Speed loss in waves

(1)

SPEED LOSS IN' WAVES.

by

Prof .ir.J. Gerritsma

and

I.r.J.A. Keuning.

Reportnr

772-P

March 2, 3 and 4

HISWA-Symposium 1988

Deift University of Technology

Ship Hydromechanics Laboratory Mekelweg .2

2628 CD Deift The Netherlands Phone 015 - 78 68'82

(2)

11151/LA

_{SYMPOSIUM 1988}

Under the auspices of:

HISWA,, Wéesperstraat 93,

1 018 VN Amsterdam,, The Netherlands

and

Waterkampioen Magazine,

Postbus 93200,,

2509

BA

The HagUe,

The Netherlands.

Production:

Eelco Piena/Waterkampioen

Cor van Horick/Scheepstechniek.

Publisher:

Koninkiijke

Ned'erlandse Toerlstenbond ANWB,

P0 Box 93200,

2509 BA The Hague,

The Netherlands.

(3)

SPEED LOSS IN WAVES

by

Prof. ir. J. Gerritsma

and

Ir. J.A. Keuning

6.3

has 'been calculated- using the data of

Series 1.

The results are compared- with mod-el tests results.

The correlation is satisfactory,. even though the actual

beam-draught rati.o exceeds the max-i-mum beam-beam-draught ratio of the Series I b-y a-pprox. 17%.

The original Deift Series I was set up in 1975 and reflected

-the design trends of that time-.

Now ada-ye mode-rn design may differ considerably from the

original designs: light displacement yachts have beam to draught

ratio' up to 9 or 10, and in the' case of a maxis

and very large cruising yachts the length beam--ratio's are also exceeding, those of the original e-ries-.

Therefor it,was decided -to extend 'the Delft -Systematic Series

with another 6 'models.

-The main particulars of these models are given in Table 2. The length--ratio varies from ₅ to 8,, the length-beam

ratio va-ries from

3.5

to

5.5

and -the beam-ratio ranges from

2.to

_12.5.

(6)

-86-The series of models has been developped in cooperation with Van der S't'ad.t and Partners.

Model k06 is the parent model of the Series and model O7 is

equal to model LfO'8 but with a.iarger displacement,. Figure 3a.

All six models have a prismatic coefficient Cp = O.5k8 and the same longitudinal position of the centre of buoyanc:

LCB = -2%

The bodyplan of the parent is' given in Figure 3b, together with the parent bodypian' of the Series 1.

The line plans of all models of the new Series II are given in the Figure #..

The wide range of variation of the considered' parameters is clearly demonstrated.

it is considered tha,t the parameters tested in the combination of both series will cover the past, present and future design at least for the foreseab].e future.

S'ince velocity prediction programs based on the Delft Systematic Series are being used for handiôaping yachts the problem of Incorporation the different the behaviour of various yachts in a seaway has come up.

The present state of the art Velocity Prediction Programs all presume ideal sailing conditions i.e. constant windspeed and no waves.

For handicap reasons this would be acceptable, since the only goal is to compare different yachts, if all different

type's Of yacht's should be affect.e,d by the waves in, a simular way.

That this is not the case has been clearly demonstrated in

Ref.

(3)

as early as

_1973.

In general seawaves have an important influence on the per-formance of a sailing yacht, in particular when the wave

direction is forward o,f the beam, and the wave length is

ap-proximately one or two' times the length of the yacht.

In this respect it. was shown (Ref. (3')) that a 'low L/V1/3 ratio

induces a higher speed loss in waves and also that concen-tration aT the mass near 'the midship is effective to increase the relative pitch damping and so to reduce pitching and ad-ded resistance in waves.

(7)

-In this Reference the windward performance of three sailing

yachts with equal wa.te;rlinelengtha (i'Orn') but different displacement

(8.2, '9.8, 11.1. tons) in irregular bow waves 'has been calculated

to demontrate the effect ofadded resistance in waves on the windward performance and the influence of the displacement and the concen-tration of mass.

In figure ₅ the speed made good as calculated for the three yachts is given for three true wind speeds: VT.W = 7

Kn.,114

Kn. and 20 Kn. on a base of significant wave height.

in figure 6 the optimum' true 'angles are given for the lightest' yacht (4 = 8.2 tons) in the same wind and wave conditions. In these calculations it was assumed that t'he added resistance in waves is not influenced b:y heel angle.

The results demonstrate a considerable influence of waves on the performance of a sailing yacht.

