stable vortex patterns. Such patterns have been documented by the authors in Ref. 12. The different patterns are most likely triggered by model irregularities on the order of the machining tolerance which occur in the vicinity of the nose tip. Unsteadiness can also contribute to the lack of repeatability problem. Free stream turbulence causes the vortex pattern to jump from one stable configuration to another. 1 3 In the present study, crossflow plane velocities and surface pressures have been measured on sharp and slightly blunted tangent ogive models at an incidence of 450, under the condition of laminar separation. The sharp model was tested with and without a nose trip, which was designed to stabilize the flow field. Results obtained on all runs are presented in this report. This includes a listing of the measured velocities and surface pressures which are tabulated in Appendices A and B respectively, and an analysis of the data which is discussed in the main body of the report. The data presented in this report differs from previously available information in that it probes in detail the secondary flow regions near the model surface as well as outer or primary areas of the crossflow plane. The resulting measurements allow the presence of secondary vortices and shear layers to be determined. Further analysis is carried out by integrating the crossflow plane velocities to determine the crossflow plane streamlines. The resulting streamline patterns are interpreted in light of topological considerations. From this point of view it is possible to gain an alternate perspective on the onset of asymmetry and the process of vortex shedding. 7

10 CHAPTER 2 NOMENCLATURE Cp average value of (p-p.)/(qsin 2 a) for 100 data points taken at each visit to a pressure tap SF y/(dqsin 2 a) Cypeak D Fy q Re s U 0 maximum Cy value. model diameter (5.715 cm) side force per unit length free stream dynamic pressure Reynolds number based on freestream properties and D/sina freestream velocity v,w velocity components in y, z directions x, y, z cartesian coordinates (see Figure 1) I angle of attack r circulation (m 2 /sec) Xr/(wDU 0sina) (sec - ) * circumferential angle (windward is * f 1800) acp Vc standard deviation of Cp /Ov2+awl, where ov and a w are the standard deviations of v and w respectively. model roll orientation [r/unit area] D/(7rUosin) 8

11 CHAPTER 3 DESCRIPTION OF THE MODEL, INSTRUMENTATION AND EXPERIMENT The experimental model shown in Figure 1 was a cm in diameter tangent ogive with a nose fineness of 3 and an afterbody length of 9.6 calibers. The sharp nuse tip could be unscrewed and replaced with a 10% blunted (spherical) nose tip. Six cross sectional stations were each instrumented with 24 pressure taps located circumferentially at intervals of 150. Pressures were monitored using three internally mounted +.1 psi Setra differential pressure transducers. Each of these devices was connected to a 48 port internally mounted Scanivalve allowing all 144 pressure taps to be sampled. In order to maximize the response of the pressure measuring system the lengths of the tubes connecting pressure taps to Scanivalves were minimized. Pretest calibrations indicated that pressure fluctuations on the order of 500 Hz could be measured. The crossflow planes were surveyed using a two dimensional, two color backscatter LDV system shown schematically in Figure 2. In order to adequately survey the entire leeward flow field, the model was mounted on the tunnel wall opposite the window through which the LDV measurements were made. The refraction resulting from the oblique passage of the laser beams through the glass was compensated for by optically alligning the focal volumes of the two different components inside the tunnel. Off-axis collecting optics were used to minimize the focal volume size which was estimated to have a diameter of.37mm and a length of 1.47mm. Directional ambiguity for both components were removed with the aid of Bragg cells. A coincident circuit was used to insure that both components of velocity were measured within a pre-selected time window. In general most of the optical and electrical components for the LDV system were manufactured by TSI (Thermo-Systems Inc.). This included beam splitters, color separators, photomultiplier tubes, Bragg cells and counter type signal processors. Scattering particules consisted of olive oil atomized to a 1.5 micron diameter by a Laskin nozzle. The aerosol was injected upstream of the turbulence damping screens to minimize flow disturbance. Experiments were conducted in the Naval Academy lm by 1.3m subsonic tunnel which has a nominal free-stream turbulence level of 0.1%. Tests were restricted to an incidence of 450 and free-stream velocity of 24m/sec which produced an Re s of 1.5(105). As discussed in Ref. 15, this resulted in a laminar boundary layer separation. The wind tunnel model was mounted on the side of the wind tunnel wall illustrated in Figure 3. To increase the rigidness of the mounting, four support wires were attached to the model at a distance of 12.6 calibers from the nose tip. Pressure alone tests were initally made on the sharp untripped model at the twelve roll angles; 00, 300, Measurements were integrated to determine the magnitude of the normal and side forces. The model was then positioned to a roll orientation featuring a maximum side force and detailed flow 9 M-

12 surveys were initiated. Unfortunately, the flow field exhibited a tendency to change levels of asymmetry during a test and side force levels were also not repeatable from test to test. Accordingly: a trip was added to the model nose tip to stabilize the flow field. The trip, shown in Figure 4 consisted of 0.45mm grit glued to the model surface near the nose in a strip 5mm long and imm wide. Pressure alone tests were then repeated to determine a roll orientation which produced high side force levels and flow field surveys were than conducted at this roll angle. A final series of tests were also made on the blunted model using a roll orientation which produced the highest observed blunt model side force. An outline of tests in which LDV data was taken is provided in Table 1. The surface pressure data were acquired three ports at a time using the internally mounted Scanivalves and transducer arrangement. At each pressure port 100 samples were taken which allowed both pressure mean and standard deviation values to be determined. The LDV velocity data were measured by focusing the system on a specific point in the flow field. Velocity measurements were acquired whenever both v and w components were measured within a 100 p sec. window. Here 100 samples were also taken at each point in the flow field allowing both the mean and standard deviation values to be calculated. In the secondary flow region near the leeside of the model surface, measurements were taken with a y, z spacing which varied from.76mm near the model nose tip to 1.27mm on the afterbody crossflow planes. This spacing was increased by a factor of 3 to 4 in the outer portions of the flow field. Pressure alone tests could be completed in about 10 minutes while the LDV surveys which measured velocities at as many as 950 points in a crossflow plane lasted up to three hours. 10

13 CHAPTER 4 INFLUENCE OF THE NOSE TRIP During the long experiments in which crossflow plane velocities were measured, the flow field occasionally changed level of asymmetry. This was determined by monitoring the surface pressures throughout the tests. Measured variations in the side force during the two sharp, untripped model tests are shown in Table 1. The level of variation was felt to be unacceptably large, hence the previously described trip was added to the model nose. Trips applied near the model nose have been successfully used by other investigators to stabilize the flow eld 1 6. The magnitude of the peak local side force, Cypeak, with and without the ip in place is illustrated in Figure 5. The addition of the trip usually i eased Cypeak, particularly at roll orientations which featured low side force s in the untripped case. The grit trip also was found to produce a side f, which was repeatable throughout long experiments. In successive experim the repeatability degraded somewhat as can be seen in Appendix B, howeve._ak was still well reproduced. Application of a tape trip with a similar pla,.urm was found to produce a more drastic effect which included reversal of the side force direction. This is more in keeping with the results of Ref. 16 where a tape trip was found to control the side force direction except at roll orientations which placed the trip near the windward plane. Although addition of the trip stabilizes the flow field, it is relevant to ask whether the presence of the trip alters the fundamental character of the flow field. It was noted in Ref. 12 that a side force characteristic which appears repeatable from test to test and facility to facility is the relation between the axial location at which Cypeak or Cy = 0 occur and the magnitude of Cypeak. If the character of the flow field is unchanged by the addition of the trip, the tripped data should reproduce the previousl, observed relationship. As is shown in Figure 6, data taken on the untripped model from both this study and Ref. 12 are in reasonable agreement with the tripped results. This suggests that the trip locks the flow field into a pattern typical of the untripped model and does not fundamentally alter its character. 11

14 CHAPTER 5 PRESSURE AND FLOW FIELD MEASUREMENTS Pressure coefficient and standard deviation data taken on the sharp tripped and blunt models are illustrated in Figures 7 and 8 respectively. During these experiments, results repeated reasonably well during each test and from run to run. The data provided in these two figures is representative of the sharp tripped and blunt model pressure measurements respectively. During the sharp, untripped model tests, the level of asymmetry was low and the measured side force changed during each run. In Figures 9a and 9b are illustrated the circumferential Cp distribution corresponding to the lowest and highest side force levels encountered during runs I and 2. The measured crossflow plane velocity vectors taken in the tests on the sharp untripped, sharp tripped and blunt model are illustrated in Figures 10, 11 and 12 respectively. Clearly visible in these figures are points located adjacent to the model surface where the velocity component parallel to the surface reverses direction. These locations are interpreted as attachment and separation points and are marked by an S and S s respectively. Also marked by S s are the windward separation points on each side of the body whose locations are estimated using both velocity and pressure data. Evident in Figures 7 and 9 are locations where maximum values of C 0 occur. Such points are marked by P in Figures 10 to 12. Similarly, regions on the leeside of the body exhibiting large 1--essure gradients in Figures 7 to 9 are marked in Figures 10 to 12 by a G. As is evident in Figures 10, 11 and 12, the crossflow plane surveys consisted of closely spaced measurements taken near the model surface and measurements taken farther from the model surface which are located a greater distance apart. Along the interface between the finely and coarsely spaced data occur points which have been probed twice; once as part of the finely spaced measurements and once as part of the coarsely spaced measurements. In Figures 10, 11 and 12 both sets of data have been plotted which provides a measure of the repeatability of the results. Near the outer edges of the crossflow plane coincident velocity measurements are generally indistinguishable, but in the vicinity of vortices a difference can often be seen (e.g. Figure lob). The vorticity throughout each crossflow plane is calc lated by dividing the surveyed area into quadrilateral elements with corners located at points where flow field velocities are measured. The circulation associated with each element is determined from: r v.t = 1/2 [nl2.(vl + v2) + n23"(v2 + V3) + n34"(v3 + v4) + n41"(v4 + Vl)] (1) 12

15 Here nij is the vector connecting element corners i and j while vi is the velocity at corner i. The computed circulation is assigned the location of the element centroid. Isovorticity contours resulting from this calculation are displayed for the sharp tripped, sharp untripped and blunt models in Figures 13, 14 and 15 respectively. Also indicated in these figures are regions of high velocity fluctuations in which the standard deviation of the crossflow velocity, 0 Vc, exceeds.3uw. A convenient method of characterizing the crossflow plane is to divide it into the regions shown in Table 2 which contain vorticity of the same sign. The circulation computed at each element in the crossflow plane is assigned to one of these regions allowing the total circulation in each region to be calculated. The few elements which do not possess a symmetric counter part with respect to the pitch plane are excluded from the summation. The outer portion of the crossflow plane is divided into two primary regions, designated by a P, which contain circulation of opposite sign. Secondary flow structure often is visible near the model surface. On each side of the model the secondary crossflow plane areas are divided into two regions, S and S2 which contain circulation of opposite sign. The boundaries between all three regions are somewhat subjective. Most easily determined is the dividing line between regions containing circulation of opposite sign where the zero vorticity contour provides a convenient demarcation line. The boundary between the primary and secondary regions with circulation of the same sign is taken to be the contour with the minimum vorticity value. The calculated circulation of the primary and secondary regions are provided in Table 2. In two of the cases listed in Table 2, the strength of one of the secondary region, )Sl, is marked with an asterisk. Here the surveyed portion of the flow field clearly omits areas of high vorticity and the calculated strengths is unreasonably low. These tabulated values are estimated using the known ratio of ASl left to As 1 right from nearby crossflow planes and the measured value of XSl right- It is important to note that the circulation contained in each region cannot necessarily be associated with a vortex since not all regions contain vortices. Also, in region S1, there often exists both a strong shear layer which springs from the separation point and a vortex. Here the circulation attributable to each structure cannot be determined. Additional information concerning the structure of the flow field can be obtained by constructing the crossflow plane streamlines. A streamline can be generated by integrating the equations: dt dw dt (2) from a starting point. The starting points are selected by trial and error to highlight regions near the vortices and separation points. To evaluate Equations (2) a description of v and w throughout the surveyed portion of the crossflow olane is necessary. Such a description is constructed using a bilinear interpolating function of the form a + by + cz + dyz to specify each velocity component within an element. Here a, b, c and d are constants evaluated using the measured velocities at the corners of the element. This provides a continuous description 13 i iibm ~.

16 of the velocity throughout the crossflow plane. As is noted in Refs. 18 and 19 the crossflow plane streamlines are not the projection of the three dimensional streamlines into the crossflow planes, but are instead the streamlines produced by the crossflow velocity vector field. The streamlines determined by the above intcnation procedure are shown in Figures 17, 18-and 19, for the sharp tripped, sharp untripped and blunt models respectively. These figures illustrate two notable characteristics. First, streamlines originating near the estimated primary separation points do not feed into vortices but instead skirt the recirculation flow region. Second, streamlines near vortex cores often have a pronounced inwards or outwards spiral. Using the velocity measurements of Figures 10 to 12 it is possible to resolve the direction of spiral. Pronounced inwards or outwards spirals tend to occur in flow fields featuring high asymmetry. In such cases primary vortices which are clearly resolvable on adjacent crossflow planes usually retain the same direction of spiral. The more symmetric flow patterns feature vortices with poorly defined directions of spiral. Limit cycles are often observed with the direction of spiral changing across the limit cycle. In these cases it is conceivable that the presence of a spiral rather than a set of closed streamlines is a result of experimental error. 14

17 CHAPTER TOPOLOGICAL NOTIONS It has recently been suggested that the crossflow plane structure can be conveniently characterized in terms of singularities, or points where the crossflow velocity is zero. 17, 18 Several types of singularities occur in the flow fields illustrated in Figures 10, 11 and 12. Saddle singularities occur on the model surface as attachment or separation points. Also classed as saddle singularities are crossflow plane stagnation points interior to the flow field which are formed by the intersection of four streamlines, two directed towards the singularity and two directed away from it. Nodal singularities only occur off the body surface as stagnation points about which the streamlines spiral or circle. This structure is reminiscent of a vortex and in this report, the term vortex and nodal singularity will be used interchangably. For a more complete discussion of singularities, the reader is referred to references 17 and 18. These topological notions are useful in analyzing the structure of the crossflow plane for two reasons. First such notions provide a concrete definition of several types of flow field structures. A vortex, for example, must contain a singular point. Thus the left secondary flow region depicted in Figures 10c and 16d is seen to contain a vortex and a shear layer rather than two vortices. Secondly, assuming that the crossflow plane is a continuous vector field and that singularities are limited to points, it can be proved that the following relation must exist between the number of nodes and saddles: 1 8 N v - N s - (N;) = -1 (3) Here Nv is the number of nodes or vortices while N' and s represent the number of saddles on and off the body surface respectively. This rule does not define crossflow plane structure but precludes certain structures. It may also point to the existance of certain flow field features which are not resolvable with the available experimental data. The streamline integration patterns shown in Figures 16, 17 and 18 illustrate the existence of both vortices and saddle singularities throughout the surveyed crossflow planes. The primary region generally contains two vortices and a saddle point. This saddle point, which is usually located in between these vortices, is an important landmark and will be referred to as the primary saddle point. The secondary region on each side of the body often contains two vortices and a saddle point. The saddle is not always clearly visible, however satisfaction of Equation (3) mandates its existence. In other instances, only a single secondary vortex is present in this secondary region. A number of saddle points occur on the model surface. In all cases an attachment saddle is visible near the center of the model on the leeside. Also, on each side if the model a separation saddle can be seen marking the windward extend of the separation region. These attachment and separation saddles will be referred to as the rear attachment and 15

18 primary separation points respectively. When secondary vortices occur, an additional separation and attachment saddle occur on each side of the model. Not visible in the flow field surveys is a saddle of attachment which must occur on the windward side of the body, often termed the crossflow plane stagnation point. Using the results from the streamline integrations, it is possible to construct crossflow plane topologies which contain the correct number of nodes and saddles to satisfy Equation (3). As an example, sketches of the crossf low plane topology for the sharp, tripped model are exhibited in Figure 19. The left primary vortex and primary saddle are shown as combined in Figure 19c. Inclusion of these two structures would also satisfy Equation (3). 6.2 FLOW FIELD DEVELOPMENT ON THE SHARP TRIPPED MODEL The tabulated circulations on the surveyed crossflow planes are shown in Table 2. On each plane a net negative circulation occurs which increases in magnitude with increasing distance from the model nose. The magnitude of the net circulation increases in rough proportion to the size of the local side force coefficient. Also indicated in this table are the circulation strengths of the primary and secondary regions P, S1 and S2 associated with each side of the model. As expected, the largest circulation occurs in P. The circulation contained in Sl is about half as large as that in P while that in S2 is on the order of a tenth of that in P. At the forward most crossflow plane probed, which is at X/D =.75, the outer edges of two primary vortices can be seen. In this crossflow plane which is illustrated in Figure loa, the primary saddle is not fully visible, but is likely offset to the left. The crossflow plane velocity field at an axial station of X/D = 1.3 is shown in Figure lob and features two primary vortices but no secondary vortex structure. The vortices and primary saddle point appear to be symmetrically located; however, the rear attachment point, marked by an SL is offset slightly to the right. Also the velocities between the two vortices, second row behind the model are all pointing to the left. As is shown in Figure 16a, the resulting streamline pattern is highly skewed. The left and tlght vortices both spiral outwards and the windward streamline from the primary saddle point does not attach to the model surface, but moves around the left vortex and then out the leeside of the visible flow field. A topological sketch of this crossflow Plane which satisfies Equation (3) is provided in Figure 19a. At an axial station of X/D = 2.6, both primary and secondary vortices are visible in Figures 10c and 16b. The left primary vortex has moved away from the model surface while the right primary vortex ha; rotated towards the leeside. The primary saddle point has moved away from the model and to the left. The windward streamline from the primary saddle point feeds into the left vortex which has reversed its direction of spiral when compared to the axial station at X/D = 1.3 and now spirals inwards. The right primary vortex retains the outwards spiral visible at X/D = 1.3. Streamlines originating in the vicinity of the right primary separation point pass between the two primary vortices and leave the visible flow field from the left side. The streamlines originating near the left primary separation point also leave the visible flow field from the left side. 16

