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Proceedings of the Thirty-second (2022) International Ocean and Polar Engineering Conference
Shanghai, China, June 5–10, 2022
Copyright © 2022 by the International Society of Offshore and Polar Engineers (ISOPE)
ISBN 978-1-880653-81-4; ISSN 1098-6189

Potential of Energy Conservation for Multiple Ships in Different Formations
Yangying He, Junmin Mou, Linying Chen*
School of Navigation, Wuhan University of Technology, Wuhan, Hubei, P.R. China
Hubei Key Laboratory of Inland Shipping Technology, Wuhan University of Technology, Wuhan, Hubei, P.R. China

Qingsong Zeng
Green & Smart River-Sea-going Ship, Cruise and Yacht Research Center, Wuhan University of Technology, Wuhan, Hubei, P.R. China

Song Zhang
School of Transportation and Logistics Engineering, Wuhan University of Technology, Wuhan, Hubei, P.R. Chinais equal), this paper focus on the resistance characteristics of the 3-ship
formation system under unequal spacing. First, a test of the single-hullresistance is included using a towing tank to validate the numericalmethod. Then a series of numerical simulations are conducted to obtain
the optimal layout in different formation shapes in a short of time.

ABSTRACTThis paper works on the resistance characteristics of a 3-ship fleet, toinvestigate the sailing bonus in various configurations (tandem, parallel,and triangles). First, numerical methods are validated by experimental
data. Then systematic simulations based on RANS (Reynolds-Averaged
Navier-Stokes) are carried out at low speed (Fr 0.0479 to Fr 0.0958) toanalyze the relationship among the advancing speed, longitudinal
distance, transverse distance and total resistance of each ship.
Conclusions of this work could provide theoretical supports for utilizing
the bonuses of sailing in formation.

COMPUTATION DETAILS
Studied ship
The formation studied in this work is composed of three identicallymodified bare hulls of ‘WillLead Ⅰ’ MASS, which eliminate the fin andazimuth propeller, as shown in Fig.1. And its principal parameters areshown in Table 1.

KEYWORDS: 3-ship fleet; CFD; resistance reduction; energy
consumption; configuration optimization.

INTRODUCTION
Fig.1 The geometry of the ‘WillLead Ⅰ’ MASS.

In nature, emergent collective behaviors, such as goose flocks, suggestthat the followers would obtain energy benefit from positive interactionof the leader’s wake in certain configurations. This phenomenon inspired
researchers to use formation optimization to achieve drag reduction,
which has been widely used in aircraft, vehicles, autonomous underwatervehicles (AUV) (Zhang, 2019).

Table 1 Parameters of the ‘WillLead Ⅰ’ MASS.
WillLead Ⅰ
Ship length LOA
Length between perpendiculars LPP
Ship beam B
Draft T
Wetted surface area AS

However, systematic analysis on drag reduction effects of ship formationis still lacking. The exciting literature mainly focuses on the influence ofhydrodynamic interaction on maneuverability between two ships indifferent conditions. Such as moored and the passing ship (Zhou, 2015;
Kok, 2018), tugboat and the assisted ship (Zou, 2019) and replenishment
or lightering operations (Lataire, 2012). As for multiple hulls, abundantstudies can be found in trimaran (Luhulima, 2021) and catamaran (Bariand Matveev, 2016), which is capable to reduce wave-making resistancebased on the adjustments of the hull configuration. But the multihull
vessels are connected rigidly, which is different from the multi-ship
formation system.
In order to enrich the previous work (the spacing between the participants

Displacement 

2.0m
1.825m
0.674m0.211m
0.675m2
140.4kg

Formation configurations
Fig. 2 (a~d) shows the three sets of formation configurations. Origin of
the body-fixed coordinate system is set at midship, and the x-, y-, and zaxis point to the bow, starboard, and downwards, respectively. The
stagger location (ST), defined as the longitudinal distances between theformer’s stern and the latter’s bow. The transverse separations (SP) mean2323