For the considered range of displacements the lightest.

IJvl/3 = 5.0

yacht has the best performance in calm water as

well in waves.

With increasing wind speed the difference between the three designs becomes smaller.

The lightest yacht in this comparison is' certainly not a light displacement yacht to modern standard with

'L/V1/3 = 5:

ultra light designs may exceed L/V1/3 = 7.

It is evident from these results that yachts with different displacements are not affected in the same way by the waves. A simuiar result has been obtained from calculations with models with' different longitudinal moments of 'inertia. It was shown that 'yachts with a small radius of gyration

perform best in' waves.

in order to be able to incorporate the effect of waves in a Velocity Prediction Pograrn it is essential to validate

the use o,f 'strip t'heory calculation of motions and added

resistance a's arelativel' easy and reliable tool.

To validate t'he u'se of these methods jt was decided to measure the mOtions in waves of the two most extreme models in' the Series

ii,, i.e. model

k5

and k071 and to compare these with calculated

result's. '

(8)

-The teat should include the effect of heel and leeway on the motions and added resistance to add information to the' long lasting discussiq,n about the importance of the parameters on both the motions and the added resistance.

in this paper the results of the experiments of the models.

1407 and '1455 will be given., in particular with regard to the

motions and the added' resistance in waves.

Model 1455 has a moderate volume of displacement V = in3

arid' a very small beam-draught ratio BWilT,c = 2.4, whereas model 407 has Yc = 3.2 ni3 and Bw1JT0 = 9.6..

The experiment'el results for pitch, heave and add'ed resistance

are compared with stript.heory.ca.lc,uiations, takingint'o account the effects of the'.hee'l angle.

In addition the added resistance has been calculated for b'oth models in realistic, irregular waves,, assuming that the wave direction is equal to the wind direction.

MODEL EXPERIMENTS

1. Resistance and side force in calm wat'er

The experiments have been carried ou't with 2.3 in GRP models in the nr.i towing tank of the Deift Ship Hydromech'anics Laboratory.

Keel and 'rudder a'r.e identical to those o:f the 'Series I, see Figure 1.

The models were equipped with a turbulence stimulator as described in (i).

From a Prohaska's plot.: CT/CF versus Ffl4/C.F a form factor 'of 1.12

for model 1455 and a factor 1.22 for model 1407 has been found from

the upright resistance tests 'in calm water, see Figure 7a' and 7b. These plots indicate a satisfactory turbulence simulation in both

cases.

The differ.ence in form factor 'reflects' the different hull form of the' t.wo considered canoe bodies..

In Figure 8 full scale upright resistance are give.n on a base of forward speed. (LWL i in).

The difforence.between themode.rate and the light displace-ment'yacht is clear: a steep increase o'f resistance for the

heavier' dispbcement yacht 'for speeds 'exceeding, the hull speed (V 7.7 kno!ts)., wheras the. light yachts resistance

curve resembles that_of_a_piani.nghull_tosome extend.

.Some points, are calculated with 'the 'existing polynomical

(9)

expression for the upright resistance derived form Series I.

Therefore the test with the light models of Series II have been performed to much highe,r model speeds in order to be

able tO predict the sped of these yachts in higher true

wind speeds more accurate.

For both models resistance and sidefo,rce has been measured for a range of forward speeds, leeway angles and heel angles. In Figure 9 the dimen8ionle5s sideforce is plotted on a base

of leeway angle.

The influence of the larger asymmetry of the underwaterpart of the light displacement hull is clerly demonstrated.

With a 30 degrees heel angle the light yacht needa approximately a

₅

degrees leeway for zerO sideforce,, whereas the other hull form needs only I degree, asäuming that the extrapolatios. of the experimental, data to zero sideforce is permisseb].e. The difference between the heeled resistance R and the upright resistance RT can be expressed by equation

Ci):

R

(C0 + c22 )F

'+ C3

(1)

qS

where: . - heel angle in radians.

The coefficients C0 and C for both models have been determined from the model exper.ment and are given in Table 3. The first term in (i) may be regarded. as the induced resistance., whereas the second term represents the resistance due to heel only.

in Figure 10 the experimentel results and their representation by Iquation (1) are given.

The results show that the heel angle has a large influence

on the heeled resistance in case of he light yacht , with the high beam to draft ratio when compared with the moderate and small

displacement yacht.