19 As can be seen in Figures lod and 16c, the same flow field structure which exists at X/D = 2.6, persists at X/D = 3.6. The left primary vortex has moved farther from the model surface, but it still spirals inward and is fed by a streamline from the primary saddle point. The right vortex continues to spiral outwards, except very near to the vortex core where a limit cycle occurs. The topology sketched in Figure 19b which satisfies Equation (3) is representative of the crossflow plane structure at X/D = 2.6 and 3.6. The maximum measured side force coefficient occurs at X/D = 4.7 and the accompanying flow field structure differs from that at X/D = 2.6 and 3.6. In Figure 10e only the right primary vortex is clearly visible. The distance between the left primary vortex and primary saddle point has decreased suggesting that these two structures have combined. The term combined is applied since both structures must disappear simultaneously in order to satisfy Equation (3). A careful construction of streamlines in the vicinity of the left primary vortex and adjacent saddle which is shown in Figure 16d indicates that the process of combination is not complete. The right primary vortex retains the outwards spiral visible at upstream stations and has moved leeward to a position nearly behind the model. The secondary region has become highly skewed with the rear attachment points and secondary separation points rotated in a counter-clock-wise direction. On the right side of the model, two counter-rotating secondary vortices are present while on the left side only one secondary vortex which rotates in a counter clock-wise manner can be seen. The clockwise rotating vortex and adjacent saddle point visible on this side of the model at X/D = 2.6 and 3.6 have combined to leave a strong shear region. An examination of the flow field adjacent to the left primary separation point indicates the formation of a region of counterclockwise rotation. Although this is not particularly evident in Fig. loe, the circulation of a number of adjacent elements in this region is positive suggesting the formation of a new secondary vortex. The calculated strength of this new vortex is given in Table 1. A plausible topology for this crossflow plane which satisfies Equation (3) is shown in Figure 19c. Here the left primary vortex and saddle are taken to be combined and are therefore not shown. Inclusion of these two structures would also satisfy Equation (3). Circumferential pressure profiles measured at the axial stations of X/D = 2.6, 3.6 and 4.7 are shown in Figure 7. It can be seen that flow field asymmetry produces differing levels of pressure on each side of the model. Lowest pressures occur on the side of the model with the closest primary vortex. The differing pressure levels occuring on each side of the model are bridged by sharp pressure gradients on the leeside of the model. These gradients extend from below each primary vortex core to the rear attachment point and are indicated by a G in Figure loe. At an X/D of 2.6, both primary vortices are located fairly close to the model surface and two pressure gradients of opposite sign occur. A single sharp pressure gradient exists beneath the right primary vortex at X/D = 3.6 and 4.7. Also indicated by a P in Figure 10 are points on the model surface where the pressure standard deviation reaches peak value. These peak values are located in the vicinity of the large pressure gradients and are likely caused by an unsteady circumferential motion of the vortex pattern. Such unsteadiness moves the position of the surface pressure gradients and produces large pressure fluctuations at fixed points on the model which are located nearby. 17

20 A comparison of Figures 7 and 10 indicates that secondary vortices have little discernable effect on the measured surface pressures. This is probably attributable to the small circulation strengths of these structures. Table 2 indicates that the circulation contained in the S2 region is typically small. The strength of the vortices in the S1 region cannot be determined since this region contains both a strong shear layer and a vortex. 6.3 FLOW FIELD DEVELOPMENT ON THE SHARP UNTRIPPED MODEL On the sharp untripped model, surveys were carried out at X/D values of 2.6 and 5.7 with the latter survey covering only the secondary region. From Appendix B it is evident that the side force levels on the untripped model are much lower than those measured on the tripped model. As was previously mentioned, fluctuations in the surface pressures were noted in tests involving the untripped sharp model. The level of variation is indicated in Table 3 where samples of side force data spanning runs 1 and 2 are shown. The crossflow planes at X/D of 2.6 and 5.7 were probed in runs 1 and 2 respectively. It can be seen from Table 2 that side force levels in both of these runs were fairly steady at the axial locations where the velocity measurements were made. At the axial station of X/D = 2.6 little asymmetry is visible in the crossflow velocity vector plots and streamline contours of Figures lla and 17 respectively. As is shown in Table 2, the net circulation is nearly zero and the side force coefficient, although fluctuating slightly, is also small. The crossflow plane clearly contains two primary vortices and on each side of the model two secondary vortices. The streamlines originating near the estimated primary separation points do not roll up into the primary vortices but skirt the recirculatory region and pass out of the surveyed portion of the flow field on the side of the model from which they originated. This is in contrast to the asymmetric case shown in Figure 16b where the streamlines originating near the right primary separation point pass between the two primary vortices and out of the visible portion of the flow field from the left side. Another notable aspect of the streamline pattern is the windward streamline from the primary saddle point. As in the asymmetric case this streamline does not attach to the body but circles around the left vortex. Neither of the primary vortices has a well defined direction of spiral and limit cycles occur near each vortex. At an axial station of 5.7, only the secondary portion of the flow field was surveyed. The primary vortices appear to have moved to the right since the rear attachment point is on the right side of the model. On the left side of the model two counter rotating vortices are visible in the secondary region shown in Figures llb while on the right hand side only one vortex appears to exist. The second vortex has presumably combined with the adjacent saddle in a similar manner to that observed on the rfrht hand of the sharp, tripped model at X/D = 4.7 (see Figure 16e). The pressure distributions on the sharp untripped model are presented in Figure 9 and display the same general features which occur in the asymmetric case. In low side force cases where the flow field is relatively symmetric, a sharp pressure gradient occurs beneath each primary vortex. A single pressure gradient occurs when a larger side force is present (e.g. Figure 9b) and is likely located below the closer of the two primary vortices. As in the case of the tripped model, the secondary vortices do not induce a discernable effect on the circumferential pressure distribution. 18

21 6.4 FLOW FIELD DEVELOPMENT ON THE BLUNTED MODEL The blunt model was tested at a roll orientation producing a Cypeak of.95, which is one of the highest values observed for this model. The velocity data was measured at axial stations with X/D values of 2.6 and 5.7. Crossflow plane velocities and streamlines at X/D = 2.6 are shown in Figures 12a and 18a respectively. This crossflow plane contains two primary vortices and two secondary vortices of opposite rotation on the left side of the model. On the right side of the model only a secondary vortex of clockwise rotation is partially visible. The primary vortex pattern is slightly offset to the left side of the model. As is shown in Table 2, the net circulation is positive as is the local side force. This is in contrast to the sharp tripped model case where a net negative circulation is associated with a positive side force. The streamlines in the vicinity of the right primary vortices show a pronounced outwards spiral while those near the left primary vortex feature a limit cycle with an outwards spiral inside of the cycle and an inwards spiral outside of it. Streamlines originating near the primary separation points skirt the recirculatory flow region and leave the flow field from the same side on which they started. The windward streamline from the primary stagnation point does not attach to the body surface, but instead circles around the right vortex. When compared to the sharp untripped model streamline pattern, a strong similarity is evident. In the blunt model case, though, the primary vortices appear to have a more defined direction of spiral. The blunt model achieves its maximum side force at X/D = 5.7. The measured flow field at this axial station is displayed in Figures 12b, 18b and shows significant asymmetry. The primary vortex pattern is offset to the left. Unlike the tripped, sharp model flow field, the left hand vortex has not moved away from the model. The secondary flow field region has two counter rotating vortices and a saddle on each side of the model but these areas are clearly not symmetric in structure or location. The attachment and separation points noted in Figure 12b are offset in a counter-clockwise direction. On the left side of the body the secondary vortex of clockwise rotation has moved away from the body surface. The net circulation over the surveyed portion of the flow field is slightly positive as indicated in Table 1. The streamline pattern which is shown in Figure 18b features primary vortices which have a well defined outwards spiral. This structure is reminiscent of that visible on the sharp tripped model at X/D = 1.3 (see Figure 16a). As in the sharp, tripped model case, streamlines originating near the right primary separation point appear to pass between the two primary vortices and then out of the surveyed portion of the flow field from the left side. An unusual aspect of the blunt model flow field can be seen by considering Figures 8 and 15b which indicate that both the velocity and surface pressures show very high levels of fluctuation. The pressure profiles on the blunted model are very similar to those on the sharp model. The different pressure levels which form on each side of the model when a side force occurs are bridged by sharp pressure gradients which occur beneath the vortex nearest to the model surface. The symmetric primary vortex pattern, which occurs at X/D = 2.6 features pressure gradients beneath each primary vortex. 19

22 CHAPTER 7 DEVELOPMENT OF FLOW FIELD ASYMMETRIES It has been suggested that flow field asymmetry is a manifestation of a hydrodynamic instability which develops when primary vortices are crowded together. 1 9 Peake, et al. 1 1 form the hypothesis, based on Nishioka and Sato's 2 0 incompressible cylinder data, that amplification of perturbations in the flow field near the primary saddle point results in the development of the asymmetric flow field. Irregularities in the model geometry serve only to determine the extent and direction of the flow field asymmetries. The results from the current study support the hypothesis that the flow field near the primary saddle point plays a principal role in the formation of the asymmetric flow field. Many of the crossflow planes surveyed appear to be symmetric both with respect to vortex location and strength. However, in all cases the windward streamline from the primary saddle point does not attach to the body surface but insteady circles about one of the primary vortices as is indicated in Figures 16 to 18. It thus seems to be this streamline which first reflects flow field asymmetry and presumably only small perturbations in the vicinity of the saddle point are sufficient to cause this streamline to detach from the model surface. Using the streamline traces of Figures 16 to 18 it is possible to construct a description of vortex shedding in terms of saddle and nodal singularities. Small perturbations near the primary saddle point leads to a detachment of the windward primary saddle streamline from the body surface, as is shown in Figures 17 and 18a. This streamline initially appears to roll up into one of the two primary vortices, neither of which have a well defined spiral direction. Figures 16a and 18b suggest that as the asymmetry in the crossflow plane grows, both vortices tend to develop a well defined outwards spiral. The windward streamline form the primary saddle now circles one of the vortices and then passes out the leeward side of the surveyed flow field. This topology is illustrated in Figure 19a and still features primary vortices which are relatively symmetrically located. As the crossflow plane asymmetry increases, one of the vortices moves away from the model and reverses its direction of spiral to inwards as illustrated in Figures 16b and 16c. The windward streamline from the primary saddle now feeds into this vortex and the resulting crossflow plane topology is illustrated in Figure 19b. Further asymmetry development leads to a combination of a primary vortex and the primary saddle. Figure 16d suggests that such a combination occurs while Figure 19c illustrates the resulting topology. Clearly, in order to satisfy Equation (3), the vortex and primary saddle must simultaneously dissappear from the flow field. It is of interest to compare the topological description of asymmetry development with the more conventional view of this process. Traditionally the crossflow plane has been visualized as containing both shed and attached primary vortices. Each attached vortex is connected to a primary separation point by a feeding sheet. As asymmetry develops and a vortex starts to move away from the body surface, the feeding sheet is torn and the vortex is shed. In the current 20

23 study the calculated crossflow plane streamlines which originate near the primary separation points do not feed into vortices. Hence the current data does not define a feeding sheet and an analog to the tearing of the feeding sheet is not evident. The clearest topological landmark visible in the asymmetry development process is the combining of the primary saddle and a primary vortex. This occurance provides a convenient definition of vortex shedding in the current study. However, the present study is limited in scope and it is not clear whether such a combination process takes place as subsequent vortices are shed or under different test conditions. Thus, the general applicability of this definition of vortex shedding remains to be demonstrated. The blunt model experiences,in general,a much lower level of side force than does the sharp model. Not only are maximum side loads lower, but average values taken over many different roll angles are significantly less. The maximum local side force occurs on the blunt model at X/D = 5.7. The resulting velocity and streamline data at this axial station are shown in Figures 12b and 18b respectively, and represent a roll orientation with the highest observed side force. From these figures it is evident that the maximum degree of flow field asymmetry which occurs on the blunt model is much less than that observed on the sharp model (see Figures 10 and 16). In fact, the degree of asymmetry is sufficiently low on the blunt model to suggest that vortex shedding does not take place. The reason for the difference in asymmetry levels observed on the sharp and blunt models remains unclear. A comparison of the blunt measurements taken at X/D = 2.6 with those at the same axial station on the sharp and sharp, tripped models indicates that the general flow field structure is qualitatively the same. Quantitatively some differences are detectable which include a 10% to 15% reduction in primary vortex strength in the case of the blunt model. An interpolation of the measured velocities along the pitch plane indicates that the primary saddle point is close: to the body surface on the blunt model than on the sharp model. Also, on the blunt model asymmetries in vortex strengths are principally confined to secondary vortices. However, it is difficult to construct an explanation for the apparent increased stability of the blunt flow field from any of these observed differences and the best hypothesis appears to concern the absence of a sharp nose tip. Near the tip of a sharp nose the local diameter is small and local irregularities may amount to extremely large local perturbations. A similar perturbing mechanism does not exist on the blunt model. 21

24 CHAPTER 8 SUMMARY AND CONCLUSIONS A tangent ogive model with nose fineness of three has been tested in incompressible flow at an incidence of 450 and with a Reynolds number producing laminar separation. The model was rigidly supported in the wind tunnel which had a streamwise turbulence level of.1%. The model's sharp nose tip was interchanged in some tests with a 10% spherically blunted one. In tests on the sharp model, a strip of grit placed near the nose was often used to stabilize the flow field. Both surface pressures and crossflow velocities were measured on several crossflow planes. A two component LDV system was used to probe the flow field near the primary separation points as well as further out from the model. Axial stations upstream of the location at which the maximum side force occured were investigated. Based on the data taken in this study the following conclusions can be drawn: 1. Use of a grit trip near the model nose stabilizes the flow field without changing its basic side force characteristics. 2. In addition to two primary vortices and a primary saddle, the flow field generally contains two counter-rotating secondary vortices and a saddle point on each side of the model. 3. The development of the asymmetric flow field on the sharn tripped model up to the point of maximum side force can be characterized by the following three steps: a. Flow field asymmetries seem to originate with instabilities at the primary saddle point. The windward streamline leaving this point detaches itself from the body surface, circles about one of the vortices and then moves out into the leeward flow field. b. The vortex circled by this primary saddle point streamline moves away from the model. c. The primary saddle and a primarv vortex appear to combine on the crossflow plane at which the peak side Force occurs. The point of combination appears to offer a convenient definition of vortex shedding. 4. Blunting the model nose by 10% drastically reduces side force and the degree of flow field asymmetry. The windward primary saddle point streamline detaches from the model and circles a primary vortex as in the sharp model case. However, at the axial station featuring maximum Cy, neither primary vortex appears to be in the process of shedding. The increased stability of the blunted model flow field is hypothesized to be related to the absence of a slender nose tip on which model irregularities become large perturbations

25 ACKNOWLEDGMENTS This project was supported by William C. Volz of the Naval Air Systems Command. The authors wish to thank Commander Paul Schlein and his staff at the U. S. Naval Academy for making the wind tunnel testing facilities available. 23

26 NSWC TR 82-39h z Y X/D =2.6 X GYWR 5,O.7 5. SUPPORT ". 3 / D 66D Figure 1. Tangent ogive pressure model arid vupport 24

27 NSWC TR 8--) 1 2-D BACKSCATTER LDV a 450 FLOW I=> 3FT x 4Ff TEST SECTION 22 COLOR COLLECTING OPTICS Fii~lire 2. 2c'homat-i e of the l,*uver i o 1-- meter 25

28 NSWC TR 82-39), ".~~emodel mounted in the wind tunnel 26

29 cm1 Fir-ure h. Nose trip wrvi e!poit 27

30 3- Cypeak 2t SHARP MODEL 3 a = NO TRIP TRIPPED -1 I 0 TRIP ONTRPO LEEWARD WINDWARD PLANE PLANE L Figure 5. C as a function of model roll angle peak 28

31 NSWC TR 82-39h 9- C y " 0 o e location 0 0 X'/D A 0 A 00-eo 0 0 AA U0 0 6A A A 6 - e o o0 Cypeak OA A location A- 8 X'/D 5 A 0 NO TRIP o & TRIPPED 4 o NO TRIP, REF 17 A NO TRIP, HIGH 3 TURBULENCE A,L 2 (i I a I I 1_1 I I Cypk Firure 6. Axial location of'!itr 1 a', faunctionl of C.Yjl-ak ypeak 29

32 r7 NSWC TR i,,c L I II o X/D = 2.6. Cy =.77 A X/D = 3.6, Cy = X/D = 4.7, Cy = Fiure 7. 2 ircumferential pressure distriutions on the sharp, tripped no(,el. (pen Symbols are anr sol i ones are o c p 30

33 0 X/D 2.6, Cy =.33 Cp, A X/D=5.7, Cy = /.2 P )or r--t- \ Figure 8. Circumferential pressure distributions on the blunt model. Open symbols are C and solid ones are a p p 31

