J. Marine Sci. Appl.

(2016) 15: x-x

DOI: 10.1007/s11804-016-1340-3

Ship Resistance of Quadramaran With Various Hull Position

Configurations
Yanuar1*, Gunawan1, A. Muhyi2, and A. Jamaluddin3
1. Department of Mechanical Engineering, University of Indonesia, Jakarta 16424, Indonesia
2. Graduated Student of Mechanical Engineering, University of Indonesia, Jakarta 16424, Indonesia
3. Indonesian Hydrodynamic Laboratory, Surabaya 60111, Indonesia

Abstract: Multihull ships are widely used for sea transportation, Quadramarans with a diamond configuration are built on
and those with four hulls are known as quadramarans. Hull position the basis of a similar concept to the trimaran, which has
configurations of a quadramaran include the diamond, tetra, and main and side hulls. The trimaran has two side hulls and one
slice. In general, multihull vessels traveling at high speeds have
main hull, and the diamond quadramaran has two side hulls
better hydrodynamic efficiency than monohull ships. This study
aims to identify possible effects of various quadramaran hull
between two main hulls. The trimaran concept has recently
position configurations on ship resistance for hull dimensions of 2 beeen claimed by Lindstrom et al. (1995), Smith and Jones
m length, 0.21 m breadth, and 0.045 m Thickness. We conducted a (2001), and Mynard et al. (2008) to have significant
towing test in which we varied the hull spacing and speed at Fr advantages over monohulls and catamarans. Xu et al. (2001)
values between 0.08 and 0.62 and measured the total resistance reported that the main and side hulls may be arranged so that
using a load cell transducer. The experimental results reveal that the the ship generates destructive wave interference to produce
lowest total resistance was achieved with a diamond quadramaran smaller waves and thereby reduce the energy dissipated in
configuration at Fr = 0.10.6 and an effective interference factor of overcoming wave-induced resistance. Yeung (2005) found
up to 0.35 with S/L = 3/10 and R/L = 1/2 at Fr = 0.62.
that in specified hull configurations, trimarans are capable of
Keywords: multihull, quadramaran, ship resistance, interference
lowering total ship resistance by about 25% at a speed of 12
factor
m/s compared with monohulls. Yanuar et al. (2013, 2015)
Article ID: 1671-9433(2016)01-0000-00 conducted studies on the effects of reducing the drag on
various multihull vesselsincluding trimarans, tetramarans,
1 Introduction1 and pentamaransby changing the shape and configuration
of their hulls.
A number of studies on multihull ships have shown them
to have better performance than monohull ships. The
development of multihull ships began with the catamaran,
which then progressed to the trimaran, quadramaran, and
pentamaran. The multihull ship is one approach for reducing
ship resistance. Studies of multihull ships have focused on
their hull configurations, forms, and composition. Multihull
ships are used as commercial and military ships, and differ
in their speed and capacities.
In general, the multihull ship has the advantages of
stability, payload, speed, and resistance. Seif and Amini
(2004) confirmed the advantages of multihull ships in terms
of their wider deck space, which yields better stability
compared to single-hull ships. Wave interferences may be Fig. 1 Ship models tested by Tuck [11]
divided into two types: constructive and destructive.
Constructive interference can amplify the effects of a wave, The quadramaran is a multihull ship with four identical
and destructive negatively effects waves. Current multihull slender hulls (high ratio L/B) that are either parallel to each
research efforts focus on identifying the configuration that other or not. Most multihull ship research is based on thin-
creates the lowest viscous resistance within a certain speed ship theory, wherein the focus is on minimizing wave-
range. induced resistance. Fig. 1 shows a range of multihull ship
models, as illustrated by Tuck and Lazaukas (1998) in their
1
Received date: 2015-06-29 study of the wave resistance of some model configurations
Accepted date: 2015-12-10 of the monohull, catamaran, trimaran, and quadramaran.
*Corresponding author Email: yanuar@eng.ui.ac.id
Three configurations of the quadramaran have been tested
Harbin Engineering University and Springer-Verlag Berlin Heidelberg 2015
 2 Yanuar, et al. Ship Resistance of Quadramaran With Various Hull Position Configurations

