ARCHIEF
Th
Case for Muthu Ships with Pr1ca Reforric
o R.tcmc Chrctrîstics
By Harrison Lackenby,' Member, and Crimpbetl Safer,2 Visitor
Twin-hulled ships have advantages where large deck oreas in relation to displacement
are required, but their resistance performance is generally worse than single-hulled ships of comparable dislacement owing to the greater wetted surface of the twin hulls
coupled with unfavorable interference of the wave systems. The paper describes ari investigation to develop hull configurations to overcome this disadvantage and particular
attention is concentrated on a special form of three-hull or trimaran configuration in
which the hulls are so disposed to give favorable interference between the variouswave
systems, especially transverse waves. The outer hulls are shaped so as not o generate wave systems outside of the craft. Model experiments have confirmed very substantial wave cancellation with this arrangement and when considered in relation to a 19½-knot conventional car ferry this has the effect of offsetting a large proportion of the resistance due to the greater wetted surface. At higher speeds the trimaran shows to advantage and the general indications are it would show promise at "overdriven" speeds where wave-making resistance would be severe. Possible applications of the multihull concept are
considered. In particular, the large deck area has obvious advantages for certain types
of ship such as vehicular ferries, roll-on roll-off ships, and for the compact and efficient stowage and dkcharge of cargo containers. In the mihtary field the concept appears at-tractive for aircraft carriers.
TWIN -HULLED or catamaran arrangements have ad-vantages for certain types of ships where large deck areas
j:elation to s amnt arc required such as ferries in
general and train and vehicular ferries, in particular in-chiding "roll-on, roll-off" ships. The concept is also at-tractive for the compact and efficient stowage of cargo
containers in container ships generally and also for fishing
vessels, particularly of the factory or freezer type where large working decks are required. Thereare also possible applications in the militar' field which are referred to later.
In this connection a number of twin-hulled ferries have
recently been built for operation on the inland seas of Japan and in Russia cargo carrying catamarans are in
operation on some of the major rivers.
A disadvantage of the twin-hulled arrangement is that
'Head, Naval Architecture Division. The British Ship Research Association. London, England.
Expriniunt Ofiier, Nnis' and Vibration Section, The British
Shio Rscarch Associatinu. London, England.
Lab.
y. Scheepsbou
Technische Hogeschool
Dell t
14-1
except under certain conditions their resistance perform-ance is generallyworse than that of a single-hulled ship
of comparable displacement for two reasons:
The wetted surface and therefore the skin-frictional
component of resistance is significantly greater.
The adjacent wave systems set up by the inner
surface of the hulls generally interfere unfavorably with each other and increase the wave-making component of
resistance beyond what it would otherwise have been.
In regard to (ii), recent work by Everest 11 2j has
shown that there can be some favorable interference of the diverging wave systems in twin-hulled craft at. speeds in
the neighborhood of F. = 0.35 or 1/'E = 1.2 (knots
and feet) over a limited rangeof transverse spacing of the
hulls. These favorable zones are sensitive to speed
changes, however, and at higher speeds the interference
effect is generally unfavorable,
The object of tise work described in the present paper
Nunìbers in brackets designate References at end of paper.
DECK OVEF D1KCO(C1DG kRCE KULL N \ ( LSPCE.1E TICKKESS O DO'OAV LKVER (b) (o) (b)
Fig. I Three-hulled configurations Fig. 2 Two-hulled configurations
was to develop hull configurations which will overcome the resistance disadvantage referred to earlier and at the same time maintain the advantages of the catamaran. In particular, attention is concentrated on a special form of three-hull or "trimaran" configuration in which the hulls
are so disposed as to give favorable interference between the various wave systems, especially the transverse waves,
and the outer surfaces of the outer hulls are shaped so as not to generate wave systems outside of the craft.
The investigations are based on model experiments which were carried out by BSRA in No. 2 Tank at Ted-dington by arrangement with Ship Division NPL.
The Mu!fihull Congurafion
The multihull configuration mainly considered in this paper is the special three-hull or trimaran arrangement,
the essential features of which are shown in Fig. i(a).
The center hull can be regarded as a more or less con-ventional hull and there are several particular features of the side hulls in the configuration:
The' are each generally similar to one-half of the
central hull on either side of its vertical middle line plane.
They are offset transversely as shown and at the
same time placed aft of the central hull, the outboard
surfaces being plated to produce a generally flat surface.
L
=
B=
b Tx,y,z =
A=
V=
R=
V=
=
length in generalhalf-length of mathematical hull breadth in general
half-breadth of mathematical hull draught
right-hand orthogonal system of axes with the x axis forward and z vertically downwards
displacement (weight) displacement (volume) resistance in general speed in general effective horsepower p
©
DECK OVEK KTECOKECNG WO HUL1\
From the resistance point of view the object of this
arrangement is two-fold:
To stagger the hulls in the fore-and-aft direction such that the wave systems produced in the interspaces by adjacent hulls are phased so as to produce favorable
interference and a reduction in wave-making resistance.
The outer surfaces of the side hulls are arranged
to he generally flat so that they do not generate any wave
systems outboard of the configuration and thereby any
wave-making resistance.
In regard to (i) above, it would be expected that
sim-ilar effects could be obtained by having the two side hulls leading the center hull. Similar effects would also be
ex-pected by having two side hulls only in which one leads
the other as indicated in Fig. 2, but in this instance means
would have to be taken to counteract any bias in course stability which might arise from the asymmetry of the arrangement. In general, one could have more than two
or three hulls abreast, that is a plurality of hulls in which
adjacent hulls are staggered in the fore and aft direction
so as to obtain favorable interfererïce of the wave systems
from the adjacent hull surfaces, the two outside hulls again being preferably "half hulls" as explained in (a) above so as not to generate wave systems outside of the
craft. Nomenclature
= mass density
= R. E. Froude's nondimensional resistance coefficitht
293SR1 (A V) = 427.1P,./ (A2 V) with R and A in tons and V in knots,
= 250/ir
RI (pV'V'() in any consistent system ofunits
= R. E. Froude's speed-displacement coefficient
= 0.5834V/A'6 with A in tons and V in knots
V/Vt' in any consistent system of units
14-2 The Case for Mu/fihull Ships with Particular Reference to Resistance Characteristics
/
Fig. 3 Thrc-hulled cross channel ferry
Referring to (ii) above. Fig. i(a) shows the outside
surfaces of the outer hulls to be quite flat and parallel to the direction of motion. Actually, with such an arrange-ment one would expect a very small amount of wave-making to be generated owing to the development of the frictional belt along the length of the surface. This could be overcome by progressively setting in transversely the
otherwise flat outsides by relatively small amounts
corre-sponding to the displacement thickness of the boundary
laver, as shown diagrammatically in Fig. 1(b).
British 3 J, United States 4], and other patents have
been obtained for these various nuiltihull configurations.
