tEOtQT
-8
PROPULSXVE PR7ORMLNCE IN IAV$.
) Ppf4j J.
'y&ts..Deift Shjbui1djrig Laborator.
PCJmsd for the Fourth fii*flnual Saostua on $hii 8pavtour at $.e
Juxis 1962.
I Intro4tction.
The resistanc. increas, ot a ship1 due to seawaves, results in many cases in a considerable los, of speed. In general this added resistanc, depends on th. dia.neions, th. form and the weight.
distribution of the ship but the quantitative knowledg, of r.sis-tance and propulsion in a seaway ii still rather scarce The
pr.-sent oonv.ntional shipfora has been developed by eaperical methods in oobination with experia.ntal work on shipaod.l..
There is no doubt that the optimum huilfora for normal cargo and passengership., sailing in still water, is closely approximated but with the present .tt. of knowledg. a naval architect cannot
claim that hi. design has an optimum propulsiv, performance in waves
It is possibl, that also in this respect th. long experience and the practical insight of the profession has led to ships that can-not be improved very much. Iumy opinion, however a definite ens-wer to thi. question cannot be given at th. moment because
systema-tic research in this area started only a few years ago.
Logbook analysis and seekeeping trials showed us th. order of magnitude of the power increase which is necessary to maintain a certain ship speed in a seaway. In a head sea and windforoe 3 a
normal cargoship needs 0% to 60% extra power to maintain th. still water speed. At windforoe 6 the extra power is approximately 50% to 100%. The usual power reserve of a ship is such smaller and in these conditions the ship has to travel with reduced speed. On the North Atlantic windforoe 5 is not an .xeeption in feat thi. value
is exesedid in about 50% of the tLme. In moderate head seas a
speed loss of I to 3 knots is not unusual for norma]. cargo.hipa at
-*
2-full power. Therefor. the investigation of the propulsive performance of a ship in waves seems worthwil.
When we limit ourselves ,to theoretical work and model xpari
acute
the research on resistance and propulsion of a ship in wavesis mostly of recent date Without being coapl.ts I mention the invee. tigations of Havelook, H.naoka, Maruc and tb. *odel
experi-ments carried out in this country, Japan, Great
In particular the recent
atodelteets
carried out at the Wag.ninj,S.ak.eping Tank can be regarded as a more systematic approach
to the
probisi, in which the influence of the shipform on th. resistance and powsr increase in wave, has been studied.A].iioet with.ut exc.ption th. experimental work has been donø
in regular waves. Until recently the relation btw..n resistanc, and power in regular waves and in irregular waves was not known to the profession. In
1957
a method was given by Maruo, to determine tb. mean rasistanca increase of a ship in irregular waves when the resis-tance increas. in regular wave components is knowfl[3J . Model .xp.-riments carried out in the D.3ft Towing Tank hay, ehown that Maruo's m.thod can be used with sufficient accuracy to predict tb. propulsive performance of a ship in longitudinal irregular waves ['.] . Loam ofthe results of this investigation are the subject of this paper. The possibility to determin, the r.aistance end the power of a ship in a given wavespeotrum allows a significant comparison of
dif-ferent hull forms. It is known that such a comparison based on r.gu-lar waveteete only, may be difficult. In regur.gu-lar head waves of mod.-. rat. height and a length which is approximately equal to the length of the ship the power morsel. may be in the order of 200% to 300%. The question of a shipowner how he could use such "unpr'aetical in.
formation" led to our experimental investigation.
XI. Pesstanc an
roulsion4n
r.u2r wavs.
Th.ory and experiments hay, shown that the, resistance increase
of a øhipin waves is mainly due to the heaving end pitching motions and the phasas of thee. *otone with respect to the wav.e fleflee.
tion effects also add to the resi.anoe but relatively thee. ffeote
seem to be amal].R
-3-Other secondary effects such as ate.ring resistance in oblique waves and the influence of a mean yawing angle in oblique waves may be mentioned too. The increase in power depends on the increase in
r.aistano., the chang. in pz'opulsiv. efficiency due to the increased
loading and th. influence of the hipmotions on the operation of the
propeller. With a linear theory )Iaruo found that the resistance
in-crease of a mathematical abipfora can be written as foilowsi
R f'j3gr232/L (1)
where is the density of the water, g is the aocel.ration of gravi-ty, r is the wave amplitude, B ii the breadth and L is the length
of th. ship.