34 NSWC TR 82-39h A) Highest side force case ac p Cp \ 0 C ~1 "'- W a A -1. X/D = 2.6, Cy =.27 0 O X/D = 5.7, Cy = Figure 9. Circumferential pressure distribution on the sharp,untripped model. Open symbols are C and solid symbols are a p p 32

35 B)Lowest side force case GCp / 40-0, ir Air 1. -~ * I0 X/D= 2.6, Cy = X/D =5.7, Cy =-.022 Figure 9. (Continued) 33

36 A) X/D =.75 Figure 10. Measured crossflow plane velocity vectors on the sharp, tripped model. S' and S' are attachment and separation points respeca s tively. The P represents peak a C locations while the G indicates regions of sharp pressure gradients 34

37 B) X/D =1.3 7//i Zi~ Figure 10. (Continued) 35

38 C) X/D =2.6,)/D2, / Tt \ \ \\ \, /7c it 1G, Figure 10. (Continued) 36

39 NSCTE D) X/D 3.6 /X 7 t Mir~ Figurle 1. (Cnt; ud -~~I -A---

40 E) X/D =.7 Figure 10. (Continued)

41 E) (Continued) Enlargement of left secondary region. 4/4 4-- Figure 10. (Continued) 39

42 E) (Continued) Enlargment of right secondary region. Figure 10. (Continued) 40

43 1 7 A X/ D 2.6N S W C TI R A) 2. X/ = * It t ' Figure ]1. Measuzred crossflow plane velocity vectors on the sharp, untri pped model. S' and S' are the attachment and separation points respectively. The P represents peak a locationls while the Gl indicates regions of sharp pressure gradients. 41

44 k B) XID \ %.4 '.r Figure 11. (Continued) 42

45 NSWC TR 82-39h B) (Continued) Enlargement of left secondary region. k- 3 + ii Figure 11. (Conti.nued) 43

46 NSWC TR 82-39h B) (Continued) Enlargement of right secondary region. A Figure 11. (Continued) 44

47 A) X/D = 2.6 Figure 12. Measured Crossflow plane velocity vectors on the blunt model. S' a and S' s are attachment and separation points respectively. The P represents peak a C locations while the G indicates regions of sharp pressua gradients. 45

48 B) X/D 57 ZIP p 4 Z~,*P p >3zv kk Fiur 12.Cniud 46

49 ~ B) (Continued) Enlargement of the left secondary region. 71 Figure 12. (Continued) 47

50 B)(Coltiflued) Enlargement of righat secondary region. 484

51 A) X/D =1.3 SHARP, TRIPPED MODEL X/D =1.3 >0ISOVORTICITY CONTOURS W.....

52 B) X/D = 2.6* C = 7 / - - ~-2.0 "

53 C) xid =3.6, Cy= / -4. / I2. ~ ~ Figur 134Cotnud 0451

54 D) X/D 4.7 C IX Figre13+(onnud +Z52

55 X/D =2.6, = I i.u +80~ onteshrun.p0dmdl - w.0 ; w j7~~lo~ /U

56 A) XID =2.6 ;C = /'.; '~ ( Figure 15. Isovorticity contours and areas of' high velocity fluctuations on the sharp, untripped model. > 0; --- w < 0 0 v /U >.3i C 54

57 ~ B) X/D 5.7, C t.0 :*~ N j) X Figure 15. (Continued) 55

58 A) X/D =1.3 Figure 16. Streamlines on the tripped model. 56

59 NSWC 'FR B) X/D =2.6 Figure 16. (Continued)

60 Nswc TB C) X/D =3.6/ Figure 16. (Continued) 58

61 NSWC 'PB D) X/D 4. Figure 16. (Continued) 59

62 Nswc TE X/D =2.6 Figure 17. ',trewnlines on the,hari, untrij'ped model. 60

63 ~ A) X/D =2.6 Figure 18. Streamlines on the blunt model. 61

64 B) X/D =5.7 Figure 18. (Continued) 62

65 a) X/D = 1.3 b) X/D 2.6 SS N N S, S, s' s,/ N Figure 19. Topological sketch of asymmetric flow development IN... II.. I I '' t'i I I = I = - II I

66 NSWC T1R ) XiD 4.7 fn 4N Figure 19. (Continued) 64

67 TABLE 1 WIND TUNNEL TESTS IN WHICH LDV DATA WAS TAKEN Crossectional Plane Surveyed Run No. Model (X/D) Comments Test No. 1 Sharp, no trip 2.6 Flow field unsteadiness occured 2 Sharp, no trip 5.7 Only secondary region surveyed 3 Sharp, tripped.75 Vortices not clearly resolved. 4 Sharp, tripped Sharp, tripped Sharp, tripped Sharp, tripped Blunt Blunt

68 TABLE -2 CIRCULATION CONTAINED IN REGIONS P, S1 and S2 X/D Left Hand Side Right Hand Side C Secondary Primary Secondary Primary _ Xs-_ ASs Ip X X?_X 2 SHARP_ TIPPED,ODEL * SHARP, UNTRIPPED MODEL " b -8 BLUNT, TRIPPED MODEL * * Estimated + Second vortex with a X =.0023 starts to form on left hand side of model. P s I Sl 66

69 TABLE 3 SIDE FORCE VARIATION Run 1 Samp le X/D Run 2 Sample X/D

70 CHAPTER 9 REFERENCES 1. Gowens, F. E. and Perkins, E. W., "Study of the Effects of Body Shape on the Vortex Wakes of Inclined Bodies at M = 2.," NACA, 1953, RM A Fiechter, M., "Uber Wirbelsysteme an Schlanken Rotationskorpern und Ihren Einfluss auf die Aerodynamischen Beiwerte," Deutsch-Franzosisches Forschungsinstitut, Saint-Louis, 1966, Bericht 10/ Thomson, K. D. and Morrison, D. F., "The Spacing, Position and Strength of Vortices in the Wake of Slender Cylindrical Bodies at Large Incidence," Journal of Fluid Mechanics, 50, 4, 1971, pp Clark, W. H. and Nelson, R. D., "Body Vortex Formation on Missiles at High Angles of Attack," AIAA Paper 76-65, Clark, W. H., "Body Vortex Formation on Missiles in Incompressible Flows," AIAA Paper No , Fidler, J. E., Schwind, R. G. and Nielsen, J. N., "Investigation of Slender- Body Vortices," AIAA Journal, 15, 12, Dec 1977, pp Yanta, W. J. and Wardlaw, A. B., "Laser Doppler Velocimeter Measurements of Leeward Flowfields on Slender Bodies at Large Angle-of-Attack," AIAA Paper , Schwind, R. G. and Mullen, J., "Laser Velocimeter Measurements of Slender Body Wake Vortices," AIAA Paper , Owen, F. K. and Johnson, D. A., "Wake Vortex Measurements of an Ogive Cylinder at a = 36 Degrees," Journal of Aircraft, Sep 1979, pp Wardlaw, A. B. and Yanta, W. J., "Flow Field About and Forces on Slender Bodies at High Incidence," AIAA Journal, 19, 3, Mar 1981, pp Peake, D. J., Owen, F. K., and Johnson, D. A., "Control of Forebody Vortex Orientation to Alleviate Side Forces," AIAA Paper , Yanta, W. J. and Wardlaw, A. B., "Multi-Stable Vortex Patterns on Slender, Circular Bodies at High Incidence," AIAA Journal, 20, 4 Apr 1982, pp Lamont, P. J. and Hunt, B. L., "Pressure and Force Distributions on a Sharp- Nosed Circular Cylinder at Large Angles of Inclination to a Uniform Subsonic Stream," Journal of Fluid Mechanics, 76, 3, 1976, pp

71 14. Wardlaw, A. B. and Morrison, A. M., "Induced Side Forces at High Angles of Attack," Journal of Space Craft and Rockets, 13, 10, 1976, pp Wardlaw, A. B. and Yanta, W. J., "The Flow Field About and Forces on Slender Bodies at High Incidence," AIAA Paper , Canning, T. N. and Nielson, J. N., "Experimental Study of the Influence of Supports on the Aerodynamic Loads of an Ogive Cylinder at High Angles of Attack," AIAA Paper , Hunt, J. C. R., Abell, C. J., Peterka, J. A., and Woo, H., "Kinematical Studies of the Flows Around Free or Surface-Mounted Obstacles; Applying Topology to Flow Visualization," Journal of Fluid Mechanics, 86, 1, 1978, pp Tobak, M. and Peake, D. J., "Topology of Two-Dimensional and Three Dimensional Separated Flows," AIAA Paper Keener, E. R. and Chapman, G. T., "Similarities in Vortex Asymmetries Over Slender Bodies and Wings," AIAA Journal, 15, 9, 1977, pp Nishioka, M. and Sato, H., "Mechanism of the Determination of the Shedding Frequency of Vortices Behind a Cylinder at Low Reynolds Number," Journal of Fluid Mechanics, 89, 1, 1978, pp

72 APPENDIX A This appendix provides a listing of the measured crossflow plane velocities and standard deviations. The symbols using in the listing are defined as follows: X,Y,Y - x,y,z coordinate (see Figure 1) V,W - v and w velocity components VS,WS - standard deviation of the v and w velocity components. In some cases the standard deviation values are not available. In these instances the listed value is A tape containing the information provided in this appendix is available on request. A- 1

73 * *..t I ** 9~Oi* P.~*,. P. fo IS On *gia5 SO4. q.6.t :2*- P.O~~S~iP.AsOI* 00 NNO4O.~ ~ 0*O "1.e4 oqpagp-.hillis -. 0 ftosa-o0 U4 ft :4*"Wfo00P.*WtsmO.oeP... P-q.M-o~po 01*...Aa4 P.*N~P4GaP.P504~Gd* 5*4W EEOE~SP.REV P O 650I5 Its U50UEaOo M ose to *4m a0~jm~4 lists 0~.. I05~P M45 *N4tftmm5.4.PJ G4P.44uA4M:@ NP54*P..OOlIV.A4NN U- S-**--P*. 00 Oo * Snia9-.4a0.. ~..-GJaS~~~ t V t... fillo 9 o 4o 5 4 P 4 o~s o P e e e eo ~ o 5 n - 44P5Mr.4*0P ftp5p54...e*oep ft c 2M: - o': 14. ~ P a1.. aa..- t! t. It ft av. S n..-."nf gatasa P *.. o fu. 0 * P0 PP ~ 00004E---~-e-o.- N4 etea.m P-fl. *5P.P.4445*00*54405*.gSP40N*E.P* A-2~..* *ase~p-*5d1@*j 0500*-*4P.446.5l4604*0eP00e.Omom.5

74 NSWC TE *ego 0 o-p-gv4 *40 04 a 4040m. O4FiN@44iMoi 4PI-N. *.iv~~~~~~~~~~ 44 *9 1 P.40l0v m-u d IZ v A-- -2 v-n 4 "P. N. -asli 0 a x- *Ud lp- 044iv -vnovv@pet-~v~o 0 4-:0 cy,u npuo40"".v ON 0N4~ # N49OON4iO e vo e.. i.e 4 4#04P44.4 *4 Ntive 4q~n Vo... o!..... t... *..... iviv-lfllivvivivvvvi -- *~s,a16g,,iiora II if.g9eal Z "a iv *******@O*~~~ ~0O@iii.i0iiiiiiiiii.i-ii 0 I-O0 ~~~ i.vqv.iinmv.vv.p - On~ P@8- O P ft- - vi vi dn-n-iv-i T"-i v- i N O--N 24N! uz -; -o - IOU &-4p ~e~e~e* 3-1 mea, : Ina.gig~ osn iiiiiiaiiivvvvvvvvvvv N..mfl.U~.. It IWiI VV Ivliv@p4 M. I* n.0 0 no.6 11,01% f"w N~aIv..4 O U*6 *P OP O@ *U 444@ v* ff S@ 54 6*.@4 ivion iv..... * lo-... i :. J4. I......e..... t v.- V! 6* W6 4 0 N 4N 4 4 *v..e44z or;,.; * i i iv. i~ P~I. oilp W-. og4.p aa emp4aen.6w ivi-iv.. to...4 J *42 mn o J4o m A m ~' --- los 0, v@.4... ON49.@i40..m P 4 alma. usage ml--- *I m.nu--n N---- lam.~~~ a.m a.s as. S5S

75 g Ai:.:..: AmQdze0d :4 M 0IN*m Ad*.t.uWQIm d 2 a g AO. A * Ip li Ad~M000 00*0d~4..A0 3 d*i004. m O 4 OO O O -0 0N4oul"OMOO0 -.!*. * 4 * ta geeeusa 0: i as P. 1.a o (E()( AdtOdO-f.00v -M OO 0 S P P. *AT. p O OM N.2::S~. *oooeooeoooooooooeeoooo00oo0.oo~oeoooooo~oo o OO e Om4m u ms eonoooo m aa A. hipa~ l.0 A... A AdhNWIA.0p " NA-NA - -Ad P:M ft 04 * mp fth oft-.ea 44ANdp.0 n4 400AdP0h ~ h *n 4 Ad- P-- N 4-0 4M M 0. 0 P.~ 4 0 *- ft - 4h-A~45N.A*Il4.A4 M 454 h0~d N 4 N a 4 a,~ 4t'ASto. P. m*wm 4. S 4 A *0 A04Ad- f4 N4 N#P.Ad ind*& h 0 P. *0Ade *.MPh M.SS4A PA ba 0 A.. A h.f... I. U.. ~ ~ sl d d~. &=I u lyar)~-e... o~ * E -p w ~ r- 0 h g *-- 4 do. Z *6... A d ~. d i~ ~... d h 4 N d 044n ~ d ~ 4 d ~ d 4 * P h d ~ Pip- d N U 4 1. l* E, ~ ~ ill d E * 10a, 51.i P h.. * * h fld..~n I N N.i 1... I.. w l A~.d. 00 h h 0 A d4.42 P.. S... t "'. 1.. It..1. d NN- ~timmo,1 =! li -lii Add.A~~dd -. d~~ A~dd.- ~~ Adth411A. *.... A...A~hP 00-A~h5A 00 A~ A-4

76 * ** ** * **********... -ffn fp Mae.BN. 0 F. -tse910" *SfO 00F-UB-a.F-PW)@ :0 OF-6464*F00M.F 4CS@a-. es000w..600p. X...S.o....S.S.S Sat.**.*.****It*. o... m -P * NN A so -00 * I anuinhe io~l *00mv on - N :ft- -02 N **Oc, O. fn in is C, 0, n 0 Oa:NSov ini*na n01.0aai nc 0t _f na: n 0 ' to~a i,#d~ JNN -i a n N Nm1 Ina IS t' Z' m 0M' Iw,. Mea Vilt f......s......@.0 I BN~f -- BN NN N N U I555 ItI lilt I#u &t to# o S S O9 S N N N d~op, AxBOIBO0f m. aa hi ~ ~ ~ : * rf"u,:1 4y 1 : F@. *..*. FU - a DDOJ*(wruyN_ * m d- NW OF@0-4 gl-n E@ I 400 N, a *:am* *Sf~I- MAOEO Il V = F-.F-- -m - * It I ItN...! C4I uc uf tf v' v0 u1 uyr 4vNNr Yl uc s9 yc yc vne yt m e y9 uf un U N.0 is$$ - 0S I N0 N F oi BOS Iotle N0~ hi _ 1:_ NNN NN NN NN NN NONN NN NN NNN NN NN NN NN onnft"n NN 'f-0 B ~ X N 4 ui 4N 0 0 S -*0 S.. S.-. 9N 40 4 *PIOF-00F00N900.@ 04 N-4F0F F--9N0~~AAAN ~9N.S00-oNFs~~pSm.NS94N.4FS4N-00FF-~I~..A-5.SrO

77 10-1U4xN4A - U1* Ca Ea.Oe E.A..**.. i *O4S00293AC Etuw0"s..4 "... "I M 9u8ee~M -on.2 NEO "44"T 0M 4 ooo asa 40 4Ioo M4.N*.-.i a-ooo *o.ineo OO6C 00mlla00.6 ao4o -o NOONON@ -- a-oeo MmN P ac I:--ooo o *... *...*... * **... ** *** em c a.. *N MSEO a 2 I I 1;m I! 9nrI aslms4ie*.0amm *UOIS4ONUNF o 1of I II oncp I..t I -- o mm5i N-- 4 I N O... N... **... *..... pla N o*m..c..ssified PC.. C eeoeeoeeeeeeeeoeoeeoeeoe.o..eoe.o.oee.eooeooeoe IIICtllllllllmlllllll.llllllllllllmO00.000OOee@ 65 0 *00.0o000mm* A 0'. Yi4Na-N..4N...PiN05 e0...a-e 0..NECP~*... MM M -NN. - 4t 'A4: P90-0.0m.0 P owes :a m O op.p.o00 0 q0 One: A- - 05Na-m~Oa-0P-*4a-UNCLASmS IFINED.N-..e4e.C~n~au~~

78 In 0 P..P. 0 in Ma of- am F." Sop Ion ii in@4 a *0 N~ 0 N4NPAI00N*4N- * NN tyf t------f yi ~ a ~ ~ S@0nln ~ olne 0 S A-N