The heeled resistance, which for the major part consists of induced resistance, differs approximately by a factor 2 for equal sideforce

(10)

2. EXPERiMENTS IN WAVES

Eperiments in waves have been carried out with the two models to compare the. pltchihg and he heaving motions as well as the added resistance.

The tests were carried out in regular head waves both in the upright condition and with a heel angle of 20 degrees.

in addition the influence of a leeway angle has been studiied by inciuding in all test conditions zero and 5 degrees leeway.

The experiments were carried out at one constant speed:

Fzi = 0.3O, corresponding to 7.1 knots for LWL =i4 m, in wave lenghta variing from 1 to 2 Lwj and wave heights up tO 0.025 LWL.. The models were free to heave and pitch, but restrained in all other modes of mOtion.

The pitch radius of inertia in both cases was 0.245 LOA. The experimental set up is given in Figure 11.

This drawing is not to Sca1e: the aft guidance. of the model

is a very light conàtruction to avoid unacceptable variation in the pitch mass moment of inertia.

The experimental results are given in Figures 12a and 12b, where the dimensionless heave and pitch amplitudes and the added resistance are plotted on a base: of the. ratio wateriine length / wave lenth. The dimensionless motion amplitudes and added resistance. are

defined by:.

heave:

pitch: = OáL/2lrCa

added resistance:

R/gL c

From the results it ma be concluded that the leeway angle and

therby the produced sideforce on the keel and rudder has a. negligable influence on both the motions and the added resistance in waves for both models investigated.

So for measuring the: motionS of a yacht in waves itis not necessary to carry out tests with leeway.

(11)

The effect of the heel angle of 20 degrees is very small for the light displacement high beam over draft ratio yacht: the heave and the pitch motion are hardly affected and the added resistance tends to be slightly lower in the. heeled condition.

In the case of the medium displacement ]ow beam to draft ratio yacht the heave and pitch motion are ølightiy smaller in the heeled

condi-t ion.

Consequently the added resistance for this hull form is also smaller in the heeled condition.

Comparison of the measured mo.tions of both models yields that the maximum motion amplitudes of model 1.55 are approximately twice as large as thos.e of, the light displacement hull. This results from the relatively low pitch and heave damping of the moderate displacement hull, wich has a small beam-draught ratio.

Linearity of the motions with wave amplitudes in the considered range of wave heights (up to 0.025 L) was quite satisfactory.

To compare the performance of the two hull forms as sailing yachts., ballast 'weight and sailpian have been determined using the following reasoning.

For model 407 a specific weight of 40 kg/rn3 for the yacht without

ballast. keel has been' assumed and for model 1+55: 6.5 kg/rn3. The height

of the centre of gravity, has been located at 80% of the depth of the canoe body.

The differance of this weight and the weight of total displacement give's the maximum possible ballaSt weight.

This has been placed in the identical keels 'beginning at the bottom

Of the 'keel.

The sailpian follows from the ratio of sail area moment and resul-ted. stability moment at 30 degrees heel angle, as taken from excisting satisfactory designs.

These consideratiOns have, led to the following 'stabilities and: sail dimensions (see table 1+).

Velocity predictions have been made for both yacht's. A speeds polar diagram for. a true wind speed VTW = 15 knots is given i.n figure 13.

(12)

-The optimum true wind angle close hauled is _{37 degrees for model} 455 and. 43 _{degrees for model LfO7 and the optimum speed made good}

are respectively 6.2 and

_5.8

knots.

However for true wind angles larger dan 90 degrees the light yacht is faster, the maximum yachtspeeds beiing 9.0 knots for model. ₄₅₅ and 10.2 knots for model 407.

This seems to agree with practical experience: light _displacement yachts do not point as high as heavier sailing yachts.

For light yachts a suffiont righting moment is very important. If

model 407 should; 'have a GM = 2 rn, _{inStead of} ₃ _{m, the maximum speed}

made good would decrease 1 knot at _VTW= _{15 knots!}

EXPERIMENTAL AND CALCULATED N0TI0!S AND ADDED RESISTANCE IN WAVES

1. Regular waves

To investigate the possibility to include the effects _{of seawaves}

on the velocity prediction of sailing yachts, the motions and the added resistance of the two considered hull forms have been calculated

by using a strip; theory method. The added resistance caIculatio is based on the method given in (4), assuming that this _resistance component is realated to the radiated damping, waves, which are

generated by the pitching and heaving, yacht. ajid the corresponding relative motion of the hull with respect to Surrounding water. Damping coefficients and hydrodynamic _{mas of 2-dimensonal}

cross-sections have bee.n determined with Frank close fit metod (6), including the case with 20 degrees heel angle.

