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Transcription

1 a C * N T > <; HYDRMECHANCS AERDYNAMCS STRUCTURAL MECHANCS v.v.v.* M 0: & Xv -y VV; MDEL NVESTGATN F STABLTY AND CNTRL CHARACTERSTCS F A PRELMNARY DESGN FR THE DEEP SUBMERGENCE RF.SCUE VESSEL (DSRV SCHEME A) by Jerme P. Feldman Q Ul *8 w r* C>, fe < P S s «L 'S : EC c! '-2 = u 5 V The dstrbutn f ths reprt s unlmted {ek» P-M ~:&'A APPLED MATHEMATCS V.V HYDRMECHANCS LABRATRY RESEARCH AND DEVELPMENT REPRT ACUSTCS AND VBRATN June 966 Reprt 2249 PRNC-TMB-648 (R«v -64)

2 ^teäü MDEL NVESTGATN F STABLTY AND CNTRL CHARACTERSTCS F A PRELMNAJY DESGN FR THE DEEP SUBMERGENCE RESCUE VESSEL (DSRV SCHEME A) by Jerme P. Feldman The dstrbutn f ths reprt s unlmted June 966 Reprt 2249

3 TABLE F CNTENTS ABSTRACT NTRDUCTN DESCRPTN F PRTTYPE AND MDEL 2 TEST APPARATUS AND PRCEDURE 2 REDUCTN AND PRESENTATN F DATA 6 DSCUSSN F RESULTS 7 DYNAMC STABLTY 7 SHRUD CNTRL EFFECTVENESS 3 THRUSTER EFFECTVENESS 4 Standstll Mde 5 Frward Speed Mde 4 Bradsde Mde 34 CRTCAL SPEED AND EQULBRUM CNDTNS FR LEVEL FLGHT 34 CNCLUSNS 40 ACKNWLEDGMENTS 42 APPENDX A - LNGTUDNAL STABLTY AND CNTRL CEFFCENTS 43 APPENDX B - LATERAL STABLTY CEFFCENTS. 5 REFERENCES 57 Page T"' - -3«

4 ptf «Shr, LST F FGURES Page Fgure - Sketch f DSRV Scheme A wth Prncpal Full-Scale Dmensns 3 Fgure 2 - Phtgraphs f Mdel f DSRV Scheme A 4 Fgure 3 - Varatn f Vertcal Plane Stablty Rts wth Speed.. Fgure 4 - scllatry Characterstcs wth Speed 2 Fgure Fgure Fgure Fgure Fgure 5 - Effect f Velcty Ceffcent n Nrmal Frce Ceffcent fr Frward Thruster Par Effect f Velcty Ceffcent n Nrmal Frce Ceffcent fr Aft Thruster Par Effect f Velcty Ceffcent n Trque Ceffcent fr Bth Thruster Pars Effect f Frward Speed n Nrmal Frce fr 0 Shaft Hrsepwer n Each Thruster Par Effect f RPM n Nrmal Frce fr Varus Frward Speds and Shaft Hrsepwers fr Frward Thruster Far 2 Fgure 0 - Effect f RPM n Nrmal Frce fr Varus Frward Speeds and Shaft Hrsepwers fr Aft Thruster Par.. 22 Fgure - Effect f Velcty Ceffcent n Nrmal Frce Ceffcent fr the Frward and Aft Thruster Pars peratng Tgether 24 Fgure 2 - Effect f Velcty Ceffcent n Ptchng Mment Ceffcent fr Frward Thruster Par 25 Fgure 3 - Effect f Velcty Ceffcent n Ptchng Mment Ceffcent fr Aft Thruster Par 26 Fgure 4 - Effect f Velcty Ceffcent n Nndmensnal Thruster Center f Actn fr Frward Par 27 Fgure 5 - Effect f Velcty Ceffcent n Nndmensnal Thruster Center f Actn fcr Aft Par 28 Fgure 6 - Effect f Velcty Ceffcent n Ptchng Mment Ceffcent fr Frward and At Thruster Pars peratng Tgether. 30 n

5 Fgure 7 - Effect f Velcty Ceffcent n Lngtudnal Frce Ceffcent fr Frward Thruster Par 3 Fgure 8 - Effect f Velcty Ceffcent n Lngtudnal Frce Ceffcent fr Aft Thruster Par 32 Fgure 9 - Effect f Velcty Ceffcent n Lngtudnal Frce fr Frward and Aft Thruater Pars peratng Tgether Fgure 20 - Effect f Velcty Ceffcent n Lateral Frce Ceffcent fr Frward Thruster Par n Bradsde Mde f peratn 35 Fgure 2 - Effect f Velcty Ceffcent n Yawng Mment Ceffcent fr Frward Thruster Par n Bradsde Mde f peratn 35 Fgure 22 - Effect f Velcty Ceffcent n Lateral Frce Ceffcent fr Aft Thruster Par n Bradsde Mde f peratn 35 Fgure 23 - Effect f Velcty Ceffcent n Yawng Mment Ceffcent fr Aft Thruster Par n Bradsde Mde f peratn 35 Fgure 24 - Elffect f Reynlds Number n Crssflw Drag Ceffcent.. 36 Fgure 25 - Effect f Sdewse Velcty n Lateral Frce fr Frward and Aft Thruster Pars peratng Tgether 36 Fgure 26 - Effect f Metacentrc Heght n Crtcal Speed.., 38 Fgure 27 - Effect f Crtcal Speed n RPM fr Aft Thruster Par 39 Fgure 28 - Ptch Angles and Shrud Angles Requred fr Level Flght.. 4 Fgure 29 - Varatn f Nrmal Frce Ceffcent wth Angle f Attack.. 44 Fgure 30 - Varatn f Ptchng Mment Ceffcent wth Angle f Attack 45 Fgure 3 - Varatn f Lngtudnal Frce Ceffcent wth Reynlds Number 46 Fgure 32 - Varatn f Lngtudnal Frce Ceffcent wth Prpulsn Rat 47 Page V

6 .' Fgure 33 - Varatn f Nrma] Frce Ceffcent, wth Sternplane Angle 48 Fgure 34 - Varatn f Ptchng Mment Ceffcent wth Sternplane Angle 49 Fgure 35 - Varatn f Ampltudes f n-phase Cmpnents f Nrmal Frce Ceffcent wth Lnear Acceleratn Parameter 50 Fgure 36 - Varatn f Ampltudes f n-phase Cmpnents f Nrmal Frce Ceffcent wth Angular Acceleratn Parameter 50 Fgure 37 - Varatn f Ampltudes f Quadrature Cmpnents f Nrmal Frce Ceffcent wth Angular Velcty Parameter ' 50 Fgure 38 - Varatn f Lateral Frce Ceffcent wth Angle f Drft 52 Fgure 39 - Varatn f Yawng Mment Ceffcent wth Angle f Drft 5 3 Fgure 40 - Varatn f Rllng Mment Ceffcent wth Angle f Drft 54 Fgure 4 - Varatn f Ampltudes f n-phase Cmpnents f Lateral Frce Ceffcent wth Lnear Acceleratn Parameter 55 Fgure 42 - Varatn f Ampltudes f n-phase Cmpnents f Rllng Mment Ceffcent wth Lnear Acceleratn Parameter 55 Fgure 43 - Varatn f Ampltudes f n-phase Cmpnents f Lateral Frce Ceffcent wth Angular Acceleratn Parameter 56 Fgure 44 - Varatn f Ampltudes f n-phase Cmpnents f Rllng Mment Ceffcent wth Angular Acceleratn Parameter 56 Fgure 45 - Varatn f Ampltudes f Quadrature Cmpnents f Lateral Frce Ceffcent wth Angular Velcty Parameter 56 Page

7 LST F TABLES Page Table - Gemetrc Characterstcs f Prttype 5 Table 2 - Nndmensnal Stablty and Cntrl Ceffcents and Prttype Cnstants 8 Table 3 - Nndmensnal Stablty Dervatves 0 Table 4 - Dmensnal Angular Acceleratn Parameter versus Tme t Reach 5-Degree Ptch Angle Usng 5-Degree Sternplane Angle fr DSRV Scheme A 3 Table 5 - Frce Ceffcents and Trque Ceffcents fr Thruster Par at Staudstll 4 Table 6 - Frces Delvered by Thruster Fars at Maxmum RPM (0 SHP) at Standstll 5. V