79 .. **.***... U1.1 RUN..****t**. *... ~~~N4PI *~~44fl4Fb 4~b ~ 4 Ma4. nn NP.04*.PINO4.@N4@P@4@ZP 6 p0n-t -PmPA..P64u.g 20 V. 44n I05.N 4@ I "oi f mi *4N ~ I t 1 P.O a 111.N-. 43P44~ 6P.P.4 N4PO@4 u. *J 5I.. I ~ M NN..a -t.p ~- e e * ee e e ~ e e e ~ eo e o M e OFee ~ o M 40 w -n 4 40 n 0 w P Pe z N N N NNNANNN N N aw 0: 0 a'.. ;4 aa t :14 7 na. I% CQ o, Ww 1V IIi.I-.:... t...i PSSP4@I@40P.P.44.,...PNP P~~e. 0 M &0 D - 9 a.4m.n-.a I m 0P.4.M4M0 N PSP. 1 i....vv.... i...p...p4.4..p.p..4.4@.s. t4o.o4bn4e V N.t " ** 0 *09 9: S am : e, M*: P ; P.' 1*14 0 g 01 4: 1M P U P0.IP e..4.u CNN@P PtNN 45P N ft P "M Man M in on s4,5 -

80 NSWC mr ~...I.1 N U1O.. Vi : aa v -0 d - t. vt. on4*n ft"a aen..nn MWiN O MNNff ON *0 i41e- e&mo M"* m InN~a# NOw..e44 lo In5 " 's1, *am 14 Na 10 44U n am.q 44 "In Mona OMM ft IM.NA.9 4 m@n54on50p 0N* 4.*~O #0 40WOMe oniin wto M *o a, ama i t m N-.ma* N-iqN.@.. 1-.*j..*..... Vt P I ~ ~ ~ ~ ~ Si ~ INIf.. 144t ~ ~ ~~I ON ~aa~f... Ifh~4....i~S@,$ og maee i,2=! 96N N 6 : 0 9 0N4 0:%'! le *04t es.n O NI NNNNN ) OU ** a* N~~ ma a am m u,.. ~.a.iaa. z P 0 0! P-4 4t0- AMiOni Naam iaor-e 44o- aa o 444-pr-p o MP- JJ. 4 4f 4 *a P00"o' W 054t4N6.U *4 N N 4N 44d4 N4 4N N N..... * d --- ~ii-ni N a N---.. m...-- I aaamaa m i iana"m m00iia oeo oe- oeo-oe-e oo ee"e pd40044 h le 0044 di.ma*0a*.~m.44*eaooa-9m.1a

81 NSWC Tii It On 0 ~. 61PI 0 P1 60a0 -Ns *.i t t 1 *W0 oex 1O- Ap-.OO1PN4 0 0* :f *1-WIN 0N",,t :41P0 0% NN..NN..... N1It ***I..- III. flloti!-ittt*ttpti--ot.--.-'n = 1"W" XeS6 P 4N0 4 N 0 4 P of o IV P 11. N:s MM 0r -0P 4 : 104 -O g ag- d 14 mcne V-2& 4:0 4mO -MeO 4UIN f moo *4 P4..6 mv 0OS2" 000:I OINP N ai " * X_140 ftp 0.0P 04-0 U 'a o 't.-tNN M.0.00.N I ~~~~~4 0 n041, , n I -t n !l w -P o o a tnn NNNNNN NN 2..N. -N. t Gt 4-0 4t0.NO.... i N. v! 01-4N01 - ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ 0 0l1 NO 1O.. 4 P N 00P P00NNN 00O00*6N4 10 0D2O m.. om M * O NO-0NP10-4N01NM01...0N01640Soop moo!*0114p04 :O 'a -2 P10N N400p.P1444p ~..p.. 'a. p.. o o 1400 N.NN* N. 4 NN - -- II II -- NNYI ey"cum I I I -f~n NP1NPINNPI *U~lt;i:::mst mam 0 0*I.IS 00w "P M,00 04P0NN1I-0% M U M IP-20440sfl P in's-of"4n 0 P P 0 4N0:,t inN0U4.0 Of : Itn: NP 0N U0 0PI NN...!! g"-n _ a ~ S ~~~~ I I I a S~l a m u s g m a ~~ mm N 0 O 0 O m0 0 - m NO 0m NO - It Nw N1 NN No No N N, N N N Nm ~ Nm N ~ - ~ - NNwh -NNNNP ~ Nt c Nm 1P P 1000P N NO@ A a

82 OO N NN- Nom 14'.6 A Ill, 0N.. 46 VA 0 2 AA nt o 0.0 em.4 'a P. O N1N tufn 0 I N0 N NN 01~n N~e N101"o io N1-i~ ~I 0.N ~~~ ~.NN N p.. o - f e ftlof*4) cc N N 1 1 N A f -ml nnnnnnnnnnnnnnn I pv.n 0 In ag1o * N N N N C AnAI4A n0. IAAI A-N N a10

83 *~~~O64~ NU * U 4 N p- *IA4ON00F ~4*M NP40IPIh* -a~e-~ %27n:" :2264.M*,~**** ~ U00N...4@N4 0 om4m:_i : ;N NI.044 in0n00 noaaa@pi O.- 40F. Z00 *4O p n,4-o P MI0 A 4IA44M M NN Mv N N ~ M 4 0 ni n 00 a 0I a cc a.i M m 0 V4 UO.0x0P, 4 In MO fm 10Z s 00 On,.ej z Tmm AIA loon Xno001: ma000 NM ta M:! n a in oin A ninNNN ci NNN M Mt * I I A a I04a P-0 0:!2 0 X:=z9 zn e l.. 4M:. = - o" M4 N*0~ A4~ 0 ~0 44 O A4 0 4M... A No.0 A--

84 NO.N. P-..0..NN ! t PNN 40 4ft.O.. N Ui4NNE~~~~~O4~ N ~ f4.f.- N.N.t 9. 4.i.N I. O.. p 00 a n 0# I M: 0r a 0M 0-tU, CP O --- M Nft 0mQ P -o 4N 1-.4 N O fd F4 0 a N a4 4 4 CO InI,0I ni 4NwNN11 a N a 44,1 0. l- O 4a9 OD0' 0 D40. N O. O N,0 40 4#4 m mmmm mm mm N N O *P ftIn 440 v.n014.4n N NU4PC n I4n 0 N6 a 0In94 NO 4'a ZON4 DCUW O.. 0%n'a 4 010,01, 4N z0 0 N N O N 4 N U * tt N t N N z ~ t N N N N f N N N N N N N N N N N N N N N cc N N 4 N 04 0 N N N NN N ' N 04 4N NN m- 1444NCON - N4 0 oo:=u N 4 -. z4~ 00 4 N- NN, 4N 40044m 04 N = a,0 m'momm m N N 4 4 4N N 0 4 ome t C, o o o o o o o o oo o o o o o o o o oo o o o o o o o o CID NN NNN NNN M m a m 4a449-! N 2 N20 - z ~ ~ ~ M N4 N N N9N N MD N 00N N - M- I.-9 P N N 404' N N1 N -,a-. M4 44 w40 044M4A 4444 UN N NN N NN tutu N 4m ON 4 N fl44p N NN 44 N4 N ON N Al4 MNN N NM Yf N 4N M4 - : N 0 n0n4.4.n.9. I ~ ~ ~ ~ ~~~~m MD N C 00N 0. N N-N4-,Nso, 04= N MD C009NOO N p N049N Nm.O4404C0404~ON40N0.4'404.N9. 0 ONON094N NN40 40N44 04N.0 4N N 4-NA4 0094N

85 *.P04 N! P. t 04 0.O4 M 4 N! P P0 N..4 N 10P P No' 4P.1- M,.n MM P N00.a. 40,0 M Mae0 N- X!Wl MOO.. 44N1.. O. 0. 7NP 11. PP N.N4.00P.P 0%.. i...4p N % x:0-m4n00p1- o M04M0.OOOOOO.4P P0FP O 0~~~~~~~~~~~~~~~~~~~~ P. 0 MOP N 1P 0.P P 4P. 0P O..1 *~~~~~~~~~~~~~~~~~ 4C P14z P P1P P-N. - MY0 1 ~ ~ ~ Nc Nm, c 4 P140M M on00 4 OP N OP In P 400 N N. N- 40NP 040 P1 0m000 N - P.440 m0- P400P1M 0P0 P.4 NO am..~04p M 004 M.- 4N 40 5* N...MMO4000N-.0P S M 0 0 ~ ~ 0 0 ~ 0 0 ~ 0 ~ ~ 0 0 ~ 0 ~ 0 0 e 0:004a o Y- N N NNNMN -NNNN *~~. e s aii I aa 5I5 a, 1 II M 5 0 ~. 4404P..PP.,P..P M * N 00 a N0- - ly l V N NNNNNNNNNNN!c u N N tveu(v N CY NNAl NcN C ~Noc N N 0ic Ilt Nt VV4 4 0 P M.1 M O.0P0P MNP It0I P.M 0O in00 NP NO.. N N0 04do 0MO.0.0 0N.P P1MNN.-. MMNN..- 04P1N.. O4MN-.- OM P. P. P. P. I44N0NMON 400 N P1 C%0 P1.O 0. N1. N10P... N.3 I N P.M P.M P - - M N..4

86 ~ *e p. 4*=0 * ~ e 4Omer M- mn.4.-0 O~..~ omo. o o 0 4 N040. a0. U0.4. : : ~ *N~ EN4 wo 0NQ0-40NiN 0 * N n. N0, ~ ~ 000!. %!.... I9P N I O NMN 0 -yyuni 4 0 CD 0 omee 0 M x Z~ N0 N~M 4 NO00 fe O P.-0 M c. 0-r :,r-rn,nn 4 N4~UU M4 OflPAa. 4 4 MOO N I- P. P*N0 f :44 cop4e 04 t 4 4 P 4U, ol04 *t.. A o imoen ",i b _0 QNO O # 0 : 44,1K * l 4. N*...0-.~.. * 0NNN-~0U00006P~.00pU; m n 0*P. Oj;..~Nml l *~ * fu N N-.-N N nmmt o0# tm cmnnnnn i'n Z ~~ M ~ N M o rymmp~ O * E E * 4 * 4 A-1-5

87 NSWC TR 8a-394 lot: 0 0,0* 0N I5 0N P 40dy *5A0N~4P-4m 00N045 40N00N~-~0~FIN aa~4.wa0 44P~al0a0- a ~0fl 4ON fl05 4O00l.U N00 p.*..n@... 0 S~4 34 4NN0 4NN~ ;";e N Nowa 0@ pa e -..N...0 P.fN... P0 P P P N 40 0N.0.. 0@0@ NOON~~~~nJONl 4004o N.NaO In IM ni4 A0 nol N -a~~@ N44~o0N 404 e~o~o~ N~o~oe~t-~ oa~ N@4 Mfl 300 ON fo W N4 N fo ON N 00 4 Mi...fO fo. r:-a. None M* Om I. a,~ N- tm0 N@ NN -mm NmN ft.. onn o.oen-fton.ooo.p mfl M00000a 00 M004 A 040 P~~~~~~~~s~~~ N al N m-..n , o 00010@A mass,, im Ina gs ow ma ml 00 sam 0, ase man ga ma a11 mamasma...aa ac N0 04al4N A ini0 ID Z z z P1.15 PS SN3 0 * 0N40 0P M 041% 404P0NP A N P1PSPS0N0 1 0t 3 04 N 0 M A 0 0 v PS' 0 S0 0P 0 0P S4P M l.. 0 N N 4 0al4 0 N4N N NNNN N4 4 4NN*p.0 1 A N nm a4m go oc ' 44N fl- CP, P, pm ym P.004P '10Z0 NM M ' oio 4 4 * In S P 10 0 P i o ll n 3 N o0 PS 44 Ne P 0, 4 0 D N O N ;: N S - IP ll# Q o S 40.N0 SISM 0MMAZf 01,010 W. P P 0 N0 f4 0 0.N N 4 0. a lo NNNN NNN NNN NNNNNNN N N N N N N N NN N N N N N N N *I 0 Np N 041, 0, N N1 4 & 4, N, 0, N, P0 0, 0 N N, a. N, a P (p QS4P 0 0 a o.00, 'p ll 00,00 #.....~NN. 4 4 P ~... o o.p a mm m mn N N a NN NN N-N NN A O

88 INSWC m em.m e..m*.. N.A4* * *me00 I'n# *n Oi Mol a & IV n P@-0 4M m0'"nef ec4t,..me...e... *mcem4.~~~~~~~.a ~~~~~.1..m~.Nm 0mo.N s :Omec,.. t. Ion In 0m*.. *0N -nmmmny- -- mninu- - - e ~*...*c~.0. -N m ~.0 m 4 4. M~ m Ili V~ I~l It*on *c 4 0.Na 4N V..0.m4. e~ m m 2 men XeN N-N ap a 10 In F- ~ nm us4i re 0. NO slalswlmu W acy inr. 4 & l,. -- l 0 mo - M0 0 *' ". w.. i q0mw t I :... :. V t 1.II" @.oc.a O a a ~ 4... o c. P. 4gum4Mp4 0 a = lAopP-N cum444 NN p - N.01 n4w.. Cm i 0 ;t 4Na0.m0.N0c -m04e'..40 X oy a.nm4n NNm. Ne 0.N0yc * ~mn: 0 M em a 4. Z2-4042,:4 0!4 N 2 F0 0 M-400' N m 4 0 : a-' P0-40' af-i 44 1 UI~~~~~~~~~ 04 N 4. N 00 NNo0NN40 a. 04N0..fI 0 0 :0 0 N.0- N em M '0.. m4 4 - o~ ~~....'.0.40 N.... N 4.a t N. 4 It N.0 Nf..- - a: ee. m- nu vf ri 04m4- nf Mf unt omae-w u#.wn ui !2N444In-.0 C. 7o 0f 'r in.. II-N ;on0..4.n Nf,.l.40 N , 4 0N W atf Ma. o e n M o fcpo-a *fw - a- n _ ~ m lo :,P,....0N0.... N-.0fI~-4... % N.04. : m.0.04 MN.'a40a -. 4N4-0 04N.-N-N 00..N'M N '-0--0ainO O~~~~~~ 0. 4 N N ONN C N N N.-.. N. - N N a N004 0,V N0 N.. N N. N 4 N N a 0 N4.4 0.e0a4. N en.. 04gi0 IA 44P-4 *O44AsNNP-0f-io N00a00 4N N N.. N- -- -'~.~a N m0 m-0-n- - ~ ~ ~ -a.-0n-4m-nn~f14n4naa. -17eO.0N-NN04NO4AaN.m

89 4-4w,*in* * *on 0# ino- 14It n o o f P @ O O P15.0.i.I Vi.... *. 0 0.@... t55j.a1.. t * *,,.0i 00. e0-=0 of z0602w v: 6000-M:O X0:o0. &0-000 M00000~ ~~ i... 7~vSv4a-vS.i.. :... iv S ~ * :-0 ccn O O O S UO S O O O O O O O G o eo O oe o o o o ooo n 0 4M & O 1 oeoe eoeoeoo oooooo S.000U@ P,I- q It44 a,44 111:..ivviiU.iiv t! M M m M t M Mm 44~mn M z in ii S-0 *v 4-. S.P..0 0P M Vt v.o~6P0.P. 4-P S-5 p..:for vi4 44 I rep.54 v4 Or ; #421. i 0 p2m@-lvi:,io N co, 4 4 ft M70 *Odi..ivvi4..004PS..ivO. M M i~iv.v M4iiis~i446iSv~ievv4vv Vi. if... c P " him M *vngan6 Mw 1 N M 4 *N f $ 1 7 0? 6 t i Z ~ ~ ~ ~ ~ ~ ~ S0NP.-iOivv0-Ovvo.94v..v;o400 N N N 5-4i..0vi V0 4t ile!s..., i V ips P.5.4v. i. ~ ~ ~ ~~~~~~~,40 nat 6:11110i~i04.646vv..440~i.v..PS.i 5~ ~ vi v-p4s.4s4v~op~vvs... ~ ~ ~ ~ ~ ~ i.. v...4v4~o54vvi.o i fh t 4t l1 4 14NNNNNNNNN N N N N 5.U05.44iv44SPivv444viv44ivv4e444viA-18PS~i

90 NSWC TB o ti t o tic t.i ti 000Oa aoaoooooooooooooo OO It 0000 It 0 Ct 8 I t c o t ti P It It... :I i o C.ItC o.ooo... Ct 0 POP-pet. M0 YF a #N00a M0"0 -F-0@ ",,,,M N M MO N.0 * 4 0 F 0 N - 0 N 0 N..- 4 N ~ - P1 0 N 4 0 0n A' 0 fu 0 N M. 0,AF 0 P1 0 Foo 0o44oo o4ooooooooooooo-ooo4ono-0ooooooooo 0oM 30 -F M-..F-0-..O4ONOO F- M F N F 0 N F000M0000o00N0M mflN -- o Mooo oooooooo04moooo -o 4MMooooooooooooooooooooooooo ooo4 0~~ IIIuS ~ 10o0 ooooo oooooooa oo o o.oo o.. o o o o o o o N..N F- M N 00NM N 00 P.00;: NM 00 P. N40 a-,n #.2NM 40 OF- 40 N0 sm M NM40F-00.NM40F-08.M400F000.m *-00 40F00-N I - A-19

