INTERNATIONAL STANDARD ISO 13643-1 Second edition 2017-02 Ships and marine technology — Manoeuvring of ships — Part 1: General concepts, quantities and test conditions Navires et technologie maritime — Manoeuvres des navires — Partie 1: Notions générales, grandeurs et conditions d’essais Reference number ISO 13643-1:2017(E) © ISO 2017 ISO 13643-1:2017(E) COPYRIGHT PROTECTED DOCUMENT © ISO 2017, Published in Switzerland All rights reserved Unless otherwise specified, no part o f this publication may be reproduced or utilized otherwise in any form or by any means, electronic or mechanical, including photocopying, or posting on the internet or an intranet, without prior written permission Permission can be requested from either ISO at the address below or ISO’s member body in the country o f the requester ISO copyright o ffice Ch de Blandonnet • CP 401 CH-1214 Vernier, Geneva, Switzerland Tel +41 22 749 01 11 Fax +41 22 749 09 47 copyright@iso.org www.iso.org ii © ISO 2017 – All rights reserved ISO 13643-1:2017(E) Page Contents Foreword iv Scope Normative references Terms and definitions Axis systems 4.1 4.2 4.3 Position coordinates Angles 6.1 6.2 6.3 General Earth-fixed axis system Ship-fixed axis system Angles o f flow 6.1.1 Angle of attack 6.1.2 Drift angle Angles o f flow at parts o f the ship Eulerian angles 6.3.1 General 6.3.2 Nodal axes 6.3.3 Eulerian angles between earth-fixed and ship-fixed axis systems General quantities 7.1 7.2 Physical quantities Geometrical quantities 7.2.1 Symbols for manoeuvring 7.2.2 Additional and alternative indices 15 7.3 Mass quantities 17 7.4 Velocities and accelerations 18 7.5 Forces, moments and their coe fficients 18 7.6 Control quantities 20 7.7 Propulsion 21 7.8 Derivatives 23 7.9 Dynamic stability 25 7.9.1 General 25 7.9.2 Dynamic stability o f the coupled dri ft, yaw and roll motion (horizontal plane) 25 7.9.3 Dynamic stability o f the coupled heave and pitch motion (vertical plane) 27 7.10 External disturbances 28 General test conditions, documentation 29 8.1 General 29 8.2 Environment 29 8.3 Ship 30 8.4 Test reports 31 8.5 Model tests 31 Annex A (informative) Alphabetical list of symbols 33 Bibliography 41 © ISO 2017 – All rights reserved iii ISO 13643-1:2017(E) Foreword ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies (ISO member bodies) The work o f preparing International Standards is normally carried out through ISO technical committees Each member body interested in a subject for which a technical committee has been established has the right to be represented on that committee International organizations, governmental and non-governmental, in liaison with ISO, also take part in the work ISO collaborates closely with the International Electrotechnical Commission (IEC) on all matters o f electrotechnical standardization The procedures used to develop this document and those intended for its further maintenance are described in the ISO/IEC Directives, Part In particular the different approval criteria needed for the di fferent types o f ISO documents should be noted This document was dra fted in accordance with the editorial rules of the ISO/IEC Directives, Part (see www.iso org/directives) Attention is drawn to the possibility that some o f the elements o f this document may be the subject o f patent rights ISO shall not be held responsible for identi fying any or all such patent rights Details o f any patent rights identified during the development o f the document will be in the Introduction and/or on the ISO list of patent declarations received (see www.iso org/patents) Any trade name used in this document is in formation given for the convenience o f users and does not constitute an endorsement For an explanation on the meaning o f ISO specific