A MATHEMATICAL MODEL TO ANALYZE THE STATIC STABILITY OF HYBRID (AERO-HYDRODYNAMICALLY SUPPORTED) VEHICLES

Transcription

1 THETIL OEL TO NLYZE THE STTI STBILITY OF HYBRI (ERO-HYROYNILLY SUPPORTE) VEHILES ollu, H Ptel, F Trreux, rnfeld Unversty, UK PRESENTE T THE 8TH SYPOSIU ON HIGH SPEE RINE VEHILE, 1- Y 8, NPLES SURY mong te new concepts developed for g speed mrne vecles over te lst two decdes [1], te erodynmc llevton [] pproc conssts n usng n erodynmc surfce to llevte te wegt sustned by te ydrodynmc lft. Suc vecle experences erodynmc nd ydrodynmc forces of te sme order of mgntude, terefore te dynmc models developed for rborne nd wterborne vecles re not sutble. onsderng vecle vng g-speed prsmtc plnng ull nd one or more erodynmc surfces, te utors propose two mtemtcl metods. Te frst one clcultes te equlbrum tttude of te vecle t gven speed nd ts numercl mplementton s been used to undertke prmetrc nlyss of te nfluence of some confgurton crcterstcs on performnces. Te second metod nlyzes te sttc stblty of te HV. Strtng from te dynmc nlyss prevously proposed by te utors [], te crcterstc polynoml of te HV dynmcs s derved nd sttc stblty crteron s proposed. NOENLTURE ptc moment rm of F [] ero- nd ydrodynmc dded mss mtrx ptc moment rm of ws ptc moment rm of ws F η (kg),(kg m) j j erodynmc center of t-erofol [B] ero- nd ydrodynmc dmpng mtrx F η (kg s -1 ), (kg s -1 m) B j j c ptc moment rm of N c L, Lft coeffcent of te -t erodynmc surfce c, rg coeffcent of te -t erodynmc surfce c m, Ptc moment coeffcent of te -t erodynmc surfce [] ydrodynmc restorng mtrx F η (kg s - ), ( kg s - m) j j G center of grvty [] erodynmc WIGe mtrx plnng ull erodynmc drg -t surfce erodynmc drg F ydrodynmc frcton drg F η ( kg s - ), ( kg s - m) ws F HV L lcg ydrodynmc wsker spry drg surge (1), eve () force or ptc (5) moment Hybrd Vecle -t surfce erodynmc lft G longtudnl poston, from trnsom m mss of te HV t equlbrum (kg) -t surfce erodynmc moment mc men erodynmc cord of te -t erofol N ydrodynmc potentl force (N) R/W totl resstnce-to-wegt rto RUL Rectlner Unform Level oton S Reference re of te -t erodynmc surfce T trust force (N) TP trust force pont of cton V velocty t equlbrum stte (m s -1 ) vcg G vertcl poston, from te keel W wegt of te vecle (N) WIGe Wng In Ground effect wrt wt respect to β dedrse ngle of te plnng ull ε ngle between te drecton of T nd te keel ζ coordnte of te -t pont n te body-fxed xes system, z xs η egt bove te surfce, pos. upwrd (m) η 1 surge dsplcement (m) η eve dsplcement, postve downwrd (m) η 5 ptc rotton, postve bow up (rd) η η t η ( t) η η ρ τ ξ ngle between te -t wng mc nd te keel densty (kg m - ), ρ r, ρ sewter trm ngle (deg), ngle between te keel of te plnng ull nd te wterlne coordnte of te -t pont n te body-fxed xes system, x xs