The Model Experiments
¡n the first place some exploratory model tests were
carried out to ascertain whether the principles already
de-scribed were effective and this proved to be the case. A
mudel of mathematical hull form was used for these tests which was similar to that used in the investigation on the
interdependence of the components of ship resistance 5,
6). The effect of varying the fore-and-aft "stagger" of
the hulls was investigated and also the effect of changes in the transverse separation of tile hulls. Although the
tests proved the effectiveness of the principles involved, the frictional component of this mathematical form of
very fine block coefficient was unusually high in relation to the wave-making resistance, with the result that in
ternis of total resistance the gains due to
wave-cancella-tion effects were relatively small .An account of this
ex-ploratory work is given in tile Appendix.
A description is given here of a more comprehensive
series of experiments on what was considered to be a more practical type of hull form for which the frictiona' re-sistance was a smaller proportion of the total.
One advantage of employing a wave-cancelling svsteni
Fig. 4 Body plan for three-hulled ferry form
might be that it would enable the hulls to be designed
pri-marily with a view to facilitating construction and there
would be less need to adopt forms of low wave-making
re-sistance. In developing the lines for the new model and in fixing the main proportions, possible eventual
appli-cations to cross-channel ferries, stich as that shown sche-rnatically in Fig. 3, were also borne in mind.
Particulars of the center and side hulls are given in
Table 1. The side hulls are centerline "splits" of the
center hull as previously explained. The body sections are shown in Fig. 4. Experience with the mathematical hull form had shown that in certain circumstances very steep waves were formed in the space between the hulls and for this reason the new models were given generous
freeboard. Turbulence stimulation was by means of studs
as in the previous experiments and the hulls were con-nected together b' a specially built towing frame of more rigid construction than that used in the previous tests. This permitted the fore-and-aft displacement of the hulls
to be varied up to a maximum of 6 ft and the overall beam
to be varied from 4 to S ft; the towing point was about 12 in forward of amidships of the center hull and 2 in
above the load waterline.
Resistance experiments covering a range of speeds were made for each of five different fore-and-aft settings
of the center hull relative to the side hulls: and in four
of these cases the effect of increasing the transverse
spac-ing of the hulls was also investigated. As before, the two side hulls were tested separately as a catamaran with a
The Case for Mu/i'ihu!! Ships with Pcirìicu!ar Reference to Resistance Characteristics 1 4-3
Table i
Center Hull Side Hull
Length bp, ft 10.00 10.00
Breadth, ft 1.08 0.54
Depth, ft 1.50 1.50
Draught, ft 0.729 0.729
C', 0.53 0.53
Displacement, lb (fiesh water) 260 130
MODEL SPEED Y REH SEC)
Fig. 5 Three-hulled ferry form.
Resistance with fore-and-aft setting 3 ft O in
MODEL S'REO v(rt PER SEC)
Fig. 6 Three-hulled ferry form.
Resistance with fore-and-aft setting 3 ft 6 in spread of 5 ft, but it was not possible to test the center
hull as a separate unit because of its lack of stability. The
basic results are given in Figs. S to 9 for fore-and-aft displacements of 3 ft, 3 ft 6 in, 4 ft, 4 ft 6 in, and 5 ft, re-spectively. In each case the resistance curve for the two
O LS
5 6
MODEL SDEED V SER SEC )
Fig. 7 Three-huBed ferry form.
Resistance with fore-and-aft setting 4 ft O in
side hulls alone is shown for comparison with that for
the three-hull unit.
The vertical line marked Linterference speed" on these diagrams corresponds to the speed at which the transverse wave systems would be expected to interfere most
favor-ably with each other on the assumption that there were no other interaction effects between adjacent hulls. That is, the speed of the model at these points is equal to the
speed of a wave whose half length corresponds to the
fore-and-aft stagger of the center and side hulls. This
need not necessarily coincide with "minima" in the
re-sistance curves, however, because of blockage effects in
the interspaces and interference between the diverging wave systems. This is evident from Figs. S to 9.
It is clear from Figs. S to 9 that the introduction of the
center hu'l produces some favorable wave interference
which becomes progressively more pronounced, and moves
towards the higher speeds, as the fore-and-aft setting of the hulls increases in stages from 3 ft to 5 ft. This is to be expected because there is more to be gained in this
respect the more severe the wave-making. At all settings
above 3 ft 6 in the introduction of the third hull actually
reduces the resistance over part of the range while
doub-ling the displacement of the configuration. In Fig. 9, which shows the results for the 5-ft setting, the resistance
at the highest speed of 8 fps is 14 percent less with the
third hull.
It is apparent from Figs. 5to 9 that the wider 5-ft spac-ing of the side hulls can produce significant improvements
in resistance over parts of the speed range as compared with 4-ft spacing. Some of the irregular interference
ef-14-4 The Caso for Multihu!! Ships with Particu!ar Reference to Resistance Characteristics
THREE OVERALL HULLS BERM 4O T ii
¡z
-/
/
/f
I
--RDE HULLS ALONE SEI SPREAD --HAEE HULLS OVERALL BEAM A' O OVERALL SEAM -cf-
-j
f.
i_
S -. J /_.SLOE HULLS ALONE SET RPSBCADI
THREE HULLS OVERALL 05ERLL BEAM 4-0 BEAM S0 I -- ----\-
\__/
J J,//
//t--HULLS ALOSE SET SP RE U D ¡-7---/
/
0 32 0 30 O 26 O 25 o 24 0 22 20 0 8 o o LA 028 V. 0 22 0 20 0 3 0 3E 0 LS OR 0DB 026 0 32 0 30 o 28 026 o 2A 0 27 0 70 O a OL S OUS 6 7
400EL soso v' se ssc)
Fig. 8 Three-hulled ferry form.
Resistance with fore-and-aft setting 4 ft 6 in fects shown on these figures may be due ¡n part to trim effects. The three-hull units were rigidl interconnected
and when trimming under-way the immersed form of the
center hull would tend to differ from that of the side
hulls especially for the larger fore-and-aft settings.
Tn both the preliminary and the present tests ¡t was
noted that there was generally little wave disturbance be-hind the three-hull units with the optimum configurations, which confirmed substantial wave-cancellation.
From the design point of view perhaps the best way to
consider the results is to compare the three-hull
configura-tion with the two-hull unit and a convenconfigura-tional single hull
on the basis of a common displacement, and this is shown
in Fig. IO. As the basis of comparison a displacement of
3730 tons has been taken which corresponds to that of a car ferry having a length of 331.5 ft and service speed
of l9 knots. The corresponding lengths of the indi-vidual hulls are given in the table on Fig. 10, as well as the overall lengths of the three-hull configurations. The various © curves are ship predictions basedon the ITTC line without Eiallowance.EE The curve for the single hull
has been estimated from Taylor's Series, but using the ITTC prediction method.
The main features of Fig. IO are the relatively high
re-sistance at lower speeds of the multihull arrangements and the superiority of certain of the three-hull arrangementsat
the higher speeds. The former effect is due, of course,
to the greater wetted surface of the multihuil
arrange-ments and the effect of this on the skin friction which
pre-ponderates at the lower speeds. In this connection it is of interest to note the wetted surface area of the different
configurations:
Single hull 18.000
Double hull 31,750 sq ft
Triple hull 31,300
At its service speed of l9,V2 knots the single hull has 13
percent less resistance than the best trimaran, but the
- .,00s soso v(rî BES SEC)
Fig. 9 Three-hulled ferry form.
