Technische Hogasdiool
Delft
S H I P B U I L D I I V G
MARINE T E C H N O L O G Y MONTHLY
CONTENTS I N F L U E N C E OF S T A R T I N G A C C E L E R A T I O N A N D TOWROPE L E N G T H O N TOWED B A R G E TRAJEC-T O R Y by R . Latorre and M . M . BernitsasA P R A C T I C A L C A L C U L A T I O N M E T H O D OF SHIP M A N E U V E R I N G M O T I O N by S. Inoue, M . Hirano, K . K i j i m a and J. Takashina
A P R A C T I C A L C A L C U L A T I O N M E T H O D O F SHIP M A N E U V E R I N G M O T I O N b y
S. Inoue*, M . Hirano** , K . K i j i m a * and J. Takashina**
Summary
This paper presents a practical calculation m e t h o d o f the ship maneuvering m o t i o n using the p r i n c i p a l par-ticulars o f ship h u l l , propeller and rudder as basic i n p u t data. The m a t h e m a t i c a l m o d e l , w h i c h describes the ship maneuvering m o t i o n , is developed e m p l o y i n g the coupled equations o f surge, sway, y a w , r o l l and p r o p e l l e r r e v o l u t i o n . C o m p u t a t i o n s are made f o r various k i n d s and types o f the merchant ships and f o r wide range o f the maneuvering characteristics. The c o m p u t e d results show satisfactory agreements w i t h the full-scale t r i a l results. I n a d d i t i o n , as an a p p l i c a t i o n study, the e f f e c t o f the loading c o n d i t i o n o n the ship maneuverability is investigat-ed t h r o u g h the s i m u l a t i o n calculations. The conclusion is t h a t the calculation m e t h o d o f the present study is v e r y u s e f u l and p o w e r f u l f o r the predictions o f the ship maneuverability at the t i m e , such as the i n i t i a l design stage etc., w h e n the p r i n c i p a l particulars o f ship h u l l , propeller and rudder are k n o w n .
1. I n t r o d u c t i o n
Recent development o f the m a r i t i m e transportat i o n has produced various transportatypes o f ships, such as h i g h -speed container carriers, r o l l - o n / r o l l - o f f ships, pure car carriers and o i l tankers f r o m handy-sized p r o d u c t carriers t o ULCCs. I n r e l a t i o n t o the problems o f the m a r i t i m e t r a f f i c safety, the diversification i n ship types o r the g r o w t h i n ship sizes, m e n t i o n e d above, has enhanced the significance o f the maneuverability as one o f the f u n d a m e n t a l performances o f ships. N a m e l y i t has become very i m p o r t a n t t o predict pre-cisely the ship maneuverability at the stage o f the ship i n i t i a l design. I n a d d i t i o n , at the t i m e o f the ship c o m -p l e t i o n , i t has become necessary t o -p r o v i d e the ma-neuvering i n f o r m a t i o n s f o r p o s t i n g i n the wheel house o f ships, as is recommended b y I M C O [ 1 ] and required b y Panama Canal Regulations [ 2 ] .
F o r these k i n d s o f purposes, the s i m u l a t i o n cal-c u l a t i o n tecal-chnique o f the maneuvering m o t i o n may be t h o u g h t to be the most u s e f u l and p o w e r f u l t o o l . Paying a t t e n t i o n t o this p o i n t , the authors have been m a k i n g extensive e f f o r t s t o develop a calculation m e t h o d to simulate the ship maneuvering m o t i o n d u r i n g the last several years [ 3 ] , [ 4 ] , [ 5 ] , [ 6 ] , [ 7 ] . I n the previous r e p o r t [ 8 ] , estimate f o r m u l a e o f the h y d r o d y n a m i c forces acting o n ship h u l l i n the ma-neuvering m o t i o n were presented, where the f o r m u l a e were given as f u n c t i o n s o f the p r i n c i p a l dimensions o f ship h u l l . Succeeding the previous r e p o r t [ 8 ] , this r e p o r t presents a practical calculation m e t h o d o f the ship maneuvering m o t i o n using the p r i n c i p a l par-ticulars o f ship h u l l , propeller and rudder, w h i c h are usually k n o w n at the i n i t i a l design stage, as basic i n p u t data.
*) Faculty of Engineering, Kyusiiu University, Fukuoka, Japan. * * ) Akishima Laboratory, Mitsui Engineering and SliipbuUding C o . , L t d . , T o k y o , Japan.
The study i n this r e p o r t consists o f three phases. A t f i r s t the m a t h e m a t i c a l m o d e l o f the ship maneu-vering m o t i o n is developed e m p l o y i n g t h e c o u p l e d equations o f surge, sway, y a w , r o l l and p r o p e l l e r r e v o l u t i o n . T h e n c o m p u t a t i o n s are made f o r t y p i c a l merchant ships covering various k i n d s and types o f ships. Comparing the c o m p u t e d results w i t h t h e results o f the full-scale trials, the v a h d i t y o f the c a l c u l a t i o n m e t h o d o f the present study is examined f o r w i d e range o f the maneuvering characteristics. I n t h e last phase, an apphcation study w i t h the c a l c u l a t i o n m e t h o d proposed i n this r e p o r t is made. The e f f e c t o f the loading c o n d i t i o n o n the ship maneuverabiUty is investigated t h r o u g h the s i m u l a t i o n calculations t a k i n g three t y p i c a l factors i n t o consideration: the d r a f t , the t r i m and the immersed r u d d e r area, w h i c h are t h o u g h t t o a f f e c t the ship maneuverabihty i n connec-t i o n w i connec-t h connec-the change o f connec-the loading c o n d i connec-t i o n .
The maneuvering m o t i o n treated i n this r e p o r t is t h a t i n calm and deep water c o n d i t i o n , and t h e ma-neuvering m o t i o n w i t h m a i n engine operation such as the crash stop maneuver is n o t i n c l u d e d here.
2. M a t h e m a t i c a l m o d e l 2.Ï. Equations of motion
The ship maneuvering m o t i o n has generally been treated as the c o u p l e d m o t i o n s i n the h o r i z o n t a l plane, namely the c o u p l e d m o t i o n s o f surge, sway and y a w , assuming t h a t the h o r i z o n t a l m o t i o n s could be separat-, ed f r o m other types o f m o t i o n . I n the d e r i v a t i o n o f the m o t i o n equations o f this study, the f o l l o w i n g considerations are p a i d t o the equations o f the h o r i -z o n t a l m o t i o n s .
1. The coupling effect due to roll
Some ships such as high-speed container carriers and r o l l - o n / r o l l - o f f ships p e r f o r m considerable r o l l i n
their maneuvering m o t i o n . The recent study by the authors [ 9 ] reveals that the maneuvering m o t i o n o f ships w i t h large r o l l m e n t i o n e d above should be cal-culated t a k i n g the c o u p l i n g e f f e c t due t o r o l l i n t o consideration.