91 O 1 N V.. N.. 0e MA t. o~~ NN0N@ 44O0 NN I* p-N 19 S A I No.e01 S O o.n 19 of 0019 t0 " g M : m 2' 3000 NEI-N N00 Ao0N 000 a.n No P;.190.S. OO l ti N a.t I 0 N. t i a.1a1.n O.0.N. ~ N N NG.i. 0 0 IA 9 Iq I 0 01N N N lo AO01tA l to N 00O is$@ - $ISO*$ I..Ali N N O O a, a00 00 M0 00 & m m & 0m 0 0, a Of4Z. 0av9700 Na 4F,m F Vs m;,.nm m N N AOO OO.. N NO 00n.19N60lm 0 000N0N0 0N - N a em1:1o, NNoN.'-.'NNN M A M 0 N no0 As 14 N. 00N N MN N 0(9 cu NOM N N M0.- A N 0 0y u; 0 N A N Nv t;0-40 Nz z Z N010N lot t0 O l sa10 0,1 IA o m1 N I'N,: 0. c 00, N r Fin P : N a mn go "M I9 9 NN 1. A-2

92 9*** *.. *** Eq~~og~ Eq4 4 Eq9 N.-- 4 a 0010, or- 00.* V gas~m ~ ~ m g- 00 N No FlS -11 I - S I I I l es t on I I INN I 0- lstli *Mom MN t4tt... C!.111 1! V!d tv IllNb"ON No NN N N N N MO N 00 : 4 00.ooo inm4 N y. o VtV e 4I 0, MM-MI... MN0ooM mo-o- -eo o-oomoo oo ooonmo 0 ~ 00 ~ 00~ ~ 0:;00z o N~fmlmOOo 00om W~~~N ' N NCI 0 MNN NN N NN NN N 34-. N 00a.. ~ 94 P N0 4ENEqNq 0 Eq -. N- 4 o -9 q 0 N 9 0 N44 4N N q9 N N 4Eq q4 4E 0E 4E 09N N Ny1 I 0 ~ ~~~~~~~~~~~~ 4qq44N444q-E44q...4qq..- E N t 0 yi1 4 -D 0172 :! ~~~~~ 00 Eq 00 P. t- P. a a N.. 0 in e MN N ~ ~ ~ ~....N. 4O.N4...N.... ; 0 0 4E 4.* N,, l s Ito qn.eq Is, I it, E E Nmo0eo N m m - -~N q - q -N N 9 0 E 9 N N N 4 44N 9 E 4. 4N NN N4 06E 4N 0 N4 E N q0aq 4EqNEqE

93 Nswc TR a f.: V240 * m* EM 440ii Otu 44 0 InN@ 00, 4N O 4. * 1. m.n. to0m e gempop-kan OcoON ANN400I -04 Aon 4 P ello IME 0U **.. ff 0 00q:4 ea NN M* A *44 JA A A A 4 j jenn. *~~~~~~~~~~~~!m *00 4O044 ON MEC 0 N e EEN..NMQ um.nn0-00n0-eoog0pnnn0e.oan m4*m4o* 400*I E4M4 0U0-U -SNM ON IU OG m * m.0 go 4 EO N O P- m V : VN 4 N A 0 0 QN EN.- 4-4WN 4 4- E E em.ne 41, P W EO N * * 4M - M O NO M W m0n00n440' M NN"WM o ~~S000P10n P. & a m c 4In ma n 0r-a ai-- I 441NMN - -. NNN omf, Itself#es *i m*i t ai II, Cmes M CUM4 ao!9= 404p In z Z U N O N N N NM MNM MN w Ps0 N C n0 m 0 &4 P , 0 *q 0 F40 - o M0* NO 00 N MN N at c.0 n Itm min m40 400N4"0 oc)m cc* M rnm i. ME ENc 0 am 4M3N.-t-0 *30 n ym a - d ND 01l o; N,oP M 4 W M M W 33N OWE * mn 00m ME M M N m4w4 N 0' N EN N N ox me 44 m ae ; N 0 0N P.4 3- NO 0 P4 W 30 N M' N *400 N ~ ~ * ~ 4No ~ -N00 E4 2m 0 M -N - z pitmy I4*400 0MM4 4f*2 N'a** N.M* o N4 ~ N 00 4 o.. ~ N *W ~ m - MNm N 33MW ME 4W - 4. P,0* 0W O. N m o o N MN. NON 4 NP 0 N N 3 - MW 0 z NO AIN NO O O - ON M O E - N. E O N * 0.. M 0 M M O 0 3 ~ 4 M IA N0 N- EN 0E 0~Iq W4 0* 0N o0m.. N4 o0 0e 00*A-22M N3

94 .*.7tv v N 4%4 *4 N ~ CU A % M onn N v MM f N9449. C 0 i eyiv 4.. tnno N W ON V t ew.. M 4 In *0&9In.0NN-m4 4 M ty n40 4N 4 cu9n NNN N..... t iv,...% 1... a a I -* 0.V i 1 N4N-MON ON O N 0~ NN W N400 9NN 9N400.-N40994N PN94.. It, w.* N :N1!0 I..l.m.lamliIt I 4 ynn------wnnnl N N N N N------N N N------N N 0 0 N4a-0= 0-.N... N op..n14j..: N----otmm *4 4To om.m. o o o o om o o a e o o o o o o m o m o o o o e m... N40N N49m 49~ O9-N40 O9.~N40 N49 4O9N049 4O9..N~ N M4M * 0 xnfl "nnnn JNNN- - -NINNN- - -* 10-NNAIEmma MNmm U ~ 4m aml, m cmc,, s ms alg i,, l m0. 1 otinr sva a 4 a llnamasmo z a 4 O en 90 N 9 N4 m4. e.n 90 N 9 N MM a 4 m4fn Pi:0 ~ o o oo ~ ~ 4~ ~~~~~~~~~ O 9 4 e n. N M P. 4 ZM! U' m 0s ON 4 m mn4 1J 0 F- am" N---14 o TO ONNN MN.4 OO 4p- 4 04m 90Me w4no N4N N 10= momoo0404mo WN.I Ne90m44NN N NO u N mu 0 N N4 N N N.4 N NN N moo N C9 cu 04 N4 Y cy m N NN 4 O 00N MN m m-od m m * 0N In N N mm 0u N 0 mm N N P. L0O = Ng M ON WI N 000. t. N N0 N 49 9 I~ O u N u i n N 0D, F-. N M N N a,0 4 N N M NNNN NN N-N--NNN-NN NNN-NN -NN- -N --- N-- N 0N 0 4 N49.0 V- 444 N SO,04044 % NM Nlo NO-N 4#0 N. 0 * 9-.-O4N mo M409N.0 N 4 N0 00N.4 N 490 M MM M N N0.09N N ~N0p NN 9.iN 04940N *0N 4N 494N -4AON NNNN49NN-...~~~-mom Uuw l.-n N N0-.b

95 NSWC TB *...* ti*. 4! lo tl'ti t k1 %.. 09Nn: v- MA NAMM Nmmf MN N MAI N9000l-ONOE~n~n E I00: 0:003-0: N...l NM #4N #0010O NO O0N E ~n In LO n inno0 in 00ENO n 0In x I N111j l. g. gii zm o la ala In N ~ ~~~~~~.N. N. N - N - N N N N.N '~. -~ -... In In In In: In In In In In In In In In In 00 0 It In In In In In In In In In ti in i Z* 0 in 00 0 In 09 P. ONMM0 0 mn 0 N 6 0M IInN 00 9 in -1 cm nn9 N- n0 *MN fue Al aft-oft O PE NN a PN Innn E NnN9nnE EE~ M.nnn ~ 0In ein 0n~ li:.0!: l.i I!E...N.. -~ 00,00000N0MN90n0I 0:2-N SMInnNna N... o ~~~~~~ ; 1;N 1; 1N;0N. nm N N n~e I~n O 0 E9 O N 9N O N 04 O~ -03O~~N6N0Itn9oIrE-nnM~~CnnIMIENN.I0 ~ N 0 N E n n N.o n * E M I n N N 0 E E E - I O n E E E E O I 0 N * E M E M n M N I 1 C,4 4 0 A-2

96 NVWC TR ly Pool- MMMV * ~ M -O. -4 1, G in 404In444:44444N0M me.a 5ea O E M N O E N M00:4E0E=NE. M ;;N;:NN ; :09 CEN 4mgN 000 9; 0 09: EN0E0 o: Z9.~~ *.% N.. NN. M...MO...N M N0 NM. E 0O 4 N0 "a0t N M 0~. NMM NO000 M..-.NMM *C -Na1 x I 00v O 'D o 0 me a K., :.:.0.. g t... ~ CN2 V (yiyynuztt n!5; z 400W. P,I SP Te ONMOM MM N N In401 a W, OM NM OM t Vi ino 0M E Vi040 : N40N.0...N.O.4.E.N.N.O.E.O.O.N.O.O.O.O.O.O.O.N.O E 0 N.0 N E N 00 N N - EM-0 00EE 000 E OEMN MN 0 M 400 E 47 N N N 00 enfmn0i NN MNM MM MMM NN -. N MM MMM MEM MMM NM

97 *94 ~ ~~aimm9o.449mma l.v I1i i ii e4el '. 1 N..... %. N 4 It.444l.N*44.-. N V (100 4dlooN an v4.a M 0or MO ;:M 4A OOifilfi.00 0 NB9 M 0 V1I0 a-0.0,0 0 0 a,.o.oe e 00=. NOO. 0.0* OO0NN N. 0 N 0 9 * O o O a.i.is.'!., 'ir 1,, 1. 1 ia. %. am I N N 0 N N NM *0 M 00 f" M0 N -.N M N M N M M N - N ,P 00 m M M AL4 1G1tV Va tc! l 1 ON 04- on ooo*oonao vko oo o o o o o oo o o e o o oo o o o o o o o ~ 1 We o NJtNN NNtNNN0N Oa oaoz' got* 11 1i A-2

98 p. p0 -NO p0m l Nu NO' 404 m04 P14 m4 p. eu m 04 mmn Num P10 0 p O 1 1 N 0 N 0.. P1 4 o - 1 P P 0 0 P 0 1 P ma, Pp 44 N PN 140 p 400.o4~o PO- 4P.U N0 ma p mol0n0.. pnom 4p.04p P4-POof.P1NP MN m P10 I I 1 N - N NI O U P1PN 1 N-aOO NO 04,, N! cu0np40pn4014.n '. 4P0N04PN10p4. P1 100 N!U* 00- Z!! ON 4.NP 00 z NO 04 P I. %4 ON P10.0. p P1 if NN.N.N N.N...N N-- mmm ~ at Cc a NNNNNP1P11P1zPNP1M V40000 I Ic Q cy m N InoNoma m 3,J 00 CMQpG mn NmNN NP.NNN.NN.NNN. NN.NNN.1P.1P.PP.PP1.P1n P11P01PP1.P1.P11.P1.P1.P viez a No O a zp N Vt. 00!1 t. : 1 : 0 ti! I! 0 : 0 0OK -,np n p.1 P41 Np P N O0 p O0 - V1-,4Pw-0~ P1-44 P O-00 N p40 N P0 Cc0 P N N P, p0 ~ mo vp010n0001p.0.n.m0~~. mom1'1' z;:op-p#poopto-o 0o 4 ~0 p0.4e'p14n NO O0.g -.. of =!:2NO'1~4444 MI- M-- m w.. Ol %, T Z ~ ~ 4 1 ~ 00 0 ~. 00 ~ 0... Ao VI0P INP14(Y14P11*'A0dl.r0pgo. 1 Nm4 0 4Pm1PvmN4o n D. C, ey u0u -Ptv-u m qonpi" N 0umN t"n 4. fu..0p10m1to 'D 'D'D p a o 40 ' N'Q C N..-.0p fuo u y r N Y NN v ty1 NICY 0P..0~N NrVN V U N 4 IV0ryN N.. prup.0p1r ItI

99 M mamam AD0-AI 'VORTEX ASYMMETRY"DEVELOPMENT ON A TANGENT 002 VE(U) NAVAL SURFACE WEAPONS CENTER SILVER SPRING NO W J YANTA ET AL. OCT 82 NSWC/TR SBI-AD-F5OO 119 CESZFZED E/E 20/4 ML

100 IIHI II-' I-0 MICROCOPY RESOLUTION TEST CHART NATIONAL BUREAU Of STANDARDS, 1963-A

101 :910MA 4 *4.0 o4 r OPN.N.m #34.0MMMfW otn m... 0M...M mo M4 n 0 ap411 -o f p ao 0&.0p0a o.00 OftqONmIt *orn.*&r-00- OpN on MoItI * ibn 0p- 0 NNNN-P NMf om o~fnfp-0o.in N.4N.*. 0 0 to0.0i..n in Va00'0.0'0 ' M Z0. E0. N 1 ~ E P R4.O.M N' an 0. 4 ONN4 o :1 0 01, 0Nn0.p.- 0 NO.NM.O N.N-f 6.044'anAgo0-. 0 M!! SoES M. 'a ej00 N O=. 3,S0S~ S 55.SS : 0 0M.0 0,0 000 M.0 1AM4n I 0n n 00In.0 4 ItN in000 At 0 I f t y o00n5.on 4 M 00 00o p-0 00-e"FNot00i000- I I ~O , s. Sf ~0 0,110000o o o o o 0 o 0 o o o o e 't 00 tt.:- : ' v a z o~. 'O N 'N '' M N. N ngnr M000fan AM N.0In.00t0)M in 0 0 -P.n 4NN 0PI 0,.o t N4 M0= c 4 C nc~ P. - 0NO..466N99..10fn0'0NO- o ;c a!: O-;O conapin0 N OM 4's,.EE 0''NO 'a' w t %t!i MOO0e :1a... t ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ l s IM-6 E0 M 0.0oilP MI.. 1 on 0. a'0. I-...N. i. SN:1 :....N I N gi ms '-.ME N4-040cp '0.N 9.0 N. N9-N f) F.0 N- N p N0 NO NO 0: we NI 00N N. O......NO~...00.N... ~..0 ~ ~ ~ ~. N M 4 A WX A 07 O im *,A a &.0E.N0 O0 N N0.... i N.N - - M -NN *;N *,gm - V -- n M InNNM-M N--- omnn0..0nn N-. N I NN O0 NM -. O...' NM OO NM O ON M NMA

102 NSWC mr p- ft---- MM MISMSOM 0 :ON4-O ad 4044m040 a, SOWON46N12l~oa oan oni lv 0******* ** p P.0I io O m M0Ne 4- wee.00 0 In ~ ~ n *N4.. P4P'. 4 P.0 16N. N I6MI N. 0i 4 M N N N N N6N NN 6 N N ' i i 4 N N N N N " 4 O 0N-o6N of.0n N.C6NinF 60 0 i 06 lmne~ o.0,,i 4 o.. i l$ I of I il ln. ~ I, I, oil I of.- i ~ 0- oc 00 eo ~"Mon *~~~~ i.n..n.i~..n.. 0. S. n.n G0.i.~f.4. 0 V0i i 040 i 0 4 in 0 40in * N I -- 4S 0K 4 W41agNM40. MM M M in A0in i.0n N N N~ MnoM N M in( inm N CYN in - ~ N in 100N0i -. -n ~0-. n0 NlLN i...4nn i0 M n4' ned N O0 6n N i.- A N N ; OGn6l:40infIN 4M A. m :: 6 mo 4 MM z N; 0P t; 6pn 0 9i 0 ni 0-N4044 4a 4inoN 49 eno..0 MO44N N 9.N N060.N.in0.M NWN0 9O O",2 0~9 in44%nn44itnnpi4; iajm0in6.n...n.0.n. It M O Ocm 6O MNyNNNNNNNNr ynf 0 ZN 7N mat unnf 0o w#7o-o ni, m m - 4 N N.. N~n'Do n i 0. 6 N4 1 N N 0 n i 0. 6 IO N N in... 0~ 0 n 4t. M 0 N.. N I... 0 N... i E M. 6 O N N O...n... N ii. N I N-..NN N N----F,9N MN NN Ii~ O n O f-NMIJNO.00 N.N00.0i0436.i19~ n1inn N U0 Ni. 4 f~ n *i N 1 1 N 4-0 N N N.i i NNNXNN in 6N in.0 4i4Nn. N.60in0O6 N6 9N 4N O0.. CA-29n 44

103 21 Vt i.s N.aa.O.N *6.. A0..A...- o It0.. i... AAA44PNIo -r tfa Ml ft.6 on 0 *44E*4A 4E4 t! O ~ i ee-.. ga OA4 4A-4A0*P A044-fuO4*4*0n 000" M.. p & O*-4A1*ft M?. a O6a fta t *40-0Na'aI.0A-A0N -P..4o. ft.a44ft0a ~ ~ ~ ~~~~0 m0 P40 MO m 7:04F no4i n4i 06- INO" aq.0 a a, 0. O0N4-0.. ONOnOg 3 *4* t t0.at* 0.0 N coo 4.A0~a 6 A "10 mo fmq -0 a m v "1 A MO,064 s A A -A -.. A.0.6A. ON P A.0. *! '" 000 *a O N.. t4 0M.N o0nmwa0 o2n*%0 ma~0 sa.e a, 0# all o.. 1*- A.. Mon *M* 0 0- no-0~@ AA**000r : , N N 00M* 4,00 0a-60 o a o 00 4 a 0. o set'd4 m N 0 A ~ ~ ~ ~ ~ sas ~ ~ eas. ~ ~ ~ ~ ~ t. a e smss.s.e Itse Itma Is 1.aig 4A a.2wn 6 0. dlm A o 0 nm. 4 Con N 0 A 04 O9 ft0 m A0 44o0 0. A 4 p *~O OM-1 I- loop--- 0 QID 'ma0 0AAAA.0 'a.00.0*.0moo It w A0N- e tt A N iti.46 N*0 tic APO.0.. vt 0 -~ It 060 1: 1: 4N4. 1: 15-: ( 44 M00-...A0 M.l Am 4*.A,aA I 10 6 t.m N00 0t #. N_ 402 O o. o0 t0 :t.i..v I, -o' i o # 0.4 e ;o0=12;o 94 ;Z009 -~ ~~~~~ o A t o 0e 0N 0N q o... A~. A-3