Resistance with fore-and-aft setting 5 ft O in
TWO HULL S NU L E
o
I0
Fig. 10 Comparison of resistance characteristics of
multihull forms and conventional single-hulled car ferry.
Resistance coefficients © are ITTC ship predictionB (without allowance). All units have the same total
displacement of 3730 tons
wetted surface of the latter is 74 percent greater. At this speed the two-hulled catamaran has IS percent more
re-sistance than the trimaran and 31 percent more than the
single hull. The trimaran shows to advantage at the
higher speeds, equalling the performance of the single hull
at about 23 knots and at 24 knots it is 10 percent better;
INaNE HULLS OVE8AL ØCUM a' 0
oVEAUsoJ:i2
J_
SEDE HULLS BEONE 52E SORE NO ESSES NULLS O/ERALL OVERALL SEAU Q BEAU 5'-O -SIDE NULLS ALONE SET SBWEAD/
/
KEY OPENNDHFTKETPNG OF HALLS HULL LENGTH HT) c.,ER*LL LFNC.YU (ET) / I / J / I S ,/' ¡
-3O. L
:
45% L tU. L 250::
aso 350 325 ::: n, iTS-
SIDE HULLS/ /
/
/
i /
/
/
/,f
/
/
COGKENYOSNL::.
O EO1/sUEHss HALESf/
//
/,/
///
SERVICE SPEEDThe Case for Multihull Ships with Particular Reference to Resistance Characteristics 1 4-5
--
-''r
-O 5 20 25 SPEEO (aNOTE) o at o 2U o M o 22 V. 0 20 o 's o lt Ola 40 30 © 20 03 02 02 O 2a a (lb) VE 0 22 020 0 8 0 6 O 4at this speed the trinaran has less than half the resistance
of the two-hulled catamaran.
It should be pointed out here that had the single hull been designed for 24 knots, its form characteristics and length would doubtless have been different and a more favorable resistance at this speed may have resulted. On
the other hand, some optimization to suit different speeds tiìight well be possible for the multihull arrangements and
in particular Fig. 9 suggests that, with wider spacing of the hulls, the trimaran might have done better at these
higher speeds.
The general indications are that at high or "overdriven" speeds where wave-making preponderates, the particular type of trimaran considered shows l)romise. Reference is being made here to the speed range beyond the "boundary speed" as defined in a recent paper by Silverleaf and
Dawson 181.
General Comments
Apart from the resistance advantage at overdriven or
high wave-making speeds there are a number of other
con-siderations in the trimaran arrangement, namely: The main characteristic has been referred to al-ready, namely the large deck area in relation to the dis-placement. This is particularly suited for the carriage of deck cargo especially roll-on roll-off cargo-carrying ve-hicles, rail transport of all kinds, and road transport gen-erally. The deck could also be used for the construction
of accommodation spaces and passenger amenities. From the strength point of view at least two decks
spanning the hulls would be desirable and these could
form a more or less open-ended 'tween deck which would be eminently suited to "roll-on roll-off' vehicles, rail-way, and road transport.
The arrangement could usefully be considered for
container ships of all kinds including those short-haul operations from the main container terminals as well as the transoceanic ships. A particular point of interest here is that the configuration is very amenable to separating
the "cargo carrying" part of the craft from the "buoyancy
portion" the shape of which is conditioned by hvdrodv-namic considerations and not generally suited for the
ef-ficient and compact stowage of standard rectangular
con-tainers or unitized cargo. This is a problem in the design
of high-speed single-hulled container ships and reference
has also been made recently to the difficulty of handling
even general cargo in the narrow wedge-shaped end com-partments of modern high-speed cargo liners of very fine
form. On the other hand, the wide rectangular dçk space of the trimaran lends itself to the development of box-like superstructures and the "buoyancy" or
"hydrody-namic" portions could then be used to house the
pro-pelling machiner-, fuel, and stores. Moreover, as men-tioned in (b), the. box-like cargo carrying superstruc-ture could be easily arranged to be open-ended to facili-tate removal of the containers horizontally rather than
vertically. !.
The large deck space and stable platform might be considered appropriate for the operation of aircraft
14-6 The Case for Mujfjhu(( Ships with Particufar Reference to Resistance Characteristics
and the arrangement might therefore be considered for aircraft carriers of all types.
A large 'tween deck and associated deck area would also be attractive for freezer or factory fishing ves-sels with a view to improving working conditions and pro-viding a stable platform for processing work.
(J) As already mentioned in (c) , the supporting hulls
would normally accommodate the propelling machinery and as these would be more slender than conventional
single hulls they would be particularly suited to compact prime movers such as gas turbines. The higher powers
as-sociated with these would also be appropriate in achiev-ing the higher than conventional speeds where the wave cancelling effects are more pronounced. Even so, it is expected that in the central hull there should be adequate
space for conventional machinery. In the particular ap-plication considered in the previous section the 250-ft long central hull would have a beam of 27 ft. The
sup-porting hulls would he used for the carriage of fuel. stores, and perhaps some cargo.
( g) The trimaran arrangement, of course, would have
greatly increased stability as compared with conventional
single-hulled ships and therefore would have 'more
re-serve in this respect.
The presence of three independent hulls with
ap-propriate subdivision would considerably improve the
underwater integrity of the craft consequent on broaching due to damage of any kind, as compared with conventional single-hulled ships.
In nuclear ships the reactor could be placed in the central hull and thus be well protected b the side hulls and deck against collision damage which is a
par-ticular hazard in single-hulled ships.
The flat vertical sides would facilitate berthing alongside quay walls and jetties and also facilitate cargo handling generally, particularly containerized cargo and
roll-on roll-off cargo-carrying vehicles.
Unlike conventional craft the shaped portions of the hulls need not be specially shaped so as to reduce the wave-making resistance of individual hulls to a minimum
bearing in mind! that the wave systems are intended to
be largely self-cancelling. This would be conducive to the development of simple hull shapes with curvature lamgely in one direction which would ease and cheapeh the
pro-duction processes.
(i) The arrangement is conducive to the development
of deep-draught, largely wall-sided hulls, slender in
rela-tion to their length, where the buoyancy would be deep-seated in the water. This would make the craft less al-fected by surface waves and rough water than
conven-tional ships.
Owing to the very significant wave cancellation
and! absence of wave s'stems outside of the craft there
vill be a niinimuni of water disturbance or "wash" due to its passage, even at high speed, which will be advantageous when operating in rivers or restricted estuarial waters.
Propellers and rudders could be fitted to the hulls .
may be some virtue, however. in fitting iropellers on struts or propulsion pods between the htills in the region of the after cud. In these positions there is likely to be
a very significant "wake gain" clue to the venturi effect as the vater slows down on expanding into the enlarging cross-secticnal area. This would lead, of course, to high propulsive efficiency.