by Tuck, including the tetra (TET), slice (SLI), and diamond Bm 0.2 0.2 m
(DIA). Three configurations of the Wigley quadramaran Hm 0.205 0.205 m
were numerically investigated by Peng (2001). Tm 0.045 0.045 m
Quadramarans with tetra and slice configurations have been Cbm 0.469 0.469
tested by Yanuar et al., which have separate stern and Sm 0.429 0.429 m2
transom hulls. We continue this research, focusing on Dispm 12.5 12.5 kg
quadramarans with diamond configurations, and then
compare the results with those from a previous experiment.
The purpose of this study is to identify the possible effect
and influence on ship resistance of a quadramaran with
various position and hull spacing configurations in which
the dimension of each hull are L: 2 m, B: 0.21 m, and T:
0.07 m. The dimensions of the models used in this
experiment are appropriate for the size of the towing tank.
Fig. 3 Design configurations of diamond quadramaran
Towing test speeds varied at Fr values between 0.1(0.6.

2 Experimental Set-ups
Our study was performed in a towing tank with calm Fig.
water. Fig. 2 shows the experimental set-up in a towing tank
40 m long, 10 m wide, and with water 2 m deep. The
equipment consisted of a load cell transducer, the ship
models, an electric motor, a data interface, and a computer.
The ship models were pulled by an electric motor and
maintained a constant speed, and we measured the pull force
using a load cell transducer for each run at various velocities
(U). The computer recorded, translated, and calculated the
data from the load cell to obtain the total resistance (RT).

4 Diamond quadramaran configuration types

Fig. 2 Experimental set-up in the towing tank

Each quadramaran hull model was slender with an L/B =

10, and the transom form and hull specifications are shown
in Table 1. The quadramaran in our experiment consisted of
four identical hulls in a diamond configuration, with the
model designs shown in Fig. 3, and a distance between the
two central main hulls of 0.1 m. We classified the ship
model configurations into seven types and arranged each
type by their transverse distance variations (hull separation, Fig. 5 Tetra and slice quadramaran configuration types
S/L) and longitudinal distance variations (staggered hull, from Yanuar et al. [10]
R/L), as shown in Figs. 4 and 5.
3 Test analyses
Table 1 Model hull specifications
The International Towing Tank Conference (ITTC-2002)
Dimension Main hull Side hull Unit (2001) classified ship resistance (RT) in calm water into two
Lm 2.0 2.0 m components: wave resistance (RW) and viscous resistance
Lwlm 1.873 1.873 m
Journal of Marine Science and Application (2015) 14: x-x 3

(RV). Wave resistance relates to the Froude number (inviscid CT

flow) and viscous resistance relates to the Reynolds number
1 (9)
CT NI
(viscous pressure). There is an air resistance which can be where CT is the total
ignored because the model testing does not include the resistance coefficient of a quadramaran model and CT-NI is
superstructure. Total resistance can be defined as the total resistance coefficient of a non-interference
. (1) RT RW RV quadramaran or the summed individual resistances of the
The coefficient of four hulls.
total resistance can be written as
CT CW CV (2) 4 Results and discussion
where CW is the
coefficient of wake resistance and CV is the coefficient of The total resistance is dominated by the wave and viscous
viscous resistance. resistance components. According to Prohaska, the viscous
resistance may be decomposed into the frictional resistance
The total resistance coefficient CT is calculated as that is influenced by the form factor, and wave resistance
RT (3) can be divided into two componentswave-induced
CT 2 where resistance and wave-breaking resistance. To explain further,
0.5 SV is water
density, and S is the the interference of waves on the quadraraman hull can
wet area of the ship hull. generate a phenomenon called hump and hollow at various
The Froude number Fr and Reynolds number Re are speeds. Constructive wave interference increases wave
defined as: resistance to form a hump, while destructive wave
(4) interference reduces the resistance and forms a hollow. The
V
Fr (5) V L experimental results are shown on the graphs as a
gL Re function of the Froude number, with the total
where V is the speed of
the ship, L is the length of the ship, g is the acceleration of resistance coefficient and the interference factor. An
gravity, and is the water kinematic viscosity of fresh optimum configuration can be obtained from that with the
smallest resistance value (CT).
water.
Prohaska defines the three-dimensional form factor k as
follows:
C CF CV (6)
k V 1
CF CF where CF is the
coefficient of
friction resistance. The friction resistance coefficient is
calculated according to the ITTC-57 model-ship correlation
line as
0.075 . (7)
CF
(log10 Re 2) 2 For multihull
ships:
CT CW (1 k ) C F (8)
Fig. 6 Total resistance coefficient CT of diamond
where is the quadramaran configurations
interference factor of the form resistance (from pressure
field changes), is the viscous resistance interference factor
(from the increasing velocity stream around the multihull),
and is the wave resistance interference factor. According to
Insel and Molland (1992, 1996), it is difficult to separate the
two factors and by experimental measurement. For
practical purposes, therefore, we combined and into a
viscous resistance interference factor , in which (1+k) =
(1+k).
To evaluate the hydrodynamic interference effects of
individual design configurations, Hafez and El-Kot (2011)
Fig. 7 Total resistance coefficient CT of tetra and slice
suggest that we can calculate the interference factor as the
quadramaran configurations (Yanuar et al. 2015)
difference in total resistance obtained when moving from
four separate hulls into one bonded quadramaran. It is
convenient to express this difference as a ratio of the non-
interference total resistance, as in Equation (9):
 4 Yanuar, et al. Ship Resistance of Quadramaran With Various Hull Position Configurations