8 NTATN The fllwng nmenclature s n accrdance wth Techncal and Research Bulletn Number -5 f the Scety f Naval Archtects and Marne Engneers and Davd Taylr Mdel Basn Reprt 39 t the extent applcable. A supplementary nmenclature s prvded t defne thse quanttes whch are nt ncluded n these references. The pstve drectns f axes, angles, frces, mments, and velctes are shwn n the accmpanyng sketch. The ceffcents and symbls are defned as fllws: Symbl Dmensnless Frm Defntn A ' Prjected area f bw planes 2 Prjected area f rudders f Prjected area f stern planes AP After perpendcular AR Aspect rat B B' B ±pl 2 V 2 Buyancy frce CB Center f buvancv f submarne CG Center f mass f submarne Dampng cnstant Crtcal dampng cnstant d'-sl Dameter f bdy FP Frward perpendcular h Depth f submergence t center f mass ',. ',. '. * pl* Mment f nerta f the bdy abut», y-, 2-axs vn

9 K' -m ^ l^' 3 " Hydrdynamc mment abut a^-axs thrugh center f gravty X K 'm Jt '- *, Dervatve f mment cmpnent wth respect P ^^ * 84 * t angular velcty cmpnent p H'- K. ^P m Dervatve f mment cmpnent wth respect p t angular acceleratn cmpnent p K t. K 'r "r Km v Dervatve f mment cmpnent wth respect t angular velcty cmpnent r f(. Kf* m «;' Dervatve f mment cmpnent wth respect t angular acceleratn cmpnent f K 'v Ä «! K *' m. *«v " 3 " Dervatve f mment cmpnent wth respect t velcty cmpnent v K' *...'. K$' m. K Dervatve f mment cmpnent wth respect lp{ 4 t acceleratn cmpnent v *5 r v. r, «? Dervatve f mment cmpnent wth respect "fr n 8r l, 3f2 r K 2 P t rudder angle cmpnent S r v ' L Dervatve f metacentrc mment cmpnent wth ^ ^32 respect t rll angle cmpnent 0 P 2 k k k'~ - Radus f gyratn f shp and added mass f shp abut y-axs ' Characterstc length f submarne M M'~ M Hydrdynamc mment abut y-axs thrugh pl 3 y 2 center f gravty 2 vu

10 M, M ' - *. t yu Dervatve f mment cmpnent wth respect t angular velcty cmpnent q *> * ; Dervatve f mment cmpnent wth respect t angular acceleratn cmpnent q M. M "w f M w p't Dervatve f mment cmpnent wth respect t velcty cmpnent tc H w,» M m w ' ^ Dervatve f mment cmpnent wth respect t acceleratn cmpnent w M 5, ^5 M*' m S «S "' " 2 Dervatve f mment cmpnent wth respect t cntrl surface angle cmpnent 5 M Sb M 8b M 8b lp 3 ^2 Dervatve f mment cmpnent wth respect t bw plane angle cmpnent 5 fc Mt W 5 S "B. p3^ Dervatve f mment cmpnent wth respect t stern plane angle cmpnent 5^ M e " & ^0 p'f Dervatve f metacentrc mment cmpnent wth respect t ptch angle cmpnent 6 M M '.. ". p3^ Hydrdynamc mment at zer angle f attack m N N. m'»> f' 3 # - A " 3 " 2 ' v. "r p' 4 f Mass f submarne, ncludng water n freefldng spaces Hydrdynamc mment abut 2-axs thrugh center f gravty Dervatve f mment cmpnent wth respect t angular velcty cmpnent r X ^jm-^wm^rr^r < ~:. :vt'jm -J j-j^-aa

11 *; Dervatve f mment cmpnent wth respect t angular acceleratn cmpnent r N V (V '-. V «" p'^ " -A Dervatve f mment cmpnent wth respect t velcty cmpnent v Dervatve f mment cmpnent wth respect t acceleratn cmpnent v "8r t Dervatve f mment cmpnent wth respect t rudder angle cmpnent 5 r V v-' Angular velcty cmpnent relatve t x-axh P 2 v u 2 Angular acceleratn cmpnent relatve t "» axs? n' ql Angular velcty cmpnent relatve t y-axs 9 'u* Angular acceleratn cmpnent relatve t y-axs r r ''-' >"$ Angular velcty cmpnent relatve t a-axs Angular acceleratn cmpnent relatve t 8-axs t^ Tme fr scllatry mtn t Hamp t ne-half ntal ampltude U t' = Velcty f rgn f bdy axes relatve t flud n feet per secnd Vk Velcty f rgn f bdy axes relatve t flud n knts

12 , V Cmpnent alng y-axs f velcty f rgn f bdy relatve t flud V'' Cmpnent alng y-axs f acceleratn f rgn f bdy relatve t flud w V Cmpnent alng a-axs f velcty 0 rgn f bdy axes relatve t flud t xv ' * H V 2 Cmpnent alng 2-axs f acceleratn f r- gn f bdy axes relatve t flud X' l P l*u> Hydrdynamc lngtudnal frce, pstve frward The lngtudnal axs, drected frm the after t the frward end f the submarne wth rgn taken at the center f gravty X B' B B B 5 B "B -T Crdnates f center f buyancy wth respect t bdy axes * n T l p^ ^v Hydrdynamc lateral fr^e, pstve t starbard Dervatve f lateral frce cmpnent wth re spect t angular velcty cmpnent r * y-. r V ^' 4 y. p' 2 f Dervatve f lateral frce cmpnent wth respect t angular acceleratn cmpnent t Dervatve f lateral frce cmpnent wth respect t velcty cmpnent v y«'.. ^ ' V " ' Dervatve f lateral frce cmpnent wth re- spect t acceleratn cmpnent v x:

13 y «* Z 8 y 5 '- g Dervatve f frce cmpnent wth respect t cntrl surface angle cmpnent, 8 8r *' p'v' Dervatve f lateral frce cmpnent wth re«spect t rudder angle cmpnent S r Dstance alng the transverse axs, drected t starbard wth rgn taken at center f gravty Z',,^ Hydrdynamc nrmal frce, pstve dwnward V-T p'v Dervatve f nrmal frce cmpnent wth re- spect t angular velcty cmpnent q Z " lt w w Z* " ^ Z- Dervatve f nrmal frce cmpnent wth respect t angular acceleratn cmpnent q Dervatve f nrmal frce cmpnent wth respect t velcty cmpnent w Dervatve f nrmal frce cmpnent wth respect t acceleratn cmpnent w '8b '56 ' 5fc lpl*ü 2 2 Dervatve f nrmal frce cmpnent wth re- spect t bw plane angle 5 fc 'S» ' 5s lpl 2 U 2 2 K Dervatve f nrmal frce cmpnent wth re- spect t stern-plane angle cmpnent S Z ' Nrmal frce at zer angle f attack * p 2 t 2 2 K Dstance alng the nrmal axs, drected frm tp t bttm (deck t keel), wth rgn taken at center f gravty xn

14 The angle f attack; the angle t the lngtudnal bdy axs frm the prjectn nt the prncpal plane f symmetry f the velcty f the rgn f the bdy axes relatve t the flud, pstve n pstve sense f rtatn abut the y-axs ß The drft r sdeslp angle; the angle t the prncpal plane f symmetry frm the velcty f the rgn f the bdy axes relatve t th.e. flud, pstve n the pstve sense f rtatn abut the a-axs S Angular dsplacement f a cntrl surface S, Angular dsplacement f bw planes, pstv tralng edge dwn 5. Angular dsplacement f rudders, pstve tralng edge prt Angular dsplacement f stern planes, pstve tralng edge dwn The angle f ptch; the angle f elevatn f the ar-axs pstve bw up p'- Mas? dsty f water a. -a. ' U Rts f stablty equatn, «, 2, A The angle f yaw J CL) C. U Crcular frequency f scllatn (Ü t> = V Natural frequency f undamped scl'atn xu