terms and expressions related to formity assessment, as well as information about ISO’s adherence to the World Trade Organization (WTO) principles in the Technical Barriers to Trade (TBT) see the following URL: www.iso.org/iso/foreword.html The committee responsible for this document is ISO/TC 8, Ships and marine technology, Subcommittee SC 6, Navigation and ship operations This second edition cancels and replaces the first edition (ISO 13643-1:2013), o f which it constitutes a minor revision with the following changes: — Table , CC-Code VK symbol “N” to “ν”; — Table , CC-Code RHOWA symbol “P ” to “ρ”; — Table , CC-Code OMN symbol “Ω” was changed to “ω”; — 7.9.2, Equations (1) and (2) in the last term Symbol “φ” was changed to “ϕ”; — 7.9.3 , third sentence of the subclause “where as q = θ and q = θ well as w = z and w = z ” was changed to “where q = θ and q = θ as well as w = z and w = z ”; — 8.2 “a) stopping test” has been inserted A list of all parts in the ISO 13643 series can be found on the ISO website iv © ISO 2017 – All rights reserved INTERNATIONAL STANDARD ISO 13643-1:2017(E) Ships and marine technology — Manoeuvring of ships — Part 1: General concepts, quantities and test conditions Scope This document applies to manoeuvring tests with surface ships, submarines and models T h i s c u ment defi ne s concep ts , s ymb ol s and te s t cond ition s s tituti ng genera l fu ndamenta l s wh ich are to be applied for the description and determination of certain ship manoeuvring characteristics to ge ther with the re s p e c tive te s t- s p e ci fic phys ic a l qua ntitie s conta i ne d i n I S O 43 -2 to I S O 43 - T he Normative references fol lowi ng c u ments are re ferre d to i n the tex t i n s uch a way th at s ome or a l l o f thei r content s titute s re qu i rements o f th i s c u ment For date d re ference s , on ly the e d ition cite d app l ie s For u ndate d re ference s , the late s t e d ition o f the re ference d c ument (i nclud i ng a ny amend ments) appl ie s ISO 19019, Sea-going vessels and marine technology — Instructions for planning, carrying out and reporting sea trials Terms and definitions For the pu r p o s e s o f th i s c u ment, the fol lowi ng term s and defi n ition s apply ISO and IEC maintain terminological databases for use in standardization at the following addresses: — IEC Electropedia: available at http://www.electropedia org/ — ISO Online browsing platform: available at https://www.iso org/obp/ 3.1 manoeuvring manoeuvres all (3.2), manoeuvring tests (3.3) and tests or other methods, such as computations, simulations, etc to establish manoeuvring characteristics N o te to entr y: M a no eu vr i ng i nclude s me a s u re s to m a i nta i n c r u i s i ng co nd ition s u nder e x ter n a l d i s tu rb a nce s 3.2 manoeuvre ship operation measures to change course and/or speed, and in case of submarines, depth N o te to entr y: S p e c i a l ac tio n s ta ken , e g included fo r c a s ti ng- o ff, tu r n i ng a s ide or re s c u i ng ( p ers on o ver b o a rd) , a re 3.3 manoeuvring test test conducted with a full-scale ship, submarine or a model to determine and evaluate the manoeuvring characteristics under standardized conditions N o te to entr y: M a no euvr i n g te s ts a re o ften s i m i l a r to m a no euvre s , but orga n i z e d i n s uch a m a n ner th at, a s fa r a s p o s s ib le , s p e c i fic m a no euvr i n g ch a rac ter i s tic s c a n b e me a s u re d i nd i vidu a l l y © ISO 2017 – All rights reserved ISO 13643-1:2017(E) 3.4 CC-Code computer compatible symbols introduced by the 14th International Towing Tank Conference 3.5 manoeuvring device rudder, azimuthing thruster, hydroplane, cycloidal propeller or equivalent system used to manoeuvre (3.2) a vessel Axis systems 4.1 General Axis systems are three-dimensional, orthogonal, right-handed systems Earth-fixed and ship-fixed axis systems are defined in Tables and 4.2 Earth-fixed axis system Table — Symbols and their definitions for the earth-fixed axis system Symbol O0 a CC-Code ORIG0 SI-Unit Term Position Positive sense — Origin, earth-fixed Arbitrary, but pre ferably — Origin, ship-fixed Pre ferably according to — O ORIG — y0 x0 X0 Y0 z0 Z0 in the water surface m m (moving with the ship) Table — In the horizontal plane a Transverse axis In the horizontal plane a Right-handed m Vertical axis Down Assuming earth or water surfaces to be plane In the direction o f gravity Arbitrary system with x0 , z0 4.3 Ship-fixed axis system Table — Symbols and their definitions for the ship-fixed axis system Symbol O x y z CC-Code ORIG X Y Z SI-Unit Term — Origin, ship fixed m m m Longitudinal axis Lateral axis Normal axis Position For surface ships in CL at the height of DWL at MP For submarines on MA in the lateral plane of B∇ In CL or MA Perpendicular to CL In CL Positive sense — Forward Starboard Right-handed system with x and y (under normal cruising conditions down) © ISO 2017 – All rights reserved ISO 13643-1:2017(E) Position coordinates Table — Symbols and their definitions for position coordinates o f points under consideration Symbol a CC-Code SI-Unit Concept x ( ) a X ( ) a m Longitudinal position y ( ) a Y ( ) a m Lateral position z ( ) a Z ( ) a m Normal position ( .) = S up p lement to s ymb o l/C C - C o de b y co de le tte rs Code letters for the following special points: A antenna (reference point); B Definition or explanation Term Distance between point under consideration and origin O measured parallel to the ship’s longitudinal axis (see Table 2), positive if point under consideration is forward of origin O Distance between point under consideration and origin O measured parallel to the ship’s lateral axis, positive if point under consideration is starboard of origin O Distance between point under consideration and origin O measured parallel to the ship’s normal axis, positive if point under consideration is below origin O fo r p o i nts u nder co n s ideratio n centre o f b uo ya nc y (s tatic) ; BB bow plane (reference point); F s tab i l i s i n g fi n (re ference p o i nt) ; G centre o f g ravit y; L lateral area below waterline (centre of area); LV lateral area above waterline (centre of area); P propeller (reference point); R manoeuvring device (reference point); S stern plane (reference point); T thruster (reference point) EXAMPLE zR resp ZR: Normal position of manoeuvring device (reference point) © ISO 2017 – All rights reserved ISO 13643-1:2017(E) 6 Angles A 6.1.1 n g l e s o f f l o w Angle of attack T a b l e — S y m b o l a n d d e f i n i t i o n f o r t h e a n g l e o f a Concept Symbol α CC-Code SI-Unit ALFA rada Term D e f i n i t i o n o r explanation Angle of attack t t a c k Axis of rotation Measurement plane y xz Angle by which the projection o f the direction of heading through the water upon CL has to be turned about lateral axis y, such that it coincides with the x-axis arctan w u arcsin a w u2 + w2 For angles, the unit ° (degree) may be used 6.1.2 Drift angle T a b l e — S y m b o l a n d d e f i n i t i o n f o r t h e d Concept Symbol β CC-Code BET SI-Unit rada Term Drift angle D e f i n i t i o n o r explanation Angle to the principal plane of symmetry from the vector of the ship’s speedb relative to the water, positive in the positive sense of rotation about the z-axis arctan – v arcsin u r i f t a n g l e Axis of rotation Measurement plane z xy –v u2 + v2 a b For angles, the unit ° (degree) may be used Re ference point for the path through the water within