Th. resistance increase coefficient is given as a function of the heave and pitch amplitudes and the wave amplitude
and the phases of heave and pitch with respect to the wave ,
namely:
Pr
Di,(i)2 + D22()2+ D12() (-v)
Oaar
9.
005
pD23(.j)
005
+ 1)33Karuo found that the resistance increase in waves is
indepen-dent of the still water resistance. Iurthsrmors it appeed that pit.
ching motions are the main Cause for resistance inoreas.\. Reflection
effects, represented by th. coefficient D33 are email. This is thus. trated by figure 1 which is taken from Naruo's paper. For small mo-tion amplitudes the reflecmo-tion ff.øts are relatively more important but then th. absolute magnitude of the resistance increase is very
small The same conclusion can be derived from model experiments * in
short waves the *otion. and the resistance increases ar. both small even in relatively high waves.
The largest resistance is found in th. region of pitch and heave resonanoc and this region may differ from that where maximum motion amplitudes occur.
In order to study the various aspects of tbe performanc. in
waves in more detail extensive model .xp.rint.nts were carried out
iith a 7+ f..t model of the "Maaadea", one of the ship. of the Holland America Line (figur. 2). This ship is ik m long and is
built on conventional lines corresponding to a still water speed of
about 17+ knots. The b]ockooefficient is 0,65 arid th. longitudinal
radius of gyration ii 23% of the length. Reei.tano and propulsion tests were carried out in still water end in regular wass of diff. rent lengths and heights. In each wave condition the mean values of speed, thrust and torque were measured at oonutant revolutions
of the propeller. The results for a wavelength .qa]. to tb. ship-.
length an, shown in figux'. 3. In total six wavelength, were conaide.
red covering the range
AlL -
0,6 toAlL a
1,6.It is important to note that th. propulsion tests were carried out with constant revolutions1 That means that at a certain .ed'th. revolutions did riot vary as a result of the varying propeller lea-.
ding which is caused by shipatotion. and wave action. Various auths have proposed three alternative methods for propulsion tests in waves n*nelyi constant revolution., constant torque and constant
power. In each of these oases an electronic control of the propel-.
1cr Motor is necessary,
Model experiments carried out at the seakeeping tank at
Wageningen have shown that within the experimental error, the three asthods give the saMe result. with regard to notions and propulsion. These results are given in Zigure 4 The constant revolutions Method was preferred for our teats because of the simple and accura-te control sysaccura-tem. The other values such as speed, thruit and tonqu.
show cyclic variations as a result of the atodel motions and th.
ac-tion of the way... Their mean values a Eth. analysis. An im-pression of the magnitude of the torque fluctuation. is given in figure 5. A comparison with the torque fluctuations measured on board of th. Japanese cargoehip 'Niussi Maru" show. that the same order of magnitude is found in practice, [] see figure 6.
The fluctuations of torque and thrust do not have a high come lsuon with the heaving and ptohing motions. Probably the variaUori of horiaontal flow in th. propeller reaniting from eurtng and the orbital motion in th. waves is the main cause for the variations in
torque and thrust
6]
. Unfortunatelythe eurging
otione were not
measured and therefor, a further analysis of thee. effects could not be made.
Th. tests in wavas were analysed in th. following way ftrst of
all the inor.aa.. of r.aistanc, thrust, torque and revolutions with regard to the .tilt water valuse war. dividod by the squared war. amplitude. Par resistance this seemed a logical approach since
theory has indicated that suob a reeiatanoe inoreaee coetfit,ient must
be constant for constant speed and wavelength. The experimental data
confirm that this assumption ii valid within the experimental acoura..
cy as shown in figure 7 where the dS.merizdonle.. resistance
coeffi-cient f!p is given for on. particular speed as a function of
wave-length. In the same figure the dimensionless increase coefficient. for thrust, torque, revolution, and power, as introduced by Voseera
[s]
ar. given nt.:S
nD3V
a
,
Kp
ObvioLu3ly all th. increases are approximately proportional to
the square of the waveheight. That means that at constant speed the
increases of thrust, torque, revolutions and power must be
approxima-tely proportional to the resistance increase. To investigate this in more detail the measured valuee of thrust, torque, revolutions and power in waves have been plotted in figure
8
on a base of resietano.at constant speed. Alec the atiDiwater values corresponding to the self-propulsion point of the ship are indicated in this figure and consequently the increase due to the waves can be read off easily in each Ca... In addition the results of overload teats in still
wa-ter are given.