2 INTROUTION Te ybrd vecle (HV) confgurton nlyzed ere s composed by g speed prsmtc plnng ull nd one or more wngs. In prtculr, beng t low egt bove te surfce, te wng experences te wng n ground effect (WIGe), postve effect tt nfluence te lft, drg nd moment. Terefore, n order to develop model wc studes te dynmc of te HV, reserc on dynmc models of prsmtc plnng ull nd WIGe vecles s been crred out. 1.1 WING IN GROUN EFFET VEHILES Reserc on WIGe vecles s mnly been crred out n te former Sovet Unon, were tey were known s Ekrnoplns. Te entrl Hydrofol esgn Bureu, under te gudnce of R. E. lekseev, developed severl test crft nd te frst lne producton ekrnoplns: Orlyonok nd Lun types [4]. In te mentme, severl reserc progrms were undertken n te west to better understnd te peculr dynmcs of te vecles flyng n ground effect. Irodov [5] nd Rozdestvensky [6] [7] mde mportnt contrbutons to te development of WIGe vecles dynmc models. In te 6 s nd te 7 s, Kumr [8], [9] strted reserc n ts re n rnfeld Unversty. He crred out severl experments nd studed te stblty ssues of vecle flyng n ground effect. Stufenbel [1] n te 8s crred out n extensve work on te nfluence of te erodynmc surfce crcterstcs on te longtudnl stblty n wng n ground effect. He obtned expermentl dt wt te WIGe vecle X-114 bult by Ren-Flugzeugbu n Germny n te 7 s. Te equtons of moton for vecle flyng IGE were defned, ncludng non lner effects. In te US, Ger [11] used te Stufenbel s work to nvestgte te stblty of Russn ekrnopln, usng te vlble dt for te F-14 rcrft, vecle wt n erodynmc lyout smlr to te Russn vecle. Te pproc s smlr to tt used for conventonl rplne, even f te model s not so ccurte (cnges of stblty dervtves wt egt not tken nto ccount). Hll [1], n 1994, extended te work of Kumr, modfyng te equtons of moton of te vecle flyng n ground effect, tkng nto ccount te nfluence of perturbtons n ptc on te egt bove te surfce. 1. PLNING RFT Reserc on g speed plnng strted n te erly twentet century for te desgn of seplnes. Lter, te reserc focused on pplctons to desgn plnng bots nd ydrofol crfts. urng te perod 196 to 199, mny experments ve been crred out nd new teoretcl formultons proposed. Svtsky [1] crred out n extensve expermentl progrm on prsmtc plnng ulls nd developed mtemtcl metod to estmte te equlbrum tttude of plnng crft. rtn [14] derved set of equtons of moton for te surge, ptc nd eve degrees of freedom nd demonstrted tt surge cn be decoupled from eve nd ptc moton. Te model of Svtsky s stll under development, s sowed by recent rtcle of Svtsky, elorme nd tl [15]. It s stll one of te reference metods used for te prelmnry desgn of plnng crft. 1. HYBRI VEHILES ONEPT In 1976, Spps [16] nlyzed new knd of rce bots, known s tunnel ull rce bots. Te dvntges of ts new confgurton come from te erodynmc lft. In 1978, Wrd et l. [17] publsed n rtcle on te desgn nd performnce of rm wng plnng crft: te KUU II. Ts vecle, wc conssts n two plnng sponsons seprted by wng secton, ws ble to run t 78 kts (lmost 145 km/), tnks to te erodynmc lft llevton. In 1978, Kllo [18] performed comprtve tests between te KUU II nd te K. Te K s conventonl mono ull plnng crft. Te dt obtned durng comprtve trls sowed tt te KUU II ptc moton, n se stte, t bout 4 to 6 knots, ws bout % to 6% lower tn te conventonl plnng ull K. In 1997, octors [] proposed new confgurton clled Ekrnoct for wc e mentoned te erodynmc llevton concept. Te wegt of te ctmrn ws llevted by erodynmc lft, tnks to more stremlned superstructure tn n trdtonl ctmrns. Te teoretcl nlyss nd computed results sowed tt reducton n te totl drg of round 5 % cn be obtned t very g speed. Russell [19] developed n nlyss of erodynmc nd ydrodynmc forces nd moments ctng on tunnel rce bot. Ts pproc s tlored only to te rce tunnel bot, terefore cnnot be used to desgn nd evlute dfferent confgurton. In te followng references [16][17][18] some expermentl dt, teoretcl nd computed results on vecles wc cn be clssfed s HV re presented, but none of tem presents n nlyss of te sttc stblty of vecle vng bot ydrodynmc nd erodynmc surfces.

