Predicting method of wave loads for ship’s route

(1)

ÀRCHEF

Predicting Method of Wave Loads for Ship'8 Route #

by

Osamu TSUKAMOTO* Toshiaki MORI*

Mitsubishi HeaIndu2tries, Ltd,

Nagasaki Shipysrd & Exgine Works

1-1 Alcunoura-Machi, Nagasaki 850-91,

Japan

# Summarized from the paper (in Japanese) published in

Transactions of the West-Japan Society of Naval Architects,

No. 47, February 1974.

Lab. y. Schepsbouwkunde

Technische Hogeschoo

Dell t

(2)

1. Introduction

As a moans cf predicting the ship motions and the wave loading in

irreilar waves, it has been gaining an increasingly

eat favor

recently to estimate ihe ship response in

irregular

waves

by first

determining

the ship response in

regtilar waves

and then linearly

euprposing this ship response and the wave spectrum.

And. for use in prtJicting the longterm distriuui.nL o

tzie ship

response in waves, various kinds of wave statistics have been Introduced.

by Walden, Roll, Yamanouchi, et al., of which the modified. Walden's

wave freq'.encic.ì

prepared by Fkuda now finds epccially wide

applica-tions.

All thee wave data, howevur, concern

mostly

the North Atlantic

Ocean and. North Pacific Ocean and differ from

sea

conditions usually

encountered by very large ships, ouch as oil tankers, ore carriers, etc.,

in their trade routes.

It therefore is felt necessary to have moro

pertinent data on sea conditions in the tr1e routes frequented by such

large ships, in order to achieve proper ship structural design.

The authors rearranged th wave data compiled by Hogben and Lub

2)

and

by Ynanouchi

3)

so as to represent wave frecuenoies in sea areas located

along four major trade routes.

Using the wave frequencies thus obtained,

the authors then made longterm predictions of the wave loading on an

oil tanker and a container

ship

and. compared the results with those

obtained using

the modified Walden's wholeyear wave frequencies.

It

is to be noted, however, that the data pxepared by Hogben and Lumb

and by Ya.manouchi are not tho resulta of systematic observation by

weather ships, etc., but of accumulation of reports from ships which

happened. to sail

through

the sea areas and. hence may lack the details

and. validity of the Walden's data.

(3)

2. Long-Term ñ d.iction of Sea Conditiori and Ship Reponße

If 'the ship recponae function in reulzr waves and irreular-ave

apectr'um are known, the variance of nhip response will Le given 'by the

followirì equation.

50

jA(w, - x)) 2[f(W x))2dxd (i)

whre

R2 variance of akjp response

Aiw, - x) ship response function

1(w, x))2 - wave spectrum

anulo between ship heading and mean wave direction

x angle between mean wave direction and

component

WaVe

Using the 1550 wave epectruni taking into account the distribution of directionality, a '.ive spectrum is given by the following equation.

[f(w, x)' 2 .- -f(w)2cos2x, (-lt./2 ¿ x

<7C/2)

₍₂₎

O (elsewhere)

where

[f(W))2 _- O.11O9H2w(w/w1)_5exp_O,4436(u/v)

Asuininr the diiiribution of peak values of ship

response to

folloi the Rayleigh distribution, the long-tena exceeding probability of the

ship response exceeding a certain valuo x will be given 'by

the following

equation.

2

prÇJQ

X

Q

,Ç,

)

erp(-

2)P(If, T)dHdT

(3)

where

_Q

- lcng-tcrrn exceeding

probability

H, T)

wave frequency

H - significant-wave

height

T ineaxi wave period

(4)

The longtertn prediction for each trade route

will

then be

given by substituting the wave frequency in that particular trade

route for the wave frequency P(T,

H)in Eq.(3).

For this purpose,

h ver, 'the WaVe fi ueicy in each trade route is determined 'by

raultiplying the íave freçuoricy in each of sea areas located along the

route 'by

the wei.-ht

_{cûefficient which takes into account the tiie}

required 1'o a Lhi2 'to

Lail

ti'ough that sea area and 'by inIirig up

the iav frequaoiea sir4lrly caloulated for all the sea areas.

N

Ph(i{, 'i) -Wi?i(}{, T)

(A'

_{kt i}

i=1

T)

have freiency in

trade route

Pi(H, i') wave freqeacy in st.a area located

alone the trade route

Wi _{'eeiht coefficient for}

iea arca

I; . nunbr of sea areas locatea

along the

trade

route

Prou Eq. (3) and Eq. (4), the longterm exceeding

pro'baUlity

for eaoh trade route will 'Lo given 'by the following equation.

2

Q

los

L'() (- ) i'(ii, T) diIdT

₍₅₎

o'

3. Results of Long',i'ari.i Pred,ictiona

3.1

Wave Frec1'uenoy

As mentioned earlier, the authors rearranged the wave data

of Hc'ben and Lub

and of Ywnanouchi as regards the

sea areas

indicated 'by

'bicok nuntters in Fie. 1.

Table i shows the nun'ber

of Waves oLzerved in each sea area, and Tables 1 - 14 wave freqcncies in sc'ie of these sea areas.

tihun

applying Eq. (4), three different weilit ooefficierits

_A,

B, and C, pluu

the Jalden's wholeyear wave frequency D, wore

(5)

i)

_{eit CeïÍicient A}

1he '.eiht coefficient A iake into accouit th

lerLt.h ot

roì.te in ezich uca e-ua, or the ti.e reruired for a uhip to uil

throuh that eea area at a coniitant

pl.cd.

;iiht Cofficiet B

The

1.ht coefficient B cor.iid.eru that the tiíe required

for a zh±p to eau through one cea area wil]. Le the ee ao

the time to call throuh other sea ara.

;ei,ht Coofficient C

The wiht coefficient C le -the owa of iiwrbere of

wjvC$

obcerved in

peotive se

arcas located

ll a1ori

(.Wh iracle

route.

Ii.

_{is jouible, however, that if one}

_{ca area}

_hiìit

a veri lc runber of oberved ;aveu as coeipard with other

sea arcu, that pariculi sea area will txcrt dc4naxit

influence oa the total

number of avs ccu.ntd for the trade

route.

:oi:ht Coefficient D

The woiht coo fficient D le the 1alden' wholeyear wave

l're que ncy.