the ship usually is the origin O o f the ship-fixed axis system © ISO 2017 – All rights reserved according to Table ISO 13643-1:2017(E) A n g l e s o f f l o w a t p a r t s o f t h e s h i p T he defi n ition o f angle s o f flow at p ar ts o f the sh ip i s to as far fol low from a s p o s s ible T hei r s ymb ol s are to b e derive d subscripts (for a selection, see Table 3) EXAMPLE αS angle of attack at stern plane (see Table 4) βR drift angle at manoeuvring device (see Table 5) 6.3 6.3.1 the defi nition o f the sh ip’s angle s o f flow tho s e i n 6.1.1 and 6.1.2 b y me an s o f s u itable Eulerian angles General Eulerian angles are described in Figure and Tables and 6.3.2 Nodal axes I n th i s s ub clau s e, the ro tationa l p o s ition o f two a xi s s ys tem s relative to one ano ther i s de s c rib e d by Eu leria n angle s wh ich a re defi ne d with the a id o f no da l a xe s (s e e T Symbol k1 k2 k3 a b l e — S y m b o l s a n d D e t h f i n e i i t r i o d n e f i o r n e i t x i p o l n a s n Table 6) a f o t i r o n o d a l a x e s n f x onto the horizontal x0 y0 -plane Positioned with respect to y0 as k1 to x0 f z0 onto yz-plane P roj e c tion o the lo ngitud i n a l a xi s P roj e c tion o ver tic a l a xi s © ISO 2017 – All rights reserved ISO 13643-1:2017(E) Key plane xz0 plane xy plane x0 y0 F i g u r e — A n g l e s b e t w e e n e a r t h - f i x e d a n d s h i p - f i x e d a x i s s y s t e m © ISO 2017 – All rights reserved ISO 13643-1:2017(E) For submerged vessels at large distances from the surface and the bottom (e.g submarines): Z z = Zθ = Mz = (27) The general solution for z and θ σ1 , σ2 and σ3 can be obtained from the following third-order equation: c an then b e re duce d by one term e ach T he s tabi l ity i nd ice s (28) B3 σ + B σ + B1 σ + B = In this case: B3 = ( m − Z w ) ( I yy − M q ) − ( mx G + M w ) ( mx G + Z q ) B2 = (29) ( m − Zw ) ( mux G − Mq ) − ( mu + Zq ) ( mx G + Mw ) − Zw ( I yy − Mq ) − Mw ( mx G + Zq ) (30) and B1 and B0 are: B1 = − Mθ ( m − Z w ) + Z w ( mux G − M q ) − M w ( mu + Z q ) (31) (32) B0 = Z w Mθ T he s tabi l ity cond ition i s unchange d for σ1 , σ2 and σ3 the s tabi l ity i nd ice s 7.10 External disturbances T Symbol a b l e CC-Code — S y m b l s a n HS m ψU PSICU rada PSIWA rada d t h e i r d e f i n i t i o n s f o r e x t e r n a l d i s t u r b a n c e Concept SI-Unit HS ψ WA o Term D Wave direction f i n i t i o n o r e x p l a n a t i o n — S ign i fic a nt wave height Current direction e D i re c tion to wh ich the c u r rent flows , rel ative to a n e a r th- fi xe d a xi s s ys tem Mean direction to which the waves p ro gre s s , rel ative to a n e a r th-fi xe d a xi s s ys tem a 28 Fo r a n gle s , the u n i t ° (de g re e) m ay b e u s e d © ISO 2017 – All rights reserved ISO 13643-1:2017(E) Table 17 (continued) Symbol CC-Code SI-Unit ψ WR PSIWREL rad a ψ WT PSIWABS rad a Concept Term Relative wind direction D e f i n i t i o n o r e x p l a n a t i o n Direction from which the wind b lows , rel ati ve to s h ip -fi xe d a xi s s ys tem True wind direction Direction from which the wind blows, relative to a n e a r th-fi xe d a xi s s ys tem ψ + ψ WR + arcsin − a 8.1 V K V WT sin (ψ WR + β ) Fo r a n gle s , the u n it ° (de g re e) m ay b e u s e d General test conditions, documentation General T he cond ition s wh ich genera l ly apply to a l l mano euvri ng te s ts accord i ng to the I S O 43 s erie s a re compi le d here b e c au s e they form a re c u rrent p a r t o f the c u mentation T he re qu i rements la id down in ISO 19019 shall also be taken into consideration 8.2 Environment For ver y c a l m cond ition s (wi nd force no t exce e d i ng B e au for t ) , te s ts may b e s tar te d i n any d i re c tion With