15 SUPPLEMENTARY NMENCLATURE Symbl Defntn C nr, Crssflw drag ceffcent based n prjected lateral area. d Dameter f thruster duct K^^' Ceffcent representng the nnlnear PP varatn f K' wth p' K 0 Trque ceffcent fr thruster par (trque)n 2 d 5 K ' Ceffcent representng the change n ^ the varatn f K' versus q' wth r' K^ ^J' Ceffcent representng the nnlnear v v varatn f K' wth v' K^^' v w Ceffcent representng the change n the varatn f K' versus v' wth w K ' Ceffcent representng the change n ^^ the varatn f K' versus w' wth p' t M Hydrdynamc mment abut y-axs due t a par f thrusters n peratn M T pad 4 M ' Ceffcent representng the change n UM the varatn f M' versus q' wth 6 s M ' Ceffcent representng the change n " the varatn f M' versus r wth p' M rr ' Ceffcent representng the nnlnear varatn f M' wth r" M ' Ceffcent representng the change n ^ the varatn f M' versus v wth p' M vr f Ceffcent representng the change n the varatn f M' versus v' wth r' x v

16 M ' vv M w q M w N ' pq N M N v t 6r r N l M V N ' wv n n" Ceffcent representng the nnlnear varatn f M' wth v' Ceffcent representng the change n the varatn f M versus w' wth q' Ceffcent representng the nnlnear varatn f M' wth w Ceffcent representng the change n the varatn f N' versus p' wth q' Ceffcent representng the change n the varatn f N' versus r wth 5 r Ceffcent representng the change n the varatn f N' versus v' wth r Ceffcent representng the nnlnear varatn f N wth v' Ceffcent representng the change n the varatn f N vesus w' wth v' Revlutns per secnd fr thruster P-at f rdered speed t nstantaneus speed f submarne Shaft pwer f thruster par U Velcty ceffcent Ucüd Hydrdynamc frce alng x-axs due t a par f thrusters n peratn X T Wd 4 X qq X r P X ' rr X ' vr ' Ceffcent representng the nnlnear varatn f X' wth q' Ceffcent representng the change n the varatn f X' versus r wth p' Ceffcent representng the nnlnear varatn f X wth r' Ceffcent representng the change n the varatn f X' versus v' wth r' xv

17 X ' Ceffcent representng the nnlnear vv varatn f X wth v X ' Ceffcent representng the change n ^ the varatn f X' versus w wth q' X ' Ceffcent representng the nnlnear ww varatn f X wth w X ' Ceffcent representng the nnlnear varatn f X' wth 6 s x ' Ceffcent f lngtudnal center f actn fr a par f thrusters n peratn,.e. -MV Y Hydrdynamc frce alng y-axs due t a par f thrusters n peratn Y T pa?d 4 Y j ' Ceffcent representng the nnlnear PP varatn f Y' wth p' Y ' Ceffcent representng the change n the varatn f Y' versus p' wth q Y > ' Ceffcent representng the change n ' the varatn f Y' versus r' wth 6 r Y^ ^ ' Ceffcent representng the change n v r the varatn f Y' versus v' wth r' Y^^' Ceffcent representng the nnlnear v v varatn f Y' wth v' Y ' Ceffcent representng the change n " the varatn f Y' versus w' wth p' Y ' C ffcent representng the change n wv the varatn f Y! versus w' wth v' Z Hydrdynamc frce alng z-axs due t a par f thrusters n peratn Z T AüJ 2 d 4 Z ' Ceffcent representng the change n '"' the varatn f Z' versus q' wth 6 Z ' Ceffcent representng the change n P the varatn f Z' versus r' wth p xv

18 '-«r ' Z Z Z ' Ceffcent representng the nnlnear varatn f Z' wth r' ' Ceffcent representng the change n the varatn f Z' versus v wth p ' Ceffcent representng the change n the varatn f Z' versus v wth r' Z vv ' Ceffcent representng 6 the nnlnear varatn f Z' wth v Z Ceffcent representng the change n '^' the varatn f Z versus w' wth q' Z w w ' Ceffcent representnc r b the nnlnear varatn f Z' wth w' 0) Thruster frequency n radans per secnd A Abslute value f A Subscrpts ndcates value fr a par f thrusters xvu

19 0) > t en Ö 0) f-. Q J > r-l H W 0 -P c a b0 a s ß X XV

20 ABSTRACT Stablty and cntrl ceffcents, derved frm mdel tests usng the DTMB Planar-Mtn-Mechansm System and supplemented by analytcal estmates, are presented fr use n detaled smulatn studes f the mtns f a prelmnary desgn fr the Deep Submergence Rescue Vessel (DSRV) n sx degrees f freedm. Analyses are made t evaluate the nherent dynamc stablty and cntrl effectveness characterstcs f the vehcle fr mtns cnfned t ether the vertcal r hrzntal plane. The results f a specal nvestgatn t determne effects f frward speed and bradsde mtn n the perfrmance f the thrusters are als presented and dscussed. NTRDUCTN The Specal Prjects ffce requested the Davd Taylr Mdel Bajn t prepare and execute a prgram f captve-mdel tests t determne the stablty and cntrl characterstcs f a prelmnary desgn fr the Deep Submergence Rescue Vessel (DSRV). l The prmary purpse f ths prgram was t prvde all f the hydrdynamc ceffcents requred fr cnductng detaled smulatn studes f the mtns f the DSRV n sx degrees f freed ncludng hverng and pvtng mdes as well as crusng mdes. n addtn, the ceffcents were requred t serve as a bass fr the desgn f the autmatc cntrl system. The DSRV s a small submersble desgned t rescue persnnel frm dsabled submarnes and t transfer them t anther submarne. The cncept f the subject desgn ental, the use f ducted thrusters t prvde the precsn cntrl necessary fr the matng peratn n cnjunctn wth an allmvable shrud fr cntrl at the hgher speeds asscated wth search and transprt. T carry ut the afrementned bjectves, tl Davd Taylr Mdel Basn cnstructed a ne-thrd scale mdel and carred ut a cmprehensve prgram f tests n the DTMB Planar-Mtn-Mechansm System. Ths prgram ncluded nt nly the types f stablty and cntrl tests perfrmed n cnventnal submarnes but a specal grup f experments t determne the cntrl frces due t the thrusters. An ral presentatn f sme f the results f these tests was made at the Davd Taylr Mdel Basn t the representatves f the Specal Prjects ffce n March 966. Ths reprt descrbes the prttype and mdel, utlnes the test prcedures and presents the fnal results f the test prgram. T facltate the smulatn studes, a cmplete set f ceffcents t be used n cnjunctn wth the DTMB submarne equatns f mtn s prvded. n addtn, an analyss s made f the nherent stablty and cntrl characterstcs ncludng the determnatn f stablty ndces, neutral angles, crtcal speed, and cntrl effectveness f bth the mvable shrud and the thruster system. References are lsted n page 57.

21 DESCRPTN F PRTTYPE AND MDEL The cnfguratn f the subject desgn fr the Deep Submergence Rescue Vessel, desgnated herenafter as DSRV Sceme A, s shwn n Fgure and by mdel phtgraph n Fgure 2. The prncpal dmensns f the prttype and mdel are gven n Table. The basc hull s a bdy f revlutn feet n length and 8.0 feet n dameter. Supermpsed n the basc hull s an bservatn dme n the tp and an escape hatch n the bttm. A tal assembly cnsstng f a shrud and sngle screw prpeller s prvded fr prpulsn, cntrl, and dynamc stablty n frward flght. Frward and aft pars f transverse thrusters, each unt cnsstng f a tube r duct enclsng a screw prpeller, are prvded fr cntrl n hverng, pvtng, and bradsde mtn. These thruster unts are referred t by N nbers thrugh 4 n sequence frm the bw t the stern. The subject desgn s represented by Mdel 5036, a ft lng mdel cnstructed f mahgany. t shuld be emphaszed that, t expedte the test prgram, the smplfed thrust unts rather than the refned TMB desgn unts were used fr the stablty and cntrl tests. These emplyed cmmercal utbard mtr rght angle drve urts whch necesstated the use f relatvely large prpeller hubs and supprt struts. As the result, the prpeller hubduct dameter rat was abut 0,42 cmpared wth the cntemplated fr the TMB desgn. TEST APPARATUS AND PRCEDURE The experments were cnducted n the deep-water basn n Twng Carrage 2 usng the DTMB Planar-Mtn-Mechansm System descrbed n Reference 2. The mdel wac supprted by tw twng struts wth supprt pnts spaced 4. 5 feet apart ( ±2. 25 feet frm the reference pnt, r prttype center f gravty lcatn). The lngtudnal, lateral, and nrmal frces and ptchng, yawng, and rllng mments were measured by means f tw sets f gages nsde the mdel, ne set at each strut. The hrzntal plane was smulated by relcatng the dme by rtatng t thrugh 90 degrees abut the lngtudnal axs. The escape hatch, hwever, was nt relcated, but nstead was remved and a cver plate attached n ts place. The expermental prgram ncluded all f the types f statc stablty and cntrl tests and scllatr tests that are nrmally carred ut fr submarnes. 2 n addtn, a specal grup f tests was cnducted t determne the ceffcents requred t smulate the actn f the thrusters n varus mdes f mtn. The statc stablty and cntrl tests were cnducted at a speed f 6 knts (crrespndng t a Reynlds number f. 3 x 0 based n the length f the submarne). The angles f attack and drft n ths grup f tests were carred ut t ±8 degrees. The maxmum angle n the all-mvable shrud was 5 degrees bth n the sternplane and rudder mdes. The scllatr tests were cnducted ver a range f speeds frm 4.0 t 6.0 knts, nclusve. 2

22

23 f Fgure 2 - Phtgraphs f Mdel f DSRV Scheme A 4

24 TABLE Gemetrc Characterstcs f Prttype Agency Specal Prjects ffce Prttype Deep Submergence Rescue Vessel Mdel 5036 Lnear Rat 3. 0 Prttype Length, feet Maxmum dameter, feet 8.00 Fneness rat 5.4 Vlume, cubc feet Lngtudnal dstance frm FP t CG and CB, feet 9.85 Heght f CG abve baselne, feet 3.83 Heght f CB abve baselne, feet 4.00 Shrud:! Planfrm area, square feet 5.25 Span at leadng edge, feet 7.79 Span at tralng edge, feet 7.46 Chrd, feet 2.00 NACA Sectn prfle 000 Thruster: Tube dameter, feet.50 Lngtudnal dstance f tube axs frm CG, feet # (frward) 6.86! #2 (frward) 5.2 #3 (aft) 4.9 #4 (aft) 6.65

25 n each f the fregng tests, the man prpeller was drven at the rpm requred t gve a net lngtudnal frce f zer, as ndcated n the gages, fr the cndtn f zer bdy angle, zer shrud angle, and n cntrl thrustng (pnt f prpulsn fr the mdel assembly). Hwever, a specal grup f tests was cnducted wth the rpm n the man prpeller vared t gve varus verlad and underlad cndtns requred fr predctn f acceleratn and deceleratn characterstcs. Three types f thruster cntrl tests were cnducted: ne wth the mdel at standstll; the secnd wth the mdel twed at varus frward speeds; and the thrd wth the mdel beng twed nrmal t ts lngtudnal axs (bradsde). Prr t the cntrl tests, a set f tests was cnducted t determne the pwerng characterstcs f the thrusters and the results f these tests are reprted n Reference 3. Durng the curse f these tests, t was nted that the thruster frces asscated wth frward speed were substantally lwer than thse btaned at standstll wth the same thruster rpm. Cnsequently, when the thruster cntrl tests were run, a ecal effrt was made t nvestgate ths pthenmenn n great detal. The thruster cntrl tests were carred ut by cverng as brad a range f rpm as pssble wthn the capacty f the mdel equpment t ensure hgh enugh Reynlds numbers t prvde relable data. The thrusters were perated as fllws: wth frward par nly, wth after par nly, and a lmted number f runs wth bth pars peratng n unsn. n each case bth prpellers f a gven thruster par were perated at equal rpm. n the frward speed tests, a range f mdel speeds f frm 0. 5 t 6. 0 knts was cvered. Ths range verlaps the range f full-scale Reynlds numbers based n vehcle length up t a full-scale speed f abut 2. 0 knts. T nvestgate the lss f thruster frce wth frward speed, the tests were cnducted n tw ways; frst by varyng thruster rpm at each f several dscrete mdel speeds and then by varyng mdel speed at each f several cnstant values f thruster rpm. n the bradsde tests, the mdel was twed at a drft angle f 90 degrees wth zer rpm n the man prpeller, frst wth thrusters nperatve and theu wth varus rpm n the frward thruster par. Bradsde tests wth a varatn f rpm n bth thruster pars were cnducted n cnjunctn wth the pwerng tests. 3 REDUCTN AND PRESENTATN F DATA The results f the captve-mdel tests are presented n the appendxes as curves f nndmensnal frce and mment ceffcents versus the apprprate parameters. The lngtudnal stablty and shrud-cntrl ceffcents fr the DSRV Scheme A are presented n Appendx A. The lateral stablty ceffcents are presented n Appendx B. Theye ceffcents apply n the strct sense t the Scheme A desgn wthut escape hatch. Hwever, t s assumed that the escape hatch wll nly have a neglgble effect n the ceffcents whch vary wth drft angle. The thruster cntrl frces and mments are presented and dscussed separately n the bdy f the reprt. Detaled data n the pwerng characterstcs f the thrusters and the man prpeller are pre nted n References 3 and 4, respectvely. t shuld be emphaszed that all f the data apply n a strct sense t the specfc desgn (DSRV Scheme A) de^cbed n ths reprt. Hwever, sme f the data may be nterpreted t

26 explre ther desgn pssbltes wthn the same desgn cncept. The stablty and cntrl ceffcents f the equatns f mtn requred fr use n cmputer studes f the mtns f DSRV Scheme A n sx degrees f freedm are summarzed n Table 2. These ceffcents cnsttute a cmplete representatn f all f the lnear, nnlnear, and cuplng effects requred t study all mdes f mtn (except steady astern mtns f the deeply submerged vehcle). Ths ncludes mtns nvlvng angles f drft up t 90 degrees. t shuld be mentned that althugh the nmenclature used s the same, the quanttes Z w ', M^', Y^, N v and K^ are ceffcents n the strct sense rather than the stablty dervatves custmarly used wth the lnearzed equatns f mtn. Cnsequently, these ceffcents may nut be numercally equal t the crrespndng stablty dervatves. Therefre, these lnear ceffcents shuld nly be used n cnjunctn wth the nnlnear ceffcents n Table Z. T prvde data fr stablty analyses based n lnearzed equatns f mtn, the stablty dervatves are lsted n Table 3, DSCUSSN F RESULTS The prmary purpse f the subject nvestgatn was t prvde the means t establsh a mathematcal mdel fr subsequent smulatn studes f DSRV Scheme A. Snce the subject vehcle s n the prelmnary stage, t s cnsdered pertnent heren t present a bref analyss f the nherent stablty and cntrl charcterstcs f the prpsed desgn. Unless mentned therwse, all dmensns apply t the full-scale versn f DSRV Scheme A. DYNAMC STABLTY The dynamc stablty characterstcs f DSRV Scheme A are analyzed heren n the bass f the characterstc equatn usng the dervatves lsted n Tables 2 and 3. A submarne s dynamcally stable f when t s dsturbed frm a cndtn f equlbrum straghtlne mtn t returns t a cndtn f straghtlne mtn after the dsturbance s remved. Ths cndtn crrespnds t havng all negatve real parts fr the stablty rts f the characterstc equatn. The rts f the characterstc equatn fr the DSRV Scheme A n the vertcal plane are shwn as a functn f speed n Fgure 3. Snce the real parts f the rts art always negatve, the submarne s ndcated t be dynamcally stable at all ahead speeds. Tl.«degree f lngtudnal stablty s quanttatvely ndcated by numercal measures f scllatry characterstcs such as thse gven n Fgure 4. At speeds abve.4 knts the dampng rat s between 0. 7 and.0 whch s cnsdered t be near ptmum frm the standpnt f nherent dynamc stablty. f

27 TABLE 2 Nndmensnal Stablty and Cntrl Ceffcents and Prttype Cnstants x j M ' vp y M ' vr ' ' l M ' vv K ' K P PP K. P K ' qr r M w ' M ' ' w ^ j Ml'! W W j M w,' K ' r.! 6s r 0. 0 'V! M e v k K ' V! K v v r K v w ' K.' v K ' wp! 6r j Ky; M ' ^ M,. ' jq 6s M.' q M rp M ' rr : M,' j m' N ' P 0. 0 j N ' N.'! p 0. 0 N ' r ! N l U ' N.' r 0. 0 N ' v 0. 0! j r 6r j N ' v r N, ' v v N.' V