On the debit side might vel1 be the question of "slam-nìing" of the (teck in rough weather. This vill b
influ-3cnced
tinderdeck. This problem svili need careful consideration,I)V freeboard and also the shape of the exposedbut is 1)robablY not insuperable.
Interestingly enough sonic very recent model work by Lewison 9 at NPL Feithani on the seakeeping perform-ance of niultihull craft is cncourazing in this respect. This
involved tests in simulated head seas corresponding to Beaufort Numbers up to 6 on a catamaran model and an equivalent trimaran both of which represented a proposed
multihullcd container ship of 2600 tons displacement.
The trimaran configuration was somewhat similar to the
three-hulled arrangement considered in the present paper
in that the central hull lead the side hulls with a view to
obtaining favorable interference of the transverse wave
systems. The side hulls, however, were symmetrical in
plan view about their own' middle line plans and did not
have flat outer surfaces. They were also somewhat shorter than the central hull. The resu]ts were extremely
inter-esting in that it was concluded that the trimaran was
Po-tentially the more seaworthy for ocean-going commercial
service. In particular, it was immune from slamming whereas this vas pronounced on the underside of the open
deck of the corresponding catamaran. The motionswere
slightly less than those of the catamaran.
The wave forces and moments on the interconnecting deck of a trimaran are an important consideration and
BSRA is presently commissioning a comprehensive series
of model tests in waves on the particular trimaran con-figuration considered in this paper. Thèse tests will in-clude the measurement of all six force components be-tween the hulls iii-a series of simulated sea states at
var-ious headings. It is anticipated here, of course, that the
transverse wave bending moments are likely to he uf the
same order as the longitudinal moments. The opportunitY
will also be taken to measure motions and slamming
be-havior.
Also ori the debit side is the fact that the structural weight will also be greater than a comparable conventional single-hulled ship, but this might be accommodated if the
other advantages were sufficientlyattractive in a
particu-lar application. 1f necessary this could be particu-largely
over-come by the use or partial use of light alloys if economic
considerations made it practicable.
There is also the question of docking these very wide
craft. In the aJ)plicatiun considered earlier, the configura-tion with 250-ft hulls would have an overall beam of 125 ft at the wider and 100 ft at the narrow spacing. This
would doubtless severely restrict the (locks available, but would not he insuperable.
Conclusions
it has been shown that with the special three-hull
con-figuration considered, very substantial wave-cancellation can be effected leading to considerable reductions in
wave-making resistance as compared with cons ntional
single-hulled craft or twin-single-hulled catamarans. When considered
in relation to a l9-knot car ferry, however, this advan-tage is more than overcome by the greater skin friction brought about by the increased wetted surface area of the trimaran. Nevertheless, the total resistances at this speed are flOt greatly different. The trimaran is signifi-cantiv better than the equivalent twin-hulled catamaran at this speed.
1f there is a need to increase the speeds of ships
sig-nificantiv above present levels, that is, well into the "over-driven" range where wave-making would be very severe,
then the indications are that this special trimaran shows
promise.
In sonic applications the multihull arrangement would
be particularly suited to the installation of advanced prime movers such as gas turbines and the associated high-power outputs obtainable would complement the trimaran
principle in breaking through into significantly higher
speed ranges than practicable with conventional craft.
Apart from considerations of resistance and propulsion
the most obvious characteristic of multihull craft is the
large deck area which can be made available and this has
obvious advantages for certain types of ship such as ve-hicular ferries, roll-on roll-off ships, and also for the
com-pact and efficient stowage and discharge of cargo
con-tainers as described in the paper.
There are many other points in favor of multihull ships
as already discussed. There are also some disadvantages, but these are not considered insuperable.
It is considered that the trimaran principle described
warrants further investigation and that design studies should he made for particular applications.
Acknowledgments
The authors express their thanks to the Council and
Director of Research of the British Ship Research
Associa-tion for permission to publish this paper. They also wish
to acknowledge the assistance given by M. N. Parker,
B. Eng., BSRA, in carrying out the work, and of staff
members of Ship Division, National Physical Laboratory,
Teddington, England.
References
i J. T. Everest, "Wave-Making of a Catamaran
Ship.' National Physical Laboratory, Ship T.M. 151,
November, 1966.
2 J. T. Everest, "Further Measurements of the
Wave-Making Resistance of a Catamaran Ship," National
Phys-ical Laboratory, Ship TM. 167, March, 1967.
3 H. Lackenby, "Improvements Relating to Multi-plc-Hulled Vessels," British Patent Specification Yo. I,-052,497 '1966 (Application Date: November, 1963).
4 H. Lackenby, "Improvements Relating to
Multi-plc-hulled Vessels," U. S. Patent Specification No.
411,-519 1966.
The Case for Multihu!! Ships with Particular Reference to Resistance Characteristics
SIDE HULL
DIRECTION OF MOTION
Fig. 11 Basic model configuration
o
EOUATIOB' OF SURFACE !.'
Fig. 12 Mathematical hull form
5 H. Lackenby, 'An Investigation into the Nature
and Interdependence of the Components of Ship
Resist-ance," Trans. RINA, London, Vol. 107, 1965, p. 474.
6 J. R. Shearer and J. J. Cross, 'The Experimental
Determination of the Components of Ship Resistance for
a Mathematical Model," Trans. RINA, London, Vol. 107,
1965, p. 459.
7 G. H. Gadd and N. Hogben, "An Appraisal of the
Ship Resistance Problem in the Light of Measurement of
Wave Pattern," National Physical Laboratory Ship Re-port No. 36, October, 1962.
8 A. Silverleaf and J. Dawson, "Hydrodynamic De-sign of Merchant Ships for High Speed Operation," Trans.
RINA, London, 1967.
9 G. R. G. Lewison, "Seakeeping Performance of a
Tri-maran and a Corresponding Catamaran," National
Physical Laboratory, Ship T.M. 172, April. 1967.
Appendix
Exploratory Experiments with a Model of Mathematical Form
Infroductory
To achieve the type of wave cancellation intended it was essential that the transverse wave systems front the two side hulls should be similar to those set up by the
center hull. As explained in the paper this was brought
about by making the center hull symmetrical about the middle line, and making the side hulls each identical to one-half of the center hull when split tlown the middle. The arrangement is shown in Fig. 11. These preliminary
experiments were based on a mathematical hull form sym-îEzs bO E
±
bO t O IA O LF O 04 3 4 6 74OHEL SACEC V (FT N SEC)
Fig. 13 Mathematical hull form.
Resistance of center hull when towed separatelyand
of two side hulls towed as a catamaran. Water temperature 62 deg F
Table 2
Center Hull ' Side Hull
Length 10 ft O in 10 ft O in Beam 1 ft O in 6 in Depth 11.5 in 11.5 in CL, 0.444 0.444 Displacement 173.6 86.8 lb \Vetted surface 14.88 sq ft 13.69 sq ft
metrical fore-and-aft which was chosen because the
wave-making and viscous components of its resistance had al-ready been well established from previous work [5-71.
This form was of extremely slender proportions, however.
with the result that the wave-making was relativelysmall
in relation to the viscous resistance.
