A Simple Method for Determining the Manoeuvring Indices K and T from Zigzag Trial Data

Transcription

1 Rind 8-- Wbsi: wwwshimoionsnl Ro 67, Jun 97, Dlf Univsiy of chnoloy, Shi Hydomchnics Lbooy, Mklw, 68 CD Dlf, h Nhlnds A Siml Mhod fo Dminin h Mnouvin Indics K nd fom Ziz il D JMJ Jouné Dlf Univsiy of chnoloy Absc Nomoo s fis od modl is h simls mhmicl modl o dscib shi mnouvs Clculd mnouvin d hv bn nlysd h o dmin h lion bwn h mnouvin indics K nd of Nomoo (96) nd ziz mnouvin chcisics h suls hv bn flcd in hs, which cn b usd hn o dmin hs indics fom cul ziz mnouvs his o is nslion in Enlish of o in Duch of h uho, Jouné (97), on his oic Inoducion h hoizonl moions of vssl du o udd dflcion cn b dscibd by usin mhmicl modls h mos siml sysm, h fis od modl of Nomoo (96), is comomis bwn h dmnd fo siml mhmicl modl nd fi oximion of h cul mnouvs of h shi Nomoo hs ublishd som mhods o sim h mnouvin indics K nd fom (full-scl) ziz il d Bu, usin hs indx simos, i s ofn h h clculd mnouvs dvi considbly fom hos msud on h shi Bcus of his, mhod hs bn dvlod o dmin hs indics in such wy h h diffncs bwn clculd nd msud d, s f s yw iod nd ovshoo concnd, s low s ossibl Usin Nomoo s fis od modl, l numb of ziz mnouvs hv bn clculd h cicl n of K nd vlus hs d hv bn nlysd nd h lion bwn h ziz mnouvin chcisics nd h Nomoo indics K nd hv bn flcd in hs Rvsd, hs hs cn b usd hn o dmin hs indics fom cul ziz mnouvs

2 Equion of Moion h fis od modl of Nomoo (96) ds s follows: In h: & & & && + & = K K ( ) Equion () Yw nul cclion Yw nul vlociy o of un (d/s o d/s ) Yw nl (d/s o d/s) Acul udd nl (d o d) Effciv udd nl (d o d) Pooionliy consn (/sc) im consn (s) h lvl of h udd nl, h udd nl which h shi sils sih cous nd & h of un of h udd h followin ms hv bn obind fom h comud cous hisois: h iod, h mn cous nd h mximum cous dviion liv o o void nsin ffcs, h hid iod hs bn usd o dmin hs mniuds, s fiu 3 Acul nd Idl Kmf Ziz Mnouvs An idl Kmf ziz mnouv hs o fulfil h followin quimns h: qul bsolu vlus of udd nls, qul bsolu vlus of udd nl vlociis nd udd-od whn = I is obvious h n cul ziz mnouv cn fulfil hs scific dmnds xcly I is ossibl howv, o nsfom n cul mnouv o n idl mnouv wih sufficin ccucy hfo, comud idl Kmf ziz mnouvs hv bn nlysd h 4 Anlysis of Fis Od Modl Usin Nomoo s fis od modl, l numb of ziz mnouvs hv bn clculd cicl n of K nd vlus, wih h followin ms: Fiu Idl Kmf Ziz s h followin lions hv bn found by nlysin hs clculd d: = C + C + = + K K C = C5 9 K 3 Equion () + C4 Equion (3) Equion (4)

