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

www.isope.org

The Impact of Added Resistance of Short Wavelength Region on Fuel Consumption
Munehiko Minoura1 and Naoki Yokotani11

Department of Naval Architecture and Ocean Engineering, Osaka University, Suita, JapanABSTRACT

as we mentioned, the added resistance in waves has an impact on fuelconsumption. Therefore, the uncertainty in the frequency domain has animpact on ship eﬃciency. The purpose of this study is to investigate theimpact of the uncertainty of added resistance in waves on fuel consumption and to determine how sensitive the uncertainty is to transmission
from the frequency response function to the ship eﬃciency.

There is an uncertainty in the results of added resistance in waves obtained with numerical calculation and tank experiments. In particular,
it is known very well to be remarkable in the short wavelength region.
In this study, these impacts for fuel consumption are investigated witha service performance simulation. In the service performance simulation, a ship virtually sails on a ﬁxed ocean route in a computer. Theadded resistance in waves is calculated by short-term prediction using
the frequency response function. The simulated results are classiﬁed into
several categories according to the wavelength of the encounter waves.
By deliberately modifying the frequency response function of the added
resistance in waves as a realization of uncertainty, we clarify their impact on the fuel consumption in voyages. In addition, we investigate theimpact on the fuel consumption for diﬀerent drafts, diﬀerent ship types,
and diﬀerent cruising speeds.

In this study, the impact on fuel consumption is predicted with a service
performance simulation. Tsujimoto et al. (2013) proposed the method
to predict the fuel consumption in actual seas and Tasker et al. (2019)
estimated the impact by a similar computational simulation. In the service performance simulation, a ship virtually sails on a ﬁxed ocean routein a computer. The encounter sea states change with the time scale ofthe short-term prediction. Minoura (2016) showed the method to provide the sea states probabilistically based on hindcasting sea state datausing Fourier series expansion and it is used in the simulation. Ship
speed in each encounter sea state is determined by solving the equilibrium equations concerning propulsive resistance, external force on thehull, propeller torque, and propeller thrust in each sea state. Since fuelconsumption for each encounter sea state is simulated the total fuel consumption in several voyages is obtained by their summation.

KEY WORDS: Service performance simulation; Equilibrium equation; Steady force; Ship size; Statistical analysis.

INTRODUCTION
Recently, the ship performance in actual seas has focused on from theviewpoint of environmental problems. The added resistance in waves
is particularly important because it has an impact on fuel consumption.
Energy Eﬃciency Design Index (EEDI) came into eﬀect by International
Maritime Organization (IMO). To calculate the evaluation value of EEDI,
the speed loss of a ship due to the added resistance in waves is demanded;this is also one of the reasons the added resistance in waves is focused on.
The added resistance in irregular waves such as actual seas has been estimated by the short-term prediction with the frequency response function.
These days, however, the ship performance in actual seas has been estimated using the on-board monitoring data, but the short-term prediction
method using the frequency response function will continue to be usedin the future. The frequency response function of the added resistance inwaves is calculated in many ways. However, there is an uncertainty inthe results of added resistance in waves obtained due to the mathematicalmodeling, the instability of calculation, and the nonlinearity concerning
wave steepness. Even in tank experiments, it exists due to the quality ofwave generation and the measurable time. In particular, it is known very
well to be remarkable in the short wavelength region. This uncertainty
has almost been discussed in the frequency domain. On the other hand,

The simulated results are distinguished into three categories according
to the wavelength of the encounter waves. By deliberately modifying
the frequency response function of the added resistance in waves as arealization of uncertainty, we clarify their impact on the fuel consumption
in voyages. The original response function is provided by the potentialbased linear calculation method (EUT: Enhanced Uniﬁed Theory). Since
the results are expected to be diﬀerent with the ship size due to the change
in the ratio of wavelength to ship length, calculations are performed withseveral analogous ships.

THEORY OF SERVICE PERFORMANCE SIMULATION
Equilibrium equations
The coordinate system is shown in Fig. 1. In the service performance
simulation, ﬁve balances are considered, which are longitudinal steadyforces, lateral steady forces, turning steady moments, propeller and engine torque, and propeller and engine power. As the steady force andmoment, propulsive resistance and external force on the hull are consid-

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