The computed motion amplitudes and added resistances agree very well with the corresponding experimental values in case of the light yacht, as can be concluded from figure 12a.

The moderate d'isplcement hull heave motion correlates satisfactory with the calculated results, whereas the m&ximum pitch amplitudes are under estImated by the calculation in both situations with _and without keel.

This phenomenon is also known from calculations _{performed for fast} and slender Cargoships.

In general the agreement between experiment and calculation improves with

increasing beam-draught ratio.

(13)

-In the upright condition the result of the calculated added resis-tance in waves is close to the experimental results for the moderate displacement low beam-draught ra'tio hull.. For the heeled condition however the calculation yields

higher

results.

This could be due to guidance apparatus aft used during the teats. In the case of the heavy models this may not have been sufficient-ly strong and as a result o.f this the resistance measurement may have been slightly erroneous. For the determination of the added' resistance

two rather large quantities have to be substracted which aggreviatea the error made.

In general the experiment's show that for a light displacement yacht the heel angle has only a very limited influence on the motion

ampli-tudes and the added resistance,. This was :to be expected since the

motiOn appeares to be highly dampened. This trend is confirmed by the calculations so that the results are most certainly correct in a qualitative sense.

In the case of the medium displacement low beam to draught ratio hull the measured motions are slighti.y smaller in the heeled

condi-tion.

In particular the added resistance in waves is smaller when heeled fOr this hull.

The calculations do not confirm this trend, however:: added resistance is hardly affected by the heel angle.

It should b,e noted however that the model shape used for these ex-periments are quite extreme considering the present day designs. This holds in particular true for the model Zi55, which resemble's

probably most to a 12 m when beam to draught iatio is concerned. For these types of vessels Kakla and Penrose

(5)

found an even bigge.r difference of measured added resistance between the zero heel upright and the heeled condition.

2. Calculation' of added resistance in irregular waves

The added resistance in irregular waveahas been calculated for a range of wave spectra with wave periods from 1.5 a. to & a. and' unit wave height.

(14)

For the wave spectra the formulatio _{by Brètschneider for a. long} created sea has been used:

S C(.w)

A5 exp(-Bw'.)

(2)

with: A = 173 H213/T and;: B = 691/T

where; ui,3

_{- significant wave height}

- 2irm0Jrn1,, average

_{wave period}

Also the influence of directional spreading of wave energy has been considered, using, a cosine squared spreading _function:

S'(w,i) = 2/v cos'p

_{. S()}

_(3')

where,: - wave: direction

In view of a velocity prediction for all headings, it has been assumed that the wave direction is equal to the wind direction in all cases. In Table '5 the calculated added resistance is given for one speed Fn = 0.30 (V 6.83 kn, _{=1r4 rn.), amd a uniform}

wave height of 1 meter, as a function of _{the wave period and t!e true}

'ind-wave angle.

It, should be mentioned here that _{the added resistance is to a fair} degree proportional t wave height squared.

For instance1 when H1/3 = 0;.'5 _{in the values in, Table 5 should be}

mul-.t'ipli,ed by (0'.5);2 = 0.25.

The data in Table 5 show that _{in a sea with directional spreading} of th.e wave components the added _{res1st'ance. is abou.t 10}

- 15% lower than in un'idiectional long crested _{waves. The veioc:ity pxéd'iction}

in waves w.ii, be carried, out for _{'long' crested seas only.}

The difference in added resistance for the tw,o hull forms is clearly shown in table 5.

The ligh't yacht ha's' _{a much lower added' resistance,, alSo taking the}

displacement into account.

It should' be kept in mind' that

the added resistance fop 455 is over-estimated by approximately 30%. when the _{yacht has a heel angle of 20.}

(15)

This contributes t approximately

5 -

10% increase in total resistance. Maximum added resistance in the close hauled condition (true wind

angle 1+0 - 50 degrees) occurs at a wave period T1 =

2.5'.3

s. for

model 1+55 and at T1 = 2.2..₅ s. for model 1+07.

This corresponds to: the dif.ference in the natural pitch periods, of the two considered hull forms:: the light displacement yacht has the smallest pitching period.

By using the data in Table 5 a velocity prediction in waves has been

made for both yachts, in particular for wind and wave directions 490 degrees.

In Table 6 the wave conditions, as used in the calculations, are

summarized..