104 NSWC TB N oneqlq~-.. InI - -n!!2 a r 4-0- * a :4 0 O -n-s- * 4 ma- a lase l. e s sella 102=1g ga ise- I A 0 ;c o g N 44 4 d l- 1~ge m m tt,1 ga ls 1,Ile ag gg g A,ng mi m I..I.I. i m.i.i. m gage 6 0 C4 0 0 a 1 N 04 6 N a l N 0 0 ~~~~~~~~~~~~0. N 4I M d A 600 F eg0eg aa, Kn O d. l P.~0-.10~ U O o l6 e a N N.0..N N * % 0 IV 44 N 9" Ift M M 4 inn M I 4 MM M O. N-. M dn * 0 l * ln~l~4m PCN -- Mne.N..- -W 4N Mm am 1 4 :1. 6 UIP N M4 - t4*n00 A0e10 4M-0alI N 0a60-NN0.0f*01 0 "!Um~1 00 am Nip I..... " * S. V:.a4d.14la Ni N M ~ i ViN..04NN-P.J 0.1l 6 04 all 0 - * -~~~. N 4. N 0 N.4 C6 11 J0 11 N 6 00c * 1 J E.. N. N.~ ~~~$l 0'0E N...N l e l l 0 6 N 4.. t777,e00 M..g l 1 NN IV N N ni nr tie -t ' N N 0 N 4 N l f 0 N 0 f ~ f a 0 4 ( O N~~~mflO~~~aflO~~~~iO~~~llO~ n.0.o0.o0sao elo0. a1.0. 1e.1.0. le.s. N001144N~ E N 0.4 N 66.N g N aa.4o.ea10o SJ1JNIJ a~e~~ a-...nn N N ~ ~ e~ A

105 NSWC TH 82.,30..i..O.. an- ~ -. 4 di,0, So*lO A;@ 3* tun-.44qe*4*n**4ndnipsplaem *...E.E.4.u.a.O.e. alti.i 17.1tit il *... *...0 ** * * *.. I ow 00: 0. P.,I*, M& 0 1".ON44,N0 O ON*Po-.*44O N4~ Nr ~ i-o-n SON,,, 7:4 i N S O - *.. e e *. N ~ n, 4, N : : As.44 N #Nr ai4,40 n 1 0 ~ O 0~ i M4N.MOO...0N0 0NO.O :~ It * 1: @.. 17 Vt 0: 1. P: 0!O..di@*O.i.d. 0 I INInONM fl n NO4ft fyn U ua O i UI MO4,i S4, - -, -5- N d, VC N,,,,,,-----NNNN,,,444E.---4NNN44444s N MO MT O W ~ ~ ~ ~ ~ ~ ~ ~ ~ 00 ~ 0 I It Itlt IV@000s V 000In P00 00 di I ~ d at4 4,, di" d d di i i i id d 4 4 &n, M*Mdd 44 4 ~ N... n.wn nm "... n n ,10... ooc4ma m o s a e a e em m caaw ~ i 0 0~ ~~~~~~~lm i o i e N a G wng e a 4N O@ N 3Occ~. ~ ~ ~ ~ ~ ~ N N :N 4444,,,,44ddiiiid~i w ~ *igfliiiiiii44444nx~p.-.0n40 em0 40M00O, o*llat-nn 10-M top ON Fte - 466N04 N 0 N000o 1s0s~, 0 MOO N N Mz --- tn M - M O M 3 EN~fl. C N -,0 - N0~i,NN -., Mi (" N - 4q sg 4 fn d, N 0 N O 4, o ID0, )1 -N,, nac!, N min.-a m i. N a 0 # 4N-. a 4,, N!didi4w,.m-!.m a * ~ ~ ~ 000* ~ ~ 00d4,idi.4,O ~ ~ ~ ~ NN ~ 0 40 *O 0,iiO-',~d0 O di i O d on. N ,,,,W N00 #n in a4 p- e o, i ta on A*d,4,N N 0 In N In 0 i0.i O04 N N N N 0 Nn p,1 01,P *O N p i i, E a54 4 ~ 0.0 d 0 d 0 go, 0 0 a 4 4 N,.., 40 i 4 N0 * p04.0nn,0dn 0.d~iN.0ad@..0Nd~i 9 some a di ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ %:W a40n A-3

106 ~ *0~~11O,11'n op04,i loom*io~a6i0-060 N O*A.I4P~0A4 " ft 0 * ell Otto: ***.* IAI~mlfii*** *nn.~~p 44**ifi*f*****AIAIA*o P ine4t 2 in. IP).40- **nmu * *Inn H I now "1"" N.0 *4040 I-npoo~I *6e NA.4 ;70 i 07AO4 IOAN-N*N xin~i *006~, ao~0.na.n MN40A4AOIN.04f4 O-0 40M!!4 0f4 I, i aM.....*~ ot...o...@-.... p OIA0A@IA i ia1o2ia OIAIAIAAIAIOU "NIee, ONWIA00IAOAt AOIO*I 4 0mlI nianianin N40 0N I N N I N ~~ n A Q - 4 A S n 4 O * A * NNNflfl~fifENNNNN~ffiP 'ifif*...nnnnnflfpffp* nt ih 0 a:4s-4!:i u o o o.eoeao Po~.oeooeo oaoeo *moo oeoooeoo o *e 6ot o e 6 0 ae60 * 4*6a6a60 e e 0*se * 6ott v4tvt 6 oo ; 6a I t ~~N~ f lowipif ii i P.P. l Ain I---a I I $Ig4t s r t l ll t o f l a $ i l ~~~~~~~~~~~~~~~I ona ~aa~aa~aa~aa~aa~aa~ It IV:..a... P:. aeo N a o N 4 A N o a A N i I 4 6 O I 4 ~. - A N 0 e~ n in W tmoo *fmf*44**iiiiiiiiii44444n N N N N O UOM0 0 0 W.V00 Oa..!a.. 07 tl P: 4: :11% ftnf to I wmo f tf yf tm0 l4 % tf tf tf n4----i "P a I ti t ti 10W n0wb ni.*fi-.n.- hj Z aoKao,0 N0 p e4,s00000p,'"0 0M'"0a a z 2a4 ~ a n 0 a. N 4. * ~ 0 ~ f n~. 4 u N * a I~ cc ine N 4.mIA ~-~a.~.~a4oo NaN I49 N 0~~ I ONG.N44-0 *I~e4.lfi06040*4.a.AIA0400 4Ofi4~ hi NNN l- o-- - No g0 1. "N mln-.-* N NfiiOma AN 1I * A AN A 01 N0 -O 402ONNIA mm NIA0MM N IA CIO N e M:0IO4N0010Na0 9 *M.4IANNNI onn01-4 ;400I04. A q -. ND 4. IA- 4 - me : CO., np,,o fo;. N pm.,,, 4 D IAa Ogg:. NO MD 4 m P.P 4 a ad U N N aa 4" N IA0 M a! N. esn N , amo ftl *s 4a pmin. IAI a g...a Se n-s lema,, IA40-NIAmime" oeani40-.ni -o...- na 0 MN oiafn x 1i4N*"o. e 9-0: t ill$ I is$ its, so of $Its...,..r.of.. l , IA 14 IA m IA n IA IA IAIAAI IAI;AICAIAIOAIDAI I AI AI I AI IA AI AI AI N60 60 M 000 on 00ft00f0 -N-- t M M.M.M.M0f" N N ftff N Nq N N N 000 OM M*, 0 a0 CPO a..: :000 0 &0 aau ~ VMO0 020,0000. ts a0a0. A-33

107 NSWC TR 82-39h WfoA 00 0 ftm 4-00"SONSM.. CC 4Odi 6- ;.3AZo nn invmnin Ai F A4o on 44 C 0~4* d4cin 4 4it4 onm 4 -ft--... d ' di'tdi Tmm ~ i 4taftd * uiem I 4 * di$ A4l**(Y1 1..N - - E 1 f- F a f ~ -- -m-u-i- UTdi IAC d7i sell@ I=CO dif!di u d!d.....,d 66A.. " - " S -. - Y,,,,,C'd'Tmjiid'...i41N..... m: 9* *.4..-o.4o 34 o.o-~ *..o P. 4@S@.E4@Q4 di.d. i.. Ad-:.Fe.. 4 lil0 of" MinAdi 0 o of ooe0 10 VIe d u C.. U dd d -. d J t :!!! 2!:=a,, a a M.. Z: AddoAoi, mc m M $ 0.!I teio TAsTso n4t A-3 4W ISP9-dPA-0000P M4i 4 d C.A di.ld.dd.ld.E. -w ja-3 N SNxN2N gf nmf"mf 4 * #i no

108 NqSWC TR & 0.* P-6, NO 004 oms :!t Nr-- 640:0 z3a0 04..AO ft mno~m m 23E0-r *W.64 a.~~~~~~~ *. *...*.*.**.*.* * ownv0 u on nin..a ty I U -----m----- "OEN *o n0.4 44ON * 09. *N0I 0 OO41A44409 n 0:mA1. *...* *.*t 9a.. **t*aet * *..... am~eg~i- me a me, *InSmA UMoo460N d :%:;0S~0N 0So% 0 r.04s-@ 'noon0, 0 n- 00,0-9 OreN.a O 0 l : 0.* tIIIatv 02 ~~ ~ ~ a tm.. me.. m.m.ms.mm.eme.m..s.*.*.e.m. 31 a z 44N pit o * Y enm mit0--mm - NC m4 0 o F a0 & ap~m @ a00a 0 0 t*t.:p.. V t a.t! t l I SiSSSS P 1 InSSI 0I 1 _W_ 1905 ~ 00 ~ N ~ S. 49 ~ 00 am O $ 0UI S 9- N p 0:000; W... N N-titNNNN NNNN I Zo z4. p @*US9.04~~904EM4mom 0N..N6N90N.0.0SI94-0N4 0' In @44... A-3E5Sf miu 4N0 49..

109 N~oN~~~NN~oot...4o...aqa:1 44~~N... e0... N4. O~al ::~~al-t.:0 PN9..eA-*Ntae...N.. e4..a t.e 'a in 4Ima.0-7 W * -N e 7 zo- e * 4~a a~.#m -00 * ~ V.46-BBN.-..0e- da~a. t.... PX ft N a. a 0 e!oe a a a~ Baa a 2-O0,0 *NOWa P-a Ptum mm X 4 W,o NA 1a 1$ $t l go 44 II $ 4 e ili *N~o044N 0 N0Nea~.S ANE AIN Np 4@@G-O*f~ NNGNNBQ~ e N s -aa aa aa a-a -aa a-aa a a cc um o~ ; m no # !o~m mgr %% w 1a ,010a N N N S. ~~ 444MN r@*ONO0@00:0mm GG oooooo N... ftin N N N N NN N N N N N N M M I I. I N 0 0 F = ;l4.0~e-.np5.@0 f G agon4g 0 4~0 N a l e 44 e c. 5.M~ e i ft A o 49 On#04 I5I0 ONNG0N0 0Sp- 10 coo- :00N5PO 0 p4.4.~ N-. N...t o IA 6.N4 0 ~ O -mc 4m.* 0~Q 0 s N( O m O om M : - 4AG- 4~Il. 4@9.G@.5.Inl...N.u...4.I.G10: I* * 9 S 0 0 NN II-u II-CMI e... -NMm N-.@Iam " - IJ -- - I - - oil oil~.p. 4 o il III oi is4 m~g.e..o IN I'I4I 4 ~ e ~ ~ ~.1 ;: *aam4 an.4p.4 4II eo og1n...- NG4 mm, N te N N #NaNN.I% N NNNNNNNNN ~r in 0 MO, le,.0 1N4"Ai r-4ia4f-ne. a NO Mlow & *~MP ~@05.on 000 -a la N9.00NNN-.pG N a a -- ~n a a. a 0-N aamn.n. NU Na a-e ~aa fy N@N NNN. GN 4 NN-.NNNN p- eg. N VMN4-.5.-G 4GpA-36,~a4

110 ... *.** *.*. *... *..... *.* do66 U6I.**All.al*M4PN0 P!=!PA*ld A04qlqisAINA l'acmnm 16MAN m N Z N MIN N AIlAIN.. MAN MINU MI *~440N 940":lAl 9 am,, ego l0 Al 0 inp O l@ 1 0g A--9ll04 -.i It-IA IPE0A a g. a 40I9AMMlON * ~ ~ ~ ~ ~ 111 ti00 * ~AlA0 m44964~i1al l*~o.*4 FIlE O44hN UO o **...*...* * mm a T o4 ~ ee e~e 000 OOO O~e~ eo ee~ O@ m No S ~ fl e 000#:m l lalala A A l l lalala : Ni, a oi, AA*i nr pr -r uact n -,o yaa- ni npv n- 4 ~~~~04,m hi~ ~~~~~~~ ~~~~ l l. f A P * f 4 00 Am 1* 000A P1mf fl N, M m~~~llll111ppm OOAP mn0f-m11 I. 1 n -I. c- m ;i ya* no no n t ni ni io# ymo, m2 2M m O z m: 00ag Q~l0 AlN~000 Ifl AlP1 ln9n 10NONO O*4l.-ONO9 i 04 f l0* l 0P0 1-1U l 0NNA 0 0.P*P l00 I0 9A 'a', 4iM' Nl.l 4~.. 9 ~ 9 N ln m00 4P Al6 * M 1@... ln Alf A 0Al0 AlP P - lp U 4 N i. N A 0 r 000 f 000*. 040P lflA 0i0*.0Il :;;004A WP..* gs f0 fl fl *A0 l llp. 1P101**- -1P-1P-1P-1P-P 1.-l -Al- M4..4A~l..4l.N.4-ANEP010 Al.4 P10 fl00a-1.0lclu U1lfl11~1..PP0P. mm00u4am 4019M -. m1100m fl00ulm m l 1- UN04A~l~f9..9ONO~l~l*0p A-37NP.*0400UN*NNl.NN~

111 0PP... F0. a P. f.p.p.pi-... P.PI..0.0a.1..0P...0oft4t.0s.P..-pa Al.IA ~.... lu.. I * Iq E.O. l.... PO PI..llA A 0 a0 N.. a.n to, x P. T0 l A00 T 0 P.. t- mine m.0a li 0@ MM4 - onba bp P A P..0I... PP P..P P APP..P..P.P..P. P. P.! P.t P...P... ;411 Op. On two- 0 Novo * ~l~l~ 0 a in Gl"Do *0plbl~ a -P-4014millnto ll~~lll~~lll~~ll In " X V - l *tl-.o@.0l-- o:2 n.:bi N..a -0P- 0,.-OoMAl ~ P.0..l~.IAP.0-.l~.IAP.0AlP00000l*IA04nPn. 0000lb0IA z 0. 0 b P 4 A P 0P 0. I I 0AiP P 0 JI 0 4 b 04b00.0 IV MM0 I ha- I- J M )8- om 0 2O1 r MO N 10: 1.o! 0 o m2c Ko.I@04P.IP@ lp.. b.0. Vj4j.0P.. ~P.bi "!2.. 0 % I O4%4% Pb~~~l0 P0.4lII0b4 IA 04bP..ll.0A bl0.l0 00 c.c 0-00 bbi P. 3Al NOIN 040P410 N NOlo I', O 40 NNO 0P.l0.b0.A~I~.04O eyn ONON O o NNOOPN.I NA NNNNA N C-400IAO bi -of (A.0b~b40A~*0AP.000.OAPIA4.4A~ P Qb4l0~.P4f~I~~~blbll t : P. in N I.I - ly in M m m * 4 vp.p.p. 1IA m m P.P Aloss Is 11, of I oss~l~ ~~~lll~~lll~~~ll~~~lll~~lll~~~ll~~~ll l PblIO4A~O~4OlP00b0P.4A-.A~0PPb.A4-P..4.0A~4~OP0P0IIA..P.P... *0..AIA~l0P.F Al..l0All~bP.0~l.0IA4 Al~b.4P.AP.I000: 0P1A I *.,l! b.0a-04ip.0.i sbio 0410.P40P. 0-.IA8 0A4.. IA*P..04Al0PN.NIV A04lI0A.--40AI04.040IM-P-.OAI-AP Mmm -fcym PbP.0.00A ~~~ low o P ~.0@00@080@AIIAIIAAIAAIIAIIAA-38AAAAAIIIII0e