Four tradc routes, rinely,

Europeiorth America,

Europe-Percian Gulf', £\riian GulfJapan, and Japancrth _{Ajierica, were}

OlQcted

and wave frtp.ertoles in theue

trado ru tes were calculated1

uein

the w4ht

_{coe±'fioioni}

_{A, B, and C for the}

_opeuorth

America route asid. the weicht oocfficieit

.

for the remaining three

trade routee, with the results ae sho';n in ¶i'ables 15 - 20. 'he

coa areas and tiht co fficierits are alio indicated in thce

tables for cauy reference.

_{Figures 2 and. 3 show hi ito raia to}

illuutrte differencei

_{in frequency dictributiona due}

_{to the uiie}

of the

dirferent weicht coefficienta, and Fi-u.

₄ _and

fitiuency

dictribuiion

ja the four trade routes, all with

_{hictoLr4ne of}

the 1alcìe'u wholeioar wave t'rt.quencieu _{for oparibon.} _Ii _..jll

be SCCII frofl 2 and 3

that there ar

c.ue difrurnceu

in

frucuency di ritutiona

due to the uc of the diffret wei-ht

(6)

compared with frequencies determined using the weight coefficient D

(Walden's whole-year wave frequency), those determined using the

weight coefficient A, B, or C are higher when wave height are low nd are lower at the wave periods of

5 - 9

seconds at which ship8

undergo frequent motions, probably due to a difference in

wave-observation methods adopted.

3,2 Statistically Analyzed Wave Loading in Each Trade Route

The author3 selected an oil tanker and a container ship, whose particulars are shown in Table 21, and calculated. their

motions and hydrodynaaiic pressures at the water line on the weather

ide of two hull sections, S.S.

= 5,

or midship section, and 8.

It was assumed. that the ships were in full loaded conditions and that the speed of the oil tanker was 0.15 in Freude number (16.1 Ift.) and that of the container ship 0.20 in 1'roudo number (19.1 Kt.). Heaving, pitching, and. rolling motions calculated are shown in Figs.

6, 7,

and 8, and. hydrodynamic pressures in regular waves in Figs. 9

and 10, respectively. Also, long-term hydrodynamic pressures

determined using the wave frequencies calculated. in

3.1

are shown in

Figs. iL 16.. It will be seen from Figs. ii and 14 that hydrodyna-mio pressures calculated are nearly the same regardless of the

different weight coefficients used, showing a head difference of

about one meter at moat when Q. 10-8. _{The hydrodynamic pressures}

calculated. using the Europe-North America route wave frequencies

-and the Walden's whole-year wave frequenciee show noreat difference. Figuree 12, 13, 15, and 16 compare the long-term hydrodynaio

pressures calculated for the four trade routes using wave frequencies of weight coefficient A which is considered to be moat reasonable of all the weight coefficients, from which it will be seen that the bydrodynamic pressures in the Europe-North America route are highest

and nearly equal the hyd.rodynaaiic pressures calculated using the

Walden's whole-year wave frequencies; the hydrodynamic pressures

in the Japan-2ersian Gulf and. Persian Gulf-Europe routes are nearly

of the same order and lowest among the hydrodynamic pressures

(7)

the hydrodynaric pressures in the Japan-North America route are intermediate between those in the }urope-North America and Japan-Fersian Gu]f (or Persian Gulf-1arope) routes; when converted into

long-term exceeding probabilities calculated using the \.'alden's

whole-year wave frequencies, the bydrodynRrnic pressures in the

Japan-Persian Gulf (or Persian Gulf-Europe) and Japan-North America routes corresponding to Q lO are Q

in-5

l0 and Q = io6

i7,

respectively. Though ohip are often reported damaged off

the Cape of Good Hope, the hydrodynamic pressures in the Persian Gulf-Europe route are lowest as are those in the Japan-Persian Gulf route, as mentioned above, and are not likely to inflict such

hull damage. The difference between the actual and predicted wave

loads may be attributable to the following.

(i) The original wave data from which the authors prepared wave frequencies were based on reports from ordinary commercial ships, and it is reasonable to presume that ships generally dare not sail in rough seas violent enough to inflict damage

to them. _{It is probably for this reason that the sea area}

No.10 of Table

_4,

which represents the sea cfi' the Cape of

Good HoFe, show relatively low wave frequencies as compared

with other sea areas.

(2) _{A trade route may locally contain very rough sea areas even}

though it shows relatively low wave frequencies as a whole.

It may be suggested then that greater weight coefficients be

_12ed

considering the ship speed losses when calculating _{wave frequencies} for ouch rough sea areas, but this will not be an effectice solution since, as stated earlier, weight coefficients has little effect in

long-term prediction. It is considered, therefore, that the

ehort-term prediction will be more realistic as a means to estimate the wave loading in very rough seas.

(8)

4. Corcluior

The authors rarrined tho wave data compiled by Hoben and Lumb

and. by Yaaaxioucbi und caloula-tà uin diffcrnt wúiht coefficioiit

the wuvo f

uncie

in four taajor trada routes, namely, Europe-North

Azerica, Japan.-?eruian Calf, Japan-North Airica, and Percian

Gulf-Europe routee. Uiiig the calculated wave tre-uer.cie, the author

thxi _{tiated lonc-teru wave loadin, or hythodynamio preu.ro, on}

an oil tanker and a container ip eailin _{theoe trada routes, with}

the folloizug ccclis.

i) The hythodynio preurs calculated remain almoot

_the

eame

rerd.1eu of the

different weiit ocefficiente

_used.

T.a 1drodj-nic pruireii in the Earope-Ncrtb Arica route are

hihest, folìo.-eJ by thoee in the Japan-North Iìerica, Persian

Gul±'-h\u'ope aM Japzn-Peroian Gulf route in that order thouh

the hydrodynaciic precu.res in the last two trade rcuts are of the same order.

Converted into the lon-ti exceeuin probabilities calculated.

using the

_{Ualdn'e whole-year wave}

_{-eu.eacies, the hydrc4ynamic}

prsurs in

the four trade routes

ccrreponding

_{to Q} lO are

10 ,

or nearly eua1

to those calculated uin the

_Ualde2l1u

i

1-year wave

quencie, in the Europe-North America route,

Q 10 10 in the

_{Japan-North America route, and Q}

_lO

lO _{in the Jap n-Persian Gulf and Persian Gulf-Europe} _routeis,

respeotivly.