the wind force exceeding Beaufort 2, the approach is to be made into the wind for a) stopping test, b) coasting stop test, c) acceleration test, d) turning circle test, e) accelerating turn test, f) astern test, g) zig-zag test, and h) sine test © ISO 2017 – All rights reserved 29 ISO 13643-1:2017(E) I n genera l, it i s to b e e xp e c te d that te s ts at or ne ar the s ur face are a ffe c te d on ly margi na l ly or to s uch an ex tent that corre c tion b y averagi ng c an b e appl ie d s ucce s s fu l ly, provide d the s ign i fic ant wave height is HS L and the wind speed VWT V0 f f the approach to the test runs should be into the wind For the turning test with thrusters and for the traversing test, which are performed in both directions, i.e into and with the wind, a higher wind ≤ , 01 are a n i n herent element o ≤ (or the me an s p e e d i n te s ts where maj or s p e e d cha nge s the i nd ividua l ru n) , re s p e c tively I the s e a cond ition i s dom i nate d b y s wel l , s p e e d may b e accep table (s e e T h ru s ter tu rni ng te s t I S O 43 – and Travers i ng te s t 43 – 4.4, re s p e c tively) Sp e ci fie d l i m it cond ition s may b e exce e de d to a de gre e, provide d a corre c tion/i nterpre tation me tho d i s agreed beforehand Water dep th i n the te s ts are a shou ld a lways exce e d five ti me s the me a n d raught o f the s h ip, e xcep t that the te s ts s er ve s p e ci fic a l ly the de term i nation o f mano euvrabi l ity at l i m ite d water dep th It is preferable that manoeuvring tests are performed in sea areas with low current velocities Wave height and direction, wind speed and direction (see Table 17) and water depth prevailing during the individual test are to be recorded The description of each ship test according to the ISO 13643 series shall contain the following data or documents, as a minimum requirement: — s e a are a, p o s s ibly a char t s e c tion; — dep th, temp eratu re, and den s ity o f the water; — d i re c tion a nd velo city o f the c urrent; — wi nd d i re c tion and velo c ity; — observed sea state 8.3 Ship For each ship under ship test conducted, in addition to the requirements of ISO 19019, the following data are to be recorded once for a related sequence of similar tests: a) identi fic ation d ata; b) principal dimensions; c) nu mb er, typ e and d i re c tion o f ro tation o f prop el lers; d) nu mb er and typ e o f mano euvri ng device s/ hyd ropla ne s; e) p o s ition o f prop el lers and ma no euvri ng device s/ hyd roplane s; f) typic a l rate o f mano euvri ng device s/ hyd ropla ne movements; g) s p e ci a l ma no euvri ng s ys tem s; h) appendages on subsurface hull, e.g 1) bilge keels; 2) shaft bossings; 3) shaft struts; 4) sonar dome, including its operational conditions; 30 © ISO 2017 – All rights reserved ISO 13643-1:2017(E) 5) s tabi l i z i ng fi n s , i nclud i ng thei r op erationa l cond ition s; i) flo ati ng cond ition (d i s placement mas s , d raughts , he el) ; j) i f mano euvri ng p er formance as a n excep tion h as to b e p er forme d at a deviati ng d i s placement, i e ballast condition instead of full-load, a correction scheme has to be agreed, e.g based on model tests or simulations; k) dived depth of submarines; l) position of antenna; m) position of echo sounder transducer Pa rame ters wh ich va r y du ri ng a te s t s erie s , s uch a s s tabi l ity p ara me ters , d raughts and s ubmari ne’s d ive d dep th, are to b e re corde d s ep a rately 8.4 for e ach te s t ru n Test reports The results of ship tests should be reported using the formats of the annexes of ISO 19019 8.5 Model tests For mo del te s ts , the fol lowi ng te s t cond ition s apply: a) Model scale M o del s c a le i s to b e s ele c te d