112 NSWC TB ~ 0900:: oo g 'i. 0i... VV....#. 4:OVI A4Ii I 1a ~ 0...A4 N0@4N. 4Ad :... o..g l* O *M won m0a0a 44 Ad.a P tn, iatt... II! I I ill i od I4 0 Ad 0 lom 4 V cw 4I.i NNU cm 0 0 M 91 0 d -M 04 N A N 0 mi 4 Win 0 ~ ~ ~ ~ ~ 0N ~ d ~ ~ ' - ~ AdN ~ o p 0N40~l4 4N p- m.a~ 0 m40 4e10.l.. i adddaa.~.~.y 0,* m - I I I~ I - -~~ "a.a. P4. A a, a, Ad a 6 d m6 Ad 0 0 A 4 0A 0 Adle s I *3*g* I Is N*NNN N A4 44 a, A Ad a, 0, a 0A co N A 00 m 0A 1 N400 0-N d Ui40ad."-N0Ai 44N00 i 040N040N6. d dnd 40 00A40000 ccaa0.a0aa d d Ad N N A4A - M 0 f- 4 4 m 4004if0N m m A N me N A~ AA* N D- 0 coo- 4 =O m N *IN 4A40 Q N 40 A- AdNind0 A 04A - A 4 N. A. Ad 0:V in 0A1N.. 10 A A. N U: t Ad a 44. A N n 0 A A w 4 N O.. d 4 N O C N O A A N AN 4 A O N d.o ~ ~. 0 4 N A M 4 d d A N 0.O O N N ~ A 0.. N.. n N z VDN N N 0. A d 4 i.. b ~ 0 ~ - c a n o A 4 A.Ii d I- ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ a! O F.A. ~~~A 00Ad4 O O O ON NN m-n0 O 40N.A ina t- # 40.a 00 t 0 l(d g 0 g o : 0 O 0 ; o O O m di41. 00A d440 0 A A. P:,7,! t";. V! i -A'Od d d AA A444.Ad ddo"a AA AdNNTT-odAA If *OOOOAAA,0 0AO O O nin Anoioio W o A-39

113 NSWC Tm ~0.- m 0 t 9: eo;4=; 4 P 0 0 0: N. 2 m NM,- la4n~i-moo N000M0.A,00 4owiiO~ P.O...NO. N 0 N 4.-.N 0 N 04000in0 ToM O N0 U O MfN funualtuft..4n....j P. 4 N 0N O 4 O - O M 1~f O O N O4i 0 0a0 O M I O 00 O-g.A l Iii n~l N 0f E O M M M M O P 0 4 M N M N N......s II0l I- - - I - hi I I- NI I I * M NNNM.--. MM ,040 M M M M M IIaMM 'O"Dooecoo M 4- N Np : : M NNN N NNNP N N N')d Ny N. N t N m N Nm N N N Nnd f 0n in 1 ONl 1N0 N MN 00 In- 0 0i N0i 4 M n0 NN4 0n in-n n 10 P- *,,ann 4 No- CU..I M O.0'D MN- N NN N- in z GA 0 n.0inon0 n i M00N 0m 00-4in00 N:o.0 0 0N N am, OON EO iiii O M.o on.on inomn0on NM6-OO-O 04 - ON00. - g - mse ON 00! - N E in 00 0 in00 -N O M N i.. O M ON O O 0 N 0MM O N P 0 O0 0 N 0 WNO &0 N in ;noo M 0 in E 44 i 0 0- i 0 N M 4 N-N 4 0 ts.am - n -- i l-, ii - - -n 00I 04P nN MN.-40N0.4.. in N0 0NM 4 0.NM. M0.4 N 0 M MtnN.E4 O0 n N.. m O 00, Mc N po :!km.ol0.. N.04 O...N... 0 I O Al V y 1 " n foin 4 #4MOO.in RInM4 y no m n M NO4 MM OON N-OO N O 00 MMM lm --- 0, mii0i t 4 4 M M 4 4 P- P n n at 001 ID : zo o o o o o o o o o o o o N NNN NNN NNN 0 n n0ini i 110in0 0ini i n ni

114 - NSWC TR o o o =:2 innl 2 N-!!0000== @ *a,m.m.m In " in,inm On # 4 *In M N ---_ t... " ) 4q fu 0 N fu 0 A0000N00" in0000Ml lll4l m x 40Al 00A000 a se4 a ~0a c mei40ap4a~0~fp4ag z 0u Af1 i 0 #9ul..-- *,**MMM ff1na0 44f1l Nff1P1-i 0 ~ ~ f Sin 9P.1M40 00 OP. falnal -p P AllI IA M a 0wtv p- Z in mo in I Al44-00 m Al04 l.,110 l~f4p4a0 A oz.d I P: Al..Alt... a a.... 4t I- - - *0000 4* Alfd t lorm~... A N 00fu -Alff1444p.7mf7_7 li.0 AP 4.00.l1 4-0-l1 44 '0Af ,~f 141 *~N~1.1~P1~1It aoo.o.oo.o.ooito.oo.o.o.o l.l...~ -f ft0 MfUtM#Ml * tin A-41

115 .. N w -- 0 *M"MA f O AX Mr-s401-0 fu F.N o 44 OOI 'GR '2 4 4N.N O N N 0:N :! N0000 O-O-0N ON OIl ONCN 'no-'no4 N~~~~~~~ 0 Nfl~ 440 NN0 -eo -. -N t NNNN OO0 O N01--.0A" N* MN C 0N N 440 ON I N N M.O ~ N30N0444N00-N0144N00.- N144N000.'oN 3~ 0 N 0-0 O 0 O O 400 N N4 0 N I M - nit 44 t41.- 4J IN t , 3,-. r, nm NC-' om. 4N NC40 N 04N 4 1U FE0-.0 0, 0N S ~ ~ -40N0TN~ ~ ~ ~ 401~ ~ ~ 01. l.040t t Vt.. 41lN0t N 4 44 Er, * ~ 0 11.'~0 S N' a1 0a a0 a., 0, N,. 0 N.c 0M0- N0fn14 NeNn04 ~~~N(jNc umin fn N--N N.Z 4 N0 0- N W 0% 4001 f"* Y NN 4~ ~ ON -. 4 N N o N ON! 2=: N4N n N 01 1N.' NN N44A-42N,1

116 P.-.-40one P.-4 MN - - Nf0eW04014 PP04mF - * *.*.* ~~ 8 1P 1P lp 1P ~888 1P4 1P 11P88 on in A4F I8 N N m 66 f0 "loan 4FPP P..@F.4 P1 4WI a*000a4p will", -~8 M. 08P..F-P COS mg P108F-T 0-1PM., ~-,.e0 P1 60! on-c 4wiP- 1 O O 0,:! V.0- S1 1P P1 P1 1P P WI F-.F-881WP1F ,0,0 0, P0,00.0 P , i0io0, Do4oo pp FP o mc~ 4o C IWO IWO IWO IWO IWO W0 IWO I WO IWO IWO IWO IWO IWKIO I I l 1 g ma0 ~ ~ mmma, a- a a, mi i m ll NF on z Pa P148 N m 00 t- F- 04 mf- I8 of11p 1 110P0 I0'W " tyl 0FFP8010W01Fi8WI1WFW40 oo*:m4*4*13i4-0p1-p4w F P WIoomm Wmm W F F ~P8 P1 WI P1 - F- 4F 0F I Mm-m A-4

117 NSWC TR 82-39h it i t"in~.. t : 'i :.1..I.. Pd Pd dfii Pd- Pd - P Pd* t--l-pd *-.In*oO-wo In- d0 "0PPdt 0* M..n0 &:nt& * e "M 49 0P o.p. P. -4P 0.I t-.p t dp d to0p d P-0 np 0 di ni 0s*.w-.wIm*I P P In000P. ~ ~ oo : x ; - : -000I0P0~ 0 a :a 2 0 P. m 0 " 0P.Pt-I *.* **PtS. d4np4*.t M" Tti"M tt4~.p 4..n. *P...ditdM tw9r4own JA PIfqn44 *m Pt o *d.t t-. I on *.n-4 ~e SJ* # o -- - *wtp~nd -- mm ~ -m I i S I S O fee lloss~eo I s ll M ommom* *PP 04P.990 "S0P0M ot M M ot 41, 001*00 *P00.4n.9Ptnd0-...4P.I.S0P..... o - o o. o PP0P44n~91 1o I A ao o - Pa - U Pd in " " e po -o'o Iil * ~ i l l S S S l ~ i N~d90 Pd00..Pd...oP d...oo-- - oddoddoddos~o~aoo...o.pp...o S w 0 0oo o0o oo ,N l m I lo olso MNlllllhl 0---to = M PM" Nd M Mot% tunt! nd n Z) OP090Pd *f" M4 Mfin.4P.o4o4oo00MIn4P.-... o. 4 In* iinin r. MN InP4i0: 00 P4-40 P0~~0n.0~ 4P040II~~M. O~ f-n 4 4. P~ oo- o. i000000ooio- - o - oo. o. ooo1.o... oo oo--o-o. t. tl. hi. Inn M O1 Ml..I.... J i i l A-44

118 Nswc TR *...*%**.*.*.*.*.*.**.*.*.*.*.*.*... ***..Till 0 40SON-. 040: ff4 *Inb *40*A*0004 lflgm**ip-op. ft ASO U* O " pol0 6 N.P-0 ft m0aa * *11111SS104111S *doap 0101m1In SP.A O.0@ 4@ 1AS S00401Q* 00A 4PAP41 *014.SIA4040W@ 0110"o m 4Ifl6, 01 0SS -m *..0-1*40A@ ASASP-OWS..4AS4A P0 A 44 A P- U 6 S P0N UAS01P01@0100* P-mlP4AS..OAS6PI4.AS0AS... 0PI0.. -i4n..4j zln.44p- Ia -m 0 F- 0 0 g 1.M.N F... AA0ASN N NSI-01N-OI ~~ :44: 0 I- 0 : : : -: : 44 An 4 l l 0. In lne'in44s S a. cp. I o0o AS S S in U y 0 AAA. m#4 ).O N 0.0 ft 4N600.N.( "m1 4 M N00 4mm Am 4 4 S4 4 z 0041;1 22-IM t o ASNANASP =*4 m NN a,01me 0 ONM*P o00 NOO4N *000@ No 001N ("N 011 N;Mp AS_&; - t!.i N 0 1 NA 0 N 0-0 N 0 *-* f- as m* N m N 0m 4n 2 9;N NN4 1,4V04f4ot-o N ;:9 0 04lp NoN 0~! fr-wp o - ~ ~ ~ ~ ~ ~ ~ ~ *11144N44410N N N NN...41m a *4 f f * i o - a lo mhi X : ;4m io olk uutu cm peiet ~ nn"60n lo o o 04N40em1NJN4@00Nfu4N-N ftvztf mf tmmnf jf tzn fff mnnnmf N 44 N0 ry0m1n0m N cm fmav NNN0NN N AS00004N04A-04540N

119 NSWC TB P.. a P. - 4W 494 A4N*Na#**04 4. Ash ~ 440! %. A... o!.....aw:.. P: ~ ~ ~ ~ ~ ~ ~ M M.. 4ANP0 0" P0A N - N - N 0-0N A0.NW 'a44 aft. 4 NO 0amo 044 -TO.-0 a 04 N40N0 NO. i 00 fm.* * A i f 4N N400 N44P. ~ ft N N P4.44W0 S4.NA4...0 r- N ftonmn4 0 to- M *vi * * P. a4. I-PM 4 P. n CNP N N8 WP. 40 P. A4P0 m Am f; 4O4ON44NOPN.mNO4 40A4P.40W0N40W "n NA4P.P.4 t -4N0 10. N 4... i O...4 A 4444AVt.N.. ft- - -f N- N N N - -.n ft ON No a"a, t Na f - - O9 M,9 IIM# mm56 N4 toi4co a O - O O N. N N N N N W N N A A. N N MWON. W N ModUte- W- -N.-W W N ---- NW N 00 4 P4. #-. a a. a " W 4-0 W'4' 4N08 8W NN40 M D NA 0 A NN A1 0. E 8 A r2l 34 A4 P. A Na M. 0 A P. N 0M4p P.7 P. ANM 4 A 0000Wf. a. 00 A 4 N M0 40 N A e- N N 4 N M~ ANN in P4 N0 N0 N P00 0 P.00o0 A N0 ODW At N #0M8m8m0MM N 444 OP. 4 8 N 440 AN m C ftft4mm Nf 4 fo * ff ozoe m m'4' P c W NW N - P ;f~' o 0*04AASA4AS0P.40 (.AOP.P ',n 0A1S 0' N o N P.. P. V404P. A ~ A N1 ~ 4m Am A ~ 4 ~ N 4 I.00P440 mmmm AW 4 04P A x b 30~P.~.0 A00...0O44 40A0 A46A U 4 A 4 4 O - A4 0 N ~ P 4.

120 NSWC TR EQ Po*4P. ;:P moo "ga... oe 6e.. O *4P.*~1@...A~iI4...U Ago 2 0EU4 4!!0: Zono P t 4 ANP. 04 Air.1Aq; M!-- Ion -EEUU E -1 - *EUP.UP*U.0O.OON M04 P 00 A Meq-..*~o 0 0* * O 0 S 0 :,&, *Oif~efli"1 floo 0lIb E000-0A o NEU E P40l0E0mla0.E,~qf'a 0,PI 0a G..U EU yn ynt -E UN NN ~ *eo~e~ aeoo~e M N ty4 000 As m v 0 N 4 m@m0n0pc l-44.p..~ooe..npp OO~eOEUNUEUUEUEEUE a 4 r N ~ N bi n 4 S As -M UA I41. ma1* N- Fc ll *F-4I4P10V-etft0-VIn * 0F-04044I.00EU P N4 P S ~~~ E....EPPE.. E..t EU.. UV o1 010P 1,Tn 14 M AinW 0 n' '0 444 z o~mo n~o~ev.eu P10 ap1.o~o'aa-47hi

121 NSWC TiR s666: -MO 14 N=::4 s ~ N4 6 N N ~ e. Ae mn.4 0t I 001 OF.** : Al. Nt@ No N4... l6a0 to0 on i. P6 n IV * *...*.*.** Al~~l~l~~l~l4.l ~~f Al l l l in~~~40 4 * ~ ~ ~. 6 ~ 0"I,-06A lal44a ~ ~ ~ O 4 6A l A *~~ ~ a l A l 0 l l A 0 win In6@604640ll.4N66ll4A m4- UPof n 4 0 Al. ' F 446-0q444ll4N ici0a l40 -N o 4. - l l l ln~44. S l :_,, " 4 4 I.All.4 ~ ~ l l l. i.... * M-000 -l 4 N WON l NN 141.~I. ~ l I. *-. i *,I... i t-ti Inf- i ;0*-ga, to cm o,: II& 0~~ t -lla~-.a~~~ - New4l0'l~0.A~ 0..Als0-Aulym I OAl n 6*0--ft stl A z V A ~ 0 4 N S I.mm..ISI.m. m ,... a.a.m mm..me. 1 mi.s.s.. z0 -- uu "t f. A-4

122 Nswc TR , U.. ~ P.... 0UEiE~ I" "M qfteu on"oft N M OR O 4 V M- IV4imwu" A AAAA VI m mm 4 m " E M p Mo Oh.~~ es. 0E..0~ S- Ion a.0 A M 10. P.*wUM * *. *. *... * I0 S SS-' EE~qE1E~qAIqEE~ESE5E mq q o 445J iqn 5AUEEO Ison E Sm ~ ~ ~ S40Imiml~im~ ~ O Ses00, SS0 ~, OUS P..44E4P.q Eq.. OO O~q E 0SOOA E GNO*-.U05A 550U 0U 4O.0.-.q.A 0 S.qU VSSEO Eq ac La1. oo e11o~o o. oo e o o o o o o o o o o o o o o o o o eo00055su, OzEUUO,51 z zi M Nummn cefm AMMMI ME- Mm- 0~N GOP. 51P4A-4 4E0qE~~.. O S.lufiun i5.0. 1,a Z * 0...~ ~ ~. ~~ Neu~4U54... n g 4 4 E M 4 4qEU0E.E om m CO M A'P QI M M &: 0 0 " US E4 ~ P.q..o ~ -- q ~o..055,50e P 00~~-EP00 00 Ion IoJP Al0A~ EU01P0 040PUS.SJOOS0O..OOfUSjf~USq~0U440050P..A E

123 3,. V, ': n t nco.4!c. jtcoo',!. t. P:. onto0 P. U F.In C P- f 10-# 'C 00 to0 P 0 - F P. FnN ---On 9 C 9 M *N a.qm N In0'C9PinO' N-*..Iin O@C0'*i on..m M 4 - 'D 1nNN 4N 0 M 4 'CI~'in b L NON 0 n 0 a a, 10 a - M & a 4 0 OM O tp..op0 0 a.m'a, 'a0 440 N-.ONM SN a.i~n040i' Nn 4 4@ N NnO N 40I N 10' 11 J, 1. Mal~II4 'C 4I4I.)~ N ' n4 M 4In n 0Ia. N 9IIN0.0' zsz Ogg! v 4:0ac44 nnor- Tro..P9910II::!"4Mp.0000 I.... I %..6t.o.. 0: n n It. M-MM-- -N7N INN**NN - NN--I gas~ a'um a x z 'a O'00I.c o ~ o o o 0 O o o e o o eer o o oe o o o o o o o No e o oom o o o e o o e e 00 I 00 n I InIflIn 00IflIn n I If InIA I InIn n I InIn n I Ine 0 0 I00:000 0C a NNNN NNNC:NNN1 JN a. vv n;c ma NmA 44,,o- muo 'Cza0WO14I'C 4a0 1- :,Q M 0A.C14nC001N9I'Na01ND 0.X w ~ ~ ~ ~ m D N 0'aaaaaaa~~~~ooeo N N NN N l ~ 01 ~ 1 ~ N 19 P w 1K.. V pl. I %... C tc %0 t o,i In2,- I Ic 02M!m NO4C0 -C- '1 1''--ONC.- 4 ~ -. n 9 1 O C EnI N.,'.O~1..nN-99.C 1(.0.0N'4'~rI I.1N..l C:4 U19. m@'cc N 00. OC 9 0 4Cn.I Nn 4CC 4 N a ' O IN. 4. ' 4CC 1 ' N C N ' O ' 4 N-N C N '' 1 N nnc N 99 0 NN09;: z;c 9;;Z0 441IJNNNE194E ;go;; 4I'U'no4NNN99 au 4InC''C 'CCN NZ191;; 'D p 0 t..4 : ~ 0C n1c C' 0 9 CI aan - - Inn 9 N 1N a'~ O I N19'C'~nI N'C C4N 9I9 0In 'C4 199 nom 0,1 4' t0I c1 9.'.C....' :.N t.'.-n k0.... N~a N0. a n CN a m 1 m 4 4 m C ' C 4 4 ' n ' ' n n m o o ' ~ J, C n - - N 9 MM M MM M AMMnM M M A-5

