Table of Contents. Introduction........................................ 1 II. Ship Hydrodynamic Test Facility...................................................................... 2 1. Experimental Configuration........................................................................ 2 2. The ModelTests..................................................................................................... 3 III. LaGrangian Trajectory Analysis........................................6........................................ 1. Data Reduction............................................................................................. 6 2. Statistical Analysis and Digital Filtering.................................................... 8 3. Theoretical Comparison................................................... 20 4. Hydrodynamic Insights........................................ 21 V. Conclusions and Recom m endations........................................ 24 APPEND IX A. Test run listing........................................ 26 ~~~~~~~~~~~~~~~~~~~~~~~~~~II

List of Tables and Figures Table I. Test Matrix Summary.............................................................. 5 Table II. Transverse Wavelengths measured from Figure 22...................................... 21 Figure 1. Schematic representation of test apparatus......................................... 3 Figure 2. Wake coverage showing longitudinal and transverse dropper offsets..... 4 Figure 3. Coordinate system for analysis results............................................................ 6 Figure 4. Velocity measurement point density by bin location.................................... 7 Figure 5. Probablility density function for the bin corresponding to 37 feet (11.3 m) behind and 2 feet (0.6 m) to port of the ship with 96 data points..... 9 Figure 6. Successive superposition of centerline longitudinal wake fraction by dropper distance. A. 1.60 X/L, B. 1.60-1.00 X/L, C. 1.60-0.50 X/L, D. 1.60-0.21 X/L, E. 1.600.07 X L..................................................... 9 Fgure 7. Successive superposition of centerline transverse wake fraction by dropper distance. A. 1.60 X/L, B. 1.60-1.00 X/L, C. 1.60-0.50 X/L, D. 1.60-0.21 X/L, E. 1.60-0.07 X L........................................................................................................ 10 Figure 8. Superposition of longitudinal wake fraction; combination of starboard, centerline, and port datasets.................................................................................. 1 1 Figure 9. Superposition of transverse wake fraction; combination of starboard, centerfine, and port datasets.................................................................................. 1 1 Figure 10. Longitudinal surface wake fractions as a function of distance aft, for longitudinal slices along the port, starboard and centerline of Figure 8......... 12 Figure 11. Transverse surface wake fractions as a function of distance aft, for longitudinal slices along the port, starboard and centerline of Figure 9......... 12 Figure 12. Longitudinal surface wake fractions as a function of distance starboard, for transverse cuts through Figure 8................................................. 13 Figure 13. Transverse surface wake fractions as a function of distance starboard, for transverse cuts through Figure 9.................................................. 13 Figure 14. Longitudinal surface wake fractions as a function of distance aft after re ing the number of bins to 61............................................... 14 ii

Figure 15. Longitudinal surface wake fractions as a function of distance aft after reducing the number of bins to 61 and filtering.......................................... 14 Figure 16. Downstream surface wake fractions as a function of distance starboard, for longitudinal cuts through Figure 10, heavy filtering (o(=0.05, L=25)......... 15 Figure 18. Color contour plots showing Wx superposition after light filtering (=0.35, L5,.45,L 4)................................................................................ 16 Figure 19. Color contour plots showing Wy superposition after light filtering (&,=0.35 L=5 0.45, 4)................................................................................ 17 Figure 20. Resultant contour images of Figure 18 showing Wx superposition after light filtering ((Ox=0.35, Lx-=5,y=0.45,Ly=4)......................................... 18 Figure 21. Resultant contour images of Figure 19 showing Wy superposition after lght filtering (o=0.35, Lx=5,oy=0.45,L=4).............................................. 18 Figure 22. Downstream surface wake fractions as a function of distance starboard, for longitudinal cuts through Figure 20, light filtering (cOx=0.35, Lx=5,a-=0.45,Ly=4)................................................................................ 19 Figure 23. Cross-stream surface wake fractions as a function of distance starboard, for longitudinal cuts through Figure 21, light filtering =0.35, L =5 0.45 4)..................................................... 19 Figure 24. Downstream surface wake fractions as a function of distance starboard, for transverse cuts through Figure 20, light filtering ( =0.35, L =5, 0.45,L =4)................................................................................. 20 Figure 25. Cross-stream surface wake fractions as a function of distance starboard, for transverse cuts through Figure 21, light filtering (=0.35, L5, 0.45,L=4)..................................................... 20 Figure 26. Vector diagram of lightly filtered surface wake fraction............................. 22 Figure 27. Two-dimensional plot of Wx................................................ 23 Figure 28. Two-dimensional plot of Wy................................................ 23 i i i~~~~~2

1. INTRODUCTION This investigation was sponsored by the David Taylor Research Center (DTRC) under contract to the Department of Naval Architecture and Marine Engineering, Program in Ship Hydrodynamics (PSH), College of Engineering, The University of Michigan. The purpose of this investigation was two fold. First, to provide Lagrangian velocity profiles in the near wake region of a high speed twin screw vessel and second, to apply advanced spatial domain stochastic analysis techniques to radar images of surface ship wakes obtained during the Spaceboard Imaging Radar-B (SIRB) Shuttle mission. These two activities are related through a desire to obtain greater knowledge of the complex hydrodynamics in operation in the viscous wake region of modern surface ships and how these interactions affect active remote sensing of the ocean surface. Discussion of the SIR-B portion of this investigation is provided as a separate documert The purpose of this investigation was to provide surface Lagrangian velocity profiles in the viscous wake region utilizing the Digital Automated Radar Tracking System (DARTS). Two-dimensional viscous wake velocity profiles were desired from the stem of the vessel to as many ship length aft as was feasible within the constraints and limitations of the test basin. The "downstream" rate of decay of both the transverse and longitudinal velocity components were of primary interest for numerical model verification. The final goal of this investigation was to provide an experimental foundation upon which to guide full-scale measurement efforts. The Lagrangian velocity analysis utilized hardware and software developed in conjunction with the Digital Automated Radar Tracking System (DARTS) to acquire trajectories of tag particles seeded in the near wake region of a towed twin screwed high speed vessel model. For this application, the radar portion of the DARTS system was replaced by a conventional high resolution video camera system. Video images were digitized and examined for each particle location and velocity with successive data runs compiled in a statistical framework. As a result of this investigation, nearly 30,000 velocity observations were obtained in the viscous wake region from immediately astern of the transom to approximately five ship lengths down stream. Although towed in the Ship Hydrodynamics Laboratory (SHL), the vessel propeller bading was adjusted to simulate a self-propelled vessel. Due to limitations of time 1