It is clearly shown that the thrust and torque increase is
pro-portional to the resistance increase With acceptable error the ease applies to the increase ot power and revoldtioe. 8óe ran
Imay
be added to this result. The thrust i. related to the resistance by the well known formula:
-Zn general the thrust deduction
faoor is not constant; it
de.
pends
on the propeller
loading and on the nonaetationnapyeffects
oua.4 by' the ship motions.
XZ constant propeller charaoterietice in waves are aesiaed,
the
analysis of the wake fraction and thrust deduction factor revealsthat their' valu.s deor.aee with increasing ship motions. As a first
approximation, however, an averag, linear relation between thrust and resistance at constant speed may be accepted.
A possibi. Cxp].anatjon of the alatoet linear relation betw.eri
re-siatance and torque could b*
as followas The propulate efficiency
can be written as followit_1.v.. 't ,,
27nf.w (p',
or's
27
1..t
where is the propeller efficiency and
is the relatje rotati.
ye ffiai'enoy'. At constant speed an increase of resistance
corree-ponds to highsr
revolutionsand
lowerpropeller
ffici.nay0 These twoeffsots
811*
to eoa,p.rieite each other and as the variation to theother faøtor'. is relatively email, the torque is proportional to the
resistance at constant speed.
The revoluUons are certainly not proportional to the resistance or the thrust. In the usual range of propeller leaing we may assUme
a linelr relation bOtWSflyth thruet
conStant JC, x and theadvance ooetfioi.tj& ,
vies
+ 02
When thrust deduction factor and wake fraction are assumed to be con. etant it follows that *
B (1 - t)T + c2Vn
The exper'isent shows however,,
that
alsoin thie case the
inorea-ee of revolution. is appro*jat.ly
proportional to thi resiatanee in.
erease at constant ape.d and wavelegth
The aame applies for thi
power increase. This 5eSis more or' less unlogical, but the combine-.
-7-4?
tion of revolutions and torque appears to give a slightly curved po.. we, resistance curve and th. straight lin, approximation for the power inorsas can be accepted as an averag, solution.
It i remarkable that the still water ovsrload points plot very
well in lin, with the regular wave point.. Although th. individual wave results show some scatter it a.y be concluded that the average
propulsive **btata'. not greatly affected by the action of the way...
Finally th. influence of resonance is clearly demonstrated in
figure 9 where a. an xaaplethttr*twrets. ooefficient for various
model speed. is plotted on a base of frequency of encounter.
Maximum values are found in tie Td*.nLfy èf pitch and.kea,e re.Onan
III.
Ustflce and
ronuluion j iretiar
W)YS5.According to )(aruo th. mean increase of resistance in a given wave .pectra can be determined when the resistance increase in regu
lar wave components is known. The ordinates of the wave .pestrua
0rj ((A).) are related to the amplitudes r(''1) of the wave coaponsits
by th. well known formulaS
u . d")
(')) d r2(fJ )
C C
p
When the resiatanee increase coefficient for regular waves: is given as a function of the frequency of encounter for constant speed
the mean increase of resistanc, is:
. 2J0,., (').) or
P 2 o
gB2/L/
0 (J,) ,o ()) d(ABased on the approximately linear relation between resistance in.
crease on the one hand and the increase of thrust, revolutions and power on the other hand, similar expressions are valid for thrust, revolutions and power. 'igure 10 ilu8tratea the proceauro fo
torques the ordinates of the wave spectrum and the torque increase coefficient are aultipli.d and the surface of the resulting curv. is
.8-is proportional to the scan inoreasø of torque. It has to be emarked
that the Method cannot be used to determine the resistance co.ffi-oients frog the mean resistane. in irregular waves of which the ener-gy spectrus i. known. In this respect there is a difference with ship motions analyais where Ui. concept of a motion spectrum is used to
this purpose.