3 XIS SYSTE In ts work te sme xs systems proposed by te utor n [] wll be used. Brefly tey re: one ertxs system nd two body-xs system, rgt-nded nd ortogonl. 1.4 ERTH-XIS SYSTE (xoz) Te drectons of te xs re fxed n spce. Te z-xs s orented vertclly downwrd; te x-xs forwrds nd prllel to te undsturbed wterlne nd te orgn s fxed t te undsturbed wterlne level. 1.5 BOY XIS SYSTES Te orgn O s concdent wt te G of te HV. Te x nd z xs ly n te longtudnl plne of symmetry, x postve forwrd nd z postve downwrd. Two systems re used: ero-ydrodynmc xes (η 1 Oη ), te x-xs beng prllel to te stedy forwrd velocty V, geometrc xes (ξoς), te x-xs ξ beng prllel to te keel of te plnng ull. ero-ydrodynmc xes re te counterprt of te erodynmc xes (clled lso wnd or body-wnd xes (UK) or stblty xes (US) used for rplnes. ONFIGURTION Te generl confgurton used to represent te HV s to be ntended s modulr. Te elements presented re ll te possble elements tt cn be tken nto ccount n ts nlyss: g-speed prsmtc plnng ull (ydrodynmc surfce), wt constnt dedrse ngle β, one or more rfols (erodynmc surfces), n ero- or ydro-propulson system. Ts nlyss focuses on te g speed equlbrum stte, but te HV s supposed to ve wterborne cpblty t rest. Hydrodynmc nd erodynmc surfces cn be ftted wt control systems, but ts work s lmted to control-fxed nlyss. EQUILIBRIU STTE LULTION Ts work nlyses te sttc stblty of HV confgurton. Te stblty nlyss strts from n equlbrum stte nd studes ow te vecle rects fter dsturbnce. Te sttc stblty studes ow t rects mmedtely fter te dsturbnce weres te dynmc stblty studes f nd ow te vecle, eventully, returns bck to te ntl equlbrum stte. Te utor proposes mtemtcl metod tt cn clculte te equlbrum tttude of te HV, strtng from geometrc, nertl, erodynmc nd ydrodynmc crcterstcs of te vecle. 1.6 HYPOTHESES Te present work concentrtes on te nlyss of n equlbrum stte crcterzed by rectlner trjectory, constnt speed nd constnt lttude bove te surfce, wc wll be referred s Rectlner Unform Level oton (RUL). Te vecle s supposed to be lwys n contct wt te wter, nd n clm wter stuton. Wves re not tken nto ccount. 1.7 FORES N OENTS Te forces nd moments ctng on te vecle re llustrted n Fgure. Tey cn be dvded n four groups: grvttonl (wegt, W), trust (propulson force, T), erodynmc (lft, drg nd moment from te 1 st nd nd erodynmc surfce, L,, nd erodynmc drg of te ull bove te surfce, ), ydrodynmc (potentl force, N, frctonl force, F, wsker spry drg, ws ). 1.7.) Grvttonl force Snce te equlbrum moton nlyzed s level moton, te egt bove te surfce s constnt; terefore te drecton of te velocty t equlbrum s norml to te wegt drecton. Te wegt (W) cts t te center of grvty (G), wc s lso te orgn of te body-fxed xs system. Te coordntes of te G re (,). 1.7.b) Power force Te trust cn be provded by n ero-propulson system or ydro-propulson system. Te trust cts t te trust pont (TP), n drecton determned by te ngle ε, te ngle between te drecton of te trust nd te keel, postve for n ntclockwse movement (vew from te strbord sde of te vecle).

4 1.7.c) erodynmc forces erodynmc forces cn be dvded n two groups: forces ctng on erofols nd force ctng on te porton of te ull bove te wter. Te erodynmc force ctng t te center of pressure of te erofol, n te longtudnl plne, s usully represented wt n equvlent system of two forces nd one moment ctng t te erodynmc center of te erofol (): lft (L), defned s perpendculr to te velocty, drg (), defned s prllel to te velocty, nd ptc moment (), postve for bow up movement. L 1 1 ρ 1 ρ ρ V V V S S S c L, c, c m, mc () Usully te erodynmc coeffcents c L,, c, nd c m,, re functons only of te ngle of ttck, but n ts nlyss, lso te nfluence of te egt bove te surfce s to be tken nto ccount. Te ngle of ttck s te sum of te trm ngle nd η, wc s te ngle between te cord of te wng nd te keel of te ull. Te egt bove te surfce to evlute te erodynmc coeffcents s tt of te erodynmc center. Te dry secton of te ull experences n erodynmc drg force ( ). To evlute ts contrbuton, Svtsky [15] proposes te expresson: 1 ρ V c, were s te frontl re of te plnng ull, (), s te erodynmc drg coeffcent of te ull (pproxmted s.7). Snce t s not known were te ull erodynmc drg cts, s supposed to be ctng on te G. Terefore no moment s generted by ts force. 1.7.d) Hydrodynmc forces Referrng to te work developed by Svtsky et l. from 1964 troug 7 [1], [15], te ydrodynmc forces re: potentl force N, frcton force F, wsker spry drg WS. Te potentl force drecton s supposed to be norml to te keel nd ctng t te ydrodynmc center H. Te frcton force cts prllel to te keel lne, lfegt between te keel nd te cne lne. Te wsker spry drg WS s been nlyzed n prtculr n [15]. lso WS s ssumed to ct troug te G of te HV. 1.8 SYSTE OF EQUTIONS OF EQUILIBRIU Once ll te forces nd moments re known, system of equtons of equlbrum cn be developed. Te vecle, n te longtudnl plne, s tree degrees of freedom, nd system of tree equtons of equlbrum s needed. Te system s: surge equton: sum of te vertcl forces, eve equton: sum of orzontl forces, ptc equton: sum of ptc moments. Te G of te HV s been cosen to be te pont of reference for te moments. 1.8.) Surge Equton It sttes tt te sum of te erodynmc drgs, te component of potentl nd frcton ydrodynmc forces prllel to te velocty, nd te wsker spry drg s to be equl to te component of te trust prllel to te velocty. 1 N sn( τ ) T cos( τ 1.8.b) F ε ) Heve Equton cos( τ ) WS () Te sum of erodynmc lft, vertcl components of te potentl nd frcton ydrodynmc force nd te vertcl component of te trust s to be equl to te wegt of te HV:

5 L 1 W 1.8.c) L N cos( τ ) T sn( τ ε ) Ptc oment Equton F sn( τ ) () Te sum of te erodynmc moments, ydrodynmc moments nd te moment generted by te trust force s to be equl to zero. L T 1 [ ξ 1 cos( τ ) ζ 1 sn( τ )] 1[ ξ 1 cos( τ ) ζ 1 sn( τ )] [ ξ cos( τ ) ζ sn( τ )] [ ξ cos( τ ) ζ sn( τ )] L N c [ ξ sn( ε ) ζ cos( ε )] TP ws ws wt te condtons ws TP F SOLUTION OF THE EQUTIONS OF EQUILIBRIU () Te metod to solve te system of te tree equtons of equlbrum s modfed verson of te Svtsky long-form metod llustrted n []. In te Svtsky metod, te wegt s sustned by ydrosttc nd ydrodynmc forces, wle n ts work te wegt s sustned by bot erodynmc nd ydrosttc-ydrodynmc forces. Obvously, s t cn be seen n equtons (), () nd (), te erodynmc drg nd moments lso ve to be tken nto ccount. In te Svtsky metod, te trm ngle s not known t te strt, terefore trm ngle s to be ssumed nd, troug cycle, te rgt trm ngle tt fulfll equtons (), () nd () s eventully found. In ts work n ddtonl ssumpton s to be tken, snce te erodynmc forces depend on: trm ngle (τ) (te ngle of ttck s te sum of te trm ngle τ nd te ngle between te mc nd te keel η), egt bove te surfce. Ts leds to trm ngle (τ) cycle nested nto te egt bove te surfce () cycle, s llustrted n Fgure. ssumng vlue for te egt bove te surfce of te G ( ) nd trm ngle τ, te erodynmc forces cn be clculted. Ten te wegt sustned by te ydrodynmc forces s equl to te dfference between te totl wegt nd te sum of te erodynmc lfts. t ts pont te long-form metod of Svtsky cn be followed, tkng nto ccount lso erodynmc drgs nd moments, nd te equlbrum trm ngle cn be derved. Te egt bove te surfce of te vecle 1 cn ten be clculted. If ts 1 s equl to te ssumed, ten te equlbrum tttude of te vecle s been found. If not, new cycle s performed. 1.9.) Vldton of te mtemtcl model s fr s te utors re wre, no expermentl dt on HV trls re vlble n te publc domn, but te model proposed cn nlyze lso plnng crft confgurtons. nlyzng te confgurton B of Tble 1, te comprson between te dt obtned by te utors nd te results presented n [15] re presented n Fgure 4. Te dt re n good greement troug te wole speed rnge, bot for te trm ngle nd for te resstnce to wegt rto. STTI STBILITY nlyzng te forces nd moments under te smll dsturbnces ypotess, te sttc stblty of te HV s derved usng te Rout-Hurwtz crteron. 1.1 ROUTH-HURWITZ RITERION In generl, gven polynoml equton n s, s n n n n 1 1 s... 1 s () te Rout-Hurwtz metod determnes ow mny roots wll ve postve rel prts. If te polynoml equton s te crcterstc polynoml of te dynmcs of vecle, ts metod cn be used to determne te stblty of te vecle. In fct, f ll te roots ve negtve rel prt, te system s stble, sttclly nd dynmclly. Furtermore, Stufenbel [1] sowed ow te lst coeffcent of te polynoml ( ) cn be used to determne te sttc stblty of te system. If te condton n > ()