2. The couplmg effect due to propeller revolution
I n the maneuvering m o t i o n o f full-scale ships the n u m b e r o f propeller r e v o l u t i o n varies due t o v a r i a t i o n o f b o t h the propeller torque and the m a i n engine torque even under the n o r m a l r u n n i n g c o n d i t i o n o f the m a i n engine. This f a c t m a y suggest t h a t the varia-t i o n i n varia-the n u m b e r o f propeller r e v o l u varia-t i o n should be reflected i n the calculation o f the propeller thrust and the rudder forces. N a m e l y i t m a y be considered t h a t the couphng e f f e c t due t o propeller r e v o l u t i o n o n the h o r i z o n t a l m o t i o n s can n o t be ignored.
A set o f coordinate axes w i t h origin f i x e d at the center o f gravity o f the ship (denoted w i t h G herein-a f t e r ) , herein-as shown i n Figures 1 herein-and 2, is used to describe the ship maneuvering m o t i o n . L o n g i t u d m a l and
trans-Figure 1. Coordinate system (1).
verse h o r i z o n t a l axes are represented b y the x and y-axes respectively, and the z-axis is chosen so as t o be perpendicular t o the JcjF-plane ( d o w n w a r d positive). B y reference t o this coordinate system G-xyz, the basic equations o f the ship maneuvering m o t i o n can be w r i t t e n i n the f o l l o w i n g f o r m t a k i n g the coupUng ef-fects due t o b o t h r o l l and propeller r e v o l u t i o n i n t o consideration [ 6 ] . Surge : m{u - vr) = Xp+ Sway : m{v + ur) = Y a w : R o l l : (1) Propeller r e v o l u t i o n : 27r/pp« = Qg+Qp
where the terms w i t h subscript H represent the h y d r o -d y n a m i c forces pro-duce-d b y the m o t i o n o f ship h u l l ( w i t h o u t propeller and r u d d e r ) and acting o n i t , and the terms w i t h subscript R represent the r u d d e r forces i n c l u d i n g the h y d r o d y n a m i c forces i n d u c e d o n ship h u l l b y r u d d e r action. T h e terms Xp, Qp and Q^ i n equation ( 1 ) represent the propeller t h r u s t , the p r o p e l -ler t o r q u e and the main engine torque respectively.
2.2. Longitudinal force acting on ship hull, propeller thrust and propeller torque
The l o n g i t u d i n a l force actmg o n ship h u l l X^ can be w r i t t e n
X j j = ~m^ü+ iiHy + X^^) vr + X{u) . ( 2 ) The added inertia terms i n equations (2) and ( 6 ) ,
namely m ^ , and J^^, can be estimated b y m a k m g use o f the estimate charts proposed b y P r o f . S. M o t o r a [ 1 0 ] . R e w r i t i n g the c o e f f i c i e n t o f the second t e r m i n e q u a t i o n ( 2 ) as + X^^ = , t h e n c,,, may have approximate value o f 0,50 - 0.75 [ 1 1 ] . The es-t i m a es-t i o n o f es-the second es-t e r m can be made b y giving an appropriate value to . The t h i r d t e r m i n e q u a t i o n (2) represents ship resistance as a f u n c t i o n o f w.
The propeller thrust Xp and the p r o p e l l e r t o r q u e Qp can be w r i t t e n
Xp={l - t p ^ ) - pn^D^KMp) 2^J^^n-pn-'D'KQ{Jp)
( 3 )
Figure 2. Coordinate system (2).
The t h r u s t c o e f f i c i e n t Kj.{Jp) and the t o r q u e coef-f i c i e n t KgiJp) can be c o m p u t e d w i t h the propeller characteristic curves as f u n c t i o n s o f the advance con-stant Jp, w h i c h is expressed as
Jp=u{\ -Wp)/(nD) . ( 4 ) T h e e f f e c t i v e propeller wake f r a c t i o n Wp, w h i c h is
-t i -t y , may generally vary i n -the maneuvering m o -t i o n f r o m t h a t i n the straight r u n n i n g c o n d i t i o n .
T h e f o l l o w i n g estimate f o r m u l a is made based o n some m o d e l experimental results [ 6 ] .
Wp = WpQ e x p ( ^ j | 3 | ) , = - 4.0 ( 5 ) where t h e e f f e c t o f the maneuvering m o t i o n o n Wp is
considered w i t h the geometrical i n f l o w angle at p r o p e l -ler p o s i t i o n /3p, w h i c h is d e f i n e d as (3^ = j3 - x'pi-' .
2.3. Lateral force and yaw moment acting on ship hull
T h e lateral f o r c e and the y a w m o m e n t acting o n ship h u l l , namely and Npj, can be w r i t t e n i n the f o l l o w i n g f o r m [ 6 ] .
= - - m^ur + Yfj^{v,r) + Y^^ivj,^)
^H = - ^z/ + ^ / / o '•) + ^ ^ 1 '-.V) ( 6 ) + [ r ^ o ( v , r ) + F ^ i ( v , r , v . ) ] x „ .
T h e terms Y j j ^ i v j ) and Nj^^ivj-) i n e q u a t i o n ( 6 ) represent the f u n d a m e n t a l f o r c e and m o m e n t w h i c h play an k n p o r t a n t part m the ship maneuvering m o t i o n . T h e authors have developed the estimate f o r -mulae o f Y^giv,r) and N^^ivj), and the results have aheady been presented i n detail i n the previous r e p o r t [ 8 ] . T h e y are summarized b r i e f l y as f o l l o w s . Y^j^iv, r) and A ' ^ g ( v , /') are expressed
YH,i^A = \pLdVHYlv' + Y ' / ^Yl^^v'\v'\
(7)
+N;^vyAN;^^/\r'\] . T h e derivatives i n equation ( 7 ) can be estimated b y k n o w i n g the p r i n c i p a l dimensions o f ship h u l l , n a m e l y L, B, d, Cg and r . The estimate f o r m u l a e f o r the hnear derivatives are given i n the f o r m
r ; = [a^k+fiCgBlD] ( 1 + è i r ' ) r ; = ^ 2 ^ ( 1 + ^ 2 ^ ' )
7v; = ^ 3 ^ ( 1 + ^ 3 7 ' )
A^; =ia^k + a^k'^){\+b^T') where
k=2dlL , T' = T/d
(8)
( 9 ) and a^, a2, , ö j , ö j , etc. are the constant. Es-t i m a Es-t e charEs-ts, as f u n c Es-t i o n s o f Es-the p r i n c i p a l dimensions o f ship h u l l , are given f o r the estimation o f the n o n -linear derivatives, where the e f f e c t o f t h e t r i m is
n o t considered. I t is advisable t o r e f e r t o the r e p o r t cited above [ 8 ] f o r t h e details o f these charts.
The terms T ^jCf . ^ v ' ) and Njjj^iv.r.^p) i n equation (6) represent the added terms due t o inclusion o f the r o l l e f f e c t . A c c o r d i n g t o the study b y the authors [ 9 ] , they can be w r i t t e n
Yjf^(v,r,^) = 0
=ipL ^dV^ [ A ^ > + A^;,^, v'W\ +
(10) The derivatives i n e q u a t i o n ( 1 0 ) can be estimated b y u t i h z i n g the results o f the study c i t e d above [ 9 ] , nam-ely
( 1 1 )
where C j , Cj and C j are the constant.