and money, only the twin screwed, outboard rotation data runs have been analyzed in detail and compiled in this summary, although wake fraction survey coverage exists for single screw as well as no propeller operation cases. II. SHIP HYDRODYNAMIC TEST FACILITY The University of Michigan Ship Hydrodynamic Test Facility (Tow Tank) was the site for the model scale experiment described herein. The Tow Tank is the largest University owned model testing facility in the United States. It is 360 feet (109.7 m) long, 22 feet (6.7 m) wide and 10 feet (3.05 m) deep. Mounted on rails over the tank is the main carriage and subcarriage which serve to transport data acquisition and analysis devices, ship models and personnel at speeds from 0.25 ft/s (0.0760 m/s) to 20.0 ft/s (6.0840 m/s) at an accuracy of 0.02 ft/s (0.0061 m/s). 1. Experimental Configuration This project was a continuation of work done in 1987 under University of Michigan project number 023945. Refinement was made in the test technique and additional data acquired. A schematic representation of the test apparatus is provided in Figure 1. The purpose of this test was to optically track targets dropped at known locations in the surface wake. The drop device was the same one used in the 1987 tests. This dropper places fifteen targets (referred to as DARTS) at two inch intervals normal to the direction of model travel. Longitudinal as well as transverse offset of the DART dropper were utilized to acquire complete coverage of the wake region of interest. (see Figure 2). The targets used were luminous polyethylene 0.25 inches (63 mm) in diameter and 0.06 inches (15 mm) thick and were slightly buoyant to provide a true representation of the surface velocity. 2

SUP MAIN CARRIAGE CARRIAE C(I If D I I I IfFl ~DROPPER - DEVICE VARIABLE LENGTH CONNECTING ARMS VIDEO CAMERA - SUBCARRIA"E \ MAIN CARRIAGE SUBCA {' \. _ X DEL ^_ DROP I DISTANCE I (VARIABLE) Figure 1. Schematic representation of test apparatus. The model used for these tests (DTRC No. 5369-1) was provided by the sponsor and was numbered U of M 1597 for internal bookkeeping purposes. This was the same model tested in 1987 as U of M 1581 and is a 1:24.824 scale model of high speed twin screw vessel with a model length of 24.84 feet (7.57 m) and a beam 2.204 feet (0.67 m). The narrow beam of this ship necessitated the placement of the starboard engine room aft of the port engine room. This geometry resulted in a shallower inclination angle of the port propeller shaft. The model appropriately cdsplays this cross-ship assymetry. The propellers used in the test were also provided by DTRC and were operated with outboard rotation. 3

X X X X x o r- 0o o o o o o o - - Yip Figure 2. Wake coverage showing longitudinal and transverse offsets. The test section of the model basin was darkened and illumination of the targets was provided by an array of ultra violet fluorescent lights. A Pulnex model TM-540 high resolution nadir viewing video camera was mounted approximately twelve feet above the water surface on the dropper centerline. The video signal was recorded simultaneously in the U-Matic format on a Sony VO-5600 and in VHS format on a General Electric 9-7885. The U-Matic tapes were saved as an archival record while the VHS tapes were used for the actual data reduction. 2. The Model Tests This test series was run at the design displacement for one speed (20 knots (10.3 m/s) full-scale) in the normal, no propeller, and trail shaft propulsion modes. Propeller rotation was outboard and model rpm settings were determined from full scale trial data from the same class ship. All trail shaft tests were performed with the starboard shaft trailing. Two runs were made without any propellers mounted to compare with the 1987 data. Data runs were taken with the DART dropper on centerline and one-half model beam to port and starboard at six distances aft for both standard and trail shaft conditions. Figure 2 provides a schematic representation of the region of wave coverage. Each configuration was run a minimum of five times to indicate level of repeatability. Table I provides a summary of the test matrix. A'zero drift' was taken for one minute before each series of runs (one per camera location) to verify still water conditions in the tow tank facility using 1.0 inch (254 mm) diameter 0.06 inch (15 mm) 4

thick yellow balsa targets. For the zero drift runs the targets were scattered randomly within the field of view and video taped under fluorescent light. Individual data runs were recorded for varying lengths of time depending on the length of time it took for the targets to migrate out of the field of view. No runs were longer than sixty seconds and twenty to thirty seconds was typical. Table I. Test Matrix Summary Normal ropulsion Traiing Shaft No Aft Dist(L) 0.000.07 0.21 0.50 1.00 1.60 0.00 0.07 0.21 0.50 1.00 1.60 1.60 Centerline 8 10 5 9 6 5 5 5 8 8 5 5 2 14" Port 5 5 5 5 5 9 5 6 5 5 5 9 14" Stbd 5 5 5 6 5 5 5 6 5 5 5 6 Totals 18 20 15 20 16 19 15 17 18 18 15 20 2 Although most data runs went smoothly, a few problems were experienced early in the test sequence. The most serious problem was the loss of the starboard propeller shaft during run 10. Repairs were made and the tests continued without mishap until run 29, when the drop distance was set at 0.07 lengths aft of the model. At this point the stem wave crest was high enough to wash the darts off the dropper. Since the dropper was fixed in vertical position, the solution was to lower the water level in the model basin two inches, refocus the camera, and take a new calibration grid measurement. There were minor problems experienced in obtaining a perfect match between desired and the actual propeller rpm. In general, the variations were small; ~ 1 rpm in model scale. The actual rpm was recorded for each run. A complete list of all data runs is given in Appendix A. 5