6 s fulflled, ten te system cn be consdered sttclly stble HV HRTERISTI POLYNOIL N STTI STBILITY ONITION In [], te utors developed mtemtcl model to study te longtudnl dynmcs of te HV. system of ordnry dfferentl equtons of moton ws derved for te longtudnl plne n te frme of smlldsturbnce stblty teory. Te sme mtemtcl model s been dopted for ts work ) omplete Order System By defnng stte spce vector υ s: υ [ η η η η η ] η () te system of equtons of moton cn be rerrnged n te ucy stndrd form (or stte-spce form). Te crcterstc polynoml of te complete order system cn be derved: 6 s 6 s 5 s s s 4 Wt 6 1, te sttc stblty s ssured wen num > were nums equl to V s () () [ ( B B ) B ( )] nd s equl to [ ] ( I ) m m( 11 ) ( m ) ( m ) b) Reduced Order System () () Ts mtemtcl metod requres to be vldted gnst expermentl dt. Unfortuntely, no expermentl dt on te sttc stblty of HV confgurton s vlble n te publc domn. To pln suc experments, t s necessry to ve pyscl nsgt of te condton stted n equton (). Ts condton, ppled to te complete order system (), s reltvely complex. ssumng tt te surge degree of freedom (η 1 ) cn be decoupled from eve (η ) nd (η 5 ) ptc degrees of freedom, smplfed verson of te condton () cn be obtned, ledng to better pyscl nsgt. In [] te utor derved mtemtcl model of te dynmcs of te HV strtng from te systems of equtons of moton of WIGe vecles nd plnng crft. s regrd te dynmcs of plnng crft, rtn [14] demonstrted tt te surge moton cn be decoupled from te eve nd ptc moton. For te dynmcs of WIGe vecles, Rozdestvensky [6] proposed reduced order system were te surge moton s decoupled from eve nd ptc moton. Ts ypotess s been confrmed by, mong oters, elye [1]. By defnng te reduced order stte spce vector υ s υ [ η η η η ] 5 5 η () te ucy stndrd form (or stte-spce form) of te reduced order system s obtned. Te crcterstc polynoml cn be derved: s s s s 1 s Wt 5 1, te sttc stblty s ssured wen V ( 5 5 ) ( I ) ( m ) > REUE ORER STTI STBILITY: PHYSIL INSIGHT () () Ec coeffcent n equton () s te dervtve wt respect to: ccelertons ( j ), eve poston( j ) egt bove te surfce ( j ) of te sum of erodynmc nd ydrodynmc forces (nd moments). Referrng to [], rememberng tt te superscrpt stnds for erodynmc nd for ydrodynmc nd tt Z s te eve force (postve

7 downwrd) nd te ptc moment (postve bow up), te coeffcents re equl to: Z Z Z 5 η Z η, η,, η, Z Z 5 5 () () Te erodynmc dervtves cn be estmted wt, for exmple, [1][] nd te ydrodynmc dervtves wt te pproces presented n [14] or []. Usng tese expressons for te confgurton presented n secton 1.5 we ve ( I )( m ) > Terefore te sttc stblty condton of te reduced order becomes 5 5 > 1.1.) Smlrty wt WIGe vecles () () prllel wt WIGe vecles sttc stblty crter s llustrted. Te sttc stblty condton derved by Stufenbel [1] nd Irodov [5] s: w Z w Z < () were w nd re te dervtves of ptc moment wt respect to te eve velocty nd te egt bove te surfce, Z w nd Z re te eve force sme dervtves ( /Z s te sme s 5 / ). w /Z w s defned lso s te erodynmc center of ptc nd / Z s te erodynmc center n egt. Rememberng postve bscss mens ed te G, te condton () cn be expressed s n [7]: te (erodynmc) center n egt sould be locted upstrem of te (erodynmc) center n ptc vdng te lft due to vrton of te ptc ngle (L lp ) from te lft due to vrton of te egt bove te surfce (L egt ), condton () sttes te pont of cton of force L egt sould be locted upstrem te pont of cton of force L lp. 1.1.b) HV Sttc Stblty rteron (reduced order) For te HV, usng te expressons (), te sttc 5 5 stblty condton > () s: η Zη η Zη > () Te frst term η/z η s te nlogue of te erodynmc center n egt of WIGe vecles. Te utor proposes for te second term te nme ydrodynmc center n eve, so tt te condton () cn be lso expressed s: te ydrodynmc center n eve sould be locted downstrem of te erodynmc center n egt s before, dvdng te ydrodynmc lft due to eve vrton (L yd ) from te lft due to vrton of te egt bove te surfce (L egt ), te pont of cton of L egt sould be locted upstrem te pont of cton of L yd. PRETRI NLYSIS prmetrc nlyss s requred n te prelmnry desgn pse of new vecle. Usng te metod llustrted n secton 1.9, te nfluence of some confgurton prmeters on te resstnce to wegt rto (R/W) of te HV s nvestgted. Te Resstnce-to-Wegt rto s defned s: R / W er. rg Hyd. rg Wegt 1.1 PRETERS onsderng te ybrd confgurton of te HV, mny prmeters ve to be tken nto ccount (Fgure 1). Te erodynmc surfces prmeters re: erodynmc profle type, men erodynmc cord (mc), surfce re,