2.4. Roll moment acting on ship hull
The r o l l m o m e n t acting o n ship h u l l can be w r i t t e n KH=-J:<A - N { ^ ) - ' W - G Z { ^ ) - Y ^ - Z p j • ( 1 2 ) T h e coupling e f f e c t due t o the h o r i z o n t a l m o t i o n s o n the m o t i o n o f r o l l is r e f l e c t e d i n the f o r m o f 7 ^ • i n equation ( 1 2 ) . A s f o r the e s t i m a t i o n o f the vertical distance z^j ( f r o m G t o the p o i n t o n w h i c h 7"^ acts), one o f the authors has proposed an estimate chart [ 1 2 ] , where estimate curves o f / z ^ ( = z ^ - O G ) s h o w n i n Figure 2 are given as f u n c t i o n s o f .
2.5. Rudder forces and moments
T h e rudder forces and m o m e n t s i n c l u d i n g the h y -d r o -d y n a m i c forces a n -d m o m e n t s i n -d u c e -d o n ship h u l l by rudder a c t i o n , n a m e l y , 7 ^ , A^^ and Kj^, can be w r i t t e n i n the f o l l o w i n g f o r m [ 6 ] , [ 1 3 ] .
= - ( 1 +aj^)F^cos5 A/^ = - ( 1 +ajf)Xj^F^ cos6 Kj^ = ( 1 +a^)Zj^F^ cos5 .
( 1 3 )
I n equation ( 1 3 ) , the h y d r o d y n a m i c f o r c e i n d u c e d o n ship h u l l b y rudder a c t i o n is described i n the f o r m o f ''H^N • c o e f f i c i e n t can be estimated based o n some m o d e l e x p e r i m e n t a l results, w h i c h suggest t h a t a^ m a y be expressed as a f u n c t i o n o f Cg [ 6 ] . T h e rudder n o r m a l f o r c e can be w r i t t e n i n t h e f o r m
1 6.13X
AnV'i s i n a .
The effective rudder i n f l o v / speed and angle, namely Vj^ and i n equation ( 1 4 ) , are calculated as f o l l o w s [ 6 ] .
1. The effective rudder mflow speed Vj^
I n t r o d u c i n g the e f f e c t i v e rudder wake f r a c t i o n [ 1 1 ] , w h i c h is d e f i n e d w i t h the concept o f the r u d d e r n o r m a l force i n d e n t i t y , can be expressed i n the f o r m
= F ( 1 - w ^ ) [ 1 + ^ 2 ^ ( 5 ) ] ' / ^ ( 1 5 ) where = 1.065 f o r the p o r t r u d d e r and = 0.935
f o r the starboard rudder. The t e r m K^gis) i n equation ( 1 5 ) represents the e f f e c t o f the propeller slip-stream o n Vj^, and gis)=nK[2-(,2-K)s] sin-s)^ ( 1 6 ) where S = 1 - W ( l - W p ) / ( « P ) n =DIH ( 1 7 ) K = 0 . 6 ( 1 - W p ) / ( 1 - w ^ ) .
The estimation o f the e f f e c t i v e r u d d e r wake f r a c t i o n is made assuming t h a t i n the maneuvering m o t i o n could be c o m p u t e d b y
I^R 0 = ^pl^po = e x p ( ^ : j |3 2 ) . ( 1 8 ) The effective rudder wake f r a c t i o n w ^ ^ o f full-scale
ships m a y be o b t a m e d f r o m the results o f the m o d e l experiments i n the same manner as f o r the e f f e c t i v e propeller wake f r a c t i o n Wp^ i n the area o f the ship propulsion, namely m a k i n g use o f the technique t o estimate the full-scale value f r o m the m o d e l experi-m e n t a l results w i t h t h e concept o f the wake r a t i o . 2. The effective rudder inflow angle
T a k i n g the f l o w - r e c t i f y i n g e f f e c t i n t o consideration, can be expressed i n the f o r m
''R + « 0 - y ^ R ( 1 9 ) where /3]j is d e f i n e d as |3]j = /? - 2x'p,r'. T h e flow-r e c t i f y i n g e f f e c t m a y be consideflow-red t o be c o n s t i t u t e d by t w o kinds o f f a c t o r s . One is the flow-rectifying e f f e c t due t o ship h u l l and the o t h e r is due t o propeller, t h e n the flow-rectification c o e f f i c i e n t 7 can be w r i t t e n [ 1 4 ]
l = Cp-Cs . ( 2 0 ) The propeller flow-rectification c o e f f i c i e n t Cp is given
i n the f o r m
Cp = + 0.6v(2 - I As)sKl -s)^ A . ( 2 1 ) The ship h u l l flow-rectification c o e f f i c i e n t C^ is given i n the f o l l o w i n g f o r m based o n some m o d e l experimen-tal results [ 6 ]
Cs=K,Pk f o r ^'R^CSOIK^ C,=C,o for p;^>C,o/K, w i t h = 0.45 and C^^ = 0.5.
( 2 2 )
2.6. Main engine torque
The types o f the m a i n engine treated here are the slow-speed diesel engine and the steam t u r b i n e , and the f o l l o w i n g t o r q u e characteristics are used.
1. The slow speed diesel engine QE = \QP\ f o r l ö p l < Ö ^ M A X
Ö ^ = Ö £ M A x f o r l Ö ^ I > Ö £ M A X
-2. The steam turbine
( 2 3 )
Qr, = SHP/(27rn) ( 2 4 )
3. N u m e r i c a l results
3.1. Full-scale maneuvering trials and ship selection A t the t i m e o f the ship c o m p l e t i o n , the full-scale sea trials f o r the maneuverability such as t h e t u r n i n g test, Z-maneuver test etc. are conducted. I n this r e p o r t three kinds o f the maneuvering tests, i.e. t h e t u r n i n g test w i t h 3 5 ° rudder, the 10° - 10° Z-maneuver test and the spiral test, are taken f o r the comparison pur-pose o f the c o m p u t e d results w i t h the results o f t h e full-scale trials. N a m e l y i n order t o examine the va-l i d i t y o f the cava-lcuva-lation m e t h o d o f the present s t u d y f o r w i d e range o f the maneuvering characteristics, c o m p u t a t i o n s are made f o r the t u r n i n g m o t i o n w i t h 3 5 ° rudder, the 10° — 10° Z-maneuver and t h e spiral maneuver.
T h e ships, o f w h i c h the comparisons are made, are selected so as t o satisfy the f o l l o w i n g requirements.
1. T h e three kinds o f the maneuvering tests m e n t i o n e d above should have been conducted f o r each ship t o be selected.
2 . T h e full-scale maneuvering trials o f each ship t o be selected should have been conducted i n the e n v i r o n -m e n t a l c o n d i t i o n below the 'slight' sea a n d b e l o w 5.0 m/sec w i n d speed.
T h u s the f o l l o w i n g seven ships covering the various types and sizes o f the merchant ships, n a m e l y f r o m a general cargo boat o f 10,000-DWT class t o a U L C C , are selected f r o m ships b u i l t i n M i t s u i Engineering and S h i p b u i l d i n g Co., L t d . during the last ten years.