III. LaGRANGIAN TRAJECTORY ANALYSIS 1. Data Reduction The dart trajectories for each run were recorded on color video tape with a black and white, high resolution, low light camera using 625 horizontal lines per screen and 1/30 second between frames. A digital timer was displayed on the screen to give the elapsed time after the passage of the stern of the model for each frame. An Imaging Technology frame grabber board was used with a DEC Microvax GPX workstation to freeze every third frame and extract the X-Y position of the center of each visible dart in screen pixel dimensions. After an entire run was digitized, a specialized Macintosh computer application was used to identify each individual dart trajectory, calculate the velocity components and store this data in standardized format files. For any unrecorded, or unknown positions or velocities, a missing data value was used. The data was then analyzed for quality control and unacceptable velocity measurements, due to digitizing error, were set to the missing data value. All of the data was then transformed into ship co-ordinates, and nondimensionalized into longitudinal and transverse wake fractions. An Apollo computer application performed the co-ordinate transformation based on conversion factors for pixel size, time counter calibration, ship speed and camera position. The coordinate system is provided in Figure 3. Longitudinal positions (x) indicate ship lengths aft of the model transom. Positive transverse positions (y) indicate ship beams starboard of 7 -2 Vi! —. ---- ----- Vx I 1 - -1 Fagure 3. Coordinate system for analysis results. 6

the model centerline. Velocities indicate fraction of the model speed in the direction of ship motion (Wx) and to starboard (Wy). The approximate size of the region where the darts fell in ship coordinates was 120 by 9 feet (36.58 by 2.74 m) in the X and Y directions, respectively. For analysis, this region was divided into 120 one-foot long (0.304 m) and 19 one-half-foot (0.152 m) wide bins, for a total of 2507 bins. This was the most convenient bin size selection as it gave excellent resolution with the minimum number of total bins and even values of distances for graphical display. A further discussion of the sensitivity of the analysis to bin size selection is provided in the next section. The target position data was then apportioned to the nearest bin. Figure 4 graphically shows the number of darts found in each bin for all runs combined. It should be noted that the distribution of velocity measurements covers the entire central position of the chart up to 98 feet (29.87 m) aft. 0 1.0 ft Bins 120.16 D- 4' X-~ I I ~ _~____~~__~_ _ ____.. _..._ __ __ _~_~_.I I.=..,.I.,0~; 0 1'2 3 4 X/L 0 108 Figure 4. Velocity measurement point density by bin location. 7

2. Statisical Analysis and Digital Filterina The following discussion focusses on the statistical significance of the DARTS data set and the subsequent analysis of digitally filtered velocity matrices. The superposition of the data set is examined as well as the statistical impact of bin size selection, averaging and filtering procedures. To analyze the statistics for each individual bin, values of sample mean and variance are required. To calculate the variance, at least three data points are required in each bin. Of the 2507 bins in the 120 by 19 grid, 172 (6.8%) had fewer than three points. These were invariably along the edge where the distribution of darts dropped off to zero. Consequently, there were about 2335 bins that could be analyzed statistically. The sample mean and variance of these bins were calculated and then each point in every bin was examined to see what minimum confidence interval was required to have that point included in a normal distribution. Figure 5 shows an example of the probablility density function of one bin. It corresponds to the position 37 feet (11.28 m) behind and 2 feet (0.61 m) to port of the ship origin with 96 data points. A list was generated for points that were more than 3 standard deviations away from the average. It would be expected for a normal distribution that 0.5% of all points would extend outside those limits. One hundred ninety four (194) points (0.66%) were fund for Wy and 259 (0.88%) for Wx, out of the 29,535 points recorded. This analysis suggested that leaving all of the points in the data set for analysis would not affect the results. During a single run at one ship speed, dart dropper location, and camera position; darts were released and tracked in a relatively small area, approximately 2 by 40 feet (0.61 by 12.19 m). Therefore, it was necessary to superimpose data from different dropper locations to fill the 9 by 120 foot (2.74 by 12.19 m) area behind the ship. Initially, this was done by combining all runs for the largest dropper distance (1.6 ship lengths) and sequentially adding closer dropper distance runs (1.60, 1.00, 0.50, 0.21, 0.07, 0.00 ship lengths). 8

A ~~~B~~~~~~~~~ - D o -10 - -,e,tab *2 — Ll,,,n n, l WE m C. (-~2) Figure. ProbabSuccessive superposity function of centerin correspongitudin wake fraction bym) aft dropper distance. and 2 feet (0.6 m) port of the ship origin with 96 data points.60-0.21 X/L, A C D 0 E V A.. B. 1 0 C. 1 0 D 1.60-0.21 X/L. E. 1.60-0.07 X/L. 9