In Table 7 the speed loss due to the added resistance in waves is given as a percentage of the cairn water speed for a true wind speed of

15 knots.

The light displacement yacht has, a lower speed loss in wave.s than the medium displacement yacht.

It depends on the wave' condit:ions and the wind speed if this compen-sates the lower speed made good when sailing to windward in calm

water..

For wave directions, larger t:han' 90 degrees the calculation o.f motions and added resistance is small in this conditions and far less

impor-tant compared with sailing to windward 'as regard speed reduction. Although calculations with different Longitudinal radii of gyration have not performed with these two models it could' be concluded from the previous calculations that the effect of 'the smaller pit:ch inertia plays less impo.rtna.t role in the added resistance than. the volume of

displacement and' BIT ratio.

ThLs will in particular hold true for light B/T ratio yachts.

CONCLUSIONS

The calculations of motions and added resistance in waves compare's

satisfactory with experimental result's in the case of light displace-men'tyachta having a large. .beamdraught rati'g. For medium displacemen.t

yachts with a small b:eam-draught ratio the correlation is somewhat le8e satisfactory.

(16)

-Calculated added résistance, based on strip theory method can be used for a velocity prediction in waves.

Such information may be useful for design purposes as well as for the determination of racing handicaps.

ACKNOWLEDGEMENT

The, auteurs are indebted R. Onnink who carried out the modelexperiments and to J.M.. Journe and A. Versluis _{for doiing the} coinputercalcu-lationa for the velocity prediction in clam water and in waves.

(17)

-Nomenclature

BWL : waterline breadth CF : frictional resistance

coefficient

CT

: total resistance

coefficient

Cp

i

prismatic coefficient

sideforce

I

₁

mast height

J I

fore triangle base

: sail dimensions

P

main sail hoist

E j

main sail foot

Fn : Froude number

GM.

metacentric height

g : acceleration

due to gravity

1113 : significant wave height

LCB :

longitudinal centre of bouyancy in % LWL

LWL, L

: water line length

q stagnation pressure -

.½p2

R : total resistance with heel.

and leeway

RT : total resistance in

upright position

P.M : righting moment

RAW :

added resistance in waves

Sc : wetted area, canoe:

body

S :: spectral density

Ti : wave period T1 2irn0/m1

:

draught of canoe body

: yacht speed

: speed made good

true wind speed

: heave amplitude : leeway angle pitch amplitude

wave amplitude

: heel angle : wave length : density of water circular frequency

vóiümé of displacement., canoe body : weight of displacement Tc

vs

VMG

VTW

Za B 0a A vc A

(18)

WFJ1J)

FIGURE 1. PARENT MODEL SERIE I.

Tablel

Farm parameters Deift Systematic Series

4.3 - 5.1

LCB 0 - -5% LqJJ

CP 0.53 - 0.60

LWL/BWL

2.8 - 3.6

(19)

2 0 4 o . EXPERIMENT CALCULATION

'Jill)

6

vs

KNOTS

PICUE 2.. COMPARISON OF EXPERIMEN-TAL AND CALCULATED

UPRIGHT RESISTANCE.

Here the upright resistance of an Admiral Cupper with a

beam-draught ratio of

6.3 has been calculated using the data of

Series I.

The results are contpared with model tests results

The correlation is satisfactory, even though the actual

beam-draught ratio exceeds the maximum beam-beam-draught ratio of the

Series I' by approx. 17%.

(20)

Table

Main particulars of Deift Series 11

(Based on LWL

1,0 m.. ).

1IMIIII

UV4WI

.aaa.

_{sa a_ - - -- W}

101

--I

FIGURE 3e. BODY PLANS OF MODELS 407 AND 455. FICURZ._3b.-PARENT-MODEL--DELflSERIZS UAMD

DELFT SERIES II.

NRLWLBWL

(rn.) (:rn) Tc (rn.) Vc (rn3') BjJ Tc

V3

355 10 2.86 0.73

7974

3.50 3.9 5.0 357 10 2.8:6 0.27 3.000 3.5.0 10.6 . 6.9 .4O6 10 2...50 0.4:8 4.617 4'00 5.2, 6.0 407 10 2,.5f0 0.26 .3.217 4.O0 9.6 6.8. 4.08. 1.0 2.5:0 0.20 1.972. 4.0:0 12.5 8.0 455 1.0 2.24 ', 0.9.4 7.915

447

2.4. : 5.0 457 10 2:.2i 0.34 2.923 4.52 6.5: 7.0

PARENT MODEL. SERIES I

4.78

Nodel. 455. L..AL/B. a 3j'7

- 5,.o _4.01

LwyJDwg - 1.5 BwrJrc 2.5.