method has bien confirmed experimentally for torque, power and revolutions. This was done as followi. In irregular long
crested head waves the b*quc d t
rviIitsw
asured for a range of speed. Two wave spectra were considered; spectrum I with a significant wave height a k,13 c corresponding to 9 f.et full scal, and spectrum 2 with6,3
as c.rraaponding with the full scale value 11/3 a 14 ft. For the sase ipied rang. th. torque and the revolutions wire predicted by using th. results of the regularwave tbstd aM t seasiap £ zspa*iscn of th. predicted and
the directly seasurad values is given in figure 11, Apparently the agreement is good. It should be mentioned that in spectrum I a model
speed of 1,01, ./s corresponds approximately to the attainable ship
speed. In spectrum 2 this speed amount. to 0,95 a/s.
The curves in figure II are determined without using a friction correction on the propeller loading. The tests in regular waves were carried out by using the I.T..C. friction line correction but it ap-peared that this ooplication is not necessary because within th. .x.
perimenta]. accuracy the increase of thrust, torque and revolutions
in not influenced by the friction correction. As the thrust dynamo-meter was damaged during one of the first runs no sansuresents of thrust in irregular waves were available.
IV. £pa)iis of service performance dat*.
A large number of service performance data of the ship was available. They were collected on the North Atlantic rout. in the course of one end a half year. Each set of data contained the follo-wing observation. and measurements:
log speed of the ship
wind velocity and wind direction c) weveheight and wave direction
-9-d). shaft horsepower, aeaaured with a toreionmeter
0).
propeller revolutions f). course of the ship.At th. beginning and at the end of each voyage the draft f'4 dIft measured and th. displacement for ach serie, of observa-. tions oould be estimated. Also th. results of propulsion t..t. with a 6 meter model in still water were available. With the aid of them.
data th. tank horsepower for each specified condition of th. ship with regard to .peed and displacement could be determined. The varia
tion of displacea.nt did not exceed 15% and th.refoz. it was assumed that the tank horsepower at constant ship speed varied as
(diepisos-ment)".
Out of the 900 available sets of data, thre. groups were eeoc-ted, namelyt
smooth sea, no waves, light wind
light sea, coming in on the beam, light to moderate winds
waves on th. bow, direction of propagation within a sector from
30° starboard to 30° port1
With the data of group 'W' th. mean ship speed under ideal
condi-tions was determined. Tar all of the data in th. groups a, b and o the measured shaft horsepower ws correoted for wind resistance The wind resistance can be expressed as;
R,-where:
a coefficient depending on the dirsotion of the relative wind and the typ. of sup.ratruoture.
the density of air.
relativ. wind velocity.
A projected area above the waterline.
The power which corresponds to the wind resiatanc.
iii
p
Y2AYPR
-w
ws
the total propulsive efficiency. Th. coefficient C, was estimated
from published windtunn.l experiment, and
the known valuesofAand
.
1',
10 a
Secondly a mean roughness allowance could be determined from the d*ta of group"d'and'b"wbere the influenc, of the sea waves on
the total. resistance could be neglected.
ft
should be clear' that the r.ugbne.a. allowance in this particular ass. is assuast to beth. differenc. between the measurd power, corrected for shaft fric-tion (3%) and the sum of the power allowance for wind and the tank horsepower. Due to this definition it i pessibi. that our "rough.'
ness" allowanc. contains also a relatively small "oorrelation"
a]-lowance.
For each voyag. the mean value of
!oUhOs$
X9Wancs has (speed)been determined.
This procedure is justified when the roughness resistance
Va-riss as the square of the speed. For small variations of the speed a deviation from this assumption has only a small influence on the final reault. In this way a mean roughness allowano. could be de-termined as a function of the ship spied.Tb. data of group Q were arranged according to the wavebeight. To begin with the relation between the mean spied and th. observed waveheight was deterain.d, a.. figur. 12. Then th. power increase
due to the wa,.e was found by dedusting the tank bors.pow.r and the
allowances for shaft frietion, wind resistance and
roughness from the measured shaft horsepower. The mean power increase due to wave action as a funation of the observed waeheigbt is abown in figure13, It should be
full power of th. machinery was used to propel the ship. There was no speed reduction necessary
from the
point of view of excessive sbipmotione or slamming. To allow acomparison with the xperiaen.
ta] results two assumption. of a somewhat dieputable nature had tobe vts
for the condition.
under consideration the ship has been mc-.ving in irregular unidirectional head seas, definable by the
Neumsnh ópectruin family,
the observed wavehaight corresponds to the
average value ofthe one-third highest waves of the Neumann spectrum.