Ship A : high-speed container carrier Ship B : general cargo boat
Ship C : r o l l - o n / r o l l - o f f ship Ship D : pure car carrier
Ship E : b u l k carrier ( 7 0 , 0 0 0 - D W T ) Ship F : V L C C (270,00Q-DWT) Ship G : U L C C (3 7 0 , 0 0 0 - D W T )
Table 1
Principal particulars o f h u l l , propeller and rudder
ship A B C D E F G k i n d o f ship container carrier ballast cargo boat r o / r o pure car carrier b u l k carrier V L C C U L C C loading c o n d i t i o n container carrier
ballast ballast ballast ballast ballast f u U ballast f u l l h u l l Lira) 202.00 160.00 2 1 2 . 0 0 180.00 2 3 0 . 0 0 318.00 3 4 8 , 0 0 B{m) 31.20 2 3 , 5 0 3 2 . 2 6 3 2 . 0 0 32.20 56.00 63,40 dim) 6.93 5.20 6.29 6.80 7.24 20.58 9.64 21.85 T im) 1.95 3.78 1.13 1.03 1.05 0.0 3.95 0.0 0.518 0.600 0.612 0.566 0.820 0.827 0,788 0.826 rudder A^/Ld 1/48,1 1/37,7 1/50,6 1/34,8 1/47.9 1/58.6 1/34.5 1/53.5 =^ L 4 0 1.57 1.22 1,19 1.38 1.55 1.28 1,44 propeller Dim) 7.10 5.70 6.60 6.20 6.70 8.90 9.60 P/D 1.04 1.14 0.97 0.95 0.71 0.71 0.71 Z 6 4 5 5 4 5 5
The p r i n c i p a l particulars o f ship h u l l , propeller and rudder o f these ships are given i n Table 1. The steam t u r b i n e is m o u n t e d as the m a i n engine o n ship F and ship G , and the slow-speed diesel engine o n the other f i v e ships.
3.2. Numerical results and comparisons with full-scale trial results
Computations based o n the mathematical m o d e l described i n chapter 2 are made f o r the three k i n d s o f the maneuvering m o t i o n s m e n t i o n e d before, and the c o m p u t e d results are compared w i t h the results o f the full-scale trials as f o l l o w s .
1. Turning motion with 35° rudder
The c o m p u t e d results o f the t u r n i n g m o t i o n w i t h 3 5 ° rudder (the starboard t u r n i n g ) f o r a l l o f the ships selected are shown w i t h solid lines i n the f o r m o f b o t h the t u r n i n g t r a j e c t o r y and the m o t i o n time-histories i n Figures 3 - 1 8 , where the results o f the full-scale trials are also shown w i t h e m p t y circles. I t can be m e n t i o n e d f r o m these figures t h a t the c o m p u t e d results, w i t h respect t o b o t h the t u r n i n g t r a j e c t o r y and the t i m e -histories o f the heading angle, the ship speed and the n u m b e r o f propeller r e v o l u t i o n , show satisfactory agreements w i t h the results o f the full-scale trials f o r all o f the ships.
The coupling e f f e c t due t o r o l l on the h o r i z o n t a l m o t i o n s is examined f o r the t u r n i n g m o t i o n o f ship D , w h i c h p e r f o r m e d large r o l l i n her t u r n i n g m o t i o n . ( T h e m a x i m u m r o l l angle measured w i t h clinometer i n t h e
wheel house was about 1 0 ° ) , C o m p u t a t i o n s are made also f o r the case w i t h o u t i n c l u s i o n o f t h e r o l l e f f e c t , and the results are shown w i t h chain lines i n Figures 9 and 10. I t may be understood f r o m Figures 9 and 10 that the computations w i t h o u t consideration o f the r o l l e f f e c t give erroneous solutions, and t h a t t h e maneuvering m o t i o n o f a ship w i t h large r o l l should be treated together w i t h the m o t i o n o f r o l l simultaneously. The authors have aheady c o n f i r m e d this f a c t i n the study w i t h m o d e L e x p e r i m e n t s [ 9 ] . I n this r e p o r t the same f a c t is c o n f i r m e d f o r the full-scale ship.
The coupKng e f f e c t due t o propeller r e v o l u t i o n o n t h e h o r i z o n t a l m o t i o n s is examined f o r the t u m m g m o t i o n o f ship A , The c o m p u t e d results w i t h o u t i n -clusion o f the propeller r e v o l u t i o n e f f e c t are shown w i t h chain lines i n Figures 3 and 4, and p o o r agreements are seen between the c o m p u t e d and the f u l l -scale t r i a l results w i t h respect t o the time-histories o f the heading angle and the ship speed. Hence i t m a y be u n d e r s t o o d that the maneuvering m o t i o n o f t h e f u l l -scale ships should be calculated t a k i n g the c o u p l i n g e f f e c t due t o propeller r e v o l u t i o n i n t o consideration even under the n o r m a l r u n n i n g c o n d i t i o n o f t h e m a i n engine.
C o m p u t a t i o n s o f ship F are made f o r b o t h t h e f u l l l o a d c o n d i t i o n and the ballast c o n d i t i o n as s h o w n i n Figures 1 3 1 6 , I t can be recognized f r o m these f i g -ures t h a t the c o m p u t e d results w i t h the c a l c u l a t i o n m e t h o d o f the present study e x p l a i n w e l l the d i f f e r -ences o f the m o t i o n time-histories between b o t h load-i n g condload-itload-ions.
iln)
Figure 4. Time-Iiistories of lieading angle, ship speed and Figure 8. Time-histories of heading angle, ship speed and num-ber of propeller revolution in turning motion (ship A ) . num-ber of propeller revolution in turning motion (ship C).
Figure 6. Time-histories of heading angle, ship speed and num- Figure 10. Time-histories of heading angle, ship speed, roll ber of propeller revolution in turning motion (ship B). angle and number of propeller revolution in turning motion
PHEOICTION FULL SCALE TRIAL
6 '35'
4 y / L
Figure 11. Turning trajectory (ship E). Figure 15. Turning trajectory (ship F ballast).
Figure 12. Time-histories of heading angle, ship speed and Figure 16. Time-histories of heading angle, ship speed and num-ber of propeller revolution in turning motion (ship E). num-ber of propeller revolution in turning motion (ship F ballast).
«IL S H I P F ( F U L L )
PHEOICTIOII O FULL SCALE TRIAL
1 2 3 4 y / L
Figure 13. Turning trajectory (ship F full).
n / L S H I P G
PHEUICTIÜfl O FULL SCACE TRIAL
- 1 0 1 2 3 4 y / L
Figure 17. Turning trajectory (ship G).
Figure 14. Time-histories of heading angle, ship speed and num-ber of propeller revolution in turning motion (ship F full).
Figure 18. Time-histories of heading angle, ship speed and num-ber of propeller revolution in turning motion (ship G).
2. 10° — 10° Z-maneuver
C o m p u t a t i o n s o f the 10° - 10° Z-maneuver are made f o r ship A , B , C, E and G , and the results are shown i n the f o r m o f the time-histories o f the heading angle and the ship speed ( o n l y f o r ship C and ship E ) i n Figures 1 9 - 2 3 . Fairly good agreements between the c o m p u t e d and the full-scale t r i a l results can be seen i n these figures, especially w i t h respect t o the am-p l i t u d e and t h e am-phase lag i n t h e heading angle resam-ponse.