28 TA.BLE 2 (Cn't) N ' wv 0. 0 Y ' v r j r Y >' V j V j Y.' V X ' qq x ' rp x ' rr Y ' wp Y ' wv 6r X. u Y*' 0.0 X ' vr X ' vv Z ' q Z l q u 6s X ' wq X ' ww Z,' q rp r6r rr 0.0 6s6s vp Y ' P Y PP vr vv Y ' pq Y.' P Y ' r Y.' r Y ' v rjör' Z ' w w q Z ' w w Z w. ' 6s 7 ' xö NTE: The cntrbutn f the man prpeller t the lngtudnal frce as a functn f the prpulsn ceffcent n' (rat f rdered speed t nstantaneus speed f the submarne) s expressed as fllws fr n' greater than zer: X' = ^ n,2 and fr n less than zer: X = lgn' n 2

29 TABLE 3 Nndmensnal Stablty Dervatves K ' r 0.0 N ' V K f! 0.0 N. K ' V K.' V M ' q M.' q M ' w M.' w N ' r N.«r Y ' r Y. ' r Y ' V Y.' V Z ' q Z.' q Z ' w Z.' w V

30 * >.- D > C Ü > (N D <0 A m M «C j a ea rh > «** > C> J r M j r* r> ^ > j C (N C M 0 a x a rh >. M Ü rh > e3 V M > g < «H 73 C -M 0 -H ^ 4-> (0 C -p ^ S (J^TD)^! PUB (,^^0)9 s^y j s^jbd AJBUT3BU PUB lean a» 3

31 < > ( n 0) C X! P H? + J j ' M ^ A r V ^ f en N 0 a x a >. +J Ü 0 w Ü -M W rt e *-* 0) -p ü c«^ x: u >» u M C5 H S () U a (N 00 SpUaS UT : 9UT.L äutdubq PUB D D T^ÜH SUTCllUBa 2

32 n the hrzntal plane the stablty rts are ndependent f frward speed. Fr DSRV Scheme A the stablty rt s a! = -0.5 Tns ndcates that the vehcle wll be nherently dynamcally stable n the hrzntal plane. SHRUD CNTRL EFFECTVENESS The values f the cntrl dervatves Tsted n Table 2 d nt n themselves prvde an adequate ndcatn f the degree f cntrl effectveness avalable. Hwever, they ^an be related t certan ther hydrdynamc r mass characterstcs t prvde a measure f cntl effectveness. ne such parameter, called the dmensnal angular acceleratn parameter, cp, has been shwn t be related apprxmately t the tme requred t make an ntal ptch angle r headng angle change f 5 degrees. 5 Values fr ths parameter cp = M M. - = N. N. - and asscated tmes t change ptch angle t 5 degrees, tg are lsted n Table 4. TABLE 4 Dmensnal Angular Acceleratn Parameter versus Tme t Reach 5-Degree Ptch Angle Usng 5-Degree Sternplane Angle fr DSRV Scheme A Speed knts CP^ sec sec t may be seen frm Table 4 that the shrud s hghly effectve frm the standpnt f ts ablty t rapdly ntate a change n headng n the hrzntal plane ver mst f the speed range. Frm the same standpnt, t s equally effectve n the vertcal plane at hgher speeds but t s subject t the crtcal speed phenmena at lwer speeds as wll be dscussed later n the reprt. 3

33 THRUSTER EFFECTVENESS The effectveness f the thrusters n varus mdes ncludng frward speed, bradsde mtn, and standstll s dscussed heren. Unless stated therwse, the thruster frces (nrmal frce Z, lateral frce Y, and lngtudnal frce X) are "delvered frces," r ncremental frces prduced by the thrusters as ppsed t a thrust exerted at the prpeller shaft. t shuld be emphaszed that the frce and mment ceffcents as well as the prpeller trque ceffcents cntaned n ths sectn f the reprt are strctly applcable t the smplfed thruster desgn used n the tests. t may be reasnably antcpated that smewhat hgher delvered frces fr any gven hrsepwer wll be btaned wth the refned TMB desgn. Hwever, t s beleved that the effects shwn fr the varus mdes f peratn n thruster perfrmance wll be relatvely the same fr the new desgn. Furthermre, the fllwng assumptns have been made cncernng the thruster data cntaned n ths reprt:. The frward par (Numbers and 2) r the aft par (Numbers 3 and 4) always perate at the same rpm. 2. The trque ceffcent fr the frward par s the same as the trque ceffcent fr the aft par at standstll. 3. The desgned maxmum shaft hrsepwer (shp fr each thruster par) s 0. Standstll Mde At standstll, the delvered frce ceffcents f the thrusters Z" and Y" are essentally cnstant wthn the practcal peratnal range f full-scale Reynlds numbers based n rpm. 3 n ths respect, the thrusters have smlar characterstcs t cnvental prpellers peratng ver a range f rpm at zer advance ceffcent. Smlarly, the trque ceffcent s als a cnstant. The standstll values f these ceffcents are presented n Table 5. TABLE 5 Frce Ceffcents and Trque Ceffcents fr Thruster Par at Standstll! Frward Par Aft Par Z" Y" KQ

34 The shaft pwer requred by the thrusters n the full-scale vehcle n the standstll mde can be determned by tne fllwng relatnshp: _ 3,5 P = Ztrn 0 d 0 K Q [] where n s he rps f the thrusters, P s the shaft pwer f the thruster par, K s the trque ceffcent, and d s the dameter f a duct. Fr example, slvng Equatn [] fr the maxmum shaft hrsepwer f 0 fr a thruster par and KQ f , the maxmum rpm fr peratng at standstll s The frces at standstll fr Ce frward and aft pars peratng at maxmum rpm (0 shp) can then be determned frm the values f Z" and Y ' gven n Table 4. These values are presented n Table 6. TABLE 6 Frces Delvered by Thruster Fars at Maxmum RPM (0 SHP) at Standstll Frward Par Aft Par Z n punds Y n punds As can be seen, at equal shp, the frward par f thrusters prduces mre thrust than the aft par. Frward Speed Mde Althugh the ceffcents Z" and Y" are cnstants n the standstll mde, as ndcated prevusly, they vary cnsderably wth frward speed. Ths s llustrated by the curves n Fgures 5 and 6. t may be nted frm these 5 ~»^r «ump.» j^bta«[ fllll» "

35 ^ ( CJ f e ^ j > ) d t m a 0) -P 2 0] 3 a t. X! h a TJ a; u ü U «H 0 0 t- u 7 8 ^ a u r-l -H rh (D (-( 0 t-> 0 u 0) Ü <H S-. W h n QCD r- 0) 3 fa rh X 00 T}* 6

36 C 0> 0 00 c y nr d > 0 ' UJJ -D a > H n ] <H C C b a 0) «H <M 0) u >. M - > (9 S- S -H 0 (2 35 a a)»-. a t,.2^ Velcty Ceff( rtcent fr Aft C 0 0 Sffec Frce < > U 3 H h 0 & (N ^ C Z ^uat3tjja BJJ T«UJK 7

37 fgures that, fr bth the frward and aft thruster pars, Z" falls ff cnsderably wth an ncrease n velcty ceffcent U". n the ther hand, the trque ceffcent KQ f each thruster par falls ff nly slghtly wth ncreasng U" as shwn n Fgure 7. Ths suggests that sme f the lss f nrmal r lateral frce can be recvered wthn the capacty f a gven pwer plant. The fregng types f ceffcent curves have been used n cnjunctn wth Equatn [] t prepare dmensnal curves f the varus frces and mments asscated wth the use f thrusters at varus frward speeds f the full scale vehcle. The prcedure s as fllws:. Select a value f velcty ceffcent U". 2. Enter trque ceffcent KQ curve (Fgure 7) t fnd crrespndng value f KQ. 3. Select a value f shp fr a thruster par. 4. Substtute values f K Q, P, and full-scale duct dameter n Equatn [] t determne rpm. 5. Use value f rpm wth value f U" t determne frward speed. 6. Usng the same value f U" as was used t btan KQ, enter apprprate thruster-frce ceffcent curve (Fgures 5 and 6) t btan value f frce ceffcent. 7. Usng the rpm and full-scale duct dameter cnvert t thrust n punds. 8. Repeat steps thrugh 7 fr ther selected values f U". The dmensnal curves,cnstructed n accrdance wth the fregng prcedure are presented,n Fgures 7 thrugh 0. The effect f frward speed n nrmal r vertcal frce delvered by the frward f aft thruster par peratng at the maxmum rpm that can be btaned wth 0 shp per thruster par at any gven speed s shwn n Fgure 8. Ths presentatn clearly shws that wthn the peratng range f full-scale speeds the nrmal frce drps ff cnsderably wth ncreasng frward speed. At 3. 0 knts, fr nstance, the frce delvered by the frward par has fallen ff t apprxmately 0 percent f ts value at standstll. The decrease n frce delvered by the aft par s smewhat less, amuntng t abut 50 percent f ts standstll value. n addtn, by peratng at half f maxmum rpm, n bth cases the delvered frce at standstll s abut 25 percent f ts value fr maxmum rpm but the percentage drp-ff wth frward speed s essentally the same as fr maxmum rpm. 8