8 ngle between te keel nd te mc (η), poston of te wng reltve to te ull. Te profle spe determnes te erodynmc coeffcents; terefore te coce of te profle s very mportnt. Te nvestgton of te optmum profle for gven confgurton s beyond te scope of ts work, snce t requres toroug nlyss of te vlble profles nd F smultons. Te utor s cosen modfed Glenn rtn 1 secton. Ts profle s very poor effcency (lft-to-drg rto), but t s been dopted only to ve expermentl vldted vlues, presented n [4]. Te nfluence of te lengt of te men erodynmc cord (nd te surfce re) s been nlyzed n secton 1.1., te nfluence of η n secton 1.1.b. s regrd te plnng ull te prmeters re: bem lengt, dedrse ngle β. To ve drect comprson wt plnng crft confgurton (no wng), one of te confgurtons tested by Svtsky n [15] s been dopted: ts crcterstcs re presented n Tble 1, se B. Its bem nd dedrse ngle ve been used lso for te HV confgurtons of tese nlyss. Some mportnt crcterstcs of te vecle re lso: mss, longtudnl poston of te G, vertcl poston of te G. Te mss of te vecle n ll te nlyss s been kept constnt: te utor supposes tt te erodynmc surfce or surfces cn be exploted to, for exmple, crry prt of te fuel (lke rplnes) or oter systems of te vecle. Te vertcl poston of te vecle s been kept fxed, snce ts poston s desgned to fulfll te ydrosttc stblty crter. n nlyss of te nfluence of te longtudnl poston of te G (lcg) s presented. 1.1.) Wng surfce re nlyss Tree confgurtons ve been nlyzed:, B nd. Tey re dentcl unless for te mc lengt: confg. B, mc meter (no wng) confg., mc meters, confg., mc meters. In Fgure 5, te resstnce to wegt rto curves of te tree confgurtons re presented. Te speed rnge cn be dvded n two zones by te speed t wc te curves cross ec oter (bout Froude number.9, 4 knots), clled V X. In te speed rnge V <V X, te totl drg of B (plnng crft) s lower tn te totl resstnce of nd. For V >V X, te HV wt wng experences less drg. Ts s becuse t low speed te ydrodynmc forces experenced by te HV nd te plnng crft re lmost te sme, snce te erodynmc forces re stll low compred to ydrodynmc forces. Noneteless te erodynmc forces led to n ncrese of te trm ngle, terefore te orzontl component of te ydrodynmc potentl force (ydrodynmc potentl drg) ctng on te HV s bgger (n module) tn te sme component ctng on te HV wtout ny wng. Te vecle wt wng/s experences ger ydrodynmc drg. s te speed ncreses, te erodynmc forces grow nd te requred ydrodynmc lft force becomes lower nd lower nd, t te sme tme, te ydrodynmc drg dmnses. Terefore, lso f te trm ngle of te HV wt wng s stll bgger tn te trm ngle of te HV wtout wng, t certn speed te totl drg experenced by te HV wt wng s lower tn te totl drg experenced by te HV wtout wng. If te requrement of te vecle s to rec speed V>V X, te confgurtons wt wng wll requre power propulson lower tn te plnng crft. Rememberng tt te profle used s low effcency, wt more effcent profle te speed V X cn be lowered nd te power propulson cn be furter reduced. 1.1.b) ngle between te mc nd te keel (η) nlyss Te confgurtons nlyzed re, nd E. In order: η degrees, η E 5 degrees, η 1 degrees. Te resstnce to wegt rto of te tree confgurtons s presented n Fgure 6. Te curves re smlr to tt of Fgure 5. Ts s becuse te erodynmc lft s ncresed bot f te mc lengt (wng re) s ncresed nd f te ngle of ttck s