3. Spiral maneuver
C o m p u t a t i o n s o f the spiral maneuver are made f o r ship A , B , C, E and F , where t h e reversed-spiral maneuver computations are added i f necessary. T h e c o m -p u t e d results are shown i n the f o r m o f t h e steady t u r n i n g performance i n Figures 24—28. I t can be men-t i o n e d f r o m men-these figures men-thamen-t b o men-t h men-the c o m p u men-t e d and the full-scale t r i a l results are i n f a i r l y good agreements. Especially t h e c o m p u t e d results explain w e l l t h e sen-sitive behavior o f the steady t u r n i n g performance o f each ship i n t h e region o f small rudder angle.
o F U L L S C A L E T R I A L
A t ( m i n )
Figure 19.10°—10° Z-manuever response (ship A ) .
o F U L L S C A L E T R I A L
4 t ( m i n )
Figure 20.10°—10° Z-maneuver response (ship B).
o F U L L S C A L E T R I A L
O O O O O 0~S"Ö-.g ^ ^
t ( m i n )
Figure 2 1 . 10°—10° Z-maneuver response (ship C).
O F U L L S C A L E T R I A L
t( m i n )
Figure 22.10°—10° Z-maneuver response (ship E).
O F U L L S C A L E T R I A L
1 5 U m l n )
1-0 f 1.0 [ 1.0
H-1.0 J- 1 . 0 j- 1 . 0
Figure 24. Steady turning performance Figure 25. Steady turning performance Figure 26. Steady turning performance (ship A ) . (ship B). (ship C).
Figure 27. Steady turning performance Figure 28. Steady turning performance (ship E). (ship F fuU).
4. A p p l i c a t i o n study
4.1. Contents and procedure
As an application study w i t h the calculation m e t h o d proposed i n the present study, the e f f e c t o f the loading c o n d i t i o n o n the ship maneuverabihty is investigated t h r o u g h the s i m u l a t i o n calculations. T w o kinds o f ships are selected f o r this purpose. One is a high-speed container carrier as a t y p i c a l f i n e h u l l - f o r m ship, and the other is a 2 3 0 . 0 0 0 - D W T V L C C as a t y p i c a l f u l l h u l l - f o r m ship. T h e y are called as the container and the tanker respectively i n this chapter. The p r i n c i p a l particulars o f ship h u l l , propeller and rudder o f these ships are shown i n Table 2.
Considering the factors w h i c h are t h o u g h t t o a f f e c t the ship maneuverability i n c o n n e c t i o n w i t h the change o f the loading c o n d i t i o n , t h e f o l l o w i n g three factors m a y be m e n t i o n e d t o be i m p o r t a n t : the d r a f t , the t r i m and the immersed rudder area ( d e f i n e d i n this r e p o r t as the area o f immersed part o f r u d d e r b e l o w still water surfaces) [ 7 ] . R u d d e r is c o m p l e t e l y immersed i n water at the f u l l l o a d c o n d i t i o n i n general, and some upper part o f rudder usually emerges above water surface at the ballast c o n d i t i o n . B y e x a m i n i n g the e f f e c t o f each f a c t o r m e n t i o n e d above o n the ship maneuverability, the investigations f o r the e f f e c t o f the loading c o n d i t i o n o n the ship m a n e u v e r a b i l i t y
Table 2
Principal particulars o f h u l l , propeller and rudder o f f u l l scale ship f o r s i m u l a t i o n study k i n d o f ship container tanker
loading c o n d i t i o n f u l l ballast f u l l ballast h u l l L ( m ) 202.00 3 1 0 . 0 0 B ( m ) 31.20 54.00 d ( m ) 10.50 6.93 19.60 9.50 W ( t o n ) 3 8 , 5 0 0 23,200 270,300 124,100 r ( m ) 0.0 2.02 0.0 3.10 0.566 0.518 0.803 0.761 rudder Aj^lLd 1/60.6 1/50.0 1/61.9 1/37.5 \ 1.67 1.35 1.51 1.17 propeller D ( m ) 7.10 7.90 PID 1.04 0.73 Z 6 6
are made. I n Table 2 , the t r i m and the immersed rudder area at the ballast c o n d i t i o n are supposed t o be
1.0 percent o f the ship length ( t r i m b y stem) and t o be 8 0 percent o f the rudder area respectively f o r b o t h ships. These figures are determined r e f e r r i n g t o those o f b o t h ships and similar ships i n the full-scale trials.
I n the process o f the change o f the loading c o n d i -t i o n , namely f r o m -the f u l l load c o n d i -t i o n -t o -the ballast c o n d i t i o n , f o u r kinds o f c o n d i t i o n s s h o w n i n Figure 29 are supposed.
1. F U L L : The f u l l load c o n d i t i o n w i t h zero t r i m and w i t h f u l l y immersed r u d -der. FULL BALLAST ( 1 ) BALLAST ( 2 ) BALLAST ( 3 )
Figure 29. Concept of loading conditions for simulation study.
2. B A L L A S T (1) : A n imaginary ballast c o n d i t i o n w i t h zero t r i m and w i t h f u l l y immersed rudder. (The d r a f t is shallowed t o the mean d r a f t between f o r e - and a f t - d r a f t at the ballast c o n d i t i o n ) . 3. B A L L A S T ( 2 ) : A n imaginary ballast c o n d i t i o n w i t h
f u l l y immersed rudder. 4. B A L L A S T ( 3 ) : The ballast c o n d i t i o n .
The above f o u r c o n d i t i o n s are t h o u g h t o u t b y changing the three factors, i.e. the d r a f t , the t r i m and the i m -mersed rudder area, one b y one f r o m the f u l l l o a d cond i t i o n t o the ballast c o n cond i t i o n . I n this r e p o r t the cond i f -ferences o f the maneuverability between F U L L and B A L L A S T ( l ) , between B A L L A S T ( l ) and B A L L A S T ( 2 ) , and between B A L L A S T ( 2 ) and B A L L A S T ( 3 ) are called as the d r a f t e f f e c t , the t r i m e f f e c t , and the e f f e c t o f the immersed rudder area respectively, where i t should be n o t e d that the d r a f t e f f e c t includes the e f f e c t due t o the change o f the rudder area ratio {Aj^ /Ld) as w e l l .
The transverse metacentric height GM usually changes considerably according t o the change o f the loading c o n d i t i o n f o r such ships as the high-speed container carriers and r o l l - o n / r o l l - o f f ships. Hence, i n a d d i t i o n t o the above-mentioned investigations, the e f f e c t o f GM o n the ship maneuverabihty is b r i e f l y examined i n connection w i t h the r o l l e f f e c t o n the h o r i z o n t a l m o t i o n s , a l t h o u g h GM is somewhat d i f f e r -ent f a c t o r f r o m the three factors taken above.
4.2. Numerical results and estimate formulae for loading condition e f f e c t
The e f f e c t o f the loading c o n d i t i o n o n t h e ship maneuverability is investigated f o r the t u r n i n g a b i h t y and the course changing a b i h t y , w h i c h are the t y p i c a l features o f the ship maneuverability. A f t e r these i n -vestigations the b r i e f e x a m i n a t i o n f o r the GM e f f e c t is added.