38 u e a, a C X < H ate 3f- ed vs ff t j, J-< J ^ J r [ -.., j Tf D +J a CD m <H 0) C 0 u >, +J Ü 0 H (D (N > -- 3 cr ;< 0 H C M C 0 M a. M a u 0) 0) M Ü Cfl 3 SH U HH s (U H 0 ux: 4-> >, -!-> DQ Ü U 0 0 -H 4H a» > M c «H 0) 0 CJ -M r-t SH 0) fh H-' m 0 W U u a.urn 00 a 0) ^uajtjja nb.,! 9

39 , C *? s g s ^ a 6 S L r» X * c X a <? p * j -H *J ä a > a a 0 J '! *-» M l C C ^ ] ^ C 0 c Ck fc F f CS a «H 0 ^ J s rward [- ) -M M J r j ^ X rt JJ & 4- M <H ( <: fc] 00 c (N 00 w u 0) -M U M 3 fe t, XJ -H EH CJ X3 ^ c«^ W fl C a s- 0) J &l w a -M 0) 0 T3 t3 a ^ U ^5 PS 0 >M c ^ C +J &K «H -D rt v 0) «H X! 0 w & C -M CJ -H QJ SH m ^ -H «HW w <4- a, 0 U (N j C C spund UT JTBd Js^snaqx j aaj xetuj^ j bß fa 20

40 , > D C > 00 ^ > V_^ r'n ^y r ^ ^ 00 t V ^ > A U rl CD l u u tj tfl 3 U 0 C 3 ^ H m > t. 0 u M a S t G X! C C 0) S-c H CD «H C H CM 0 s u w u fa C75 a» 3» fa CM sja^snaqj, j abd pjbyva.j Aq paaaat^aa ajj -[BUKN

41 ' 00 M t V- ' ^ n ^ M 3 ^ V N n y A ^ A s w 3 ^ 0 0 H «M CD fr Va r epwers 0) w CJ ^ m ^ 0 u w fe H 4-> rh MH 0. SÄ u S- C 0) 0 M 55-D ^ Cß G JH 3 C («-H fc 0 es XJ w (^ H J flj Q; < <H C tfl 0 3 C «M -0 'M 0 5g 0) * (X «H 5^ +J 05 «H 0 HH W fc < <N 0 be ^ C sja^srum, j JTBd ^JV ^Q pa.aatjaa aaaj BuaN 22

42 t shuld be emphaszed that the large lsses n nrmal frce shwn n Fgure 8 apply t the case where all avalable thruster pwer s utlzed. The lss fr the case f cnstant rpm s smewhat greater as wll be shwn n the fllwng paragraph. The effect f thruster rpm n nrmal frce fr each f several speeds s shwn fr the frward and aft pars n Fgures 9 and 0, respectvely. Supermpsed n these fgures are cnturs f maxmum rpm fr equal shp. t may be nted frm these cnturs that fr any gven shp the maxmum rpm f a thruster par ncreases wth frward speed. Ths s due t the fact that the trque ceffcent decreases wth frward speed (see Fgure 7). Alternatvely, fr the same reasn, fr cnstant rpm, the shaft hrsepwer tends t decrease as the ahead speed ncreases. The relatve effects f frward speed n lateral frces are essentally the same as thse fr the nrmal frces. The magntude f the lateral frce n any gven case can be btaned by multplyng the apprprate nrmal frce n Fgures 8, 9, and 0 by N3 -. t s nterestng t nte that the separate frces f the frward and aft thruster pars can be supermpsed t prvde the ceffcents fr cmbnatns nvlvng the use f bth thruster pars. Ths s shwn n Fgure where the sld lne was btaned by takng the sum f the fared curves n Fgures 5 and 6 and the data pnts were btaned frm mdel tests n whch bth thruster pars were perated smultaneusly at equal rpm. As can be seen, the agreement between the supermpsed values and the drect expermental values s excellent. A detaled analyss f the hydrdynamc phenmena whch accunt lr the lss f delvered thruster frce shwn by Fgures 6 thrugh 0 s beynd the scpe f ths reprt. Hwever, smlar lsses n delvered thruster frces have been measured n mdel experments fr the case f a bw-thruster n a surface shp. t s beleved, that these lsses are due t an nteractn between the du^t jet velcty f the thrusters and the manstream flw abut the bdy. Thus, t s suggested that, n the frward speed mde, the lngtudnal lcatn f the thrusters alng the hull s anther mprtant factr that shuld be cnsdered n the desgn f the thruster system f the DSRV. Sme nsght ntc the nature f the effect f frward speed n the thruster frces can be ganed by examnng the accmpanyng effect n the hydrdynamc mments. Fgures 2 and 3 shw the varatn f ptchng mment ceffcent delvered by each thruster par wth frvard velcty ceffcent. t may be nted that the percentage decrease n ptchng mment ceffcent at any gven velcty ceffcent s less fr the frward thruster par and greater fr the aft thruster par than the crrespndng decreases n nrmal frce ceffcent. n fact, abve a velcty ceffcent f abut the ptchng mment ceffcent fr the aft thruster par actually reverses sgn. The reasns fr these trends can be seen frm Fgures 4 and 5 whch are plts f center f actn 23

43 X. C l < > Cfl E u - u 0 G 0 z cj x: t- a -u a) ^ M pj 0 ^ S H G U tx b b- C U - t- H Q) *-> a HH J3 «0) t«-m «l H dl m -«a u m SfH 4H >> f) <D +J +J 'M 0 H G -H u cj a «CJ >» r-h CJ t M GJ -H u > ^ 0) CJ ^- -M 0 SH 0 (fl ^ ^ M r (D U '4- «4- 'J <*H 0 'H W fe < > a- - + fwd Z4

44 , n X CD 00 ( ) C ) ( fd c L ) '"* C a 0) < -( 0) Ü >. M C f J3 fcl Ü M M H tn 0, 3 t. ö s 0 H M D c U a; rt * Ü u <th b KH 0) 0 Ur 0 u t-l >. M (-> c a; CJ 0 u rh 0) > th <«J m 0 0 u -t-> (-> u c 0) SH s 4-0 w s (N 0) c H ^natjjja ^aaj SuqTd 25 X

45 ' X tx c H t G 0 ß s H Ü -M ^- H SH < u ^M H 0) t, <H 0 0 f-l (J H 0) 0 >.-M u M C >. 't M u H,--( -H CJ a) "H 0 >*H -H 0) Ä <H 0 > u C u c m m th 0 W S 0) H N W ^UTTJJ ^umw SajmTd n 26

46 Q V > ^ k CD m r- C c H 'X D s c - 0 JH Z rj JJ C 0 D 4-> M C '«c W u u C rf «H 0 4H l+h -H «H ) -M J u < u >. -H >. ^ 0 +J - Ü u C Ü 0 0 rh -M l-l c > (D > t f ter C CJ () (N - Effe Thru C (N jxx ^uat3tjj 9 D Ja^snam j nx^av J 0 Ja^aa 27

47 n H X 00 ( > C«a ndmens r 0 Sä * a 4J b «H M M a a u <D 0) 0 m Ü c Tf G «H «H 0 «H «H -H Q) +J 0 0 Ü u U-J; >» >»=H M M 0 C y Ü f". 0 0 (H rh +J 0 a» a > (N rh f V er Ce M 4J 5 - Effec Thrus PH 0 u be -,, _ ja^snjqx j nt^y j aa^ua 28

