ON December 31, 1991 the Union of Soviet Socialist

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1 Journal of Counter-Ordnance Technology (Fifth International Syposiu on Technology and Me Proble) Hydrodynaics of Fallg Me Water Colun Peter C. Chu Anthony F. Gilles Chenwu Fan Peter Fleischer Abstract-- The hydrodynaic features of a fallg e to the water colun is vestigated experientally. The experient consisted of droppg three cyldrical odel es of various lengths to a pool where the trajectories were filed fro two angles. The controlled paraeters were e paraeters (length to diaeter ratio center of ass location) and itial conditions (itial velocity and drop angle). Results dicate that center of ass position has the largest fluence on the es' trajectory and that accurate trajectory odelg requires the clusion of both oentu and oent equations. A statistical-dynaic odel has been established to predict the trajectories of the fallg es. Key Words Me ipact burial oentu of e oent of oentu of e e ipact burial prediction odel e drop experient (MIDEX).. INTRODUCTION ON Deceber 99 the Union of Soviet Socialist Republics (USSR) effectively ceased to exist under ternational law and the Cold War ended (Fischer 999). In response the Navy-Mare Corps tea developed a new strategic concept ''Fro the Sea'' (FTS) which provides a fraework for Naval operations to the st century. FTS effectively shifted operational focus fro blue water operations to sea-based power projection to regional littoral areas. FTS the 994 revision ''Forward Fro the Sea'' (FFTS) and ''Operational Maneuver fro the Sea'' (OMFTS) all provide guidg prciples for sea-based power projection to regional littoral areas of the world. One of the greatest threats to U.S. sea-based power projection littoral areas is the naval e. Mes were first developed 77 and have been used ost ajor conflicts sce. Today an estiated 50 countries possess soe sort of g capability. (Lehr 000) Mes can be used both offensive and defensive roles. Offensively they can be placed eney waters or nearby sea-lanes order to harass ilitary and coercial shippg. Defensively they can be used to delay or prevent aphibious assaults or to deny coand of the sea. The Wonsan Korea Me Crisis and Iraq's use of es durg Desert Stor provide excellent exaples of the value of the naval e as a defensive weapon. Shortly after the Manuscript received January This work was supported by the U.S. Office of Naval Research Naval Oceanographic Office and Naval Postgraduate School. Peter C. Chu and Chenwu Fan are with the Naval Postgraduate School Monterey CA 994 USA (telephone: e-ail: chu@ nps.navy.il fan@nps.navy.il). A.F. Gilles is with Naval Oceanographic Office Stennis Space Center MS 959 USA (e-ail: gillesa@navo.navy.il). P. Fleischer is with the Naval Oceanographic Office Stennis Space Center MS 959 USA (e-ail: fleischerp@navo.navy.il). October 950 Wonsan Korea e crisis then Chief of Naval Operations Adiral Forest Sheran exclaied ``when you can't go where you want to when you want to you haven't got coand of the sea. Coand of the sea is the bedrock for all of our war plans. We have always been subare-conscious and air-conscious. We have now coenced to becoe e-conscious begng last week.'' (Boorda 999). With the past 5 years three U.S. ships the USS Sauel B. Roberts (FFG-58) Tripoli (LPH-0) and Prceton (CG-59) have fallen victi to es. Total ship daages were $5 illion while the es cost approxiately $0 thousand. (Boorda 999) Mes have evolved over the years fro the dub ``horned'' contact es that daaged the Tripoli and Roberts to ones that are relatively sophisticated - non-agnetic aterials irregular shapes anechoic coatgs ultiple sensors and ship count routes. Despite their creased sophistication es rea expensive and are relatively easy to anufacture upkeep and place. As such they are an efficient yet potent force ultiplier and are widely available to any country or group who has a odest ability to purchase the. Naval es are characterized by three factors: position water (botto oored risg floatg) ethod of delivery (aircraft surface