individual resistances of the four hulls, and negative values

indicate a detrimental interference. The highest interference
factor for this experiment was 0.35 at Fr = 0.62, obtained by
the SLI-C2 configuration. For the diamond configuration,
the greatest of interference value obtained was 0.3 at Fr =
0.62.

Fig. 8 Total resistance coefficient CT of each optimum

quadramaran configuration.

Fig. 6 shows the total resistance coefficient of

quadramarans with a diamond configuration. The least ship
resistance in this experiment was obtained in the DIA-A3
configuration, which utilizes ratios of S/L = 7/41 and R/L =
3/82, particularly at high speeds, Fr > 0.35. Longitudinal
distance variations that are more to the front (smaller R/L
ratio) and wider transversal distance variations (bigger S/L Fig. 9 Interference factor ratio of each configuration
ratio) contribute to decreases in ship resistance at high Fr
values, as well as reduced hump sizes. 5 Conclusions
Fig. 7 shows the total resistance coefficients of
This paper experimentally investigates the influence of
quadramarans with tetra and slice configurations. The slice
different hull position configurations and side-hull spacing
configuration has lower ship resistance than the tetra
variations on the hydrodynamic interference of quadramaran
configuration over most of the Fr range. Nevertheless, the
ship models. Hull separations with greater S/L ratios have
ship resistance on the tetra configuration is more stable at
the least resistance in each configuration at high speeds (Fr
low to medium speeds. The lowest ship resistance in this
> 0.4), i.e., the configuration type A3 has lower resistance
experiment was obtained by the SLI-C1 configuration,
than A1 and A2, with similar results for the B and C
which utilizes ratios of S/L = 1/5 and R/L = 1/2, particularly
configurations. The staggered hull generates the least
on low to medium speeds of Fr = 0.904, and at high speeds
resistance in each configuration, i.e., the configuration type
of Fr > 0.4. The least ship resistance was obtained on the
A3 has lower resistance than A2 and A1, C1 is lower than
SLI-C1 configuration at ratios S/L = 3/10 and R/L = 1/2.
B1, and C2 is lower than B2. The test results also show that
Thus, a longitudinal distance variation of the ships main
an effective interference factor of up to 0.35 can be achieved
hull that is more to the front (bigger R/L ratio) and a wider
with the TET-C3 configuration (S/L = 3/10, R/L = 1/2).
transverse distance variation (bigger S/L ratio) contribute to
a reduction in ship resistance at high Fr values, as well as
reducing the hump.
Acknowledgement
Fig. 8 shows the total resistance coefficient for each This work is sponsored by the Directorate of Research and
optimum quadramaran ship model. Of the three ship hull Community Services, University of Indonesia (Hibah PUPT-
configurations, the lowest ship resistances for most of the Fr Tambahan UI 2015)
range (0.10.6) was obtained by the diamond
configurations. The reducing trend of ship resistance on the References
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