The iald.en'c Wave

freqienoieo, when

ed in th

analyses of

atruetural atrength of ships

ailin

outside the North Atlantic

Ocean, wiil supply the over-estimated wave loadß.

The structural aiialyuee of ships in service should, therefore, 1

mada properly a the oise may warrant having due

rear

to the oa

cond.itionii in th ship' trade routes.

(9)

5)

It i

poriUe to ieii th required ctreithin'to chipa

according to th uea conditions in thuir expected. trìì3 routes.

Hovr, it i

necbary io ue the

hcrtteni prediction when

evi1atinL their

truci.urul øtrngth if the trEde routee locally

contain very rcgh ea axeas.

(10)

Re f er ence s

i)

uda, J.;

ictin Ln

Trends of Deci

¿etnes for 3hipo

in Ooan Uvo

(i Jpnco) Journal oi tht

;ociety of Nawl rchitctu

of Jpn V1. l

(19&3)

iiobui

ii. ansi Luri,

cmn 1ave Statiutic'

Ymamuchi, Y., Uno:i?

. and anda, T.

Ûn the Uindi and Uaveu on thu

)orthera

rth !ac.i±'ic Ccan nd South Adjacent

of Japan aa the

Environiental CóJ1teìuj tcr thc Shipu' Papr of

ip icearch Institute,

(11)

o 60 ¿0 20 0 20 i i i r i r T j r i kXO60TP2 TO riCiriU l JIiI)1AJI GTLJ.)L KA

---.-WA) tLMLLJ U

lo

-AXI0II0 TO YhiWiUtNl h 1;

FIR. i flock nano

'i'rablc I Block llame and nunrlrer iii ot2seryed wav

z---w

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Ti Tri 1* iir.riOrii &_rh L1O*.)

T ?lrir*iiI 1) 21 r 31 2) / ..13 .r ¿2 ¿ li

Iiu)

Il 14 _Ii)i44 ________li 2( ¡ri 1d.I9 L. IT li ¡7 1* 4 2 _{____._____»} 211 i 21)Oj 21 4//.017 1:1 ¡O 24 16 _T2 _'.fl I.. 21. 12,V 11. 1 '1S it

_14

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1i

T J I i r r T I J I i

r_r ii irr ri

11.0 1*0 it 140 120 100 *2 I i r r t i r r r

ii ri ii

t 20 0 20 40 t.,0 *2 1 20 O

(12)

-05 B 005 C = 0.0& I»0.34 = 0.0 - OUL r 040

r--i

WEIGHT-A

r-k-i

.

WEIGHT-B

WEIGHTC

;

WEIGHT-D

C = Q.o f)

rL9

A ..o.0 C A =0.02 C r0 Q r -Q.02 Ö 0,02 D -H Cm) FLG.2

HISTGRAM FOR THE ROUTE

EUROPE -NORTH AMERICA

(BASED ON MEAN WAVE HEIGHT)

'IO _4c3 300 2cK loo, H 13 IS

r-;

WEIGHT-A

WEGHT-B

WEiGHT C

'-i,-,

ViEIGHT-D 17 - TcSEC

FIG. 3

HISTORAM FÖR

THE ROUTE

EUROPE-NORTH AMERICA

(BASED QN MEAN WAVE'

PERIOD)

400rn Io 075 275 4.75 6.75 75 10.75 2.75 I 4.75

(13)

IO' 400 ₃₀₀ 200 loo

0'5

/

275 415 Fk75 8.75 b o.o C =O. D O06 O3 d C.O D = 034

FIG. 4

HISTGRAM

FOR 4 ROuTES

(BASED ON MEAN WAVE

HEIGHT)

WEIGHT A

C = 0.0 d o.o_ J_ì0J I 10.75 2.75 14.75

H (In)

0O2 C =.00 D rOC8 300 203 5 7 9

ii

13 15 ¡7 T C SE C.)

FIG. 5 HISTGRAM

FOR 4 ÍOUTES

(BASED ON MEAN WAVE PERIOD)

WEIGHT A

EUROPE-NORTH AMERICA() JAPAN-PERSIAN (b)

>-

o

Li

o

LU cl:: u--3 _lo

400

EJSVPE-NORTH AMERICA JAPAN PERSIANG.

AMERICA ,JAPAN-NORTH JAPAN-NORTH AMERICA (C) PERSIAN,GEUR3PE PERSIAN G-EUROPE(d) WALDEN WA C LDEN O) loo O

(14)

C,

t

t5 Ui to 4,0 20 O G -18cl

T'JXER

(Fr-O.15) - 00NTAR (Fr -02Q) TANKEP (Fr-0.)5) c0NTAR(Ft0,20) '/SHLP LENcrH/wvr

FIG.6

HEAVING MOTION

05 1.0 1.5

JSHP LENGTh/WAVE LENG1

FIG.7

_P;TCHING _MOTION

60

TANKER (Fr-0J5)

CONTM'ER(fr-02O)

05 1.Q

/SHIP LEMGTH/ WAVE LENGTtI

FIG.8

ROLLING MOTION

1.5

(15)

ti-LU cr

D

(J) (J-) LU Cr: Q-LU u-) U) LU er:

Q-z

>-'J

o

Q

2.0

o

S.S: 5

LOAD WATER LINE

WEATHER SIDE

s.s:8Y2

LOAD WATER LINE

WEATHER SIDE 14

-/

/

I-I

/

.

/

-

w--/SHIP LENGTH/WAVE LENGTH

FIG.1O

HYDRODYNAMC PRESSURE

IN REGULAR WAVE

leoIogo Fr

TANKER

!---.