subsurface) and ethod of actuation (acoustic and/or agnetic fluence pressure contact controlled). The littoral battlespace is divided to five regions based upon water depth. With each of these regions naval forces can encounter ultiple types of threats (Fig. ). The littoral regions are: Deep Water (DW). Water depths: > 00 ft. Threat: aly oored and risg es although a few large botto es exist. Shallow Water (SW). Water depths: fro 40 to 00 ft. Threat: botto oored and risg. Very Shallow Water (VSW). Water depths: fro 0 to 40 ft. Threat: botto oored risg and controlled. Surf Zone (SZ). Water depths: < 0 ft. to the beach itself. Threat: sae as VSW but land es and obstacles can also be encountered. Craft Landg Zone (CLZ). Water depths: the beach itself. Threat: conventional land es and obstacles. (U.S. Naval Me Warfare Plan 000) The shift focus fro the blue water to the littoral has brought any new challenges to the warfighter. The greatest is what ipact will the highly variable littoral environent have on future operations particularly e countereasures (MCM). The ost fluential environental paraeter to successful MCM operations is the local bathyetry character of the botto. This key

2 Journal of Counter-Ordnance Technology (Fifth International Syposiu on Technology and Me Proble) paraeter often deteres whether an area should be swept or hunted. Botto clutter the for of rock outcrops coral reefs an-ade debris and irregularities slope provide false contacts or create shadow zones that crease overall clearance ties. Soft botto sedients such as are clays and silts cause a high degree of e burial upon ipact. These buried or partially buried botto es are of greatest concern to the MCM planner. Environental data collection a potential adversaries' littoral region is often hapered by accessibility. This lack of accurate data causes a certa degree of uncertaty MCM planng. As a result several nuerical odels for predictg e ipact burial (IB) have been developed. The ost proisg IB odel was origally developed by Arnone and Bowen 980. Later iproveents by Satkowiak (987) Hurst (99) Chu et al. ( a b) and others have resulted the current version IMPACT 5. IMPACT 5 creates a twodiensional tie history of a cyldrical e as it falls through air water and sedient phases. IB prediction is largely calculated fro the are sedient characteristics and e ipact orientation and velocity. Chu et al. (00) found overprediction of burial depth by IMPACT5 after analyzg the synchronized environental and e burial data collected durg the Me Ipact Burial Prediction Experient (MIBEX) the Monterey Bay June 000. The essential eleents of the e ipact burial odel translate to the science and engeerg of hydrodynaic process of a fallg object and of sedient transport. Any solid object fallg through fluid (air and water) should obey two physical prciples: (a) oentu balance and (b) oent balance. The current IMPACT5 odel only considers the oentu balance of the e and disregards the oent balance of the e. Such an coplete hydrodynaics the odel leads to unrealistic prediction of the e fallg the water (no helicoidal otion). If considerg oentu and oent balance the fallg object should have a helicoidal otion. Without the helicoidal otion the IMPACT5 ay over-predict the ipact burial depth. In this study a nonlear dynaical syste is established for the oveent of a nonunifor (center of gravity not the sae as the center of volue) cyldrical odel e the water colun. A e-drop experient was conducted. The experiental results show the nonlear characteristics of the trajectory pattern. The data collected fro the experient can be used for e ipact burial prediction odel developent and verification.. DYNAMICS A. Earth Coordate Syste Two coordate systes are used to describe a e fallg through the water colun: earth and relative coordates. The earth coordate syste is fixed to the Earth surface with horizontal sides as x and y-axes (along the two sides of the pool) and vertical direction as z-axis (upward positive Fig. ). Suppose a e fallg to the water colun. The e rotates around its a axis (r ) with an angle ψ and an angular velocity of Ω. Its position is represented by the center of ass (COM) and its orientation is represented by two angles: ψ and ψ (Fig. ). Here ψ is the angle between the r -axis and the horizontal plane; and ψ is the angle between the projection of the a axis the (x y) plane and the x-axis. The angle ψ + π / is usually called attitude. The relative coordate is rigidly connected with the e. The orig (O) of the relative coordate syste cocides with the center of ass (COM); the r -axis is along the central le of the e; the r -axis is perpendicular to the plane constructed by r -axis and z-axis (r -z plane); and the r -axis lies the (r -z) plane and is perpendicular to r -axis. The selection of axes (x y z) and (r r r ) follows the right-hand rule. Let V = (V V V ) be the three coponents of the velocity of COM i.e. be the orig velocity of the coordate syste (r r r ). The geoetric center (GC) is located at ( 0 0). For GC below COM > 0 and for GC above COM < 0. The relative coordate syste (r r r ) is obtaed through the translation and two rotations ψ and ψ of the earth coordate syste. Let the position vector P be represented by P E and P B the earth and relative coordate systes P E and P B are connected by Figure. Littoral e threat (fro Rhodes 998). P E cosψ sψ 0 cosψ 0 sψ = sψ cosψ P + B 0 0 sψ 0 cosψ z () x y

3 Journal of Counter-Ordnance Technology (Fifth International Syposiu on Technology and Me Proble) where (x y z ) represent the position of COM the earth coordate syste. B. Nonlear Dynaical Equations Any solid object fallg through a fluid (air and water) should obey two physical prciples: () oentu balance and () oent of oentu balance. Let V w = (V w V w V w ) be the water velocity and ( ω ω ω ) be the coponents of the angular velocity referrg to the direction of the relative coordate syste. The dependent and dependent variables are ade non-diensional by: t = g t L ω L = ω V = g where g is the gravitational acceleration and L the length of the e. The non-diensional oentu equations for COM are given by (Mises 959) V gl Figure. Earth coordate syste. dv ρ ρ F w + ωv ωv = sψ + (a) ρ ρgπ dv + ω = F V ρgπ (b) dv ρ ρ F w ωv = cosψ + (c) ρ ρgπ where Π is the volue of the e ρ the e density ρ w the water density (F F F ) the coponents of water drag. The non-diensional equations of the oent of oentu for axial syetric e are dω J J LM + ωω = (a) J gj dω Π( ρ ρ ) L w = cos ψ + LM (b) J gj ω LM = d gj (c) where is the distance between COM and geoetric center (GC) (M M M ) the coponents of the oent due to water drag (J J J ) the three oents of gyration J = ( r + r ) d J = ( r + r ) d J = ( ) r + r d. (4) The orientation of the e ( ψ ψ ) is detered by dψ = ω dψ ψ = (5) cos ω. Figure. Cylder orientation and relative coordate syste. The eight non-diensional nonlear equations (a-c) (ac) and (5) are the basic syste for deterg the e oveent the water colun.. MODEL MINES A. Description Three odel es were used for the drop experient at the Naval Postgraduate School swig pool. All had a circular diaeter of 4 c however the lengths were 5 and 9 c respectively. The bodies were constructed of rigid plastic with aluu-capped ends. Inside each was a threaded bolt runng lengthwise across the e and an ternal weight (Fig. 4). The ternal cyldrical weight ade by copper was used to vary the e's center of ass and could be adjusted fore or aft. The center of gravity of the odel e is the orig of the body fixed coordate syste. The odel e is coposed of six unifor cyldrical parts (Fig. 4): (a) a plastic hollow cylder C () with ass of outer and ner radii of R and R length of (L -l ) and the center of gravity for the part (COMP) to be at its geoetric center located along the r -axis at r = ; (b) an aluu-capped left end (Fig. 5) solid cylder C () with ass of radius of R length of l and COMP located along the r -axis at r = L/- l / + ; (c) an aluucapped right end solid cylder C () with ass of radius of R length of l and COMP located along the r -axis at r = L/- l / - ; (d) a cyldrical thread C (4) with ass of 4