48 f nrmal frce ceffcent versus velcty ceffcent. The nndrnensnal center f actn x ' s defned as -M, Z,, and s expressed n bdy lengths wth respect t the center f gravty. Fr the frward thraster par, the center f actn mves frward frm the centerlne f the thruster par untl t reaches a pnt abut 3. 2 bdy lengths ahead f the center f gravty. n ths case, the mvement s benefcal frm the standpnt f cntrl snce the lever arm wth respect t the reference pnt s always ncreasng. Thus, fr a range f speeds up t 3 knts, althugh the nrmal frce decreases by abut 90 percent, the ptchng mment nly decreaser 40 percent. Fr the aft thruster par, the center f actn als mves frward wth ncreasng velcty ceffcent but nt at as great a rate as fr the frward par. Hwever, t mves frm a pnt aft f the center f gravty t a pnt n the center f gravty at a velcty ceffcent f and, then, at hgher velcty ceffcents t actually mves frward f the center f gravty. Ths llustrates the cause f the change n sense f the ptchng mment whch was mentned prevusly. As fr the nrmal frces, the ptchng mments develped by the separate thr. cter pars can als be supermpsed. Ths s shwn by P'gure 6. Agan, n sp.te f the cmpletely dfferent character f the center f actn curves fr the frward and aft thruster pars, the agreement between the supermpsed and expermental values s excellent. Ths ndcates, that fr all practcal purpses, there s n nteractn between the frward and aft thruster pars. The effec.rward speed n the center f actn f lateral frces s the same as th e tr the center f actn f the nrmal frces. Cnsequently, the yawng mment ceffcents prduced by the thrusters can be determned by multplyng the apprprate ptchng mment ceffcents n Tgures JZ and 3 by [J~. n addtn t the effects n nrmal and lateral frces and ptchng and yawng mments prduced by the thrusters, there s an attendant ncrease n lngtudnal (resstance) frce wth frward speed. Ths s shwn n Fgures 7 and 8. t can be seen frm Fgure 7 that, when the frward thruster par s used, the lngtudnal frce ceffcent des nt change sgnfcantly untl a velcty ceffcent f abut Hwever, abve ths pnt there s a cmparatvely sharp ncrease. n the ther hand, when the aft thruster par c used, there s a large ncrease n lngtudnal frce ceffcent wth frward speed startng mmedately at a velcty ceffcent f zer. Ths s cnsstent wth the fact that the flw abut the afterbdy f submerged frms s much mre crtcal nsfar as resstance s cncerned than the flw abut the frebdy. Althugh the change n lngtudnal frce caused by the frward par s much dfferent than that prduced by the aft par, the separate effects can be supermpsed as shwn byfgure 9. 29» WC^K.WW'T- "

49 C H K 00 ; r c D f^ tchng Aft A C 73 a a ^ 0 c«z -M TJ -M D f ^ () M 0 a ^ H 0) 0 m m fa be Ü «H Ö 0) S-> -H M HH ^ rt 0) SH 0 u M a a ; >> -H f 4-> tfl r-l -H ^ (U «H -H > «H «H () Cl( 0 «H 0 > 0 u ^ -M -M -M C [fl n Effe Mme Thru + a * < 7 (N -l CD (D U bd (N CD

50 C K f D 00 0 CD u a 0 0 'H JQ j q a>! 0 y *-> c u (H MH 0) 0 u u 0 M <-' C Ö 0) J -H u u -H <*-( <«th M 0) 0) 0 0 uu >> 0) M U U u 0 0 t* > «HH -H H 0 " U -H efl 0) be j«<»h C S-c m W J EK -*!. eg 0) M J rh 3

51 C l-l X 00 f* ^0 rt ngtudn Par J a a) 0 V z M 3 a a j- a> x3 p H H 0 Ü 0) (-> m «H «M U «H < H 0) «H <H 0 <D «H 0 >. Ü a >> Ü 0) f +J 0 -H ^ Ü 0) -H 0 > «M -^ <H J «H a> > 0 0 n QJ Effe Fre (N 00 0 u p be rh en x QJ.0 TBUTpn^jaaq 32

52 ^ Tr~^5-^ K 00 f M c (D «H «H 0) u M Ü 0 ^H u rt 0) a M M TJ D 3 u t-> x HH be a 4J "M J<: flt3 c es M a T3 Q - CJ u ^ SH 0 ^ «M b 0) 0) 0 u 4J u 0 0) <+H be >> 0 +J V EH c 0) bc C3 r-l Ü M > <w aj «M S u (-> u () 0 0) Ü u «n }-. H «fh 0 03 H (>4 CX cn ^ +J 0) S-. 3 be fc + ' J f. X n AJ r-l WX ^nat^tjj^ ^-j BUTpn^TSuq n 3 3

53 n summary, there s substantal decrease n nrmal frce, lateral frce, ptchng mment, and yawng mment and a substantal ncrease n lngtudnal frce wth frward speed fr any gven thruster rpm r thruster pwer. Ths s beleved t be due t an nteractn between the thruster jet velcty and the manstream flw abut the bdy. The nteractn apparently cause«large changes n pressure dstrbutn abut the bdy as evdenced by the large mve - ment n center f actn f the thruster frces wth frward speed. t s cncluded, therefre, that the aft thruster par, n partcular, s neffectve as a cntrl devce when peratng n the frward speed mde abve a speed f ne knt. The frward thruster par may have sme usefulness fr peratn n vertcal-plane maneuvers belw crtcal speed as wll be dscussed later n ths reprt. Bradsde Mde The effects f bradsde mtn n the lateral frces and yawng mments s shwn by Fgures 20 thrugh 23. t may be seen frm Fgure 20 that the lateral frce delvered by a thruster par decreases wth bradsde speed, bth when the thruster frce. appled n the drectn f the mtn and when t s appled n the drectn ppsng the mtn. Fgure 24 presents the crssflw drag ceffcent as a functn f Reynlds number. These data can be used n cnjunctn wth the ceffcents n Fgures 20 thrugh 23 t make predctns f equlbrum speed as well as acceleratn and deceleratn n the bradsde mde. Such a predctn s made n Fgure 25 whch shws the varatn f lateral frce delvered by bth thruster pars and drag wth speed n bradsde mtn. The thruster frce crrespnds t the case where the thrusters are perated at the maxmum rpm that, can be btaned wth 0 shp n each thruster par (amuntng t a ttal shp f 20). The fgure shws that the ttal frce delvered by the thrusters decreases wth bradsde speed and at abut 0. 9 knt s equal t the crssflw drag at 550 punds. Cnsequently, the full scale vehcle can be prpelled bradsde untl t reaches a steady speed f 0.9 knt r, alternatvely, t can be held statnary n a bradsde current f 0.9 knt. The fregng estmate may be ptmstc snce t assumes that bth thruster pars can smultaneusly develp ther full rated shp. At ths cndtn, a steady equlbrum cannt be mantaned snce the vehcle wll have a yawng mment. Cnsequently, an equlbrum speed (zer mment case) f smewhat less than 0.9 knt may be mre realstc especally f the pwer lmtatn s at the separate prme mvers as ppsed t the ttal capacty f the battery. CRTCAL SPEED AND EQULBRUM CrTTNS FR LEVEL FLGHT The crtcal speed, defned as the speed belw whch "cntrl reversav effects ccur, can be determned frm the fllwng relatnshp: v ^'V 'A 34» - «fc--

54 Prpulsln n drectn f ntn Prpulsn n drectn ppsed t mtn (read bth scales as negatve) 60x0" Velcty Ceffcent U" Fgure 20 - Effect f Velcty Ceffcent n Lateral Frce Ceffcent fr Frward Thruster Par n Bradsde Mde f peratn Prpulsn n drectn f ntn Prpulsn n drectn ppsed t ntn (read bth scales as negatve) Velcty Ceffcent U" Fgure 2 - Effect f Velcty Ceffcent n Yawng Mment Ceffcent fr Frward Thruster Par n Bradsde Mde f peratn 60x0 0" 3 x 20 > 0 - +* c fc «j0 (3 2% Prpulsn n drectn ppsed t ntn (read b< th scales as negatve) Prpulsn n. drectn f mtn 40xl0-3 Velcty Ceffcent U" Fgure 22 - Effect f Velcty Ceffcent n Lateral Frce Ceffcent fr Aft Thruster Par n Bradsde Mde f peratn 8 Prpulsn n drectn ppsed t ntn (read bth scales as negatve) J 4.^Prpulsn n drectn f ntn Velcty Ceffcent U" Fgure 23 - Effect f Velcty Ceffcent n Yawng Mment Ceffcent fr Aft Thruster Par n Bradsde Mde f peratn