1. The turning ability
The f o u r indices, i.e. the advance ( 9 0 ° heading), the transfer ( 9 0 ° heading), the tactical diameter Z)^ and the dimensionless t u r n i n g rate /•' (steady t u r n i n g ) , are generally e m p l o y e d as the indices w h i c h represent the t u m m g a b i l i t y . The c o m p u t e d results o f these indices f o r the f o u r k i n d s o f conditions are s h o w n i n Figure 30 f o r the container and i n Figure 31 f o r the tanker, t a k i n g the rudder angle i n abscissa. T h e y are based o n the results o f the s i m u l a t i o n calculations f o r the t u m i n g m o t i o n . The e f f e c t o f the loading c o n d i t i o n o n A^, T^, and r' can be u n d e r s t o o d f r o m Figures 30 and 31 t h r o u g h the e f f e c t o f each f a c t o r , i.e. the d r a f t , the t r i m and the immersed rudder area, o n t h e m .
F U L L BALLAST ( 1 ) BALLAST ( 2 ) BALLAST ( 3 ) CONTAINER I 1 \ ^ A d ^ X 15 2 5 35 £ ( d « g ) 14 12 8 10 CONTAINER
1
\\
\\
\\\
\ \ \ \\ \ V \ \ \ \ y y . y' 0.8 0.4 0.2 15 25 36 6(degj F U L L BALLAST ( 1 ) B A L L A S T ( 2 ) BALLAST ( 3 ) 15 2 5 35 S t d e g ) 14 12 10 T A N K E R / 1 / 1i
V \ W D , / L ^ ~ 1.2 1.0 0 8 0.6 0.4 0 . 2 15 25 35 £ ( d e g ) 0 . 0Figure 30. Computed results of advance, transfer, tactical Figure 3 1 . Computed results of advance, transfer, tactical diameter and dimensionless turning rate for the Container. diameter and dimensionless turning rate for the Tanker.
The full-scale maneuvering trials are usually con-ducted at one loading c o n d i t i o n , namely either at the f u l l load c o n d i t i o n or at the ballast c o n d i t i o n . I t m a y be considered t o be very u s e f u l i f the estimation o f the t u r n i n g ability at a loading c o n d i t i o n f o r w h i c h the fuU-scale trials are n o t conducted can be made b y u t i l i z m g the full-scale t r i a l results at the other loading c o n d i t i o n . Hence an a t t e m p t is made t o develop es-t i m a es-t e f o r m u l a e o f es-the f o u r indices w h i c h express es-the relations between the f u l l load c o n d i t i o n and the baUast c o n d i t i o n w i t h a r b i t r a r y d r a f t , t r i m and immers-ed rudder area. T h e results obtainimmers-ed are w r i t t e n i n the f o r m y l ^ ( B a l l a s t ) ={\-A^d*){\'rB^T*') ( l + q a * ) - ^ ^ ( F u l l ) r / B a l l a s t ) = (1 -A^d*-) (1 -^B^T*) (1 t C j a * ) - r / F u l l ) Z)^(Ballast) = (1 ~ A^d*) (1 + . 0 3 7 * ) (1 H-C3a*) - i J / F u l l ) r' (Ballast) = ( 1 +A^d*) (1 -B^j*) (1 - C 4 a * ) - ; - ' ( F u l l ) where d* = \ - d g / d p T* = l O O r / Z ( 2 6 ) a* = 1 ^A^/A^o . (25) T h e c o e f f i c i e n t s A2, — , 5 ^ , — , , — etc. i n equation ( 2 5 ) can be determmed based o n t h e results s h o w n i n Figure 3 0 or Figure 3 1 , and t h e y are given i n Figure 3 2 f o r b o t h the contamer and the tanker.
TANKER CONTAINER 0.2 0.0 0.6 0.4 0.2 0.0 1.2 - 3 A<
V
B2 B3 x^ 5 15 2 5 35 5 15 25 35 5 15 2 5 35 5 15 25 3 5 S ( d . g . )Figure 32. Coefficients y l j , A2 etc. for indices of turning ability.
2. The course changing ability
A t f h s t the procedure o f the 1 5 ° / 7 ° course changing maneuver is b r i e f l y explained b y m a k i n g use o f the figures shown i n Figure 3 3 . The rudder e x e c u t i o n o f
S.'P / / 1 / S = 1 5 ' / ! \ T2 s = o° <S=-7" 6 = 0° at ( = T2
Figure 33. Illustration of course changing maneuver with rudder angle of 15°/7°. F U L L B A L L A S T ( 1 ) B A L L A S T ( 2 ) B A L L A S T ( 3 ) (deg)
Figure 34. Computed results of new course distance and new course angle for the Container.
5 = 15° is ordered at the t i m e o f r = 0, atid the
check-ing rudder w i t h 5 = - 7 ° is taken w h e n the headcheck-ing angle grows t o 1// = 1// j . The course changing maneuver is ended b y r e t u r n i n g the rudder amidship w h e n the t u m i n g rate becomes zero. The heading angle at the end o f the course changing maneuver, i// 2 > is called as the n e w course angle, and the distance s h o w n i n Figure 33 is caUed as the n e w course distance.
T h e course changing a b i l i t y is generally discussed w i t h the indices o f i// 2 and . The c o m p u t e d results o f these indices f o r the f o u r kinds o f c o n d i t i o n s are shown i n Figure 34 f o r the container and i n Figure 35 f o r the tanker, taking the heading angle o f i n abscissa. T h e y are based on the results o f the simula-t i o n calculasimula-tions f o r simula-the 1 5 ° / 7 ° course changmg maneuver. T h e e f f e c t o f the loading c o n d i t i o n on
1 / / 2 and can be understood f r o m Figures 34 and 35
F U L L
B A L L A S T ( 1 )
B A L L A S T ( 2 )
B A L L A S T ( 3 )
15 3 0 4 5 «l», (deg)
Figure 35. Computed results of new course distance and new course angle for the Tanker.
TANKER CONTAINER o.e 0.6 - 0 . 2 0.2 A s Bs Be 0,3 0.6 0.4 0.0 60 15 +1 (deg) 30
Figure 36. Coefficients A^, etc. for indices of course chang-ing ability.
t h r o u g h the e f f e c t o f each f a c t o r , i.e. the d r a f t , the t r i m and the immersed rudder area, o n t h e m .
The same a t t e m p t as f o r the estimate f o r m u l a e o f the indices on the t u r n i n g a b i l i t y is made f o r the i n dices on the course changing a b i h t y . N a m e l y the f o l -l o w i n g expressions are obtained,
i/zjCBallast) ={1-A^d*)il-B^T*)
(1 +C^a*) • V/jCFull)
(27) i ? ^ ( B a l l a s t ) = ( 1 - ^ g t f * ) ( l - 5 g r * )
( l + C g a * ) - D ^ ( F u l l )
where the coefficients A^, A^, - -- etc. i n equation (27) can be determined based o n the results s h o w n i n Figure 34 or Figure 35, and t h e y are given i n Figure 3 6 f o r b o t h the container and the tanker.