i n s uch a way that mo del s i z e and mo del Reynold s numb ers are as large as possible It is to be observed that for Froude numbers (see Table 8) of more than 0,25, re s u lts are no tice ably i n fluence d b y wave e ffe c ts For wi nd tun nel te s ts , the blo ckage ratio s l l b e le s s th an % and the Reynold s numb er no t le s s than × 10 b) D i men s iona l acc u rac y For ship models, the deviations from the nominal offsets shall not exceed ±0,25 % For dimensions of less than 200 mm, deviations shall be less than ±0,5 mm This refers also to appendages as shaft bossings, bilge keels, bow bulbs and sonar domes as well as for hull openings (e.g for thrusters) For pro fi le d app endage s s uch as s ft bracke ts , no z z le s , fi n s , e tc , the devi ation s from the nom i na l offsets are to be not more than ±0,2 mm For rudders on which measurements are performed, attempts should be made to achieve deviations from the nominal of not more than ±0,1 mm c) Materials M o del s for s ur face ve s s el s for tan k te s ts s l l b e made o f wo o d or s ynthe tic materi a l; s ubmari ne mo del s sh a l l b e made o f wo o d, s ynthe tic materi a l or me ta l For app endage s , wo o d (e g te a k) , s ynthe tic materia l s or me ta l may b e u s e d d) Sur face fi ni sh Ta n k mo del s and thei r app endage s s hou ld b e hyd rau l ic a l ly s mo o th, i e roughness height of the surface and kperm = 10 ν/V, where ν speed representative for the test For wind tunnel tests, all edges shall be kept sharp © ISO 2017 – All rights reserved k < kperm Here, k is the V is the i s the ki nematic vi s co s ity a nd 31 ISO 13643-1:2017(E) e) Stabi l ity a nd i ner ti a For ma no euvri ng te s ts with of inertia (see Table 11 f) Propeller fre e -ru n n i ng mo del s , the tra n s vers e s tabi l ity and the ma s s moments ) a re to b e adj u s te d a s clo s e a s p o s s ible to tho s e o f the ve s s el I f no mo del s o f the fi na l prop el lers a re avai lable, s to ck prop el lers may b e u s e d te s ts G e ome tr y and p er formance data (s e e fi na l prop el ler T he ma i n p a rame ters have to b e given the fol lowi ng 1) diameter; 2) number of blades; 3) pitch ratio; 4) area ratio g) Test data For each model under test, indications a) to i) according to 8.3 shall be recorded once for a related series of similar tests: 1) model scale; 2) water temperature; 3) towing tank dimensions; 4) water depth 32 for the mano euvri ng Table 15) should be as close as possible to those of the ran ki ng: a nd add itiona l ly the fol lowi ng data © ISO 2017 – All rights reserved ISO 13643-1:2017(E) Annex A (informative) Alphabetical list of symbols Table A.1 — Alphabetical list of symbols Symbol A AC AE AL A LT A LV AM AP AR A RF A RP A RT A RX A SK AX A0 B B BB BDWL BL BÑ b bR bRF bRT bRX b SK C CL CC-Code Key word A AC AE AL ALT ALV AM AP ARU ARF ARP ART ARX ASK AX A0 B Reference point of antenna Canal cross section Blade area, propeller Lateral area below waterline Cross section of lateral thrust unit Lateral area above waterline Midship section area After perpendicular Rudder area Flap area Rudder area in the propeller race Total rudder area Fixed post area of a rudder Skeg area Maximum transverse section area Propeller disc area, propeller swept area Breadth B C entre o f b uoya nc y BDWL BL — SP SPRU SPRUF SPRUT SPRUX SPSX FNORM CL © ISO 2017 – All rights reserved Reference point of bow plane Breadth of design waterline Baseline C entre o f b uoya nc y o f for m Cross force Centreline plane 21 20 21 9 d i s p l acement Rudder span Rudder span Flap span for a rudder Total rudder span Fixed post span for a rudder Skeg span C Page 10 19 10 33 ISO 13643-1:2017(E) Table A.1 (continued) Symbol Q* T CTH CT * C C c c m