55 M!"r? «3 3 * 5-6 -!! : TTTT: : :: " '! cw j J t rj;: t-~]-t-4 T3 T t t ( > "t >>,n, Q rr-js Reynlds Number Based n Maxmum Beam 20xl0 5 Fgure 24 - Effect f Reynlds Number n Crssflw Drag Ceffcent (0 u & u 0) (0 (0 3 TJ S* C M C >» «M - 0) y <M 0 b.m a t k. «Q b J) T3 «a 4 a f A Drag J 400 y Thrus ter P ars Speed n knts Fgure 25 - Effect f Sdewse Velcty n Lateral Frce fr Frward and Aft Thruster Pars peratng Tgether 36

56 Based n Equatn [2] and the dervatves cntaned n Tables 2 and 3, the crtcal speed fr DSRV Scheme A s fund t be abut. 6 knts. The crtcal speed and asscated cntrl reversal effects can be demnstrated and bserved n peratng submarnes by perfrmng a partcular knd f lv.-speed dvng maneuver. Fr example, f whle prceedng at a speed belw. 6 knts wth the full-scale cunterpart f DSRV Scheme A the shrud was set at a large dve angle,the vehcle wuld assume a dve ptch angle and frst change depth n the dve drectn. Hwever, when a steady ptch angle s reachedjt wuld start and cntnue t rse whle mantanng a dve ptch angle. Thus, ths maneuver shws that even belw crtcal speed the ptch angle always has the crrect sense wth respect t the shrud angle but there s an ambguty n the depth change. Cnsequently, the shrud s cnsdered t be a relatvely neffectve cntrl devce fr depth-changng maneuvers f the DSRV Scheme A at speeds belw. 6 knts. t shuld be mentned that the crtcal speed f. 6 knts s based n a BG f 2 nches. The crtcal speed culd be reduced by lwerng the value f the BG, as shwn n Fgure 26. Hwever, t may nt be desrable t lwer the BG snce t wuld make the vehcle extremely senstve n ptch and rll at the hverng cndtn. n addtn, t may lead t ncreased rllng n turnng maneuvers and n buyant ascents. n cnventnal submarnes, the prblem f cntrl at belw crtcal speed s usually slved by the use f bwplanes. Ths fllws frm Equatn [2] where, fr the case f usng bwplanes nly, the rat M. 'Z, ; s negatve resultng n ether n crtcal speed r a crtcal speed whch s hgh enugh t le utsde f the range f peratn. Fr smlar reasns, althugh DSRV Scheme A has n bwplanes, t sh d be pssble t perfrm the same functn effectvely wth the frward thru ^T par. Ths can be shwn frm Equatn [2] whch can be rewrtten fr lae case f thrusters as fllws: V, =f 2 L. k ax + Z - x. w w M ' + Z J*T, " [3] Fr DSRV Scheme A, f x* s greater than 0. 2"? there s n crtcal speed. Frm Fgure 4,t may be seen that the frward thruster par satsfes ths crtern at all frward speeds. n the ther hand, there s a crtcal speed asscated wth the use f the aft thruster par. Furthermre, as mentned prevusly, at the hgher speeds there s a sgn reversal n the hydrdynamc ptchng mment prduced by the aft thruster par. The thruster rpm's asscated wth the crtcal speed f the vehcle cntrlled by the aft thruster par nly are shwn n Fgure 27. t may be seen that there s n crtcal speed fr rpm's less than 800. A regn n Fgure 27 s marked ff t ndcate the cmbnatns f speeds and rpm at whch the sgn reversal n hydrdynamc ptchng mment wll ccur. n vew f the fregng, the use f the aft thrusters as a means f vercmng the crtcal speed prblem s nt advcated. 37

57 2.0 Metacentrc Heght n nches Fgure 26 - Effect f Metacentrc Heght n Crtcal Velcty 38

58 C * H cal cty SCrt Vel [ J, y 0 ^ et m u ) > a D M 0 c 0 y 00 (N (N CD (N 00 0 * > 75 3, '«X r H - c fj u -, M -( -a <. 3 3 u C E a.. Vn u u s tj tj 5: C C Cd c >, n ±J 'J tfl M 0 M u u 0 0; X3 c > X > < a a C U-l -H -^ -< 0 0 ^H '^ u a. >> P5 c X *-> M m -J -H -H 4- (fl Ü M 0 C J f- - ^ fl X ^ ^3 B a- x J: u th U W 'H 0 (L S 3 t-> n 0 0 -H V4 a; CJ (D S H J3 ^ 4-( -H ** e«w 04 r^ fnj u 3 hc abd JQ^snam, ^JV J WdH 39

59 U Due t asymmetres, a submarne usually has t carry a steady ptch angle and steady cntrl-surface angle t mantan a cndtn f hrzntal equlbrum flght. The varus cmbnatns whch wll gve equlbrum level flght can be estmated fr DSRV Scheme A frm the statc stablty and cntrl dervatves lsted n Tables 2 and 3. The equlbrum ptch angles and shrud angles requred fr level flght f DSRV Scheme A when cntrlled wth shrud nly are shwn as functns f speed n Fgure 28» At speeds greater than 2 knts r less than. 5 knts, the equlbrum ptch angle s less than degree and the equlbrum shrud angle s less than 2 degrees. Hwever, between.5 and 2.0 knts, the equlbrum angles are large and nclude a case (crtcal speed) where n cmbnatn f fnte shrud angle and ptch angle wll prduce a cndtn f steady level flght. CNCLUSNS Hydrdynamc ceffcents, derved frm tests f a ne-thrd scale mdel, are presented fr use n detaled smulatn studes f the mtns f a specfc desgn fr the Deep Submergence Rescue Vessel (DSRV Scheme A ). Based n an analyss f these data, the fllwng cnclusns are made cncernng the stablty and cntrl characterstcs f DSRV Scheme A :. The submarne wll have near-ptmum dynamc stablty n the vertcal plane f mtn (dampng rat between 0. 7 and.0) at all peratng speeds greater than. 4 knts. 2. The submarne wll be dynamcally stable n the hrzntal plane f mtn and, therefre, shuld have gd cursekeepng qualtes. 3. Usng the all mvable shrud nly, the submarne wll have gd cntrl effectveness n the vertcal plane at frward speeds abve crtcal speed and n the hrzntal planes at all frward speeds, as evdenced by ts ablty t ntate a dve r change headng rapdly. 4. n general, the thrusters wll be relatvely neffectve as cntrl dc'ces fr peratng n the frward speed mde; the nrmal frce, lateral frce, ptchng mment, and yawng mment prduced by the thrusters wll decrease substantally and the lngtudnal frce wll ncrease substantally wth frward speed fr any gven thruster rpm r thruster pwer. The pr perfrmance f the thrusters s beleved t be due t an nteractn between the thruster jet velcty and manstream flw abut the bdy whch causes large changes n pressure dstrbutn abut the bdy as evdenced by the large mvement n center f actn f the thruster frce wth frward speed. 5. t shuld be pssble t prpel the submarne bradsde untl t reaches a steady speed f abut 0. 9 knt r, alternatvely, untl t s held statnary n a bradsde current f abut 0. 9 knt. 40

60 m 0) > X +» a cr C n a) y U NJ N M a) > d h w S n ^> s CD V -H 00 Ü ft 00 N saaasap uj S Q QSuy pnajs puc e 8T3UV p:*td 4

61 6. The crtcal speed f the submarne fr cntrl wth shrud nly wll ccur at abut. 6 knts. The frward thruster par can be used n leu f the bwplanes fund n cnventnal submarnes t prvde gd cntrl at frward speeds at r belw. 6 knts; the aft thruster par s nt recmmended fr ths purpse because f the sgn reversal n the hydrdynamc ptchng mment that wll ccur wthn the range f usable speeds. ACKNWLEDGMENTS The authr s grateful t Messrs. E. Dttrch, T. Mahney, A. Magnusn, N. Kng, and B. Carsn fr ther assstance n the expermental wrk; and t Messrs. M. Gertler and G. Hagen f the Stablty and Cntrl Dvsn fr ther cntrbutns and gudance. n addtn, the helpful suggestns and partcpatn n the test prgram f Messrs. J. Beverdge, F. Puryear, and G. ber f the Prpeller Branch are greatly apprecated. 42

62 APPENDX A LNGTUDNAL STABLTY AND CNTRL CEFFCENTS (Fgures 29-37) 43