For five wind speeds up to 30 knots the N.uiinñ
peotra for
fully developed s wn iedtopredict the power increase at sea. - 11
For that purpose the powea' increase coefficients derived from
the mod.ltaete in regular waves were used. The r.ults are Shown in figure 14 whir, the power increase are labelled with the mean of th. one-third highest waves In combination with the speed
ob-served wavebeight (fjgure 12) relation, the power increase as a func tion of the wavebeight could be determined as given in figure 13, Obviously the power increase derived from the servics performance
data agrees 'very well with the prediot.d values.
In figure 15 th. total horsepower, consisting of tank boree'
power and the allowances for wind, roughness and waves is ihown as a function of waveheight The total. power developed is independent
of the weveheight. For waveheighta exceeding 4
meter no reliable
observations were available; in this range the
spaed..wav.heightcurv, was eiti*atsd. It is probable however, that for higher Waves
th. speed baa to be reduced because of the ebipinotione.
Xt is agreed that
the twq assumptions with regard to the formof the wave spectrum are of a.
somewhat arbitrary nsture and. oonCsiquently
not too muob vslu shouldbe attached to on. particular case
Very recently however, the thru;t ad power in seawavee of the
Britieh ship "Weather
Reporter" were analysed by using adireotl-measured sea
tste. Zt was reported that the predictions agreed
tiefactorily' with. the meaeur.d valuO [" j
The oonoluatons of the invsstigatione mar be that
a reliable
method for the prediction of the propulsive erforaance in a
given sea state is now available. The method can be used to
com-pare the performance of various
bull arid propeller designs inepsciied wavaconditione.
REFERENCES.
1, TM Hiv.lock
"The deaping end pitching Motion of a ship". Phil. hag. 'J 194Z.
T. Rnsoka.
Theorstical tnvsstigation concerning ship Motion in regular waves".
Preos.dinga Symposium on the Behaviour of Ships in a seaway,
Wagening.n 1959,
H. Memo.
excess resistance of a ship in rough see.". mt. Shipb.. Progress, 1957w
1i. J. Grritsaa, J.J. v.&. Bosch W. Beukelnan. in regular and irregular wav..t..
mt.
Shipb. Progress, 1961.0. Vose.re, W.A. Swaan,
"Soae sesks.ping teeta with a Victory model".
mt.
Shipb. Progress, 1960."Investigation into ths sea-going qualities of the single corey sargo ship "Nias.i Maru" by actual anI model ship experiments 195k".
Shipbuilding Research Association of Japan.
H.J.S. Canham, D.E. Cartwrigbt, 0.J. Ooodrioh N. Hogb.n. Seakeeping trials on OW.S. Weather Reporter".
0.75 0.75
kr
0.50 0.25 2.0 1.5 1.0 0.5-0.5
INFLUENCE OF PROPELLER CONTROL
ON HEAVE, PITCH
AND MEAN
SHAFT TORQUE FOR
IL
t°°
WAVE HEIGHT
I
RADIUS OF INERTIA 0.265 LPROPELLER CONTROL CONSTANT
RE.
0CONSTANT TORQUE 0 CONSTANT POWER 0 S 0 0.10 ' Fr PITCH TORQUE 0.20 0.30
Lit
OL
RES I STAN:C E I NCR:EASE COEFFICIENT
PITCH SYNCHRONISM D33 III I 0.1 0.2 03
- Fr
PRISMATIC COEFFICIENT
0.667
RADIUS OF GYRATION
0.25 L HEAVE SYNCHRONISM 0.4 0.5 1500 1000to
0.5 50° 0 0 HEAVE SYNCHRONISM 01 0.2 0.3 aS 0.53 3L/8=8
B/T= 2
BLOCK COEFFICIENT
U o' 150