_0.15

J--- 0.20

BI0 9.90

Fr TANKER

--- 0.15

NTAUER-

0.20

o

0.5

tO

15

--J$HIp LENGTH/WAVE LENGTH

FIG. 9

_{HYDRODyNAMIC PRESSURE}

IN REGULAR WAVE

15

(16)

tAJ cr (r) rn W :20 C) O .0

SS-5

LOAD WATER LINE

WEATHER SIDE

/

FO.I5

-y

I

L

vi

V COURSE ANGLE 3'O 60 G'0 i I COURSE ANGLE 3b _I _o _i _o i (HEAD SEAS) o y .

t.

s

a

I

t

i i

¡

4. i 80 (HEAD SEAS)

FiG; 12

_{HYDRODYNAMIC PRESSURE}

ESTIMATED

IN LONG TERM

-WEIGHTA.TANKER)

rn

30

FIG. 11

_HYDRODYNAMIC

LOAD WATER LINE WEATHER SIDE

F

O.5 PRESSURE ESTIMATED IN LONG

TERM

ROUTE; EURO.NORTH.

_AMERICA

(TANKER)

t_LÛGLJ-&

LQU $ALOjL.O.,

PLAj Q_&..

:q

I V.. _V_. 20 V o 9 o I V f V o y Io V o o ¿2 V ¿2 I y s s

t

5 + y

I

a'

y y

I

(17)

'V

o

O. 3O

SS=8

LOAD WATER LINE

WEATHER SIDE F1

0.2

y Q 'V +

_.4

£ ¡ o

i

V o s s

*

6Ö 90

IO

I8O

COURSE ANGLE (HEAD SEAS)

FIG. 1 3 HYDRODYNAMIC

PRESSURE ES11MATED IN

LONG TERM

WEIGHT-A

(TANKER)

LOG ¡

6i

V e V -o y y y A V A o

s

4 60' 90' 120 150'

(.OSEAS )

-COURSE ANGLE

F1G.14

_{HYDRODYNAMIC PRESSURE E5TIt1ATED IN LONG TERM}

ROUTE; EURONORTH

_AMERICA

(CONTAINER)

//IHf

-8 -5

e

o o Q

'V'

G

i

& 'V

o

y o V o AD5 WATER LINE

WEATHER SIDE rEuRO.N.A. Q

oil

Fr 0.15

JAPANPG.L

APA-NA.L_

A. 1çEuaLD u_

VALDEN Lv.- _{V_} 'V 'V a A y

r

u.

c 28

o

>-a

C) Q::

a

=

I

(18)

2:

>-D

o

er

D

m 10

i

S.S = 5

LOAD WATER UNE

WEATHER SIDE

F1 =02

cV

o

io

COURSE ANGLE

SEAS)

PRESSURE ESTIMATED

IN LONG TERM

WEIGHTA

(CONTAINER)

o V 4 n V o 4 o V 4 LCGO -8

-ÇUH)NA.Q o

JAPANp_

-PGEufÑ

WA LUÍ N 9 2 4

J

Q Q

,-y 4 G y q Q LI .La * LI 4

4:

o V o Q n 4 V V COURSE ANGLE o V V o e q V ò Q _q. c. V e $

.'

_t 9d 12d 150 180 (HEAD SEAS)

FIG. 1 6

_{HYDRODYNAMIC PRESSURE EflMATED IN LONG TERM}

-I?-

_{WEIGHT-A(CONTAINER}

L0G0

!-8

JAPAN.PG

JPNA,

FURl O

VLLDEN

\

D

o

oV 07

D

o

>-=

_o Q V e 4 Vo A.. A. o. 60

FIG.15 HYDRODYNANIC

S S - 8 1"2

m 30

LOAD WATER LINE WEATHER SIDE Fr

02

Ui er (r) (J) LU er L cri 20 C-)

(19)

e

J!,2r 2 Wave treqioncy in the block-I

1 Qfl.1 £5.2.

3.25.21 10.1.4

18

-1.bl ¿.13 9.0.1

Tailik .3 \V7ve frequency in the bluck-6

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,.92F.9T0.0.4

J 30.0) 0.54 0.IF 0.50 1.52 0.70 0.00., 0.34 0.10 T 4.30 0.00 1.63

l.iJ

1.64 7.32 2.lo I C.)6 s.$) 0.00 0.00 0.50 1.0'? I 0.67 C.C., 0.00 1.70 27 _0.041 0.54TO.95 0.00

C.9F.2,

coo o.c. co, _{0.c4 j} c.C. 0.30 0.11 1 i.0

c.co o.co I o. o.co o.co 0.00 0.017

O CO 000 I _0.00 0.0el0.00 _C.00 _0.20 _0.017 _0.27

COO 0.00 .c'0f o.co I 0.00 oca coo o.00

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 I 0.000.001 _0.00 _0.00 _0.00 0.00 0.00 0.00 000. 0.C'7 0.00 0.010 0.00 3.9) 0.04 0.00 0.00 0.00 1000.00 0)o.4) 1 61.1 ¿.7) 1.35 0.30 C.2.1 0.03 5.92 c.t, o 75 07) 2.7) 0.63

'

1.2.70 113.4.1 70.03 17.62 5.C- 1.37 0.39 1.6., .C.61.49 39.71 47.52 03.15 9.1' 1.42 0.4e 0.15 104.Z7 I

r-11.29 26.40 12.2) 9.99 3.52 0.9'? 0.20 ?035 0.04 1.35 9.07 9.7) 6.14. . 2.22 0.0.1 0.32 32.10

'

0.16 0.45 1,)? 1.53 0.42 DoS 0.1.4 i 0.07 5.02 3.75 75 0.60 1.01 1.02 0.0.1 0.6% 0.00 ¿.63 6 0.00 0.21 0.32 0.51 0,?! 0.15 0.00 0.0) 1.50 0.72 0.13 0.5.0 i 0.30 0.1., 0.10 0.04 0.0.0 1.14 0.00 0.02 0.07 0.00 C.0. 0.2) 0.19 C.C... 0.55 2.015 0.00 0.00 0.00 I 0.00 0.00 0.00 0.00 0.00 0.00 £ 0.00 0.00 J 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.2.7) 13.7) 9,00 0.00 1 0.00 0.00 0.00 0.00 0.00 f 0.00 0.00 _0.00 0.00 0.00 Q.C) 0.40 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.02 0.04 0.00 0.00 1.4.73 15.7) 0.0.3 0.00 0.0)0 0.00 0.20 C.03 0.00 C.00 0.00 LIII COU 42.4. _3)3.10 5.21.09 .1?o.n *7.45 33.3* 1.1.00 3.)) 1.63 1000.00