4 Journal of Counter-Ordnance Technology (Fifth International Syposiu on Technology and Me Proble) 4 radius of R length of (L - l ) and COMP located along the r -axis at r = ; (e) a cyldrical threaded bolt C (5) with ass of 5 out and ner radii of R and R length of l and COMP located along the r -axis at r = L/ - - l - l /; (f) an adjustable copper cyldrical weight C () with ass of outer and ner radii of R and R length of l and COMP located along the r -axis at r = δ + where δ is the distance between the COMP of the adjustable weight and the geoetric center of the odel e. Figure 4. Internal coponents of the odel e. B. Moents of Gyration Sce the six parts (all es) all have unifor ass distribution the oents of gyration for these parts are: () () J = ( R + R J R ) () = R J = (4) J 4 (4) = ( + R ) = R 4 J R () J = R J ( ) () [ ] ( ) () J = J = R + R + ( L l ) = J = ( R + l ) ( J () () J = = R + l ) Figure 5. Internal structure of the odel e. J J J (4) = [ 4 = R + ( ) ] J J L l ( ) (5) (5) 5 = J = R + R + l = J = (R + R + l ) () ( ) () where the superscripts for the oents dicate the cyldrical parts. The resultant oents of gyration is coputed by ( j ) = J j = L l L l ( j ) ( = = + + ( ) + + ) J J J j = L + + ( l ) + ( δ + ). (7) 4 5 Accordg to the defition of COM the coordate of GC ( ) is detered by [ ( L/ l l /) δ ] 5 = j = j l which dicates how the adjustable weight deteres the location of COM for the odel e. (8) C. Model Paraeters C.. Length/Diaeter and Density Ratios Our goal was to choose a scale that was soewhat representative of the real world ratio of water depth to e length but at the sae tie would be large enough to fil and would not daage the pool's botto. The odel es were based on the realistic assuption that a e is laid water depths of 45 thus producg a 5: ratio. The depth of the pool is.4. Fro this ratio the length (L) of the odel e is chosen as 5 c. The addition of a and 9 c length allowed for later coparison of the sensitivity of water phase trajectory to the ratio of e length over diaeter. The outer radius of the odel e is c. The length/diaeter ratios (L/D) are 5/4 /4 and 9/4. The correspondg density ratios ( ρ / ρ ) are.70 w.8 and.88 respectively. C. -Value In each of the three odel es the location of the weight (ie. the value of δ ) is adjustable. Use of (7) location of the COM ( -value) can be detered (Table ). The positive -value dicates that COM is below the geoetric center and the negative -value dicates that COM is above the geoetric center. 4

5 Journal of Counter-Ordnance Technology (Fifth International Syposiu on Technology and Me Proble) 5 Table. Model L/D density ratio and -value (unit: c). Me L/D ρ / ρ w 0 5/ / / MINE DROP EXPERIMENT An e drop experient (MIDEX) was conducted at the NPS swi pool June 00. The purpose of the experient is to collect data about e's otion the water colun for various cobations of the odel e paraeters. It basically consisted of droppg each of three odel es to the water where each drop was recorded underwater fro two viewpots. Figure depicts the overall setup. The controlled paraeters for each drop were: L/D ratio -value itial velocity (V ) and drop angle. The Earth's coordate syste is chosen with the orig at the corner of the swig pool with the two sides as x- and y-axes and the vertical z-axis. The itial jection of e was the (y z) plane (Fig. ). A. Initial Velocity Initial velocity (V ) was calculated by usg the voltage return of an frared photo detector located at the base of the e jector. The frared sensor produced a square wave pulse when no light was detected due to blockage caused by the e's passage. The length of the square wave pulse was converted to tie by usg a universal counter. Dividg the e's length by the universal counter's tie yielded V. The es were dropped fro several positions with the jector echanis order to produce a range of V. The ethod used to detere V required that the frared light sensor be located above the water's surface. This distance was held fixed throughout the experient at 0 c. B. Drop Angle ( The drop angle (itial ψ ) ) was controlled usg the drop angle device. Five screw positions arked the 