The results are shown in contour image diagrams, Figures 6A through E for Wx and Figures 7A through E for Wy, both with the camera on centerline. It can be seen that there is a minimum of variation as the additional data is added in sequence, rather, the field becomes increasingly more well defined. This self consistency also held for the port and starboard camera and dropper offset positions, but was not so clearly defined between the center, port and starboard data sets. Consequently, these three large data sets were built and it was assumed that any internal errors were random and small. It is possible that the cross-ship variations of ship structure and propulsion influence the cross-ship data set consistency. For the sake of an overall picture, all three data sets (center, port and starboard) were superimposed and are shown in Figures 8 and 9 as Wx and Wy contour images, respectively. It will be seen later in this discussion that by first filtering the three transverse offset datasets, that they can be superimposed to advantage. 20. Figure 7. Succesive superposition of centerline transverse wake fraction by dropper distance. A. 1.60 X/L, B. 1.60-1.00 X/L, C. 1.60-0.50 X/L, D. 1.60-0.21 X/L, E. 1.60-0.07 X/L. 10

20 10 U/V!0 Figure 8/9. Superpostion of longitudinal/transverse wake fraction, combination of starboard, centerline and port datasets. This data set could also be displayed along longitudinal and transverse cuts in the ship's flow field. Figures 10 and 11 show this for the unfiltered combined data along longitudinal cuts of -1.5 feet (-.46 m), 0.0 feet and +1.5 feet (0.46 m) from the ship centerline for Wx and Wy. Figures 12 and 13 show transverse cuts at 21.0, 23.0, 25.0 and 27.0 feet (6.40, 7.01, 7.62, and 8.22 m) from the stern for the same unfiltered data group. The effect of variation in bin size was negligible within the constraints of having enough points in each bin for accurate average values of wake fraction, and having enough bins to show some detail in the spatial wake variation. By reducing the number of bins, there were more points per bin, but still the same approximate proportion (i.e. 5%) of bins that had fewer than three points necessary to calculate statistical quantities. The effect, shown unfiltered in Figure 14 is similar to a crude form 1 1

0.20 - -- —.6806 Y/B 0.1: ---- 0.0000 Y/B 0.15- -----.6806 Y/B longitudinal slices along the port, starboard and centerline of Figure 8. 0.08 i * —-- -.6806 Y/B 0.06 0.0000 Y/B *t... -.6806 Y/B ~'! uch as beyond 90 feet i( to 0.00 -0.04 -0.06 -0.08 —-- 0 I 2 3 4 5 X/L Figure 11. Transverse surface wake fractions as a function of distance aft, for longitudinal slices along the port, starboard and centerline of Figure 9. of filtering, that is an average across adjacent bins. However, where there are rapid fluctuations, such as beyond 90 feet (27.43 in), the low-pass filtering is better. Note the oscillations in Figure 15 using fewer bins, compared to Figure 17 using the filter. By increasing the number of bins, the frequency response could be increased, but the frequency of interest in water waves is generally low, so that the additional computational effort was not warranted. 12

0.10............ ----.8454 X/L. — n —-.9259 X/L.......... 1.0064 X/L 0.0.... ii 1.0870 X/L = 0.04 0.02 0.00 -. ~ g,... I,, -2 -1 0 1 2 Y/B Figure 12. Longitudinal surface wake fractions as a function of distance starboard, for transverse cuts through Figure 8. 0.04 _ _ ----.8454 X/L ".m —s.9259 X/L 0.02..... 1.0064 X/L' 1.0870 XAL i / > 0.00- I -0.02 - -0.04 -2 -i 0 1 2 Y/B Figure 13. Transverse surface wake fractions as a function of distance starboard, for transverse cuts through Figure 9. The low-pass filter applied in this analysis is symmetric and non-recursive so there is no phase shift at any frequency. The lag window chosen to filter over depended on the "cutoff wavelength, co. The cutoff is in terms of a wavelength based on the size of the bins, so oc = 1.0 means all frequencies that generated waves of less than 1 bin were removed. Recall that the bins are 1 foot (0.304 m) long and one-half 13

0.20 i -____I -... -.6806 Y/B.15.. —. 0.0000 Y/B 0.15 —.6806 Y/B 0.10 0.05- -- 0.00 -0.05 0 1 2 3 4 5 X/L Figure 14. Longitudinal surface wake fractions as a function of distance aft after reducing the number of bins to 61. 0.06 ----- -.6806 Y/B 0.04 -... 0.0000 Y/B _ ~ -----.6806 Y/B 0.02 /-004 o 406..- O 1 2 3 4 5 X/L Figure 15. Longitudinal surface wake fractions as a function of distance aft after reducing the number of bins to 61 and filtering. foot (0.152 m) wide, so the same cutoff value differs in effect in the transverse direction from the longitudinal direction. Thus the lag window was chosen to be just sightly larger than the cutoff wavelength. 14

0.20, i i I I III _ -.6806 Y/B \.15 ----- ~~0.0000,Y/B 0,15 I -1 -.6806 Y/B 0.10 0.05 0.00 -0.05. ~. ~,. ~ -, 0 1 2 3 4 5 X/L Figure 16. Downstream surface wake fractions as a function of distance starboard, for longitudinal cuts through Figure 10, heavy filtering (w=0.05, L=25). 0.06....... -.6806 Y/B 0.04 -.. - 0.0000 Y/B K A. —---.6806 Y/B 0.02 -0.02 -0.04 -0.06 * ~ ~ - - *''~~' I''''' a' | 0 1 2 3 4 5 X/L Figure 17. Cross-stream surface wake fractions as a function of distance starboard, for longitudinal cuts through Figure 11, heavy filtering (co=0.05, L=25). With a lag window of 25 bins and a very low cut-off frequency of oc = 0.05 cycles per bin in the longitudinal direction only, the filter essentially generates the D.C. signal as shown in Figures 16 and 17. The average wake values fall nicely over the unfiltered plots, Figures 12 and 13, showing no distortion due to the extremely heavy filtering. 15