9 ncresed (ugmentng η te ngle of ttck s ugmented). Terefore te sme pyscl nsgt proposed for te nlyss of secton 1.1.b pples ere. Te bevor s less ccentuted becuse, wle n Fgure 5 tere s confgurton wtout wng, n ts nlyss ll te tree confgurtons ve wng. 1.1.c) Longtudnl poston of te G (lcg) nlyss Te confgurtons nlyzed re, F nd G nd te resstnce to wegt rto s represented n Fgure 7. lcg F lcg *.85 (-15%), lcg meters, lcg G lcg *1.15 (15%). In order to keep te poston of te erodynmc center fxed, te coordntes ve been cnged ccordngly (snce te pont of orgn s te G). s t cn be seen, lcg seems to ve te strongest nfluence on te performnce of te HV. Te poston of te G strongly nfluences te trm ngle of te HV, nd rerwrd sft of te G leds, t equl speed, to bgger trm ngle vrton tn te ncrese of te wng re or te ncrese of ngle η. omprng te trm ngle of confgurton wt confgurton F: Fn B 1, τ F τ 1.5 deg, Fn B 1.8, τ F τ deg, Fn B.5, τ F τ.5 deg. s explned n secton 1.1. nd 1.1.b, n ncrese of te trm ngle corresponds to n ncrese of te ngle of ttck of te wng, terefore to n ncrese of te erodynmc lft. Snce te ncrese of te trm ngle, sftng te G rerwrd, s bgger tn ncresng te wng surfce S or te ngle η of te sme percentge, te postve effect on te resstnce to wegt rto s ennced. Vce vers, te forwrd sft of te G s negtve effect. ONLUSIONS Te utors developed mtemtcl frmework to clculte te performnce of ybrd vecle, vecle vng prsmtc plnng ull nd one or more wng(s). Usng te mtemtcl model developed to estmte te HV equlbrum tttude cross rnge of speed, prmetrc nlyss s been conducted. Te results re tt: dmnsng te longtudnl dstnce between te trnsom of te ull nd te G or ncresng te surfce of te wng (S) or ncresng te ngle between te wng men erodynmc cord nd te keel (η) led to te resstnce to wegt rto of te HV to dmns. In prtculr, te postve effect of sftng te G rerwrd s more sgnfcnt tn ncresng te surfce of te wng. Te ncrese of η ngle s te smllest postve effect. Fnlly, followng te pproc of Irodov [5] nd Stufenbel [1] for WIGe vecles, crteron to estmte te sttc stblty of HV s been developed. REFERENES 1. EYER, J. R., LRK,. J., ELLSWORTH, W.., Te Quest for Speed t Se, Nvl Surfce enter, rderock vson, Tecncl gest, 4. OTORS, L. J., nlyss of te Effcency of n Ekrnoct: Very Hg Speed tmrn wt erodynmc llevton, RIN, Interntonl onference on Wng n Ground Effect rft (WIGs 97), OLLU,., PTEL,. H., TRRIEUX, F., Unfed temtcl odel for Hg Speed Hybrd (r nd Wter-borne) Vecles, nd Interntonl onference on rne Reserc nd Trnsportton (IRT 7), 7 4. KOLYZEV, B., ZHUKOV, V., SKLIK,., Ekrnoplns, Peculrty of te teory nd desgn, Snt Petersburg Sudostroyenye, 5. IROOV, R.., WIG Longtudnl Stblty rter (Krter prodol'noy ustoycvost ekrnopln), TsGI (entrl Insttute of eroydrodynmcs m. N. Ye. Zukovskj), ROZHESTVENSKY, K. V., Ekrnoplns - te GE's of fst wter trnsport, Trnsctons of Te Insttute of rne Engneer, Vol. 19, pp , ROZHESTVENSKY, K. V., Wng-n-ground effect vecles, Progress n erospce Scences, Vols. 4, pp. 11-8, 6 8. KUR, P., Stblty of Ground Effect Vecles, rnfeld ollege of eronutcs, Report ero No. 198, KUR, P., On te Longtudnl ynmc Stblty of Ground Effect Wng, rnfeld ollege of eronutcs, Report ero No., STUFENBIEL, R. W., BO-TZNG, Y., Stblty nd control of ground effect rcrft n longtudnl moton (trnslton), vd W. Tylor Nvl Sp Reserc nd evelopment enter, 1977