51.4 W4.'A YL.4-14 1. Ofli

¿.1.4.. 5L01 7 , 1.1 1) 0S 07

0.00 0.00

C00 0.00

¿.Y5 }L7.Sco l'Is cou

(20)

TL1e 4 Wave frequency in the biock-O

Tgble 5 Wave reque13cy in the bIock-7

-

19 -LLA l4Vt

P1J1X/ _£ A.LLflLIZOI 5 ' 9 0.1 1 15 17 0.73 ¿7.2.4 20.15 2.16 1.10 0.6 O.c. C.00 I 2.03 73.7 lIoso 1.t.40 76.56 24.17 9.P1 ).L 0.15 1,66 777,32 )Iß.05 1.75 I.66 6. .02 114.00 6.4,17 26.30 e.C'o 2.20 0.74 5.79 3.70 19.19 ¿3.10 ¿2.33 25. lijo 3.77 1.)3 t5.)4 4.75 0.49 4.39 13.59 16.14 -12.95 6.00 2.51 0.95 0.1) o.os 1.69 2.21. 1.66 1.11. 0. 3.!_.j?.,...,,,

.

0 24 9.4. 5.75 4.75 0.09 0.56.. 1.25 2.12 2.57 1.00 0.53 7.75 0,00 0.1 0.14 0.46 0.67 0.55 0.30 0.0)1. 2.06 0.00 0.09 0.39 0.3.0. 0.2.4 0.15 0.4/7 0.1) 1.)? 6.0 0.04 0.0 0,40 0.16 0.21 0.12 0Cl 0.00 10.75 0.00) 0.00 0./A) 0.00 0.00 0.00 0.00 0.00 10.75 Ç.C)0 0.00 0.00 0.00 0.00 0Cl) 0.00 0.00 0.0.0 1.2.75 0.00 0.00 0.00 0.00 0.00 0.00 6.00 0.0.) 0.00 19.75 0.00 0.01) 0.00 0.0.0 0.0.0 0.00 0.00 00.3 0.04) 14.75 0.00 0.00 0.00 0.00 C.C.) 0.0') 0.007 0.00 0.00 0.00 0.0.0 0.00 0.00 0.013 0.00 0.00 0.00 0.00 05,.0 4n4 091.1 AU. 164.62 215.71 2.51.4.0 101.1.4 50.44 52.'» 11.00 7.4 1.00.0.40 lILAi 6291 61314 0131.0 ¿13. F1Jt1CL5 5 7 9 11 0) 15 17 1(4.4.2 ¿6.0) 7.5e 2.70 0.6.0 0.0)7 0.00 4.3) 167.09 1.75 175.4? 133.34 73.30 22.9) 0.01. 2.04 0.61 3.50 ¿74,65 17.06 70.61 (.1,41 30.40 12,6 4.33 1.02 0,4.1 205.00 2 1.42 39.90 32.29 0.13.1.) 1.0.90 ).7'l 1.35 0.01 92.3) 4.64' 7.05 1LYO 11.45 6.70 3.11 1.02 0.14 .44.9.1 4.15 0.20 0.4.0 4.4? 1.02 0,1.1 0.14 0.00 0,00 ¿.0/? C.C/O 0,4.2 0.20 1.03 1.54 0.1.4 0.60 0.20 5.41 6.75 0.64) 0.41 0.5.4 0.11. 0.61. 0.74 0.41 0.3.4 3.79 0(4) 0.41 0.1/. 0.42 0,1/. 0.01) 0.01) 0. 1.75 0.007 0.0) 0.20 0.07 .03 0.20 0,07 0.0.) 0.0.0 0.00 0.0.0 0,04) 0.00 0.00 0.00 0.0.3 10.75 0.00 0.01) 0.00 0.00 C.C.1) 0.00 I 0.043 _.Q.0 0.00 0.06 Q... 0.00 11.7) 0.043 11.44) 0.00 0.042 0.00 0.00 1.2.75 0.00 0.00 0.0.3 0.330 0.00 0.04) 0.00 0.00 U.'?) 0.00 0,00 0.1.0 043 0.00) 0.03 C.C/O 0.00 0.00) 1075 0.00 0(30 0.0.3 O.C3 0.00 0.00 0.0.3 0.00 0.00 12.» ral0.qTh X2.19 210.20 92.62 431.72 15.74 5.54 2.0.15 1000.00

(21)

TLk 6

Wave frequency in the block-IS

TbIe 7 Wave frequency in the block-19

6LLJ 0Vt 0L.U0. _¿ AOL ns.a u » 15 17 1 126.1 55.67 1.00 2.30 c.0 T 0.1.4 0.1.2.f ¿.62. 197. 190.09 104.52. 65.6O 1.6.5.11 .4.60 2.43 1.2.1 2.06 74.97 2._7, 2.4.64 73.72 59.09I 6.EJ 2.32 0.1.4 0.75 192.4.5 s.to 23.6.6 Ï 1i.0

'.s

25h 0.52 0.29 04.77 2.06 7.06. 11.0$ 0.75 ¿.2)1 X.SS 0)7 0.39 _36.0.1 .4.7) i 0.32 0.06 1.5.0 T 0.61 0.07 I 0.00 0.0*2 $.29 5.7$ f c.fl. 2..C*D 1.72 1. i.aif 0.1.3 _coo 0.00 4.50 r 6..?) cci c.c.. 0.4) I

t.o

0.43 0.21 0.00 0.00. 1.73 775 c.0 c.25 0.39 0.22 0.04f 0.0*2 0.0 0.04. 1.15 0.7) 0.0*2 O.0 0.5.2 0.5.0 0.07 0.00 0.00 0.00 0.71 9.75 0.00 0.00 - 0.00 0.00 0.00 0.00 0.00 0.00 0.00

-10.75 0.00 0.04) 0.00 0.00 0.00 i 0.00 0.00 0.00 0.00 1.1.75 0.00 0.00 0.00 0.00 0.00 if 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.04) 0.C(j 0.00 0.04) 0.06) 0.00 0.062 0.00 1472 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.0*3

(liti '