4. 0001 6 2i r. I I I'I 3.0 0 I- - - -/- 1 -. -3.000 1-4. 000 L_-L- - 0.0000 15.00 30 00 45 00 60.00 75.00 90F00 105.0 120, 0 binCUiplot output file VX.FJlLER~g3.2.1.5.4 Figure 18. Color contour plots showing Wx superposition after light filtering (cOx=0.35,

4 000 -------------- binCTpt output fI.e VYILTERg321.5 Figure 19. Color contour plots showing Wy superposition after light filtering (x=0.35, I f 1~ ——'.0..00 7' b'F1,.., I I -4. 000. 0.0000 15.00 3000 45 00 60.00 75.00 90.00 105.0 120.( binCUiplot output file VY FlL1ER g32,1. 5 4 Figure19 l n p s n s17

For a lag window of five bins and a higher value of coc = 0.35 in the longitudinal direction combined with a lag of four bins and coc = 0.45 in the transverse direction, the center, port, and starboard data can be overlaid to advantage. Color plots of Wx and Wy are shown in Figures 18 and 19 for the center, port, and starboard cases. For Wy, only negative values of velocity were plotted for port measurements and only positive values for starboard to reduce unnecessary clutter. For Wx, the values at x = 10, 20, 30, 37 and 45 feet (3.05, 6.10, 9.15, 11.28, and 13.72 m) show the near-field peaks line up extremely well, while for Wy, the far-field peaks at 35 to 75 feet (10.67 to 22.86 m) correspond well. The outermost contour lines do not have much significance as they simply indicate the outer range of the data which, of course, changes with dart dropper location. The resultant matrix of this superposition is shown in Figures 20 and 21. Utilizing this filtering configuration, the longitudinal plane cuts look essentially 10 U/V 21 -10 Figure 20/21. Resultant contour image of Figure 19 showing Wx/Wy superposition after light filtering (ox=0.35, Lx=5,oy=0.45,Ly=4). 18

0.0000 Y/B 0. m":-8 — -.6806 Y/B.6806 Y/B 010.1 -0.05 0 1 2 3 4 5 X/L Figure 22. Downstream surface wake fractions as a function of distance starboard, for longitudinal cuts through Figure 20, light filtering (ox=0.35, Lx=5,yO=0.45,Ly=4). 0.06...,,..,.......- 0.0000 Y/B 0.04 A 686 Y/B Am — -.6806 Y/B > -,,,"V,,,A 0.00 -0.04 0.06...,.. 0 1 2 3 4 5 X/L Figure 23. Cross-stream surface wake fractions as a function of distance starboard, for longitudinal cuts through Figure 21, light filtering (o)x=0.35, Lx=5,oy=0.45,Ly=4). unfiltered up to 3 ship lengths. This is displayed in Figures 22 and 23, and can be compared to the unfiltered plots in Figures 10 and 11. The noise at four to five ship lengths is dramatically reduced. Transverse plane cuts, shown in Figures 24 and 25, can be compared to their unfiltered plots in Figures 12 and 13. 19

0.10-.8454 XA..9259 X/. 0.08 4.... 1.0064 X/L L ---— 1.0870 X/L 0.06 0.04 % 0.02,, 0.00.-..-...,..... -2 -1 0 1 2 Y/B Figure 24. Downstream surface wake fractions as a function of distance starboard, for transverse cuts through Figure 20, light filtering (ox,=0.35, Lx=5,Gva=0.45,Ly=4). 0.03 0.03- --- -------------— 8454 —-- -*-".8454 X/L 0.02-..".."""..9259 X/L of - " 1.0064 X/L.01 - -- 1.0870X. L 0.00 4~ -2 -0 12 -0.02 - -2 -1 0 1 2 Y/B Figure 25. Cross-stream surface wake fractions as a function of distance starboard, for transverse cuts through Figure 21, light filtering (ox=0.35, Lx=5,o04.45,Ly=4). 3. Theoretical Comparison For a theoretical comparison with the longitudinal plane cuts, calculations were made of Kelvin wave patterns in which the phase velocity equals the speed of the ship so that the characteristic transverse wave length X, where X= 2.x-Vp2/g. 20

For this case, V. = 6.772 feet per second (2.06 m/s) generating a wavelength of X = 8.94 feet (2.72 m). Table II shows measurements from Figure 22 that indicate overall agreement with the Kelvin wave pattern. However, the waves decrease in wavelength with increasing distance downstream. Table II. Transverse wavelengths measured from Figure 22. Longitudinal Positon - x/L No. of wave orbital cycles mean wavelength - ft (m) Oto 1 2.5.. 9.94 (3.03) to 2 3.0.8.28 (2.52) 2 to3 3.5 7.10 (2.16)_ overal 9.0 8.28 (2.52) By modelling the Kelvin wave system as if it were generated by a pressure point located in front of the ship, good agreement is reached with the measured values and the theoretical positions where the first and second wall reflections should occur. For a towing tank with 22 foot (6.71 m) width, the model should have the first wall reflection cross the centerline at approximately 28 feet (8.53 m) and the second reflection about 90 feet (27.43 m) behind the model stern. Close examination of Figure 10 shows that the level of variance in the system seems to increase at those positions. 4. Hvdrodynamic Insights The asymmetry of Wx and Wy shows a greater axial velocity at the gree surface on the port side at the free surface (the near-field peak at x=10 feet (3.05 m) is at y = 0.5 feet (0.152 m)rather than at the centerline in Figure 20) and higher transverse velocities (Wy = +0.04 for starboard and -0.035 for port at x = 10 feet (3.05 m) in Figure 21) than the starboard side. One possible explaination for this assymetry is that the thrust wake from the shallower set port propeller provides a visible contribution to the surface flow field in the near wake. 21