10 11. GER, J., Stblty nd ontrol of Wng-In- Ground Effect Vecles or Wngsps, I, rd erospce Scences eetng nd Exbt, HLL, I.., n nvestgton nto te flgt dynmcs of wng n ground effect rcrft opertng n erodynmc flgt, rnfeld Unversty, Sc Tess, SVITSKY,., Hydrodynmc esgn of Plnng Hulls, Journl of rne Tecnology, Vol. 1, pp , RTIN,., Teoretcl etermnton of Porposng Instblty of Hg-Speed Plnng Bots, Journl of Sp Reserc, Vol., pp. -5, SVITSKY,., e LORE,. F., TL, R., Incluson of Wsker Spry rg n Performnce Predcton etod for Hg-Speed Plnng Hulls, rne Tecnology, Vol. 44, pp. 5-56, SHIPPS, P. R., Hybrd rm-wng/plnng crft - tody's rcebots, tomorrow's outlook, I/SNE dvnced rne Vecles onference, WR, T.., GOELZER, H. F., OOK, P.., esgn nd performnce of te rm wng plnng crft KUU II, I/SNE dvnced rne Vecles onferences, KLLIO, J.., Results of full scle trls on two g speed plnng crft (KUU II nd K), vd W. Tylor Nvl Sp Reserc nd evelopment enter, TNSR/SP-847-1, RUSSELL, J.., Secrets of Tunnel Bot esgn, erorne Reserc, ISBN ,. OTORS, L., Hydrodynmcs of Hg-Speed Smll rft, Unversty of cgn, ELHYE, H., n Investgton nto te Longtudnl Stblty of Wng In Ground effect vecles, Sc tess, rnfeld Unversty, HUN, H. H., HNG,. H., Longtudnl stblty nd dynmc moton of smll pssenger WIG crft, Ocen Engneerng, Vol. 9, pp ,. FLTINSEN, O.., Hydrodynmcs of Hg- Speed Vecles, mbrdge Unversty Press, 5 4. RTER,. W., Effect of Ground Proxmty on te erodynmc rcterstcs of spect-rto-1 rfols Wt nd WItout End Pltes, NS Tecncl Note, Vol. -97, 196 Engneerng & Nvl rctecture Group s P resercer under te supervson of Prof. noo Ptel. Te project s prelmnry study on rne Unmnned erl Vecles (UVs) for Brts erospce. He s responsble for te study of te dynmcs of ts HV, ybrd vecle between wng n ground effect vecle nd g speed mrne vecle. He presented pper on te dynmc stblty of HV t te Interntonl onference on rne Reserc nd Trnsportton 7. Prof. noo Ptel FREng, BSc, P, Eng, FIecE, FRIN, Hon RN fter grduton from P n 197, noo Ptel strted s creer s n erodynmcst nd subsequently worked on te determnton of erodynmc gust lods on rcrft wngs before optng for cnge of creer to offsore mecncs. He estblsed lrge group workng n ts feld nd s n output of over 11 reserc ppers, books nd 8 Ptents. Hs current reserc nd work for ndustry s on combned r nd wter borne g speed vecles nd on spects of mrtme Unmnned r nd Surfce Vecles. r Florent Trreux s lecturer t rnfeld Unversty n te Offsore Engneerng & Nvl rctecture Group. Hs nterest n Hg Speed rne Vecles leds m to lunc n nnovtve reserc progrm t rnfeld n tree mn res: coupled eroydrodynmcs, novel concept desgn nd control of ybrd vecles t te r-wter nterfce. UTHORS BIOGRPHY urzo ollu GRIN grduted n erospce Engneerng (mrk 1/1) n ln, Itly. He ten joned rnfeld Unversty nd te Offsore

11 VEHILE HRTERISTIS BSI ONFIG. OPRISON ONFIGURTIONS Wng re nlyss η nlyss lcg nlyss Geometry unt conf. conf. B conf. conf. conf. E conf. F conf. G Propulson (ξ, ζ) TP [m] (, ) m ε [deg] [deg] 1 deg erodynmc surfce (one wng) mc [m] S [m ] 4 η [deg] 1 \ (ξ, ζ) 1 [m] (, ) \ (, ) (, ) (1.,) (18.7,) profle \ G.. 1 \ G.. 1 G.. 1 G.. 1 Hydrodynmc surfce (prsmtc plnng ull) Inertl bem [m] m β (dedrse) [deg] 14 deg (frontl re) [m ].67 m lcg (from trnsom) [m] (-15%) vcg (from keel) [m] 1.87 mss [kg] 516 kg Tble 1: rcterstcs of te nlyzed confgurtons (15 %) Fgure 1: crcterstcs of te nlyzed confgurtons

12 Fgure : forces nd moments ctng on te ybrd vecle Fgure : flow crt of te metod to fnd te equlbrum tttude of te HV

13 Fgure 4: Svtsky 7 (15) vs. ollu et l. Trm ngle nd Resstnce-to-Wegt rto

14 Fgure 5: nfluence of te wng re consderng te Resstnce-to-Wegt rto Fgure 6: nfluence of η consderng te Resstnce-to-Wegt rto

15 Fgure 7: Influence of te longtudnl poston of G consderng te Resstnce-to-Wegt rto