5 o 0 o 45 o 0 o and 75 o. The drop angles were detered fro the lay of the pool walkway which was assued to be parallel to the water's surface. A range of drop angles was chosen to represent the various entry angles that air and surface laid es exhibit. This range produced velocities whose horizontal and vertical coponents varied agnitude. This allowed for coparison of e trajectory sensitivity with the varyg velocity coponents. Figure. MIDEX equipent. C. Methodology For each run the es were set to a -value. For positive -value the es were placed to the jector so that the COM was located below the geoetric center. For negative -value the COM was located above the geoetric center to release. A series of drops were then conducted order of decreasg e length for each angle. Table dicates nuber of drops conducted for different drop angles and -value for L/D = 5/4. Nuber of drops for other L/D ratios (/4 9/4) is coparable to that for L/D ratio of 5/4. All together there were 7 drops. Each video caera had a fil tie of approxiately one hour. At the end of the day the tapes were replayed order to detere clarity and optiu caera position. Table. Nuber of drops conducted for different drop angles and -values for L/D = 5/4. ψ ( ) 0 5 o 0 o 45 o 0 o 75 o DATA RETRIEVAL AND ANALYSIS A. Data Retrieval Upon copletion of the drop phase the video fro each caera was converted to digital forat. The digital video for each view was then analyzed frae by frae (0 Hz) order to detere the e's position the (x z) 5

6 Journal of Counter-Ordnance Technology (Fifth International Syposiu on Technology and Me Proble) and (y z) planes. The e's top and botto positions were put to a MATLAB generated grid siilar to the ones with the pool. The first pot to ipact the water was always plotted first. This facilitated trackg of the itial entry pot throughout the water colun. The caeras were not tie synchronized; thus the first recorded position corresponded to when the full length of the e was view. B. Source of Errors There were several sources of error that hdered the deteration of the e's exact position with the water colun. Locations above or below the caera's focal pot were subjected to parallax distortion. Placg the caeras as far back as possible while still beg able to resolve the dividual grid squares iized this error. Second the background grids were located behd the e's trajectory plane. This resulted the e appearg larger than noral. This error was iized by not allowg the plotted pots to exceed the particular e's length. Third an object jected to the water will generate an air cavity. This air cavity can greatly affect the itial otion particularly at very high speeds (hydro ballistics). The air cavity effect was deeed to be ial due to the low ject velocities used. C. Data Analysis The -D data provided by each caera was first used to produce raw two -D plots of the e's trajectory. Next - D data fro both caeras was then fused to produce a -D history. This -D history was then ade non-diensional order to generalize the results. The non-diensional data was used to generate ipact scatter plots and was also used ultiple lear regression calculations.. EXPERIMENTAL RESULTS A. Trajectory Patterns After analyzg the -D data set seven trajectory patterns were found. The plots on the (y z) plane were chosen for trajectory analysis as this plane was parallel to the direction of the e drop. The generalized trajectory patterns are described Table and Figures 7-0. The water phase trajectory a e experiences ultiately deteres the ipact orientation. In MIDEX the categorizg of trajectories to general patterns served two purposes. Observed trajectories were found to be ost sensitive to -value drop angle and L/D ratio. As COM distance ( -value) creased fro GC the e tended to follow a straight pattern. As COM was oved closer to the GC (decreasg -value) the e's trajectory tended towards beg ore parallel with the pool's botto. At steep drop angles the e experienced little lateral oveent and tended towards a straight pattern. Additionally as L/D ratio decreased ore coplex trajectory patterns developed. This cluded significant oscillation about the vertical axis and creased lateral oveent. Table. Description of relative coordate based trajectory patterns. Trajectory Pattern Straight (or Slant) Spiral Description Little angular change Nearly parallel to z-axis ψ near (90 o ± 5 o ) Oscillatg (no rotation) Flip Only once as <0 Flat Seesaw Cobation ψ near 0 o (no oscillation) ψ near 0 o Figure 7. Trajectory patterns. Figure 8. Trajectory patterns. (oscillation) Several of the above patterns