P~~~~ OA.. B~~~~~~~~~~~~~~~............ I ~ i! #$l7 NI ^.O_ ti::::::::*-!*:;;^^:^:i;:';*.^:^:i:^:^!*-(l*-*:.O 41 DiSTANCE ASTjftN (feel) U_ _ __ _ __ _ __ _ __ _ __ _ __ _ __ _ __ _ __ _ __ _ _ C...........lli~ill^^liiyit'W |kij&.|...i.jj....j...::::-:;:;:;;;.::^:::::;:;:;:^-i~i:;:::^:^;:^;;^;i:^ i:.^;::^::~~;;;a>~i:;^:;:i^ ^::;::: —;.:::;;;:;p^;::ft l~gi H::;:;:=:;:;:i:;;i:.............................................:*;:;*:::*::.................................-..... 5::;:;:;::::*^:;:::::;:::;';:::h~k;"^:;;^:::^!^:;:^::!^;^;]^;:;^ ^ iI:: ^^ B:^:!^:;K oI;:::-),-;,,;;:!^!:^^!^!;^.............4. DISTANCE;:;:;:;^i::::::^::;;;;;*:|P:*y;^;:^k^;;^ ASTERN (feel) 1;:::;:::;:^;:::::::::::;::::::*::;*;:!:;*;*;:;...:||iig!!liiaillliiil~~~~lg|||||||Eii Figure 26. Vector diagram of lightly filtered surface wake fraction. 2 2................:::::i^:::;:^;ii;:. ^ ^;: i;-*;;^;W;;........~f i::::;::"i::::;::*i:!;;*;:;^*:^:P:;:::;:;:;:;:*:^^;:^;;:^i:%:-::*"*;:h^::::";;;:^:i::^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~..... ^rL^:^:!-;:::;:::::;'::':::.!:::^ "^:':^'^'1^!^1^:^:^:":;::;::;::;^ "P^ ^::. Ow i "I;:- 1::1:i:% "i;:........... *-:::: -;-:**: ":*:;::*.;-::^ *;:^? i: W::: ^: a.......... Z............ Aft.;: ~:;^:!:j!;;^::ii!^:::7:^i ^;^;::^;:^;^::::;:::' ^^^^ Qt O l ^^^ i ^ *l::^*;*;:::;:;:^..:::;:;:;**:r;:;: ^^**^:*y:::r^;:*\;:.:*.:.L**^:w*<:^':"^*^;;;^^~~ ~ ~~ ~ ~~ ~ ~ ~~~ ~ ~~~~ ~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~....... Figure 26. Vector diagram of lightly filtered surface wake fraction.~~~~~~~~~~~~~~~~~~~.....................................

Figure 27. Two-dimensional plot of Wx. Figure 28. Two-dimensional plot of Wy. 23

Based on the appearance of wave orbital velocities in the dataset, measurements of transverse wavelength were made. The average transverse wave length was similar to a theoretical Kelvin pressure point wave system. There is clear evidence of the wave reflections based on some increase in the noise of the system and comparison with presure point Kelvin wave generation, but this does not effect the oscillations of the wake patterns. Therefore, surface waves must have a small effect on surface wake, indeed, an assumption of linear independence seems justified. By combining both x and y velocities on one graph, the effects of surface vorticity may be examined. Figure 26 is a unit vector diagram expressing velocity magnitude by color. Note that the velocities in both directions are very small far down stream but the vectors retain their unit length. A significant pattern can be seen in which every three or four bins has either purely longitudinal or purely transverse velocities along the edge. This gives evidence for sustained vorticity in the flow field. Figures 27 and 28 are two-dimensional plots of Wx and Wy respectively, which may help in visualizing the two velocity fields. IV. CONCLUSIONS AND RECOMMENDATIONS As a result of this investigation and subsequent detailed analysis of the composite data sets collected (approximately 30,000 velocity observations in the near wake region) the following conclusions are drawn. With respect to the method of surface wake velocity measurement acquisition, this procedure was highly accurate. The level of error in digitizing target positions was less than one percent of the wake coverage. The use of 15 targets per run was sufficient to provide an even spread of velocity measurements throughout the wake field up to 90 feet (27.43 m) aft. The analysis could have extended farther if all records were digitized to their full 10 second extent. Statistically, the number of individual velocities in each bin that exceeded three standard deviations from the bin mean velocity was about less than one percent of the total number of points digitized and accepted. This is consistent with minimum 24

standards for a normally distributed ensemble. Within each offset dataset, repeated runs of the same conditions are virtually identical. Runs with offset port or starboard positions were lightly filtered for excellent agreement. Filtering of the final data set proved to be an effective tool in data anlysis providing insight to the hydrodynamics influencing the surface wake velocities. dclearly show the orbital velocity influence of the Kelvin wave pattern, identification of the tank wall reflection, and a surface wake perturbation possibly due to the known hull asymmetry. In addition, ft has been shown that the DARTS system could be used to detect and quantify vorticity if the the analysis is performed in a fixed inertial reference frame. Finally, extraction of all of the information generated by this technique has not yet been exhausted, but requires additional detailed analysis. The quality of the data set, however, strongly suggests this analysis would produce extremely fruitful results. 25