3 In h:,, nd in ds, nd in sconds = / & is h im of udd cion is h iod fo mnouvs wih & = nd = is h yw mliud fo mnouvs wih & = nd =, /, C, C, C 4 nd C5 funcions of h oduc K C 3 is funcion of & hs lions ivn in h fius 5, 6 nd 7 s will b dscibd fuh on 5 nsfomion of Acul Ziz Mnouvs o Idl Mnouvs h ls dviion of n cul ziz s fom n idl on is nlly cusd by no fulfillin h quimn x =, s fiu b usd o obin h vlus n idl mnouv: mx -idl -idl = mx nd fo ( x ( )) ( ) = 6 Dminion of K nd fom Ziz il As h idl vlus of, &,, nd known, h unknowns in h h quions (), (3) nd (4) K, nd hs quions cn b solvd in n iiv wy Doin his mnully, is vy im consumin Wihou l influnc on h ccucy howv, hs quions cn b simlifid by ssumin h: << C 4 5 K C 3 hn, quions () nd (3) duc o: nd = + 5 K = K Equion (5) Equion (6) Fiu Mnouv nsfomion Bcus of nsin ffcs, h scond nd h hid iod of h im hisoy hs o b usd o dmin mn vlus of, &,, nd, bin h vlus fo n idl mnouv Howv, whn suosin h & & = =, wo ddiionl cocions hv o Fom divions in h Andix follows: = 4 + λ K + 5 K = 4 + λ K Equion (7) 3

4 In quion (7) is λ funcion of K only, s fiu 4 Also follows fom h divions in h Andix h / is funcion of K only, s fiu 4 hus, wih known idl vlus of,, nd, h cofficins K nd cn b found fom quions (5), (6) nd (7) by siml nd fs iion h followin ocdu ovids h cofficins K nd in vy quick nd siml wy: As fis uss fo / : ino 5 K in quion (6) A /, fiu 4 ovids now K nd λ 3 Equion (7) ovids 4 Fom K nd follows K 5 Usin quion (6), his ocdu will b d fom s wih nw uss fo / h ocdu will b mind s K nd do no chn nymo Dlf Univsiy of chnoloy, h Nhlnds Nomoo (96) K Nomoo, Anlysis of Kmf s Sndd Mnouv s nd Poosd Sin Quliy Indics, Fis Symosium on Shi Mnouvbiliy, DRC Ro 46, Ocob 96 9 Andix Fom h quion of moion, ivn in quion (), i cn b found fo & = nd = (s fiu 3): nd & = & = + K + & K ( ) Equion (8) ( ) / ( ) Fom quions (8) nd (9) follows: = + & K Equion (9) / ( ) / ( ) Equion () 7 Acknowldmn h uho is vy ful o M G vn Luwn fo his suo whn solvin mhmicl oblms duin h nlysis of his fis od sysm 8 Rfncs Jouné (97) JMJ Jouné, En nvoudi mhod blin vn d mnouv-indics K n ui zi-z ovn, Ro 67, 97, Shi Hydomchnics Lbooy, Fiu 3 Infini Rudd R of un Vlus : Fom quion (8) follows: 4

5 & = & + K ( ) Inoin h nsin ffcs yilds: & = & hus: & = K + Equion () Fom quion (9) follows: Bcus & = + & K = + ( ) ( ) nd + K = = is: ( ) / ( ) Equion () Fom quions () nd () follows: = + K + Whn nmin: = λ, hn λ is + funcion of, bcus: = hn h followin lion s fo : 4 = + 4λ K Equion (3) Fom h quions bov follows h λ, nd K funcions of h oduc In fiu 5, hs bn lod ins wih K s m Equion (3) nd 4 his fiu show h = fo = K nd h = fo K = Vlus : Fom quion (8) follows: & = & Bcus & = is: & + K ( ) = K ( ) Equion (4) hn, fom quions () nd () follows h: λ = = + Bcus λ is funcion of h oduc K, lso will b funcion of K Fom quion () follows h: = K hus, bcus = + ( ) / = is: nd ( ) = K Equion (5) Bcus is funcion of K, lso will b funcion of K Fiu 6 shows s funcion of K Equion (5) nd his fiu show h = fo = nd h = fo K = 5

6 Howv, fom h vious follows oo h boh K nd λ funcions of In fiu 4, lod ins K nd λ hv bn Fiu 4 Pms λ nd s Funcion of K 6

7 Fiu 5 Piod s Funcion of K nd 7

8 Fiu 6 nsf Funcion s Funcion of K 8

9 Fiu 7 Cocion Cofficins 9