7 Journal of Counter-Ordnance Technology (Fifth International Syposiu on Technology and Me Proble) 7 COM Position: Me Length: 5 9 Drop Angle: 5 Straight Straight Straight-Slant Slant-Straight Spiral Spiral Slant-Straight Slant-Straight Slant-Straight Slant-Straight Slant-Straight Spiral Drop Angle: 0 Slant-Straight Slant Spiral Straight Spiral Spiral Slant- Slant-Straight Slant-Straight Spiral Slant-Straight Slant-Straight Spiral Drop Angle: 45 Slant-Straight Spiral Spiral Slant Spiral Spiral Straight-Spiral Straight-Spiral Spiral Slant Slant-Straight Slant-Spiral Drop Angle: 0 Straight Straight-Slant Spiral Straight Straight-Spiral Straight-Spiral Drop Angle: 75 Straight Straight-Spiral Slant Straight Straight-Spiral Straight-Spiral Straight Straight-Spiral Straight-Spiral Figure 9. Trajectory patterns for =. ( COM Position: - Me Length: 5 9 Drop Angle: 0 Flip-Straight Flip-Slant Flip-Straight-Spiral Flip-Straight Flip-Straight Flip-Straight-Spiral-Flip Drop Angle: 45 Flip-Straight Flip-Straight-Spiral Flip-Straight Flip-Straight Flip-Straight Flip-Straight-Spiral COM Position: - Drop Angle: 0 Flip-Straight Flip-Slant Straight-Flip-Seesaw Flip-Slant Flip-Straight Flip-Straight-Spiral Drop Angle: 45 Flip-Spiral-Slant Flip-Slant Flip-Spiral Flip-Slant Flip-Slant Flip-Spiral Drop Angle: 0 Flip-Straight Flip-Straight Flip-Spiral-Seesaw Straight-Flip Slant-Flip-Slant Flip-Spiral Figure 0. Trajectory patterns for negative COM position ). Here COM is above GC when the cylder enters the surface). B. Ipact Attitude The angle ψ + π / is the ipact attitude at the botto of the water colun. The e burial is largely detered fro the ipact attitude of the e. Mes whose ipact attitudes are perpendicular ( ψ = 90 o ) to the sedient terface will experience the largest degree of ipact burial (Taber 999). It is therefore iportant to analyze the relationship between ipact attitude and the controlled paraeters drop angle V L/D and. The experient shows that both L/D and V had little fluence on ipact attitude. The drop angle and however were the largest deterants of ipact attitude. Fro Figure it is apparent that there are several peaks centered near 90 o 40 o and 80 o. Further analysis reveals that these peaks correspond to the COM positions 0 and (correspondg to 0 ) respectively. COM positions - and - (correspondg to ) followed the sae trend as their positive counterparts. Although drop angle was not the ost fluential paraeter variations did duce changes ipact orientation. As drop angle creased the likelihood of any lateral oveent decreased. This allowed for ipact angles that were ore vertically orientated. This is priarily due to the fact that the vertical coponents of velocity were greater than those at shallow angles. Thus the tie to botto and tie for trajectory alteration was less. C. Me Tublg Not Observed The current Navy's e ipact burial odel (IMPACT5/8) was developed by the Coastal Syste Station (Arnone and Bowen 980; Satkowiak 987); subsequent upgraded by the New Zealand Defense Establishent (Hurst 99) and the Naval Research Laboratory (NRL). Soe of the ajor put paraeters to the odel are environent (sedientation shear strength water depth) e characteristics (shape center of ass weight and e deployent paraeters) deployent platfor (ship aircraft subare) speed of platfor angle of e upon enterg water rotational velocity at tie of deployent and others. The theoretical base of IMPACT5 is the oentu equations (a)-(c). The odel assues that COM cocides with GC ( = 0). Chu et al. (00) reported the discrepancy between observed and odel predicted (by