Appendix A. Test run listing 26

___odel Test Data Runs for Model 1597 un No Speed Dlst. Aft TransverseDeslred RP Actual RPMI Comments _ft/) (Lengths) Position (port/stbd) (port/stbd _ 1 6.772 0.00 center 483/483 not recorded no timer 2 6.772 0.00 center 483/483 490/483 3 6.772 0.00 center 483/483 485/482 4 6.772 0.00 center 483/483 476/482 5 6.772 0.00 center 483/483 491/483 6 6.772 0.00 center 483/483 487/483 7 6.772 0.00 center 483/483 482/483 8 6.772 0.00 center 483/483 482/482 9 6.772 0.50 center 483/483 482/483 no timer 10 6,772 0.50 center 483/483 / Stbd shaft fell out of model 1 1 6.772 0.50 center 483/483 483/481 anomalous looking pattern 12 6.772 0.50 center 483/483 354/354 13 6.772 0.50 center 483/483 483/484 14 6.772 0.50 center 483/483 482/483 15 6.772 0.50 center 483/483 483/483 1 6 6.772 0.50 center 483/483 482/484 1 7 6.772 0.50 center 483/483 485/484 18 6.772 1.00 center 483/483 483/483 1 9 6.772 1.00 center 483/483 483/483 20 6.772 1.00 center 483/483 483/482 21 6.772 1.00 center 483/483 482/484 00 *0* * 0 * *0.. zero run 22 6.772 1.00 center 483/483 482/484 23 6.772 1.00 center 483/483 483/483 24 6.772 1.60 center 483/483 483/483 ____ 25 6.772 1.60 center 483/483 482/483 26 6.772 1.60 center 483/483 484/483 27 6.772 1.60 center 483/483 483/483_ 28 6.772 1.60 center 483/483 483/483 darts didn't drop 29 6.772 0.07 center dart dropr struck by stem wave:darts washed o 30 6.772 0.07 center _ dart droppr struck by stern wave:darts washed of *waming** new focus and scale due to lowered tank water level *___ 31 6.772 0.07 center 483/483 483/483 one port side dart fell off ___ *- - I |.., * * *00_ _ 000_ zero run 32 6.772 0.07 center 483/483 483/483 four port side darts fell off 33 6.772 0.0 center 483/483 483/483 34 6.772 0.07 center 483/483 484/483 35 6.772 0.07 center 483/483 483/483 36 6.772 0.07 center 483/483 484/483 37 6.772 007 center 483/483 355/483 port rprn too low 38 6.772 0.07 center 483/483 477/482 39 6.772 0.21 center 483/483 482/483 40 6.772 0.21 center 483/483 482/483 41 6.772 0.21 center 483/483 483/482________

Model Test Data Runs for Model 1597 ____ _._ Run No Speed Dist. Aft TransverseDesired RP Actual RPM Comments (ft/s) (Lengths) Position (port/stbd) (port/atbd___ 42 6.772 0.21 center 483/483 483/483 43 6.772 0.21 center 483/483 486/484 44 6.772 0.21 center 654/345 650/450 Begin trail shaft tests 45 6.772 0.21 center 654/345 653/435___ 46 6.772 0.21 center 654/345 652/370___ _............ 0 zero run 47 6.772 0.21 center 654/345 652/345 48 6.772 0.21 center 654/345 652/345____ 49 6.772 0.21 center 654/345 652/345 __ 50 6.772 0.21 center 654/345 652/345 51 6.772 0.21 center 654/345 652/345 52 6.772 0.07 center 654/345 652/345 __ 53 6.772 0.07 center 654/345 652/345___ 54 6.772 0.07 center 654/345 652/345____ 55 6.772 0.07 center 654/345 652/345 56 6.772 0.07 center 654/345 652/345___ 57 6.772 0.00 center 654/345 650/344___ 58 6.772 0.00 center 654/345 651/345 59 6.772 0.00 center 654/345 651/345 60 6.772 0.00 center 654/345 651/345 61 6.772 0.00 center 654/345 651/345 62 6.772 0.50 center 654/345 650/345 63 6.772 0.50 center 654/345 650/345 64 6.772 0.50 center 654/345 650/345 65 6.772 0.50 center 654/345 650/346 *****.._. * *____... zero runn 66 6.772 0.50 center 654/345 353/339 both props freewheeling 67 6.772 0.50 center 654/345 353/345 por prop freewheeling 68 6.772 0.50 center 654/345 654/343 69 6.772 0.50 center 654/345 651/343_ 70 6.772 1.00 center 654/345 651/344 71 6.772 1.00 center 654/345 651/346 72 6.772 1.00 center 654/345 651/345 73 6.772 1.00 center 654/345 651/345 74 6.772 1.00 center 654/345 651/345 75 6.772 1.60 center 654/345 650/344 76 6.772 1.60 center 654/345 650/344_ 77 6.772 1.60 center 654/345 650/344 78 6.772 1.60 center 654/345 655/345 79 6.772 1.60 center 654/345 651/346 ____ 80 6.772 1.60 14" port 654/345 650/345 81 6.772 1.60 14 port 654/345 651/345 82 6.772 1.60 14 port 654/345 651/345____ 83 6.772 1.60 14 port 654/345 650/345 ___4________