Particulars of Models and Towing Arrangemeits The particulars of the center hull and corresponding
side half hulls are given in Table 2.
The three hulls were connected by an angle frame which
allowed the relative position of the models to be easily
adjusted. The maximum spread, i.e., the overall beam, of
the trimaran model allowed by the frame was 8 ft 7 in,
and the maximum fore-and-aft displacement or "setting"
of the center hull relative to the side hulls was 6 ft 6 in.
A standard model towing frame was secured to the angle
frame, and the towing position was 3 in above the water
level to allow the side hulls to be tested alone. To
stimu-late turbulence studs were fitted 1/2 in from the bow of
each model hull.
The lines of this forni together with the mathematical epression for its surface are given in Fig. 12.
Resuifs of Experimenfs
The resistance measurements with the single hull
configurations the center hull was tested alone and the two side hulls were tested as a catamaran at the
maxi-mum spread permitted by the towing frame, namely S ft
14-8 The Case for Muh'ihufi Ships with Particular Reference to Resistance Characteristics
MEASURED RESISTANCE OF 2 SIDE HULLS At .-7 SPREAD N0 'TV 4SF C RLCT LA E FAI. LINE -TIO
RESISTANCE DEDAC.EO FROM RESULTS OP EXPERIMENTS DOFT MODEL IN S.l TAOIC CORRECTED FOL XCVNOLDS
HUGRE METHOD) WITH NL -MEASURED 6ES SFLNCE 0F CENTFE HULL
- FTC. 857 LINE -CENTRE NULLPLATE FRICTION
LIGE -- SCHOESHCRR FLAT t G ES HAGERII05 FORE-AND-AFT DISPLACEMENT OR SETTING CENTRE L NE SEPARATION FULL LENGTH L O IA BÚA) v 00 008 006 OVERALL BEAM OH S PA E AO OSERULL LENGTH
2 .3 4 5 b
MODEL SPEED V ÇT PER SEC)
Fig. 14 Mathematical hull form.
Reduction in resistance with optimum three-hulled
configuration. Water temperature 62 deg F 7 in, with a view to reducing the interaction between hulls
to a minimum. The results are shown in Fig. 13.
The resistance measurements with the single hull
covered two speed ranges, namely 2 to 3.5 fps and .5.5
to 8.5 fps, respectively. No experiments were carried out in the range 3.5 to 5.5 fps, and this part of the curve shown in Fig. 13 has been sketched in by reference to the
results of the earlier experiments with the 20 ft model (5, 61. This part of thecurve is not relevant to the sub-sequent comparison with the measured resistance of the
three hull arrangements. The resistance of the 20-ft model
was corrected for Reynolds number by Hughes' method for scaling the resistance of ship forms. The agreement
between the 10- and 20-ft model results is considered
sat-isfactory having regard to the high leve] of the tow point
in the 10-ft model and the tendency for this model to
take an angle of heel at high speeds due to its poor
trans-verse stability.
Although the two side hulls had the same total
dis-placement as the center hull their resistance when tested
as a catamaran was very much greater. This is very
largel' attributable to theirhaving nearly twice the wetted
surface of the single hull. At a speed of 8 fps their
residu-ary resistance relative to the Schoenherr flat plate fric-tion is only slightly greater than that of the single center
hull, suggesting thatat the 8 ft 7 in spread at which they
were tested there was little wave interference between
them. At lower speeds, however, their residuary resistance
is very much greater than that of the center hull. The
reason for this is not clear, but it is possible that the
asymmetry of the side hulls may induce boundary layer
separation at very low Reynoldsnumbers.
The experiments with the three hull arrangements were
0-75
Fig. 15 Mathematical hull form
Variation of resistance with varying fore-and-aft
setting of hulls 022 w 020 Aj3 OIS s.-.-A-. '-s
MODEL SPEED. 5 SET PER NEC
O- OVERALL LENGTH- 1301.
- -R-- - OVERALL LENGTH 275L
OVEHALL REAM SOASAD ÇET
Fig. 16 Mathematical hull form.
Variation of resistance with varying overallbeam
concentrated at the hump speed of 5.5 fps where wave
interference effects might be expected to be pronounced. It was originally intended to make further experiments in
way of the second hump at 8 fps but this was found to be impracticable due to the very steep waves generated
in the space between the hulls in this speed range which
threatened to swamp the models.
At the speed of 5.5 fl)s the theoretical optimum fore-and-aft distance between the hulls as far as transverse
wave-making is concerned is 2.95 ft. corresponding to
one-half wave length. This was confirmed by experiment and further tests vere carried out to determine the optimum transverse spacing at this speed. In Fig. 14 the measured resistance of the three-hull unit of optimum conflguratioo
is shown in relation to the curve constructed by adding
the measured resistance of the center and side hull respec-tiveiv, i.e., the total resistance of the three hulls assuming
no interaction between them.
It will be seen that the
interaction effect has resulted in a reduction of 8 percent
in total model resistance. Thiscorresponds to 22 percent of the Schoenherr residuary or about 40 percent of the
probable wave-making resistance assuming the level of
the total viscous resistance to be as indicated in Fig. 14.
A check spot at 3 fps, in the range of negligible wave-making, confirms the curve deduced from the experiments in which the center and side hulls were towed separately. As already noted, the frictional resistance of the simple
mathematical form was reiativel' high in relation to the
wave-making resistance. The reduction in total resistance
obtainable by wave cancellation with a forni of this type
was therefore limited.
The Cose for Mulfiliu!I Ships with Particular Reference to Resistance Characteristics
14-9
® MEASURED #ESINTARCE OF THREE PULLED UNIT OS OPTIMUM cO,IEIGARArION FOR THE SPEED
SUM Of RESISTATCS NULL TOWED 2 SIDE HULLS CATAMARAN Cf SEPARATELY TOWED AS CENTRE 6/ AND A
J
/'ADÇ
02 TOISL5CSNTAf2CE 'S2 CH L2TF 'X\
POHE-AND-APE CORRESPO-401N0 LENGTH AT SF11020 TO F5 RAVES SET PER SEC -26
\
-N' N' 24 -'-s 's 'E i 's N 0 22 N 020 OMODEL SPEED.S RElEER SEC
-O--- CENTRE HULL LEADING - SPREAD
8-- 8-- CENTDE HULL LEADE2O 8-- SPREAD 4'8-- ,
- -6--- - SIDE HULLS LEADING - SPREAD 4-?
0-05L OIOL OISL 020L OPSL OTOL 035L
FORE UND -AFT SETTING IN TERMS 0F MODEL HULL LEEA3THS
025 0 26 024 0 22 V. 0 20 O IS O Io O IA 0 12
The effects of varying the fore-and-aft and transverse separations of the hulls in the three-hull unit at a
con-stant speed of 5.5 fps are shown in Figs. 15 and 16.
lt
wifl be seen from Fig. 15 that the resistance obtained atoptimum fore-and-aft setting is little affected by variation
in the spread but the results become more sensitive to spread when the fore-and-aft setting is nonoptimurn. As
was to be expected the resistance at the interference speed
was approximately the same whether the center hull led
the side hulls by one-half wave length or the side hulls
led by the same amount. The arrangement with the center hull leading gave better results when the fore-and-aft setting was nonoptimuni, however. Fig. 16 shows that for fore-and-aft settings in the neighborhood of one-half wave
L. F. Robertson, Jr., Member: I would like to express
my appreciation to the authors for their interesting work
as presented in this paper, andthank them for the
oppor-tunity to offer my thoughts on the subject.