3. The effect of
The GM e f f e c t is examined f o r the f u l l load con-d i t i o n o f the container. C o m p u t a t i o n s are macon-de f o r t w o cases o f GM, i.e. GM = °° and GM = 0 . 6 m . Figure 3 7 shows the c o m p u t e d results o f the steady t u r n i n g p e r f o r m a n c e , and Figure 38 shows the c o m p u t e d results o f the 10° - 10° Z-maneuver response. I t can be recognized f r o m these figures t h a t t h e e f f e c t o f GM o n the maneuverabihty o f ships such as the high-speed container carriers etc. can n o t be ignored i n connection w i t h the r o l l e f f e c t on the h o r i z o n t a l m o t i o n s , and t h a t the course keeping a b i l i t y m a y be deteriorated i n the case o f small GM as is r e p o r t e d b y D r . H . Eda [ 1 5 ] .
4.3. Comparisons with full-scale trial results
The v a h d i t y o f the results o b t a i n e d t h r o u g h the s i m u l a t i o n calculations f o r the e f f e c t o f the loading
r' C O N T A I N E R
1.0 r
GM =00 (WITHOUT ROLL) GM = 0.6m
J - 1 . 0
Figure 37. Computed results of steady turning performance for the Container. C O N T A I N E R ' ^ ' ' ' ' S * G M = 0 0 ( W I T H O U T R O L L ) 3 0 r G H = C . 6 m I ( m i r ) - 3 0
1-Figure 38. Computed results of 10°—10° Z-maneuver response for the Container.
c o n d i t i o n o n the ship maneuverability is examined b y comparing w i t h the full-scale t r i a l results.
1. The tuming ability
The e m p t y circles i n Figure 39 show the full-scale t r i a l results obtained i n the t u r n i n g test w i t h 3 5 ° r u d der o f 2 0 0 , 0 0 0 D W T class V L C C s . The arrows i n F i g -ure 39 mean the e s t i m a t i o n o f the indices w i t h equa-t i o n ( 2 5 ) f r o m equa-the f u l l load c o n d i equa-t i o n equa-t o equa-t h e ballasequa-t c o n d i t i o n , where as t h e value o f the indices at the f u l l load c o n d i t i o n the mean values o f the fuU-scale t r i a l results are e m p l o y e d . I t m a y be understood f r o m F i g -ure 39 t h a t adequate results can be o b t a m e d b y the estunate f o r m u l a e o f equation ( 2 5 ) , a l t h o u g h some scatter is seen i n the full-scale t r i a l results because the results o f d i f f e r e n t h u l l - f o r m ships f r o m the t a n k e r
— PREDICTION BY E q , ( 2 5 ) O F U L L S C A L E TRIAL B A L L A S T F U L L >- 3 0 c c 3 D, / L 0 c c 8 A d / L n 5 _ l
^
^
^ T p / L 1 0 . 0 5 0.10 2 d / L 0.15Figure 39. Comparison o f predicted results of advance, transfer, and tactical diameter with those of full scale trial for the Tanker.
shown i n Table 2 are i n c l u d e d there. B o t h t h e comput-ed and the full-scale t r i a l results i n Figure 39 indicate shght difference o f the indices o n the t u r n i n g a b i l i t y between the f u l l load c o n d i t i o n and the bahast con-d i t i o n , namely the incon-dices i n the l a t t e r c o n con-d i t i o n are shghtly smaUer than those i n the f o r m e r c o n d i t i o n . T h i s m a y be due t o the f a c t t h a t the e f f e c t o f each f a c t o r , i.e. the d r a f t , the t r i m and the immersed r u d d e r area, on the indices acts so as t o cancel each o t h e r as a result, while the e f f e c t o f each f a c t o r itself is n o t necessarily small as can be seen i n Figures 30 and 3 1 .
2. The course changing ability
Figures 4 0 and 41 show b o t h the c o m p u t e d and the full-scale t r i a l results f o r t h e indices o n the course changing a b i l i t y f o r the container and f o r the tanker respectively. The solid lines at the f u l l load c o n d i t i o n and at the ballast c o n d i t i o n i n Figure 4 0 , w h i c h rep-resent the c o m p u t e d results o f the container, are t h e same ones as those at the F U L L and at the B A L -L A S T ( 3 ) i n Figure 34 respectively. The same is ex-plained f o r the c o m p u t e d results o f the tanker shown i n Figures 4 1 and 35. The results o f d i f f e r e n t h u l l -f o r m ships -f r o m the container o r the tanker shown i n Table 2 are added i n the full-scale t r i a l results, namely the results o f d i f f e r e n t f i n e h u l l - f o r m ships w i t h Cg o f 0.5 — 0.6 are added i n Figure 4 0 and the results o f d i f f e r e n t h i i U - f o r m tankers and b u l k carriers are added i n Figure 4 1 . I t can be m e n t i o n e d f r o m Figures 40 and 41 that the results obtained t h r o u g h the s i m u l a t i o n calculations f o r the course changing a b i l i t y explain w e l l the full-scale t r i a l results, especially w i t h respect t o n o t o n l y the e f f e c t o f the loading c o n d i t i o n b u t also the tendency w i t h w h i c h the indices o f i/zj and Z ) ^ vary according t o the v a r i a t i o n o f \//,.
5. Conclusions
I t is the purpose o f the present study t o develop a practical calculation m e t h o d o f the ship maneuvering m o t i o n using the p r i n c i p a l particulars o f ship h u l l , propeller and r u d d e r as basic i n p u t data. T h e conp u t e d results are comconpared w i t h the results o f the f u l l -scale trials, and the v a l i d i t y o f the calculation m e t h o d o f the present s t u d y is examined. I n a d d i t i o n , as an apphcation s t u d y , the e f f e c t o f the loading c o n d i t i o n o n the ship maneuverability is investigated t h r o u g h the s i m u l a t i o n calculations. T h e m a j o r results obtained i n t h e study o f this r e p o r t are summarized as f o l l o w s .
1. The c o m p u t e d results show satisfactory agreements w i t h the results o f the full-scale trials f o r various k i n d s and types o f the merchant ships, n a m e l y f r o m a general cargo boat o f 10,000-DWT class t o a U L C C , and f o r w i d e range o f the maneuvering char-acteristics, namely f o r the t u r n i n g m o t i o n w i t h 3 5 ° rudder, the 10° - 10° Z-maneuver and the spiral maneuver.
2. The maneuvering m o t i o n o f a ship w i t h large r o h should be treated together w i t h the m o t i o n o f r o h simultaneously.
3. The maneuvering m o t i o n o f the fuU-scale ships should be calculated t a k i n g the coupling e f f e c t due t o propeller r e v o l u t i o n i n t o consideration even under the n o r m a l r u n n i n g c o n d i t i o n o f the m a m engme.
4 . The e f f e c t o f the loading c o n d i t i o n o n the ship maneuverability is investigated and c l a r i f i e d b y e x a m i n i n g the effects o f three t y p i c a l f a c t o r s : the d r a f t , the t r i m and the immersed rudder area, w h i c h are t h o u g h t t o a f f e c t the ship maneuverability i n c o n n e c t i o n w i t h the change o f the l o a d m g c o n d i -t i o n . PREDICTION F U L L S C A L E TRIAL PREDICTION F U L L SCALE TRIAL 9¬ 80 C O N T A I N E R F U L L D N / L ^ 80 30 45 +, CdfgJ C O N T A I N E R B A L L A S T D n / L ( 45 '^| (if«g)
Figure 40. Comparison of predicted results of new course dis-tance and new course angle with those of f u l l scale trials for the Container. 3¬ 80 T A N K E R F U L L
! 1
1 40 30 45 't'l (deg) T A N K E R B A L L A S Ty
y
Y
30 45 +, tdtg)Figure 4 1 . Comparison of predicted results of new course dis-tance and new course angle with those of full scale trials for the Tanker.