mR c mRF c mRT c mRX c mSK cR cRF cRT cRX cr c rR c rRF c rRT c rRX c rSK c SK ct c tR c tRF c tRT c tRX c tSK c c D DWL d h F eR e F n n F F h nÑ F 34 CC-Code CQS CT CTH CTHS CH CHP CHME CHMERU CHMERUF CHMERUT CHMERUX CHMESK CHRU CHRUF CHRUT CHRUX CHRT CHRRU CHRRUF CHRRUT CHRRUX CHRSK CHSK CHT CHTRU CHTRUF CHTRUT CHTRUX CHTSK DP DWL DH EXF EXR Key word Torque co e ffic ient To ta l re s i s ta nce co e ffic ient 21 T h r u s t lo ad i ng co e ffic ient T h r u s t co e ffic ient Chord length, general Chord length of propeller blade Mean chord length, general Mean rudder chord length M e a n fl ap chord leng th fo r 10 21 a r udder Mean total rudder chord length M e a n fi xe d p o s t chord len g th for Propeller diameter Design waterline Hub diameter 10 a r udder Mean skeg chord length Rudder chord length Flap chord length for a rudder Total rudder chord length Fixed post chord length for a rudder Rudder root chord length, general Rudder root chord length Flap root chord length for a rudder Total rudder root chord length Fixed post root chord length for a rudder Skeg root chord length Skeg chord length Tip chord length, general Rudder tip chord length Flap tip chord length for a rudder Total rudder tip chord length Fixed post tip chord length for a rudder Skeg tip chord length D 11 12 21 12 21 E C o ntrol p oi nt e ccentr ic ity o f c ycloid a l p rop el ler F Re ference p o i nt o f s tabi l i s i ng fi n FN FH FV Page Froude number 20 © ISO 2017 – All rights reserved ISO 13643-1:2017(E) Table A.1 (continued) Symbol FP f G GM g HS h hm lxx lyy lzz lxy lyz lzx J JV K K KG KP KPC KQ KQC KR KT KTC Kp Kp Kr Kr Kv Kv Kφ dyn CC-Code FP F — GM G HS DE DEME IXX IYY IZZ IXY IYZ IZX ADVC ADVCV MX — KG KP KPC KQ KQC MXR KT KTC DKDP DKDPT DKDR DKDRT DKDV DKDVT DKDPHDY © ISO 2017 – All rights reserved Key word Fore perpendicular Camber of a foil Page 12 G Centre o f gravity 12 Metacentric height Acceleration due to gravity Wave height Water depth H 28 I Moment of inertia about x-axis Moment of inertia about y-axis Moment of inertia about z-axis 17 Product of inertia J 21 Advance coe fficient Moment about x-axis Keel reference K Centre o f gravity above keel re ference 19 12 Power coe fficient 21 Torque coe fficient Thrust coe fficient 22 19 22 Derivative 24 Manoeuvring device moment about x-axis 35 ISO 13643-1:2017(E) Table A.1 (continued) Symbol kxx kyy kzz k1 k2 k3 CC-Code RDGX RDGY RDGZ — — — L L L L LF FL LDWL LPP LDWL LPP L LV M M MA MP MR Mq Mq Mw Mw Mz Mθ m N NR Np Np Nr Nr Nv Nv Nφ n n LT Key word Radius of inertia about x-axis Radius of inertia about y-axis Radius of inertia about z-axis Nodal axis 17 L Length Blade length D yn a m ic l i ft Page fo rce Centre of lateral area below waterline Length of design waterline Length between perpendiculars Centre of lateral area above waterline M 12 22 19 12 MY — MAX — MYR DMDQ DMDQT DMDW DMDWT DMDWP DMDZ MA Moment about y-axis Metacentre Main axis Mid between perpendiculars Manoeuvring device moment about y-axis 19 12 Derivative 24 Ship’s mass MZ MZR DNDP DNDPT DNDR DNDRT DNDV DNDVT DNDPHI N NLT Moment about z-axis Manoeuvring device moment about z-axis 19 Derivative 24 Rate of revolution, general Rate of revolution of lateral thrust unit 20 19 N O 36 © ISO 2017 – All rights reserved ISO 13643-1:2017(E) Table A.1 (continued) Symbol O O0 P P P P B PD P PH LT PS PSLT P p p F R p p Q R Q RF Q q q R R R R R n T r r S S S AP SBH S s T T T CC-Code ORIG ORIG0 P PITCH PB PD PH PITCHLT PS PSLT OMX OXRT PPFR PPRR Q QRU QRUF OMY OYRT R RDP RN RT OMZ OZRT S SAP SBH SP T TH © ISO 2017 – All rights reserved Key word Origin Page P Power Propeller pitch Port (side) Reference point of propeller Power Pressure hull Propeller pitch of lateral thrust unit Power Power of lateral