In the Maritime Administration we have considered the catamaran type of vessel and there is now underway a research study of the feasibility of its use in our ocean commerce. We have found that in order to maintain
com-parable costs the catamaran should be smaller than the
conventional ship. This means that it is running at a
higher speed-length ratio (V/VL) and is therefore sub-ject to higher values of wavemaking resistance than the
longer conventional hull.
For example, in developing an oceanographic vessel
with a 20-knot service speed, the 350-ft conventional ship had a speed-length ratio of 1.07 while the 250-ft catam
ran with equivalent deck area had aspeed-length ratio of 1.27 and required substantially more power.
This experience would lead us to believe that the
pos-sibility of wave-cancellation effects as discussed in the
pa-per could be the answer to the problem.
In order to compare the three types of vessels more readily. I have prepared a partial replot of Fig. IO of the
paper relating speed to effective horsepower requirements
(see Fig. 17). It may be noted from this figure that the tested catamaran always requires more power than the
conventional hull. In the trimaran hull the effect of wave
cancel]ation can be seen at about 18 knots and 23 knots,
but a real advantage over the conventional hull is not
ap-parent until we reach 23 knots, which corresponds to a speed-length ratio of 1.25 for the conventional ship with
a length of 331.5 ft. At this speed the installed power,
us-ing a 25-percent service factor and a propulsive
effici-ency of 0.75, would be about 17,000 hp. This would
ap-pear impractical in a ship of this size. It also apap-pears that the very slender center hull of the trimaran would
lead to a lower efficiency than the conventional form, and
I would appreciate the authors' comment on this. The suggestion that propellers could be placed on pods between the hulls is interesting, but it would
ap-pear impractical from a hardware viewpoint.
Discussion
In closing I would like to suggest that an attempt be macle to reduce the frictional resistance of the trimaran vessel, and I wonder whether the authors have
consid-ered using a large center hull associated with much
small-er side hulls, with spacing as required for optimum
can-cellation effects aimed at a lower speed fange, say 18 knots for the vessel studied.
Herbert A. Meier,4 Visitor: These data on a trimaran
are most welcome, even though a trimaran acids still an-other possibility to the many unusual hull types that should be considered before a final selection of hull form is made, especially when a designer is faced with unusual
reqi.irements with respect to speed, stability, deck area,
or seaworthiness.
In the realm of multi-hull ships the catamaran has
cer-tain advantages with respect to deck area and stability.
However, any gains in the speed-power relationship have
been elusive. A trimaran appears to offer all the advan-tages of the catamaran with the possibility of additional
gains in powering. However, the structural complication and weight penalty of a catamaran appear to be further compounded by a trimaran configuration. Obviously lit-tle technical information exists on any multi-hull ships sufficient for their optimization, and any generalization at this stage in their development must be cautiously
ap-proached.
Since high speed for displacement-type hulls dictates
low displacement-length ratios and hence increased length
and, since the optimum trimaran appears, at least from this study, to benefit by rather large fore-and-aft separa-tion of the wing and central hulls, the trimaran
config-uration will result in an extremely long vehicle.
For high-speed mono-hull displacement forms, this
desirability of increased length at the expense of reduc-tions in other dimensions results in a ship that has little cargo-carrying volume in the hulls. Moreover, it cannot
4Ship Concept Design Division, Naval Ship Engineering Center, Naval Ship Systems Command, the Navy Department, \Vashing-ton, D.C.
14-IO The Cose for Muh'ihul! Ships with Particular Reference to Resistance Characteristics
4
length the resistance is a minimum at a spread of approxi-mately 8 ft. The optimum transverse spacing is doubtless related to the divergence of the wave systems but no
siniple relationship to the Kelvin angle is apparent.
It was observed in all these experiments that the waves
generated by the side hulls appeared to emanate almost
entirely from their curved sides as intended. There vas practically no surface disjurbance along their flat outer
sides.
Conclusion
It was concluded from these exploratory experiments that it was practicable to achieve a substantial degree of
wave cancellation by the adoption of the three-hull
carry cargo topsides because of stability considerations. In view of this, it is apparent thatsome plurality of hulls
or other stabilizing dodge is called for. It is suggested
that a long slender hull stabilized by short SpOnSOflS, the
bottoms of which conform to the wave profile generated by the main hull, may offer the possibility of achieving the desired goals, with less structural complication and
weight penalty. A first approach to this configuration
was tested at the U. S. Naval Academy Tank with en-couraging results. This model was also tested in head seas and showed remarkably little increase in resistance at higher speed when compared to a conventional hull.
It is planned to further explore this conguration.
A. J. Vosper, Visitor: While I warmly welcome the British initiative on niultihull ships, I have some reser-vations on the grounds that the authors have done barely half of the investigation which such a novel concept merits. The mere mention of the advantages of carefully siting the propellers in order to gain from the "venturi" effect in the wake is a poor substitute for real data on
measured propulsion characteristics. I would therefore
make a special plea for this aspect to be explored as soon
as possible.
So far as the resistance data are concerned, the basis for comparison between multihull forms and the single hull,
viz., the 3730-ton car ferry, is not a very exacting cri-terion. It is not particularly difficult to find a hull form
having a resistance coefficient some 30 percent less than that of the ferry at the same displacement and speed.
Such a form would be longer than the ferry, but easier
to construct and maintain than any of the multihull
types. With this more severe standard of comparison, the virtue of the multihull form at these relatively low
speeds then lies solely with its handsome transverse sta-bility. One then wonders whether a trimaran with rela-tively small outer hulls might be an economic
compro-mise. The uthors' views on this aspect would be
appre-ciated.
Turning to the authors' suggestions for possible uses
for multihull forms, the suggestion that such a
configura-tion might be suitable as an aircraft carrier seems very
questionable, since the critical problem in aircraft carrier
design is not one of transverse stability, but rather of providing internal stowage for the vast amount of
sup-porting services, stores, and accommodations; and in
this respect it is not believed that the multihull configura-tion will show to advantage over a single hull. One
would like to see some real data on the economic aspects
of the multihull configuration, since one suspects that the trimaran will suffer from very much larger docking costs, more costly hull maintenance, and heavier
operat-ing costs, because of double machinery space and so on,
in comparison with a single-hull vessel.
Finally, seakeeping performance must be of vital
con-cern in inultihull craft, and it is to be hoped that, in
Superintendent, Admiralty Experiment Works, Haslar, Gos-port, liants, Great Britain.