IMPACT5/8) e burial depth fro a e ipact burial experient perfored near the Monterey beach California May 000. The odel describes two trajectory patterns (Figure ): (a) without any orientation change (b) with a constant tublg. For the second pattern user should put the tublg rate (Chu et al. 998; 000ab). In MIDEX e tublg was never observed even for = 0 (Figure ). Figure. Relationship between COM position and ipact attitude. Arnone-Bowen IBPM Without Moent Equation Iproved IBPM with rotation but without Moent Equation Figure. Two trajectory patterns predicted usg the Navy's Me Ipact Burial Model (IMPACT5/8): (a) no tublg and (b) constant tublg. The odel was established based only on the oentu equations (a)-(c). 7

8 Journal of Counter-Ordnance Technology (Fifth International Syposiu on Technology and Me Proble) 8 COM Position: 0 Me Length: 5 9 Drop Angle: 5 Seesaw Flat Flat-Seesaw Seasaw Seesaw Seesaw Seasaw Seesaw Flat-Seesaw Flat Spiral-Seesaw Spiral-Seesaw Drop Angle: 0 Seesaw Flat Spiral-Seesaw Flat Flat-Spiral Flat-Spiral Flat-Spiral Flat-Spiral Flat-Spiral Flat Flat-Spiral Flat-Spiral Slant-Seesaw Spiral-Flat-Seesaw Flat Drop Angle: 45 Seesaw Flat-Spiral Spiral-Seesaw Flat-Spiral Straight-Flat Straight-Flat Straight Straight-Flat Straight-Flat-Spiral Straight-Flat-Spiral Seesaw Seesaw Drop Angle: 0 Spiral-Seesaw Straight-Seesaw Straight-Flat Straight-Spiral-Seesaw Straight-Spiral-Seesaw Straight-Flat Straight-Spiral-Seesaw Straight-Flat-Spiral Straight-Seesaw Slant Straight-Flat Straight-Spiral-Flat Straight-Flat-Spiral Straight Straight-Seesaw-Spiral Straight-Spiral-Seesaw Straight-Spiral-Seesaw Straight-Seesaw Drop Angle: 75 Straight-Seesaw Straight-Flat Straight-Spiral-Seesaw Straight-Spiral-Seesaw Straight Straight-Flat-Spiral Figure. Trajectory patterns for the COM-0 position (i.e. COM cocidence with GC). 7. STATISTICAL PREDICTION MODEL Multivariate lear regression odel was established fro the MIDEX data (7 drops) to establish relationships between the put non-diensional paraeters; ψ L/D V and and the output variables (teporally varyg) such as position (x y z ) velocity (u v w) and attitude ψ at tie t. Let Y represent the output variables. The regression equation is given by Y() t = β () t + β () t ψ + β () t L/ D + β () t V + β () t. (9) 0 4 Figure 4 shows the teporally varyg regression coefficients for u v w and ψ. For the e's attitude ( ψ ) the coefficient β () t 4 is uch larger than the other coefficients which dicates that the e's orientation (versus the vertical direction) is aly detered by the location of COM. To show the dependence of ipact of e on the botto (i.e. horizontal location relative to the e's surface entry pot orientation velocity) the ultivariate regression between the put non-diensional paraeters; ψ L/D V and and the fal state (i.e. ipact on the botto) variables such as the horizontal position of COM (x y ) the velocity of COM (u v w) and the attitude ψ. Let Z represent the output variables. The regression equation is given by Z = + ψ + L/ D + V 0 + (0) 4 with the regression coefficients ( ) for the 0 4 output paraeters given by Table 4. Table 4. Regression coefficients of Eq.(0). 0 4 x y ψ u v w CONCLUSIONS () Moent of a fallg e water colun is a highly nonlear process which should be described by both the oentu and oent of oentu equations. If the oent of oentu equations are absent the otion of fallg e cannot be copletely siulated. The new e ipact burial prediction odel should clude the oent of oentu equations. () Six different trajectory patterns (straight spiral flip flat seesaw cobation) were detected fro MIDEX. No tublg of e was observed. The flip of e occurs only once for negative -values (i.e. COM is above GC as the e enters the water surface). The flat pattern occurs usually for = 0 (i.e. COM cocides with GC). The transition between patterns depends on the itial conditions (drop angle ψ and itial velocity V ) and the ternal structure of e (such as L/D ratio -value etc.). The dynaics of trajectory pattern foration and transition is very coplicated. It volves stability nonlear dynaics and