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

A 3D Panel Method for Mono-Hull Ship Motions and Loads with moderate forward Speed
Amresh Negi1), Shivaji Ganesan T1), Debabrata Sen2)
1) Indian Register of Shipping, Powai, Mumbai, India
2) Ocean Engineering & Naval Architecture, IIT Kharagpur, Kharagpur, IndiagLrzABSTRACTThis paper describes the development of a computer program based on
the 3D panel-based Green Function Method (GFM) to evaluate the ship
motions and loads Response Amplitude Operator (RAO) at moderate
forward speed. In this approach, the zero speed Green function is used
to determine the oscillating velocity potential, and forward speed
correction is implemented similar to strip theory. With the forward
speed corrections, the added mass, damping, and excitation terms in theequation of motion are modified accordingly. This method can help
determine ship motions, loads, and dynamic hull pressure RAOs forslender mono-hull ships at low to moderate forward speed. Theseresults can be further post-processed for various practical applications
within the scope of ship design assessment to check and verify
numerous operability and survivability conditions. The theoreticalassumption, mathematical formulation, and details of numerical
implementation have been discussed in particular. The computed
motion and load RAOs for four different ship geometries are comparedwith the other 2D and 3D methods and experimental results. Finally,
the significant advantages and disadvantages of the present method
over other 2D and 3D numerical methods are discussed.

INTRODUCTION
For ages, ships have been transporting passengers, cargo, and material
and therefore the ship behavior in a seaway has always remained asubject of greater interest. For a long time, ship designers, the researchcommunity, seafarers, and classification societies have focused on
accurately predicting ship motions and loads in a realistic oceanenvironment. The pioneering work of St. Denis and Pierson (1953) topredict the statistics of ship responses in seaway has set the course formodern ship seakeeping computations. Korvin-Kroukovsky & Jacobs(1957) developed the first linear strip theory to predict the ship heaveand pitch motion. A variety of strip theory versions were developed andexists, amongst which the STF method (Salvesen, Tuck, and Faltinsen,1970) has been arguably the most popular version.
In 2D strip theory formulations, forward speed corrections have been
considered in an ad-hoc manner and thus theory application for the
mono-hull is limited for Froude number up to 0.3. Strip theories are
satisfactory to compute the ship motion and load. However, the solution
is valid for the high-frequency oscillations i.e. radiated waves havewavelengths in the order of ship beam, which is already assumed to besmall. Another limitation comes from the application point of view. For
the direct load application such as performing Spectral Fatigue
Analysis (SFA), it is more convenient to map and interpolate 3D
dynamic hull pressure to the FE model than the strip theory-based
dynamic hull pressure for determining the stress transfer function or
stress RAOs. Therefore, it leads to a requirement for an efficient 3D
panel program capable of handling the forward speed of the vessel.

KEYWORDS: panel method, ship motions, shiploads, seakeeping,Green function, forward speed, RAO.
NOMENCLATURE
ρ∇
ϕ0
ϕ1-6
ϕ7ζaA33, A55
B33, B55
BCbdAcceleration due to gravity
Length of the ship
Radial distance
Water depth measured from the mean surface

Water density
Volumetric displacement of the ship
Incident potential
Radiation potential corresponding to six degrees ofmotion
Diffraction potential
Unit wave amplitude
Added mass coefficients for Heave and Pitchmotion
Damping coefficients for Heave and Pitch motionBreadth of the ship
Block coefficient
Water depth

For the past few decades, ship designers routinely used potential flowbased numerical methods to compute wave-induced ship motion andload responses. These efficient numerical techniques vary fromtraditional 2D strip theories in the frequency domain to advanced 3D
Rankine Panel Method (RPM) in the time domain. Even at present,with the available computational resources, a complete numerical

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