357.30 547.54 177.2) 73.99 25.23 6.71 2.91 1.95 3.40)3.00 1644$ ,4Y1 LW _oiut 3 3 13 ILl. flOJ005 49.76 2.1.44 5.06 1.74

f

0.54 0.29 0.21 2.00 74.50 2..7) 206.92 1)0.41 p.20

20.000)4

2.00 0.70 2.43 34).6 16.93 2.7) 04.6) 97 II_. ¿7 5.4 11.7 .6.71

r

1.31 0.37 270.33 3.46 fl. )1. 41.61 20.57 6.77 L.M C.?) 1.20 O 24.4? 9.9) 16.54 4.5.4 2.36 1.72 09.74 3.75- 0.07 2.34 4.00f 4.6.5 ).0 2.56 0.47 0.10 25.43 0.2.2 1.15 4.59 1.7.-s 2.56 1.1) 0.54, 22.59 0.2.4 0.9.0 2.22 2.4.4 2.06? 1.06 0.6.2 0.2) 9.9.4 0,05 0.70 1.19 1.72 f_1.65 1.5 0.47 0.60 -0.24 7.19 61.7) 0.05 0.72 f 0.69 1.9) 1.22 _0.162 _0.22 _6.64 9.75 10.75 0.00 0.00 0.0)0 0.03 0.0*2 0.00 0.00 0.03 0.2.2 0.00 2.6.75 0.00 0.0*2 0.02 0.02 0.00 0.00 0.06.2 0.00 0.0*3 12.7) 0.003 0.00 0.02 0.06 0.01 0.00 0.00. 0.07 0.00 3.3.7) 0.410 0,410 0.00 0.0*7 I 0.00 0.00 0.410 0.0') 0.0)0 0.00 0.00 0.03 0.01 0.00 C.C*D 0.00 _0.02 14.7) 0.00 3.5275 0000 0.00 0.02 0,02 0.03 0-Cc 0 00 0.-Os (41.5 LU. _176.7*7 239.3.) 237.04 254.15 7.4.09 2$_3$ 9.6 9.3? lccc.00

(22)

21

-j

Tabk 8 Wave frequency in ihe b!ock-20

i(1 eLiT 901e CIII s.L... 7LAI0 S 3 U 13 i 17 ¿3.79 20.31 I 3.1) 1.33 0.) 0.1.2 0.70 4.10 J 75.41. 0.73 1 XC'9.24 lc..7) 95)7 11.75 o I 20.60 I ,s.oe ¿9.0? --- '--,---¿I.9..,2.73

¿1 1,62

0.65 29.43 2.73 2.52 J 27.98-t -19.1.0 6. IS 1.92 0.3) 145.9.0 0.17 1.42, ¿.29 551 .LI..__±.'1_0.62 1.19 1 _3.70 ₁₃₈ _0.16 _28,02 C.2 1.% j 8.1.7 7.6C 5.38 2.1 .1.17 0.34 26.07 C, C.14 0.t.7 2.32 3.7e 2.84 T 1.30 0.62 0.01 t 0.001 .73 2. 2.42 1.03 0.51 0.55 1 0.07 10.75

-r--0.00

001.00

030 .1.1) 231 1.59 0.74 033 0.00 734 0.00 0.01 0.00 0.01 0.00 0.00 C. 02 I 0.03 0.0) 0.04 0.01 0.00 0.21 1.i.73

o.co I o.c ace 0.03 C.0._ C.C4 C.C1 0.00 C. L t0.00 1 0.00 j3.7 0.01 0.00 0. 00 00 0.00 0.00 0.02. 0.00 0.00 0.03 0.02 0.00 0.00 0.00 C. CO 0.05 .L4..fl coo 0.03 0.01 0.00 0.00 0.00 0.04 15.73 j OYL6 £1.3. 175.k. 290.9 258.9) 15.8.10 '70.07 27.33 10.21 10.1) 1000.00

Table 9 Wave frequency in the block-2

ii(1 3411.0 12.51 C.I.A 4.1... )U.1C$ 3 7 10 13 15 1' 74.62 30.62. 3.4.1 1.3) I 030 0.14 _C.C9 5.71 _L16..1 0.72. 1.3.76 152.02 64.95 19.09 1 9.60 I 1.90 0.8.0 2.32 3878.5 1.7> 20.31 9.13 66.0') 3,.95 12.44 3.4.7 0.93 0.5) 251.42 2.7., ¿.0 24.94. 4.4.71 32.53 U,6o 5.00 1.40 0.5) 127.90 3.75 1.56 9.76 20.29 19.97 11.01 4.41 1.92 0.70 69.62 ¿.75 I 0.58 1.29 3.05 3.15 1.64 I 0.73 0.25 0.11 10.49 5.75 ₁ I O.3 0.70 ¿.7) I 3.4.1 1.59 039 0.13 17.27 6.7, 0.0'7 0.57 2.09 2.3 2.6.0 0.7.1 0.30 CC) e.0 8 0.0.1 0.30 230 1.o.. 1.46 0.57 0.19 ' 0.10 5.37 8.75. 0.07 0.20 0.44 0.00 I 1.00 I 0.57 0.)) 0.72 4.09 0.092 0.01 0.01 0.00 0.01 0.00 .00 0.00 0.03 10.7 5-r---0.041 0.012 0.0. 0.02 0.012 0.01 0-Ce .00 0.10 11.74 0.CD 0.00 0.000 0.441 0.00 0.00 0.4.0 0.00 0.00 1.2.75-0.04) 0.00 0.0.0 0.00 0.04) 0.4.0 0.00 0.00 0.00 13.75 0.00 0.00 0.00

0.001.00

0.00 0.00 0.00 0.0*2 1.4.74 0.00 0.00 0.00 0.00 0.0.0 0.00 0.02. 0.02 0.00 15.73 5 CIII LU. 24.4.04 3)1.25 125.6) 53.90 19.54 b. 58 01.43 1000.00

(23)

g O 9.15 10.75 12.75

u."