32OOO 28.000 24.000 20.000 16.000 12 .000 o 8.000 4,000 Ui O a-W O
I
Ui > t-o LU IL UiThe Case for Multihul! Ships with Particular Referenceio Resistance Characteristics
14-1 I
.-iiu.j
_r 'i
1'
p_prì_
yi
14 16 18 20 22 24 26 SPEED-KNOTSFig. 17 Replot of Fig. 10 relating speed to
effec-tive horsepower. requirements
addition to tise comparison between catamarans and
trimarans which the authors refer to as being undertaken
at NPL Feitham, a comparison with a single hull will also be undertaken.
Ullmann Kgore, Menzbcr: Multihulled craftare often comparcd with single hulls at the saine displacement and
speed, but the comparison is of academic interest only.
Unless deadweight is to be reduced, the structural weight
of any multihulled vessel will prevent displacement parity
with a single hull.
Omission of reference to the work of Eggers ("On the
Resistance of Twin-hulled Ships") is conspicuous.
Eg-gers reported experiments on twin hulls at a wide range
of hull spacings and arrangements.
Elimination of "any wave-making resistance" by
adop-tion of flat outboard sides is a remarkable achievement.
Evidently the flat outboard sides have eliniinated not
only the divergent wave system but the transverse system as well, including the stern wave. This result is especially notable in view of the several experiments on catamarans where the opposite effect was reported.
The authors, in discussing their Fig. 10, acknowledge that "had the single hull been designed for 24 knots
a more favorable resistance at this speed may have
re-sulted." It is not clear that Fig. 10 does more than to
19A knots does not do so well at 24 knots. The possi-bility of producing the trimaran to lift the same dead-weight as the conventional ferry and to have the same displacement is remote, as stated in the foregoing.
\Vhile these remarks are provoked by the authors' un-disguised advocacy of the multihull concept, they are
not to be taken as denial of scientific value in the experi-ments they report. Whatever the value catamarans or trimarans ultimately may have, we need information.
Pending a comprehensive research program, reports on limited aspects of a broad question, such as the present
contribution, are gratefully received.
K. W. H. Eggers,5 Visitor: If we write down the
wave-resistance expression for a trimaran in terms of the
spectral function F(u) of the central hull, using
the dimensionless notation from a previous paper7 for a symmetric ship, we have:
R=
1671
fF2(u)(1
± cos2uY 2 cos wX cas uY) H(u)duwith X .
dimensionless fore-and-aft setting, V = di-mensionless sidewise spread from centerline, w = [1(I +
4u5)h/2]h/2.H (u) (1 ± 4u)'/2/2w2; for infinite X and Y, this
simplifies to
R=
111(u) du
1671
For non-hump speeds, it
is not evident to me that
optimal interference can be achieved with fixing X equal
to r corresponding to a fore-and-aft setting equal to one half wave length, though certainly the resulting wave spectrum will be absolutely annihilated for u 0, i.e.,
for the principal transverse wave.
At least regarding the system of main hull and one
side hull, I founds that a significantly favorable
interfer-ence could be established even for as high a Froude
num-ber as 0.5, if arrangement was in Kelvin angle, i.e., the
bow of the side hull located in the cusp region of the
main-hull bow wave pattern; and I could verify this
experimentally (see Fig. 18). The optimum X for this
case was calculated as X = 4 ir V2/9 and Y = X/
\/8; thus X is found less than sr, and the experiments
Daviclson Laboratory. Stevens Institute of Technology,
Ho-boken, N.J.
TK. W. Eggers, S. D. Sharma, and L. \V. Ward: "An Assess-ment of Some ExperiAssess-mental Method for Determining the
Wave-making Characteristics of a Ship Form," Trans. SNAME, vol. 75, 1967, pp. 112 - 157.
5K. Eggers, "Uber \Vidcrstandsverhaltnisse von
Zweikörper-schiffen," Jahrbuch der Schifihautechnischen Gesellschaft, Bd. 49,
1955, pp. 516-539 (now available as N.P.L. translation).
(9 L f,? (0 0.8 sas 42
b0
£ z j u I ,o 48I
1 4-1 2 The Case for Multihufi Ships with Particular Reference to Resistance Characteristics
, .-..-.,.&
8 cz=OS---.
expenmental calculated frictiona/port calculated--_ R
.rl.31e
'c/.928'
c O 42 48 45 48 (o Tandem arrangement, a = 0, F = 0.5 Tandem arrangement, a = 0, F = 0.316Cc) Arrangement in Kelvin angle, a = 1Ó028,, Fa
= 0.5
= calculated contribution of frictional resistance
Fig. 18 Total resistance of two models with 13/L
= 1/8, referred to resistance without interference
even showed an optimum for a still smaller X. It is true
that this favorable effect will be partly lessened by inter-action between the side hull; however, at least for an
arrangement of three equal hulls, my calculationsbased
on the principle of linear superpositionresulted in a
clearly favorable effect, as may be concluded from Fig. 19. \Ve should observe that favorable interaction
(a =
20 deg) happens twice against only one unfavorablein-teraction (a= 90 deg) with a distance between the bows reduced by a factor 2/3.
George E. Meese, Member: The paper is very
inter-esting, and especially so for those who are designing multihulled vessels.
In commenting on the authors' paragraph (ii), we find that catamaran hulls generally are so fine that wave making for each hull at lower speeds is quite a low
fac-tor. By configuring the hulls with the straight sides
inboard, there are no waves to interfere with each other and increase resistance very much, Of course this does not have a direct point in a study of eliminating inte
ference effects by unusual locations of the hulls.
'\'
The authors' body plan, shown in Fig. 4, could have
been designed for less wetted surface, which would have
helped the multihulls in their comparison of Fig. 10. For a more equitable comparison in Fig. 10, it would seem fairer not to base data on equal displacement, but
1.25 (5 (71 ¿o 3Y
46'
-0,6
Fig. 19 Calculated additional resistance due to wave
interference for oblique arrangements F 0.5) in ratio to wave resistance without interference
on equal deck space or container cargo volume. In this
way the compared vessels would be on the same
revenue-producing base, and the resistance data closer to those which would be realized in construction. This would
show the niultihulls to be very favorable in power
re-quired for equal speeds.
The authors' form used for study appears to have
great directional stability, but may prove very poor in
turning characteristics.
The authors have used, for comparison in Fig. 10, the trimaran which has hulls 250 ft long, a total length of
350 ft, ad has a beam of about 125 ft. There would
have to be considerable weight of steel in such a struc-titre. A catamaran of equivalent dimensions would have only half of the connecting structural weight, and less than the trimaran 3-hull structure weights. This fact puts the catamaran in a more favorable economic position
b providing more revenue-producing tons.
The authors have done a great work in showing that niultihulled vessels have potential. This field requires
a considerable amount of future work to study the many combinations possible with this type of vessel and show
how they can he designed and built for greater profits.
Reuven Leopold, Member: The authors should be com-mended on their originality and the application of funda-mental priliciples in attempting to solve the age-old prob-1cm of wave-making resistance for high-speed displace-ment ships.
Mv discussion concerns the examination of the basic
reasoning for selecting a trimaran versus a twin-hull
con-
t-Fig. 20 TRISEC configuration
figuration. First, I would like to voice my criticism con-cerning the paper's introduction where, in my opinion, an over-simplified approach was taken as to the basic design-driving forces which led to the selection of the
trimaran configuration.