PARENT MODEL SERIES It

Model 1O7

L/a½ - 6.0 - 6.0

LWIJBWL - 4.4 LWL/BWL - 4.0'

(21)

LA4JJJ

J.J/ LJLJ

LLJLV

- i .._ -

----r

-_a__

--;Figure 4. Body plans of models Seriesli.

102

L/A'FJ- 7.0 L/D - 3.5 1./A'!! - 5,0

LiD - 4.0 L/A'6 - 6.0 L/D -4.0 1./A'!) - 6.0

(22)

z

TRUE WIND SPEED 20 KN

LWLIVc'3 - 5.0

14 KN

71c

'I.

0 I 2

SIGNIFICANT 'WAVE HEIGHT rn

FIGURE' 61. TRUE WIND ANGLE IN WAVES.

1 2 I

SIGNIFICANT WAVE HEIGHT

(23)

CT/CF

1 2 3

Figure 7a. PROHASKA PLOT OF UPRIGHT RESISTANCE

TESTS.

FN'/CF

Figure lb. PROHASKA PLOT OF UPRIGHT RESISTANCE

TESTS.

(24)

15

Figure 8. UPRIGHT RESISTANCE MODELS 407

AND 45t5

0

PREDICTED USING SERIES I DATA 0 0 2 4 6 8

LEEWAY ANGLE - DEGREES

0

0 2 4 6 8 10 12

LEEWAY ANGLE DEGREES

Figure 9. SIDEFORCE

VERSUS LEEWAY ANGLE.

I0

0

(25)

10

0

Table

Reeled Resistance Coefficients

F I

MODEL 455

I I

MODEL 407

3 4 5 0 1 2 3 4

Figure 10. HEELED RESISTANCE FOR MODELS 455 AND 407.

1i06 -Model nr C0 C2 i.O3Cff 407 .2.00 '9.15 1.0.6 45.5 1.. 24 0.10 4 .0

I

U v) U.

(26)

Figure 11. EXPERIMENTAL SET UP FOR HEELED

WAVE EXPERIMENTS..

(27)

I

2.0

I

1.0 1.0 0.5 0. l of - 00

..

0° "Co 0.5 '1.0 0 0.5 11* - 1/1 A0010 IUZITANCI

. 20°

0.5 1.0 0 0.1 1.0 1./I

111

-20° 1.0 I- J I I 0 0.5 1.0 0 0.5 1.0 0 0.5 1.0 0

111 -

11* -

Ill

ICkY, I

,-00

In

L 0.5 1.0 20° 0.5 1.0 0 0.5 1,0 1/1 :1/5 £0010 IUIflAC

Figure 2a. MOTIONS AND ADDED RESISTANCE ti9ura 12b. MOTIONS AND ADDED RESISTANCE

IN REGUZR WAVES, MODEL 4O7. IN REGUER WAVES, MODEL 455.

Ln - '.5

- S rN - 0.30 rio 0.30 5 - 00 S AS

-5°

A ,

- Calculation

- Calculation - 20° ho S 0.1 1.0 In -0.5 1.0 ,0 - 00 0.4 0.2

t

(28)

Table 4

Sail dimensions and rightinq moment

Model nr. 407

Model nr.455

I 19 .23 rn 21. 42 m 6.41 m 7.14 m P 17.78 rn 19.97 rn E 5.08 rn 5.71 rn 9.90 ton 23.62 ton GM 3.Olrn' 1.22 rn

RM

5l01 Nrn/degr. 4934. Nm/degr.

TRUE WIND ANGLE

900

#44i'441%

00 1800 MODEL 407 TW 15 KN. MODEL 4

Figure 13. SPEED POLAR DIAGRAM OF MODELS 40.7 AND 455 FOR VTW 15 KNOTS.

12 10 2 0 2 1'O 12

(29)

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V

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.

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a a

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a a

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a

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U

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a

a a

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a a a a U U U

U I

U B B a I U

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U

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(30)

Table 6 Wave conditions

T1 (s) 1.50 2.00 2.500 3.0 4.00 5.00 5.5 6.0 (rn) 0.40 0.45 0.475 0.5 0.75 1.30 2.0 3.0

Table 7