13.15 I 1.h.15 35.75

Tahk IO \Vave frequency in the b!oc-24

)0..AJ 41V) i16i ___1.19.5 95 t..t9 2.1.4 0.7) 20247 7.Y7 17.65 5.19 2.1.79 73.69 6!.60 I 27.63 6.11 2.75 37.11 25.52 1.4..6C s.7e 2.31 3.75 4.75 I 0.57 5.78 11.60 _7.66 0.10 0.1.4 1.96 1.1.8 6.75 0.770.61. 2.32 3.91 c.cO 1.12 0.47 0.68 8.75 C10 o.L1. 6.75 0C 0.00 0.00 10.75 0.00 0.00 1.00 0,10 1.1.75 0.00 0.03 0.01 0.00 1.2.35 0.10 i 0.17' 0.03 C.00 33.7) CCC ox 0.00- 0.00 1.10 0.10 0.00 0.10 15.75 0.00 0.10 0.00 0.10 40_li Slfl JLA!CL 15.0.C4 57.5.. 1.2.40 I 1.50 1 1.06 U7.C1 91.59 43.93 20.31 t 3.35 33.53 120.07 121.07 2.33 6.'7 . 16.27

Table H W

(qucv in the bock-33

5.17 9.2) 0.87 2.20 1...C4_4.13 1.80 1.1'? 0.00 11.53 0.35 0.800.50 i 2.45 0.35 0.00 0.001 _5.05

22

-5.50 0.72 0.17 0.10 0.00 0.10 0.10 t 0.00 0.10 0.10 I C.00 0.00 0.00 0.35 0.40 0.40 £2 OVIL 413. 1)kI$ 23.4.16 0.1.) 7.0 0.07 311.45 ¡05 061.1 414. RRIIXS 1.15 32.57 0,0)2 ¿.19 0.00 4.73 0.05 2.02 0.18 1.10 0.00 0.37 0.00 0.00 0.00 0.04 0.00 j 0.00 9.8) 0.10 0.10 t 0.02 _{0.02 1} 0.10 0.10 0.16 t 0.00 0.36 0.00 0.00 0.00 0.00 0.1)3 0.10 0.10 0.00 0.00 0.00 0.00 0.10 Ï 0.10 0.00 0.00 0.10 0.00 0.00 0.10 0.00 0.00 Ccc 0.00 t 0.00 0.00 0.00 0.00 0.00 0.10 0.00 0.16) 0.00 0.00 0.03 0.10 0.00 o. cc 0.00 0.00 0.00 0.10 i 0.00 0.00 0.10 0.10 304.51 250.71. 217.10 96.02 ¿7.70 15.20 23.71 0.00 41.1. _3)5.30 _390.6.9 75.15 26.8) '7. b) _lbS 38.1) 6.0? 0.87 0.1) 0.00 336.57 23.13 16.27 8.40 1.47 0cc 75.54 (1.37 10.20 3.10 1.37 0.00 43.61 0.10 0.10 5.03 0.57 0.00 1.47 0.58 0.10 1.47 0.55 0.53 t 0.60 2.65 0.00 O.0' 0.00 0.40 0.10 . 0.59 0.00 0.40 7 11 13 15 17 .9 11 13 17 0.00 11.1. 0.00

sr

2k. 57 2.96 ¿96.80 0.32 199.25 0.27 68.95

(24)

Table 12 _{Wave frequency in the bock-3l}

Table 13 Wave frequency in the bock-2

23

-2 1) 2.) 17 ¡JI 071,1 412. }LA11 2)5.70J ¿6.02 1 9.00 T 0.7)- 6.50 C.CC I 2.,e'2 0.0e 203.28 1.O9 I 91.28 b).3 27.65 5.32 2.0) 7.42 0.00 299.99 27.1) 1.2.1.20 125.60 I T 9.9) 0.7 _'1.00 _328.!? 2.)) 7.47 19.9) J 32.67 21.33 5.93 1.O 0.20 2.20 ¿.10 _20.9) _17.83 _11.30

_).)

_1.20 _CX 50.09 0.7 .7) 0.73 1.9) .4.0e 1.27 0.93 1.20 0.00 11.1) 0.05 b.')) 0.1) I _3.10 0.85 1.75 1.3) 0.o5 C.CC 9.70 0.07, 0_lS Ï 2.12 0.05 0.75 0.)) C.5. COO _3.70 0:00 0.00 0.36 0.53 0.50 0.9) 0.36 0.00 2,76 0.00 9.73 0.00 0.36 C.,) C.58 C.9) C.30 0.10 2.76 10.77,- 0.10 0.0.6 0.09 0.3) I 0.14 0.23 0.09 0.00 _c.e 0.00 J_0.00 0.00 0.00 0.00 0.00 0 CC 0.20 COO 0.00 6.00 0.10 0.00 0.00 CCC COO 13.73- 0.00 i 0.02 0.00 CCC CCC C.06 6.c 0.10 0.10 2.4.73 25.75 6.00 CCC 0.00 0.10 C.C'O 0.03 0.00 f 0 60 0.00 0.082 0.00 0.0.6 0.00 I 0.00 ç .00 0.00 0.00 0.00 Ï I 2CT1.L0. 270.62 211.10 224.30 3)7.09 I 24)1 6.00 2000.00

Ie,LI lAR 811220 ota 08U

422. P1.8100'S 9 11. 13 15 37 .. 5 .r 369.07 )5.)ß 13.98 1.7k 0.24 t C.0 9.64 0.00 25.6.31 1)2.42 95.62 5.0.65 19.5.8Ï 0.8.. Ö.0# 0.0,3 311.01 1.75 39.42 117.40 94.17 30.80 7.63 1.80 6.60 C.C6 258.27 2 1.60 9.73 22.53 39.67 12.80 .4.87 0.87 C.00 71.81 0.8') 5.5) 12,27 11.03 6.77 2.67 1.082 0.00 ¿0.1.6 4..')) f 0.1) 1.)) 2,23 2.40 0.9) I 0.47 1.13 . 6.10 8.59 3.7) 0.2.0 0.5.0 1.50 0.80 1.16 0.89 0.40 0.0.6 4.55 8.7) 0.10 0.50 1.10 0.86 1.10 0.85 C.40 J 0.00 5-¿.85 0.00 01.18 0.l.0I 0.80 C.4 01.27 0,34 I 0.00 .)ó I.?) 0.00 0.18 0.40 0.80 6.49 6.27 6.22 T 0.00 2.30 9.75 0.00 0.04 0.10 0.26 6.12 C.d 0.Co 0.00 0.59 10.7S 0.00 0.00 0.C*) 0.00 0.00 COO 6.10 0.00 0.00 2.1.75 0.10 0,00 0.00 0.002 0.00 0.10 0.00 0.002 0.00 12.75 0.00 0.00 0.002 0.10 0.083 COO 0.00 0.00 0.00 13.73 0.00 0.06 0.00 0.00 0.10 0.0,3 0.10 0.00 0.00 1.4.73 0.00 0.00 0.00 0.00 0.00 I 0CC 0.00 0.00 0.00 15.75 sa 017.1 I.J. _3.69 _286.39 _209.20 _9i.8C 35.70 12.82 22.80 0.00 1000.00