124 NN.Pa-ON.NN.N vo.- -O-0. *Mp- *.0NgaiaD*i,D. *4 o O O0~o o 'MN C ON O 00t ' MONWNMOod "P. 0 ly N OM0.@0 0 N M~ N. N O aa ON N0 m0.00 * *Nf 000NO~ a 0-00 eoo1*foa.d.*...* O0**MOM JIIOMO MON 0OO 000 N 0. UNON MO MM- ef N- NNO MOONOm 00. OO ON.N ONN-O 0.0--NN. NN M ;:2 U0N MN 0 0 ON N O 0NO=O~ 0 -YC N yf N qc nmi "m nr N N N N en m " 4 N 0000 NMpON, 0 N m M m 0a N M 4 0( a 0. 0 a a a o N Mm 0~o a a.n... -N N NO-"It! 0N eooooooo~n 0g0. N 0 : M N NOO.MOO 0 'Oo O 0 0 M00 O O-MO 0 0 M 0 0 *.. NNNMMMMMM-- z -NNNNNMMMMM---NNNNM MM C*. O O O O O O oo 0.. '.. '0.Q '... N... a 00 ~~~~~~~~~~ O a0'00 0 OO NN NN N NMMM M cc4f -0 : C1 ms m m 0040 Ia N...* '0.EN0N M O OO - ON- - -N OO00NOO OON ON N M 0A 5

125 NSWC TE ox VON MEMNmp0M N!SO A aan04namt a n=avi4 tm0omma:onomn0 4 ~Is4 ME M '4M N ammmnn~mn &* *O. 4 t...1n.. ON ae O. a0.!.a0.40.n. 4N NOO- a 0--a 4 E M M -- e N 0 p ---- M ~ Mon lin.1.. ~.,I tm M E * M.. ~ ~ ~ Mp-0 ~ ~ EO ~ I EQ-N Min ON0 4 M4. t-~j N 4 M N In40 I- EM4 t 40Q.. M~oe M 0r.a.p-.o, a- P 4 N NOE M.. -~4a.0oo -. N -M o* on40n I MMI-000O00104,.0N=OaO a I f 1 e es mi aa Vi N..a E..4 00ia- 4 It ll 0N40 ea4. 040a 4 M04 M$4 ao 0 NN $0400- M- E N-~P NaN *N0 1N0M0 W1, 100 c, a No zo.0o4 *.44a I.04.a40M N-CNP440444MMMMD z 4O 400.0,0 a E44 ) z a N S D 'SS S 40,0 NN040MM 4a0-. N4 0N00-44aN0N4M0-N40 o-.a 0oM a 0- N NN M MaM- - NNNNM N N N N M M 4 M '' It I : I ti..... MM 4 4m m m U ~ ~ III00000N NO0 ~~~~:.aa 0 ~ a~~~m4a0~ 1 M 0.M4aa0M4a00.40a.z 0- am 4 c 40 Q M X N20 N2 NN:m NmMM M MM E a.aa a.aa a.a a.ao a.aaa.aaa.aoa.aaa. a z2 & z : : N 0 m 11 M# ;,04,9 ; 4M 2 mz'm-" 1 ',% 0 m 00 z - 4 NM - A0- c I P&... Il " OIMIW M., M - - a v DI coac A-5

126 NSWC TB a0 C d) inf fn4% 04 MC 9 F- 4-F P - 0MN N NC 49 C-M v 4S-C C 0 N~~~ C ~~ CCM9.C' men NNN- 9M C2 CF 0 3CCCC 9CC t9ccc C4-.F-C3NN 43a44 C 3. C F 0,:MN 4!:z *NOMMOM9Na--Ma,.MNNFam J S 4 N N 9-4. C9NM C - C 9 C C F - F - M 4 9 C-NN:9 F - C C C 9 F -0 O C F C C 4 3 C C 9nN. ~-. NN.~.~ Ei44 MMNN C4CC MNNN N 44 C9C CM4~CF 3 99 M.~.4 M O M 4 O F9 C C O.9 4 m s!w I la M4 C~404 NC C-1F-1 IC- M4 0C C MFNC CC 44 loll#$.. o0... 4O9N F-4N C CFF-C0 99CN F-C-C34 C449.C'amC-.3CCC... C - is C O. OC'O"4O C C C CO C C 0 C OC"CO O O CC C CC'C9M C CC 00000a F- O. 4 F9 N5.3 N CFC.. C-. N 4 2 NNC- C- On 00000Ma 7 9N -0rm InN 0k w 49 %)F ~C 4F-9N M -3.- ID 01 A C 0' 0"o N N a 0 N CCC NN44M A. 4NM4 1,-1 e-.0!! rqp s4mf-cccm.-1,nn 4J 99M NCNN M C N9C NOM N 0 F- -0-CCF ~ a 2-4) CIse 4NF M F M N -CC4F-NF A- M- -NN men0 MN fqM NO-N I 4F9CC-9FCOC N4-49 FCIV.9' M. -mis -,-----mu--m-----m--- iii..... i..m i.. Iu m In 94 Co 11. M1 let $I$ I- loll - so ON e $$s.. t 4 oi C l I 3 N C C O.0F 4 C N MN *A9 N0 -CD a, M * In 4 3 a C N N In 9* 9A Z N CY *A -3 a. F- Nu MC4M3-C3NF NNF- B.OF-CMNF-9C - - NMC Na M-.MNN.N innnn-lm~~mmccn~ii.- CC.A-53-F-C

127 ~N. MONOM -00,44 *P.0ON M a O 's P s f.a -. oao. ; *4 n~~.0 " 44 l-- N... #M*EEM an~mannoenmanannogl~nao woa *aannn0n-0n......%% Man*M*WIM~~~~~flI-.1 * -& *M 4nnnnnaal~.. in NN - an N NNN N NNN NN OMN~an Nan~an O0000 'tn t0 EM~anN M~e-0 -On M 0 M-in ed M 0M2 0 M0 p..ao M t- onea, 2N 0 p N N.0 coi cyo0 N &- f a a - M S 'a S a0 a ay 1 r A a aa N a 0- a a0a. an oo o~~ ~o o 0. NNN~n-00Maa..ON.a.aO.O. vanan :0..Nan CtONM:a.OO.A..an. - a.. N -NNN E- NNN~'IMM M N w NN Neoooooooeoooootooooeooooooooo 0 eoooooeoooooe Ina INnal1, Mnna M MMM4,e u n NI 4 0#O nm* mnnnnnjaaaj -nnnnaaaaann.nn-n-. 'I A 'A a : m w af 40a l a 4 N 4 N an pn 00 t N P. v zn m A m.'jno # v01 v N ana00m0c aonnnonnanonyn-noconinnoe P N -P. t.*0m -MM000N 0 *anoa c anm a00MN-M 000N cumn n--n4anm40n0-19n0twoaan x0m00man20anj SOcr.Na MN-*n0O annnnn.aaa an MMnn-- - ~.1 iaa It.17 anno1o.oo.na.o4.n n.ln.oo.o o nn a ' ian t 0~ ~ ~ ~ ~~~~~~~~~~~~10 W0aNoaa0NM00an--na00a~nnCa nc -0 00aNa '00-O~~I o0nnnn0n0-n-an~n #-n-n toao~00-ansam~np~nm -NanNMaanna0 ann -a-m n-an-07-anmoo 41nno~n-nn,.N 'c fy InM P. P a 0-ZI - AnN Naa4nnM q rn O a(mmm- - 0,, 0 A-5

128 in in: M9N0404*40 M-4 4N -4 4* It. I. N. It0 O. 9..*9O , M 0 Sy 10 a In o4 bq k M*4pm.ON 4. 9 NO AlN 4. A NNnotyly- 0 4y *0 P.. a 4E 0 * * O t N * 0 -W%1-0 0LPNG *4 NNfuNNcACYryinMMMMMM NN NNN e ~.e N..*. M..* cm 9C on z 'a M 4 9 MN0 C *- N3 IV N p. N0 N N m 4- mm. M M N ala Il S IS II I w1 IVtoa 4MCY- - -@-09M x -y NM 09 N M ma.9 N N r* NC 2 -M*' 90N14' N II N N N M M M M - - N N NN M M M 2 rmm0 a4* w :C!...0 :. I IM VI, e PeS ol- *m ~ 0 ~ ~ ~ ~ c000 ~ 00 ~ t 00 a ,4 om ot ' C 000 CC 4 40 NO : - 00 on ma 9pp p J4 VO 0o 0,c,0 s6-4p4~0n~p.4*u4n C'A-5 0 ~ Cp.~~4p

129 APPENDIX B The measured surface pressures are provided in this appendix at pressure stations 1 to 4 (see Figure 1). Due to equipment problems, data at pressure stations 5 and 6 were not acquired in all tests and this information has been omitted from the listed results for all runs. The symbols appearing in the data list are defined as follows: PHI - Circumferential angle measured from the leeward plane. X/D - x/d (see Figure 1) CP - Average pressure coefficient based on a sample of 100 measurements. SCP - Here CP is defined as (p - p,)/qsin 2. Standard deviation of the pressure coefficient using a sample of 100 measurements. CN - Local normal force coefficient: normal force/(dqsin 2 ) CY - Local side force coefficient: side force/(dqsin 2 ) In runs 1 and 2, two sets of data are.listed. During these tests, substantial fluctuation in the measured pressure was seen and the listed data sets produced the highest and lowest side force values. In the remaining- tests, pressures were fairly stable throughout each experiment and the presented data represents a typical set of measurements. A tape containing this information is available on request. B-i

130 NSWC TR 82-39h TEST NUMBEt k RUN NUMHER 1 PORT PHI X/D/2.6 x/d3.6 A/Da4.1 X/D*S.7 CP SCP CP SCP CP SCP CP SCP b S.00 *968.OjO OS O Sys S.00-10o26 osa -I.S a *144 a -S.O T S S T1.09? IS k64.11u b S6.480 IS b O.le* S I ZS 20 IOS OSO IS b S11.OS8 cn CY TEST NUMbEH RUN NUMOER 1 PORT PHI X/D*2.6 X/D3.b X/0-4.7 X/DS.? CP SCP CP SCP CP SCP CP Sc S S b TS.O * Y s2t SS b e ss.260 I / S6 i d , ,084 -.q b b S , IS be S Y CN CY B -2

131 TEST NUMbEh RUN NUMeULW PORT PHI X/0aZ.6 X/0*3.6 A/DX0.7 X/D0.7 CP SCP CP scp Ce SCP cp SCP ,U # S ? ? b -1.4d e -j * , e ,S It Z Y * _ S#S.194 lb 30: :414 : * Is : * , Iya N i.226 in o Ch CY TEST NUMBEK HUN NUMBER 2 PORT PHI X/Du2.6 X/Om3,6 A/DM4.7 X/OwS.7 CP SCP CP SCP CP SCP CP SCP o z ? lob , 7 pg SI "1.D # O d lbo Ch CY B-3

132 TEST NUMbFN NUN NUMBER 3 PORT PHI XID*2. A/0-3.6 A/O-4.7 1/0.5.7 CP SCP CP blcl. CP SCP CP SCP J * : % #J36 job * & lo.06b O a e O07b -. 6b * Sv O b -2.M is u W e % s S e.544,0t S Ch CY TEST NUMBER RUN NUMHLR 4 PORT PHI X/0-2.6 X/0=3.6 X1/04.7 X/05.7 CP SCP CP SCP CP SCP CP SCP O S ,Obb a , o ".5s$ :397 : : S il S b e d o t CN = Cy B-4i

133 TEST NUMBER RUN NUMBER 5 PORT PHI X/0-2.6 X/0-3.6 A/D)84.7 A/057 CP SCP CP SCP CP SCP CP SCP IOS t * A IS A S S CN CY TEST NUMBER RUN NUMBER 6 PORT PHI X/0.2.6 X/0-3.6 X/D4.7 X/ST.7 CP SCP CP SCP CP SCP CP SCP S OSO OS S S TS ?.23S S ? O0S SO ? S CM CY B-5

134 TEST NUMREH 81062SO2 RUN NUMNER I PORT PHI X/02.6 X/ /o04.7 X/0.5.7 CR SCP CP SCP CP SCP CP SCP * * o b ? b R o * IS o IS SO I a S o s? , SS SO SS C s CY TEST NUMBER RUN NUMBER 6 PONT PHI X/D2.6 X/0.3.6 X/034.7 X/D-S.? CP SCP CP SCP CP SCP CP SCP v S S I TS S * V ? Is * ,lio S T.116 -I ? ? * ?." I s.06? na. -) A*%v -1.6s % % * -. 0?.% ISO.#$ ? p %2.02,s sll.044 S co CT.308 A4bl B-6 -!

135 TEST NUMBEN RUN NUMBER 9 PORT PHI X/ID2.6 4/D=3.6 X/0-4.7 X/OrS CP SCP CP SCP CP SCP CP SCP b o a bb kbo b ? S * % CN CY B-7

136 DISTRIBUTION LIST Copies Hughes Aircraft Co. 1 Missile Systems Group Canoga Park, CA Attn: Mr. Henry August Calspan Field Services, Inc. 1 PWT-4T, MS 600 AEDC (AFSC) Arnold Air Force Station, TN Attn: Dr. W. B. Baker AEDC/DOFAA 1 Arnold Air Force Station, TN Attn: Mr. Thomas Best AFATL/DLMA Eglin AFB, FL Attn: Mr. Carroll B. Butler Naval Weapons Center Code 3246 China Lake, CA Attn: Dr. William H. Clark Department of Engineering Sciences University of Florida Gainesville, FL Attn: Dr. Mark H. Clarkson AEDC Arnold Air Force Station, TN Attn: Mr. Stuart Coulter AFATL-DLB Eglin Air Force Base, FL Attn: Dr. Donald C. Daniel Commander US Army Missile Command Redstone Arsenal, AL Attn: Mr. Ray Deep, DRSMI-RDK (1)

137 Department of Aeronautical Engineering University of Bristol Bristol B58 ITR United Kingdom Attn: Mr. Paul Dexter DISTRIBUTION LIST (Cont.) Copies I Lockheed Missiles and Space Co. Inc. Dept , Bldg. 154, Fac. 1 P.O. Box 504 Sunnyvale, CA Attn: Dr. Lars E. Ericsson Vought Corporation Advanced Technology Center P. 0. Box Dallas, TX Attn: Dr. C. H. Haight Nielsen Engineering and Research, Inc. 510 Clyde Avenue Mountain View, CA Attn: Dr. Michael J. Hemsch Rockwell International Missile System Division 4300 East 5th Avenue Columbus, OH Attn: Mr. Fred Hessman, D-165 Northrup Corporation. Aircraft Division Orgn 3813, Zone 82 One Northrop Avenue Hawthorne, CA Attn: Dr. Brian L. Hunt Department of Mechanics of Fluids University of Manchester Manchester M13 9PL ENGLAND Attn: Dr. Peter Lamont AFWAL/FIGC Department of the Air Force Wright Patterson Air Force Base, OH Attn: Dr. William H. Lane AFATL/DLJCA Eglin AFB, FL Attn: Dr. Lawrence E. Lijewski (2) 'V

138 DISTRIBUTION LIST (Cont.) Copies FIMG Air Force Wright Aeronautical Laboratories (AFSC) Wright-Patterson AFB, Ohio Attn: Capt. Alex J. Malanowski NASA-Ames Research Center Mail Stop Moffett Field, CA Attn: Mr. Gerald N. Malcomn Commander US Army Research Office P. 0. Box Research Triangle Park, NC Attn: Colonel Duff G. Manges Department of Aerospace and Mechanical Engineering University if Notre Dame Notre Dame, IN Attn: Dr. Robert C. Nelson Nielsen Engineering and Research 510 Clyde Avenue Mountain View, CA Attn: Dr. Jack N. Nielsen AEDC/DOFAA, DOT Arnold Air Force Station, TN Attn: Captain Alvin R. Obal Complere, Inc. P. 0. Bcx 1697 Palo Alto, CA Attn: Dr. F. K. Owen Commander Naval Sea Systems Command SEA 62R41 Washington, DC Attn: Mr. Lionel Pasiuk Mechanical Engineering Department Clemson University Clemson, SC Attn: Dr. C. E. G. Prizirembel (3)

139 DISTRIBUTION LIST (Cont.) Copies Director 1 Engineering Sciences Division US Army Research Office P. 0. Box Research Triangle Park, NC Attn: Dr. Robert E. Singleton Commander 1 U.S. Army Missile Command Redstone Arsenal, AL Attn: David Washington, DRSMI-RDK USAFA/DFAN 1 USAF Academy, CO Attn: Captain G. J. Zollars Defense Technical Information Center Cameron Station Alexandria, VA Library of Congress Attn: Gift and Exchange Division Washington, DC (4)

140