thrust unit Roll velocity 22 12 22 12 20 22 20 18 Roll acceleration Relative propeller pitch o f cycloidal propeller Q 20 Torque Torque on manoeuvring device stock 22 19 Angular acceleration about -axis 18 Torque on flap stock Angular velocity about y-axis y R Resistance Propeller radius Reference point of manoeuvring device Reynolds number Resistance Angular velocity about z-axis Angular acceleration about -axis z S Wetted surface Reference point of stern plane Starboard (side) Wetted surface of appendages Wetted surface of bare hull Track length T Draught Reference point of thruster Propeller thrust 19 22 22 18 22 12 22 12 22 37 ISO 13643-1:2017(E) Table A.1 (continued) Symbol TA TDWL TF t t t tR tRF tRT tRX tSK t°A t° W u u u V VA VK VU VWR VWT V0 v v W WL w w w wB wS X XR x x0 x( ) 38 CC-Code TA TDWL TF TI THDF TMX TMRU TMRUF TMRUT TMRUX TMSK TEAI TEWA UP VX VXRT V VA VKA VCU VWREL VWABS V0 VY VYRT WT WL WFT VZ VZRT WCANB WCANS FX FXR X X0 X( ) Draught Design draught Draught Time Thrust deduction fraction Key word Page 12 22 P ro fi le th ickne s s Rudder thickness Flap thickness Rudder thickness Rudder thickness Skeg thickness Temperature 13 U C i rc u m ferenti a l velo c ity L on gitud i n a l velo c ity Longitudinal acceleration Ship’s speed Speed of advance Speed over ground V 22 18 22 C u r rent velo c ity Rel ati ve wi nd velo c ity 18 Tr ue wi nd velo c ity Initial speed L atera l velo c ity Lateral acceleration Ship’s weight Waterline Taylo r wa ke W frac tio n N or m a l velo c ity Normal acceleration Bottom width of canal Surface width of canal 13 22 18 13 X Longitudinal force Longitudinal manoeuvring device force Axis Longitudinal position 19 © ISO 2017 – All rights reserved ISO 13643-1:2017(E) Table A.1 (continued) Symbol CC-Code Key word Page Y FY FYR DYDP DYDPT DYDR DYDRT DYDV DYDVT DYDPHI Y Y0 Y( ) Lateral force Lateral manoeuvring device force Normal force Normal manoeuvring device force Number of propeller blades 19 22 Derivative 25 z( ) FZ FZR NBP DZDQ DZDQT DZDW DZDWT DZDZ DZDTP Z Z0 Z( ) Axis Normal position α ALFA Angle of attack β β* BET BETS Drift angle Effective advance angle 23 Δ ΔF δB δR δRF δRO δS δ0 DISPM DISPF ANB ANRU ANRUF ANRUOR ANS ANRU0 Displacement mass Displacement force Bow plane angle Manoeuvring device angle Y YR Yp Yp Yr Yr Yv Yv Yφ y y0 y( ) Z ZR Z Zq Zq Zw Zw Zz Zθ z z0 © ISO 2017 – All rights reserved 19 24 Derivative 25 Axis Lateral position Z α β Δ Rudder fl ap a ngle Manoeuvring device angle, ordered Stern plane angle Neutral manoeuvring device angle 20 39 ISO 13643-1:2017(E) Table A.1 (continued) Symbol η ηB ηD ηH ηR ηS η0 Θ θ θS ΛR λ λ λR ν Key word η E fficiency E fficiency Propulsive e fficiency Hull e fficiency Relative rotative e fficiency E fficiency E fficiency 23 TETAM TETP TRIMS Polar moment of inertia Pitch angle Trim angle 23 ASRU ADVR SCALE TARU Rudder aspect ratio Propeller advance ratio Scale Rudder taper 13 23 13 VK RHOWA RHOAI σ — Θ Λ ν Kinematic viscosity Density Stability index Σ Φ Roll angle Heel (blank) angle ψ PSIH PSIY PSICU PSIWA PSIWREL PSIWABS YART Heading Yaw angle Current direction Wave direction Relative wind direction True wind direction ω OMN ψ ψU ψ WA ψ WR ψ WT Ñ ∇ AP ∇ LB ∇ SP DISPV DISPVAP DISPVLB DISPVSP ρ PHIR HEELANG ϕ ϕS Page ETA ETAB ETAD ETAH ETAR ETAS ETA0 ρA ρ 40 CC-Code Ψ Yaw velocity Angular velocity 25 to 28 Ω Ñ Displacement volume Displacement volume 28 29 18 13 14 Lost buoyancy volume Displacement volume © ISO 2017 – All rights reserved ISO 13643-1:2017(E) Bibliography [1] [2] ISO 80000-1, Quantities and units — Part 1: General ISO 80000-3, Quantities and units — Part 3: Space and time © ISO 2017 – All rights reserved 41 ISO 13643-1:2017(E) ICS 47.020.70 Price based on 41 pages © ISO 2017 – All rights reserved