(25)

TMbIe 14 Wave freQueocy in the bock-33

15 frqutcv in the route EUR.--N. A. (W'cight.A)

214

-)..L l.4.0 37 11 20 2? 24 I .11112.1 022422 231227 .223222 .111131 L5 6.471 444100 1324 3911 7 ' flL 0 3 76.96 3.! ¿.65 1.t.4 0.53 C.1l 0.13 .31 2.2.1,7 I -.ne 1.75. 61.4.1 15.1; o.ee 2..9 0.13 2.3 4.02.3) 15.95 52,01 2. 13.12 )9.ç

-

12.41 3.56 1.06 0.55 242.03

3.25 2).)! ¿.1,e.. 31.es 11.e) ¿.93 133 0.55 122,07

7.27 1. 5 4.73 15.7 . 1e.t. 3.1.26 4.35 1.75 _{C. 53} _66.61 0.15 ..20 3.05 3.4 2.11 C.90 0.30 0.11 11.25 6.35 C.?) -. 1,5) 3.97 4.9% 2. 2.68 0.74. 0.26 14.95 7.75 0.09 0.53 3.8.2 2.33 1.57 C.o1 0.4.2. 0.16 7.0 5.7) 0.05 0,33 .1.31 1.43 3.31. 0.49 t _0.32 _0.09 _3.4.4 9.75 0.04 C.X 0.67k 1.1k I 1.03 4 0.42 0.29 0,2.4 ¿.2.1 4.1.75 0.00 0.00 0.00 t 0.00 0.00 T 0.03 0.00 0.00 0.00 0,00 0.0.2 0.01 0.1.1 0.02 0.01 0.00 0.00 0. .2.2.73 0.00 0.01 0.00 t 0.01 0.2? 0.0.1 0.00 0.00 0.05 0.00 0.00 0.00 0.00 0,00 0.00 0.00 0.00 0.00 3.4.73 0.00 0.00 0.02. t 0.0.2 0.00 1 _0.00 2.00 I 0.00 0.02 45.75 0.00 0.00 . 0.00 I C.01 0.02 0.00 _0.00 _0.00 0.02 i 1

U1CW75 su..a 22s.s. _jU4..03 s.ss 20.07 7.30 9.8e 1.Q0

1ì.00 _OL1 S.J. ) i 1)1.17 ¿7.fl 2.1.40 1 0,33 ¿.26 C.00 391.1) 73j 94.3 20.70 5.00 0.?! 3.2 0.00 295.1? 3. _,15 3191)

97

57.3) C.40 o.eo 0.00 331,44 2.7) 5.33 ,5...0 24.00 2.1.07 1.i: .2C 1.20 0.00 19.6' 3.7, I s.ro 33.30 57.5 3.6) I _1.20 120 0.00 0.00 33)0 7.6.9) 3.20 211 ¿.3) 1.0 1.07 3.7 .20 200 ¡.10 135 0.90 0.4.0 C. X 9.43 5.3) 1.29 2.00 2.1: 01; 090 C.40 CX 9.4.9 7.1 0.00 0.00 4.4: 0.2. 0.93 C..Z C.4.9 0.00 5.75-0.00 0.0e i 0.40 0.0.2 - 4.5) 0.42 C..Ç 0.00 2.4e 0.00 0.00 I _0.7.0 T C.0 0.23 C.16 0.12 0.00 0.67 c.00 0.00 0.00 I 0.00 0.00 0.00 0.00 0.00 0.00 0.00 D.V- 0.00 0.00 0.00 0.00 0.00 0.00 0.00 7.2.75 3.00 3.00 0.00 0.00 1.00 COO C.00 C.00 0.00 13.75 0.00 0.00 0.00 0.00 0.0.0 0.00 0.0.0 3.00 0.00 77 COO 0.03 I 0.00 .0'0 0.0: 0.00 COO 0.00 0.00 317.61 2t..)0 239.53 105.54 ¿h.) 3.4.90. 13.)O .C(

(26)

t

To*Ile i6 \\'ave frequency in th routh EUR.---. .-\. (Woight-B)

Toihle 17 _{Wavc frequency in the routt h'R.----N. .\. (Weight-C)}

-

25

-L. La.4. 17 1 17 1. 20 i 22 24 .1.60 .104.040 I .0010 .1o04 6.8Th .714 ¿ou 082.1 ¿3h. ?U4 S 1 9 ii 13 35 17 87.071 37.2) 5.)) 3.7 0.5b 0.17 .0.5» 4.37 0.111 2.60 1369* e." 114.08 167.9 7C.24 .09.02 3,7! 1.46 4.22.5* 1.75. U.)! 3.30 0.95 0.34. 231..18 2.73 ).. 22.4.) I 37.60 13.22 I 4..5.T1 1.20] _0.53 _1.-12.07 3.75 2h30 t.ah I 37. 36 32 4. 7 3.97. 1.61 0.66 t _o. _1.01 _2.72 _2.90 .0. 0.71. 1.36 f 0.221 0.08 4.58 0.62f 0.22I 0.20 * 1 1.36 33) 4.18 I I 1.33 1.77 0.70 0.13 4.16 7.7, 003 Q.)? 0.71 1.1.3 3.01 Q.53 0.261 0.27 4.41 8._75 0.03 0113 C..)) ,90 0.7 9.7) - - 0.09 0423 0.1v 3.27 J 0.00 I 0.00 0.00 0.00 0.00 Q. I 0.00 0.00 I 0.00 10

f0

I 7.031 _0.31 _{0.03 j} 0.331 0.CG 0.03

1.0O

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