5. The estimate f o r m u l a e o f equations ( 2 5 ) and ( 2 7 ) are u s e f u l f o r the estimations o f the t u r n i n g a b i l i t y and the course changing a b i h t y at a loading d i t i o n , f o r w h i c h the full-scale trials are n o t con-ducted, when the full-scale t r i a l results at the other loadmg c o n d i t i o n are available.
6. F i n a l l y the calculation m e t h o d o f the present study is very u s e f u l and p o w e r f u l f o r the predictions o f the ship maneuverability at the t i m e , such as the i n i t i a l design stage etc., w h e n the p r i n c i p a l p a r t i c u -lars o f ship h u h , propeller and rudder are k n o w n .
References
1. IMCO: Recommendation on information to be included in the manoeuvring booklets. Resolution A. 209 (VII) adopt-ed on 12 October 1971.
2. Maneuvering characteristics: Data required, Code of Federal Regulations, 35 Panama Canal par. 103, 41a, 1977. 3. Inoue, S., Hirano, M . , Hirakawa, Y. and Mukai, K., 'The
hydrodynamic derivatives on ship maneuverability in even keel condition' (in Japanese), Transactions of the West-Japan Society of Naval Architects, No. 57,1979.
4. Inoue, S., Hirano, M . and Mukai, K., 'The non-linear terms of lateral force and moment acting on sliip huU in the case of maneuvering' (in Japanese), Transactions of the West-Japan Society of Naval Architects, No. 58, 1979.
5. Inoue. S., Kijima, K . and Moriyama, F., 'Presumprion of hydrodynamic derivatives on ship maneuvering in trimmed condition' (in Japanese), Transactions of the West-Japan Society of Naval Architects, No. 55,1978.
6. Hirano, M . , 'On the calcularion method of ship maneuver-ing motion at the initial design phase' (in Japanese), Journal of the Society of Naval Architects of Japan, V o l . 147, 1980.
7. Inoue, S., Hirano, M . , Kijima, K. and Takashina, J., 'An application of simulation study of maneuvermg motion' (in Japanese), Transactions of the West-Japan Society of Naval Architects, No. 61, 1981.
8. Inoue, S., Hirano, M. and Kijima, K.,'Hydrodynamic deriv-atives on ship maneuvering'. International Shipbuilding Progress, Vol. 28, No. 321,J981.
9. Hirano, M . and Takashina, J., 'A calculation of ship turning motion taking coupling effect due to heel into consider-ation'. Transactions of the West-Japan Society of Naval Architects, No. 59,1980.
10. Motora, S., 'On the measurement of added mass and added moment of merria for ship motions (Part 1, 2 and 3)' (in Japanese), Journal of the Society of Naval Architects of Japan, Vol. 105 and 106,1959 and 1960.
11. Yoshimura, Y . and Nomoto, K., 'Modeling of maneuvermg behaviour of ships with a propeller idhng, boosting and reversing' (in Japanese), Journal of the Society of Naval Architects of Japan, Vol. 144,1978.
12. Inoue, S., 'On the point in vertical direction on which lateral force acts' (in Japanese), Technical Report, SP 82, Technical Committee of the West-Japan Society of Naval Architects, 1979.
13. Ogawa, A. and Kasai, H., 'On the mathematical model of maneuvering motion of ships'. International Shipbuilding Progress, Vol. 25, No. 292, 1978.
14. Yumuro, A., 'Some experiments on flow-straightening effect of a propeller in oblique flows' (in Japanese), Jour-nal of the Society of Naval Architects of Japan, Vol. 145, 1979.
15. Eda, H., 'RolHng and steering performance of high speed ships', 13th Symposium on Naval Hydrodynamics, 1980.
Nomenclature
advance m o m e n t o f i n e r t i a o f ship w i t h respect t o x rudder area (immersed part b e l o w stiU water and z-axes respectively
surface) m o m e n t o f r o t a r y i n e r t i a o f
propeller-shaft-rudder area ing system
r a t i o o f h y d r o d y n a m i c f o r c e , induced o n ship J ,J added m o m e n t o f inertia o f ship w i t h respect h u l l b y rudder action, t o rudder f o r c e t o X and z-axes respectively
B breadth o f ship
PP added m o m e n t o f r o t a r y i n e r t i a o f propeller
CB b l o c k c o e f f i c i e n t L length o f ship (between perpendiculars)
Cp propeller f l o w - r e c t i f i c a t i o n c o e f f i c i e n t m mass o f ship
Cs ship h u l l f l o w - r e c t i f i c a t i o n c o e f f i c i e n t added mass o f ship i n x and >'-axes d h e c t i o n
D propeller diameter respectively
DN new course distance roU damping m o m e n t
tactical diameter n n u m b e r o f propeller r e v o l u t i o n d d r a f t o f ship (mean d r a f t ) P propeher p i t c h
d r a f t at ballast c o n d i t i o n (mean d r a f t ) r t u m i n g rate
d . d r a f t at f u h load c o n d i t i o n r' dimensionless t u m i n g rate (= rL/V)
FN rudder n o r m a l force T r transfer
GZM restoring m o m e n t lever o f r o l l ho t h m s t deduction c o e f f i c i e n t i n straight r u n -H rudder height
ho
ning c o n d i t i o n
vertical distance f r o m s t i l l water surface t o u ship speed i n x-axis d i r e c t i o n p o i n t o n w h i c h lateral f o r c e 7 ^ acts (see V ship speed (= ( w ^ + v^)'''^) Figure 2) e f f e c t i v e rudder i n f l o w speed
V ship speed i n y-axis d h e c t i o n
v' dimensionless ship speed i n j^-axis d h e c t i o n
(= v/V)
W displacement o f ship
Wp e f f e c t i v e propeller wake f r a c t i o n
Wpg e f f e c t i v e propeher wake f r a c t i o n i n straight r u n n i n g c o n d i t i o n
effective rudder wake f r a c t i o n
Wj^Q e f f e c t i v e rudder wake f r a c t i o n i n straight r u n n i n g c o n d i t i o n Xp ;)c-coordinate o f propeller p o s i t i o n Xp dimensionless f o r m o f Xp (= Xp/L) Xj^ x-coordinate o f p o i n t o n w h i c h rudder f o r c e acts xi, dimensionless f o r m o f x„ (= x„ /L) ' x^ x-coordinate o f midship Zjj z-coordinate o f p o i n t on w h i c h lateral f o r c e acts Zj^ z-coordinate o f p o i n t on w h i c h r u d d e r f o r c e Yj^ acts
effective rudder i n f l o w angle j} d r i f t angle (= - sin"^ v') 7 f l o w - r e c t i f i c a t i o n c o e f f i c i e n t S rudder angle X aspect r a t i o o f rudder p density o f water T t r i m q u a n t i t y if roU angle 1^ heading angle