The general function of ships, as a transportation
fa-cility, is to move cargo. The features of the iarticular
ship are, therefore, dictated by: (a) the desired speed
the kind of cargo (e) the quantity of cargo
The hull forni, then, depends mainly on the speed and
the kind of cargo to be transported. This dependence
can he demonstrated by examining different hull forms and their optimum application:
Cargo
Speed Stowage Factor hull Form
Low High . . Low Conventional
Medium High Catamaran
High High TRISEC (see Fig. 20)
High Low Submersible
The introduction correctly states that the two
prob-lems are:
Increased wetted surface
(ü) Adjacent wave system
However, subsequent to this statement of the problem, it is disappointing to see no general treatment leading to the suggested solution of a trimaran configuration. As
The Case for Multihull Ships wi/h Particular Reference fo Resistance Characteristics 14-13
.- '
F,,O.5
LosLI!
41
¡F
Gain) obtainede
20 2 42 oit turns out, it seems to me that by adding a third hull
at the center, the solution, in many ways, results in
op-posi te-from-desi red effects. For example:
The wetted surface of the trimaran will be larger
than for the equivalent displacement ship of conven-tional or catamaran form, since it increases as a
func-tion of the number of hulls.
The advantage of the catamaran's stability is
cained from the second term of the manient of inertia
ol the waterplane, i.e., area X the distance from the
center of the hull to the center of the ship, squared. For the center hull, this term is obviously zero.
Therefore, in my opinion, the trimaran configuration pushes to a higher speed its speed-versus-power curve's crossing point in the speed-versus-power curves of the
equivalent-displacement conventional hull, l'bus, while
at higher speeds the trimaran has advantageous effects
on wave cancellation and, thus, reduction of total
re-sistance, it has an undesirable effect at low speeds: i.e., higher wetted surface than the equivalent twin-hull or
single-hull vessel.
Authors' Closure
The question of the greater structural weight of multi-hull ships has been mentioned several times and in par-ticular by Mr. Kilgore, Mr. Meier, and Mr. Meese. This has been referred to in the paper, and T hope that I have not given the impression that it is a minor consideration.
The position is that we probably do not have enough
information to carry out a rigorous structural analysis anyway and, as I have mentioned, we are now arranging
for model tests to throw light on the forces and moments
on the interconnecting decks. This disadvantage might
be overcome by the use of light alloys, if the
advan-tages of the multihull idea were sufficiently attractive to justify the extra cost.
This leads on to the basis of comparison used in Fig.
IO, in which the relative performance of the single, twin,
and three-hulled craft are compared. This is on a basis
of common speed and displacement, and I realize the
shortcomings of this which have been referred to by a
number of discussors.
In a thorough study, of course, the weight variation
would have to be taken into account, but at this stage
the speed-displacement basis seemed to be the best
thing to use rather than attempt to make a guess at the
weight variations which must depend on particular cases. In any case, I doubt whether this would have altered
the situation to a very great extent.
Again referring to Fig. 10, there have been several
remarks on the comparison between the trimaran and the single hull at its service speed of l9 knots and the
more or less arbitrary higher speed of 24 knots. In this connection, Mr. Vosper suggests that the multihuhl
ad-1 4-ad-1 4 The Case for Multihull Shins with Particular Reference to Resistance Characteristics
vantage could easily be offset by using a longer and
pre-suniably narrower form.
I have no doubt that this is
true, but I doubt very much whether such a form could do the sanie duty as the car ferry, where deck space is
at a prenuiuni. On the other hand, I do not think one
needs to do a design study to say that the multihull is bound to be better off in that respect.
I was i'ery interested in Mr. Meese's suggestion that a
fairer basis would be in terms of equal deck space or container cargo volume rather than displacement. Ï think
this is a good point and would certainly put the
multi-hull concept way up in the betting.
As regards Mr. Egger's comments, I should underline
that we vere abhing at substantial cancellation of the
transverse 'ave system rather than the diverging waves, and] recent work by Everest at NPL has confirmed that in trimarans this is the most promising thing to go for. This work also showed that, owing to reflection and in-teractiori effects, the theory was unreliable at transverse spacings of less than half the ho]] length, which is what
ve are concerned with here. Moreover, these restrictions also apply to results based on the superposition of meas-ured wave systems.
I would like to emphasize, by the way, that ail the
results given in the paper are experimental, and conclu-sions are drawn on the premise that carefully conducted
moc]el experiments are meaningful.
Several speakers have referred to the possibility of
replacing the outer hulls by smaller hulls or sponsons, and it may vell be possible to achieve some wave
can-cellation in this way. In this connection, I was interested
to hear from Mr. Meier that some tests on these lines
already have been carried out at the U.S. Naval Academy.
Another possibility might be to have shorter middle
hulls, perhaps in conjunction with propulsion pods. Both Mr. Robertson and Mr. I'Ieese have referred to the possibility of improving the performance of the tri-maran by reducing the skin-frictional resistance, and I
agree that there is some scope here. In particular, the skegs shown on the side hulls could be removed without
detriment. They were put there to add to the directional
stability of the catamaran, but in the trimaran this is
probably unnecessary. Their removal should improve
the turning characteristics as well.
1".Ir. Vosper comments that the aircraft carrier appli-cation ¡s questionable because of the difficulty of
pro-viding adequate stowage space for stores and accomrno-dation. J cannot see the difficulty here, as one could build up as many box-like superstructures as one required.
After all, the proposed containership application needs
a fair amount of stowage space.
I do not understand either Mr. Vosper's reference to the disadvantage of having a double machinery space. In a military ship the place for this would surely be in the center hull where it would have protection from the side hulls, and in this way one could have a single
Mr. Robertson has asked nie to comment on the ques-tion of propulsive efficiency of a three-hull arrangement ith a pr)J)eller behind the center hull. Bearing in mind
that the \vettccl surface of the center hull is about 2/3
that of the single hull, one would expect the Ywake-gain"
or recovery from the frictional belt to be correspondingl'
less: This is a matter for further investigation, and J suggest in the paper that there may be some advabtage in positioning the screws in the interspaces.
In regard to Mr. Kilgore's comment on the
elimina-tion of;4anv wave-making resistance" by means of the tia t outboard sides, I would point out that reference was
being made here only to the wave systems normally
gen-crated by the outside surfaces of a multihull craft and
not to the wave-making resistance of the craft as a whole.
Finally, a few general comments: There is one com-mon factor running through all the discussion, and the paper too for that matter. namely, the need for further work. I certainly agree with this and J was glad to hear Mr. Vosper underlining the urgency for it. Funds for this work have been limited and perhaps Mr. Vosper's organization, the U.K. Navy Departmeut, can help out! T was certainly interested to hear of developments in this teld in the United States which the discussion has
brought out. In particular, I vas gratihed to hear from Mr. Robertson that the work described in the paper
may he of help in some of their problems at the
Mari-time Administration.
In concluding, T would like to express my thanks to all contributors for having taken part in the discussion.