fluid-body teraction. () MIDEX shows that both L/D and V had little fluence on e's ipact attitude on the botto. The drop angle ψ and however were the deterants of ipact attitude. For =0 the e was alost parallel to the botto. For and cases the e is alost vertical to the botto. (4) MIDEX provided nondiensional data of position (x y z ) velocity (u v w) and attitude ψ for each put cludg data ψ L/D ratio V and. The data can be used for odel developent and validation. (5) The observed trajectories were far ore coplex than those theorized by usg only the oentu equations. Siply assigng a rotation rate to the odel will not siulate the oveent of fallg e the water colun. At a iu updates to the IMPACT 5 odel 8

9 Journal of Counter-Ordnance Technology (Fifth International Syposiu on Technology and Me Proble) 9 should clude the ore realistic oent of oentu equations. () Further research on e hydrodynaics is needed. The research needs to expand beyond the siple cyldrical shaped e to those that are irregularly shaped (Rockan and Manta types). Additionally the utilization of scaled down versions should be explored. A saller e that can be odeled as accurately as its real counterpart will save tie oney and will require less logistical support. ACKNOWLEDGMENT This work was supported by the Office of Naval Research Mare Geology Progra (N00040WR08) and the Naval Oceanographic Office (N000PO00005). REFERENCES Arnone R. A. and Bowen Prediction Model of the Tie History Penetration of a Cylder through the Air-Water-Sedient Phases. NCSC letter report T4 Naval Coastal Systes Center Panaa City FL 980. Satkowiak L. J. User's Guide for the Modified Ipact Burial Prediction Model. NCSC TN Naval Coastal Systes Center Panaa City Fl 987. Sith T. Me Burial Ipact Prediction Experient. Master Thesis Naval Postgraduate School Monterey CA 000. Taber V. Environental Sensitivity Study on Me Ipact Burial Prediction Model. Master Thesis Naval Postgraduate School Monterey CA 999. Peter C. Chu (PhD 85 ) is a professor of oceanography jot warfare analysis and odelg and virtue environent siulation (MOVES) at the Naval Postgraduate School Monterey CA 994. Chenwu Fan (MA 8 )Is an oceanographer at the Naval Postgraduate School Monterey CA 994. Peter Fleischer (Ph.D 70 ) is an oceanographer at the Naval Oceanographic Office Stennis Space Center MS 959. Anthony F. Gilles (MA 0) is a Navy Lieutenant Coander who obtaed MA degree Meteorology and Oceanography at the Naval Postgraduate School Septeber 00. Boorda J. M. ''Me Countereasures - An Integral Part of our Strategy and our Forces.'' Federation of Aerican Scientists. ( Chu P.C. E. Gottshall and T.E. Halwachs 998: Environental Effects on Naval Warfare Siulations. Institute of Jot Warfare Analysis Naval Postgraduate School Technical Report NPS-IJWA p. Chu P.C. V.I. Taber and S.D. Haeger 000a: A Me Ipact Burial Model Sensitivity Study. Institute of Jot Warfare Analysis Naval Postgraduate School Technical Report NPS-IJWA p. Chu P.C. V.I. Taber and S.D. Haeger 000b: Environental Sensitivity Study on Me Ipact Burial Prediction Model. Proceedgs on the Fourth International Syposiu on Technology and the Me Proble 0 pp. Chu P.C. T.B. Sith and S.D. Haeger 00: Me burial ipact prediction experient. Institute of Jot Warfare Analysis Naval Postgraduate School Technical Report NPS-IJWA p. Departent of the Navy. U.S. Naval Me Warfare Plan Fourth Edition Progras for the Millenniu. Washgton D.C. January 000. Fischer Ben B. At Cold War's End: US Intelligence on the Soviet Union and Eastern Europe Sprgfield: National Technical Inforation Service 999. Hurst R.B. Me Ipact Burial Prediction Model - Technical Description of Recent Changes and Developents. Defense Scientific Establishent Auckland New Zealand Report 49. Lehr S.E. Me Warfare: To Enable Maneuver Aphibious Warfare Conference April 000. ( Lott D.F. K. Willias and D. Jackson Me Burial Carbonate Sedients. Proc. of the Technology and Me Proble Syposiu Noveber 99 Naval Postgraduate School. Rhodes J.E. G. Holder Concept for Future Naval Me Countereasures Littoral Power Projection May 998. ( /c.ht) 9