__ M___ odel Test Date Runs for Model 1597 _____.... un o. Speed Dlt. Aft TransverseDelsred RP Actual RPM Comments (ft/s) (Lengths) Positlon (port/stbd) (port/stbd __ _*.*' *. * *. * *.. zero run 84 6.772 1.60 14" port 654/345 655/345_____.. 85 6.772 1.60 14" port 654/345 654/345 86 6.772 1.60 14 port 654/345 653/346 87 6.772 1.60 14" port 654/345 652/345 88 6.772 1.60 14" port 654/345 652/346 89 6.772 1.00 14" port 654/345 651/345 90 6.772 1.00 14' port 654/345 650/345 91 6.772 1.00 14" port 654/345 649/345 92 6.772 1.00 14" port 654/345 648/345 93 6.772 1.00 14 port 654/345 648/345 94 6.772 0.50 14" port 654/345 650/345 95 6.772 0.50 14' port 654/345 649/345 96 6.772 0.50 14 port 654/345 649/344 97 6.772 0.50 14" port 654/345 649/344 98 6.772 0.50 14 port 654/345 649/344 _ - 99 6.772 0.21 14' ort 654/345 647/345 100 6.772 0.21 14" port 654/345 647/344 101 6.772 0.21 14' port 654/345 648/344 102 6.772 0.21 14' port 654/345 648/343 103 6.772 0.21 14' port 654/345 648/344 -04 6.772 0.07 14" port 654/345 648/344.*. ** 0 * * *... *. zero run 105 6.772 0.07 14, port 654/345 656/345 106 6.772 0.07 14" port 654/345 651/345. 107 6.772 0.07 14 port 654/345 650/348___ 108 6.772 0.07 14 port 654/345 650/346 109 6.772 0.07 14 port 654/345 650/346 110 6.772 0.00 14" port 654/345 650/346____. 111 6.772 0.00 14' port 654/345 648/345____ 112 6.772 0.00 14' port 654/345 648/345 113 6.772 0.00 14" port 654/345 647/345____ 114 6.772 0.00 1 4" port 654/345 647/345__ 115 6.772 0.00 14" port 483/483 482/482 Standard shaft operation 116 6.772 0.00 14" port 483/483 483/482____. 117 6.772 0.00 14' port 483/483 483/482____ 118 6.772 0.00 14 port 483/483 484/483___...... 119 6.772 0.00 14 port 483/483 483/482___ _ 120 6.772 0.07 14" port 483/483 484/484____ 121 6.772 0.07 14 port 483/483 483/483 122 6.772 0.07 14" port 483/483 482/482 123 6.772 0.07 14 port 483/483 483/482___ 124 6.772 0.07 14 port 483/483 482/483_____..... _ ** * * * *0 * * *zero run i el i i i i i iiiiiiiii, iiiiiiii....

'_ _'___ __ Model Test Data Runs for Model 1597 un No Speed Dist. Aft Transverse Desred RP Actual RPM Comments (ft/s) (Length) Positlon (port/stbd) (ort/stbd ____. 166 6.772 0.21 14' stbd 483/483 483/483 167 6.772 0.21 14" stbd 483/483 483/484_ 168 6.772 0.21 14' stbd 483/483 483/483 169 6.772 0.21 14' stbd 483/483 483/483 170 6.772 0.07 14' stbd 483/483 484/483 71 6.772 0.07 14' stbd 483/483 483/483 172 6.772 0.07 14' stbd 483/483 483/483 173 6.772 0.07 14' stbd 483/483 483/483 174 6.772 0.07 14" stbd 483/483 483/483 175 6.772 0.00 14' stbd 483/483 483/483 176 6.772 0.00 14" stbd 483/483 483/483 177 6.772 0.00 14' stbd 483/483 482/483 178 6.772 0.00 14' stbd 483/483 483/483 179 6.772 0.00 14' stbd 483/483 652/348 Trail shaft operation * *. *.* * * * * * zero run 180 6.772 0.00 14" stbd 654/345 649/349 181 6.772 0.00 14" stbd 654/345 650/345 82 6.772 0.00 14" stbd 654/345 650/346 183 6.772 0.00 14" stbd 654/345 649/347 184 6.772 0.00 14' stbd 654/345 649/345 185 6.800 0.07 14' stbd 654/345 650/346___ _. 186 6.772 0.07 14' stbd 654/345 648/345 187 6.772 0.07 14' stbd 654/345 645/347___........ 188 6.772 0.07 14" stbd 654/345 645/346 189 6.772 0.07 14 stbd 654/345 648/345 190 6.772 0.07 14" stbd 654/345 638/346 port pm low 191 6.772 0.21 14" stbd 654/345 637/345 port rpm low 192 6.772 0.21 14' stbd 654/345 637/346 port rpm low 193 6.772 0.21 14' stbd 654/345 638/348 port rpm low 194 6.772 0.21 14" stbd 654/345 637/347 port rpm low 195 6.772 0.21 14" stbd 654/345 652/346 196 6.772 0.50 14' stbd 654/345 648/346____7p 197 6.772 0.50 14' stbd 654/345 650/346 198 6.772 0.50 14' stbd 654/345 650/346_ 199 6.772 0.50 14" stbd 654/345 650/345 200 6.772 0.50 14' stbd 654/345 650/345 201 6.772 1.00 14' stbd 654/345 650/345 202 6.772 1.00 14' stbd 654/345 648/345 203 6.772 1.00 14' stbd 654/345 648/347 204 6.772 1.00 14' stbd 654/345 648/345__.____......*.. *..... *...* * *.. z__________ zero run 205 6.772 1.00 14' stbd 654/345 660/347_ 206 6.772 1.60 14' stbd 654/345 657/346 ____A_ 207 6.772 1.60 14' stbd 654/345 655/346____..

.._____. Model Test Data Runs for Model 1597 un No Speed Dlt. Aft TransverseDesired RP Actual RPM Comments __ (fts) (Lngths) Position (port/stbd) (port/stbd _ 208 6.772 1.60 14' stbd 654/345 631/345 209 6.772 1.60 14' stbd 654/345 632/345 210 6.772 1.60 14' stbd 654/345 630/347 211 6.772 1.60 14' stbd 654/345 not recorded 212 6.772 1.60 center no props compare to 1987 data 213 6.772 1.60 center no props compare to 1987 data