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Linearized Three‐Dimensional Planing in Deep and Shallow Water.

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Title: Linearized Three‐Dimensional Planing in Deep and Shallow Water.
Authors: Doctors, Lawrence J.1 (AUTHOR) l.doctors@unsw.edu.au
Source: International Journal for Numerical Methods in Engineering. 12/15/2025, Vol. 126 Issue 23, p1-26. 26p.
Subjects: Potential flow, Water depth, Free surfaces, Hydrostatic pressure, Empirical research, Numerical integration, Lift (Aerodynamics), Surface dynamics
Abstract: The traditional analysis of three‐dimensional planing is studied in detail using potential‐flow theory together with linearized free‐surface conditions. The work is extended here to the case of water of finite depth. The planing surface is modeled as a traveling pressure distribution. Thus, the analysis solves the inverse problem of finding the pressure that generates the hull shape. Specifically, the pressure is discretized as a two‐dimensional array of overlapping tent‐function pressure elements. The current study includes a careful study of the convergence properties of the method with respect to the numerical integrations needed to compute the response functions from the pressure elements, and also the number of elements needed to represent the pressure accurately. The predictions are compared with the available towing‐tank model experimental data for both flat and prismatic planing surfaces. There are encouraging predictions for various trim angles, deadrise angles, length‐to‐beam ratios, and Froude numbers. Additionally, the theory correctly predicts the dependence of the lift, drag, and the location of the center of pressure as the water depth is decreased. [ABSTRACT FROM AUTHOR]
Copyright of International Journal for Numerical Methods in Engineering is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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DbLabel: Engineering Source
An: 190211842
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
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  Data: Linearized Three‐Dimensional Planing in Deep and Shallow Water.
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  Data: <searchLink fieldCode="AR" term="%22Doctors%2C+Lawrence+J%2E%22">Doctors, Lawrence J.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> l.doctors@unsw.edu.au</i>
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  Data: <searchLink fieldCode="JN" term="%22International+Journal+for+Numerical+Methods+in+Engineering%22">International Journal for Numerical Methods in Engineering</searchLink>. 12/15/2025, Vol. 126 Issue 23, p1-26. 26p.
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  Data: <searchLink fieldCode="DE" term="%22Potential+flow%22">Potential flow</searchLink><br /><searchLink fieldCode="DE" term="%22Water+depth%22">Water depth</searchLink><br /><searchLink fieldCode="DE" term="%22Free+surfaces%22">Free surfaces</searchLink><br /><searchLink fieldCode="DE" term="%22Hydrostatic+pressure%22">Hydrostatic pressure</searchLink><br /><searchLink fieldCode="DE" term="%22Empirical+research%22">Empirical research</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+integration%22">Numerical integration</searchLink><br /><searchLink fieldCode="DE" term="%22Lift+%28Aerodynamics%29%22">Lift (Aerodynamics)</searchLink><br /><searchLink fieldCode="DE" term="%22Surface+dynamics%22">Surface dynamics</searchLink>
– Name: Abstract
  Label: Abstract
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  Data: The traditional analysis of three‐dimensional planing is studied in detail using potential‐flow theory together with linearized free‐surface conditions. The work is extended here to the case of water of finite depth. The planing surface is modeled as a traveling pressure distribution. Thus, the analysis solves the inverse problem of finding the pressure that generates the hull shape. Specifically, the pressure is discretized as a two‐dimensional array of overlapping tent‐function pressure elements. The current study includes a careful study of the convergence properties of the method with respect to the numerical integrations needed to compute the response functions from the pressure elements, and also the number of elements needed to represent the pressure accurately. The predictions are compared with the available towing‐tank model experimental data for both flat and prismatic planing surfaces. There are encouraging predictions for various trim angles, deadrise angles, length‐to‐beam ratios, and Froude numbers. Additionally, the theory correctly predicts the dependence of the lift, drag, and the location of the center of pressure as the water depth is decreased. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of International Journal for Numerical Methods in Engineering is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1002/nme.70147
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      – Code: eng
        Text: English
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        PageCount: 26
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    Subjects:
      – SubjectFull: Potential flow
        Type: general
      – SubjectFull: Water depth
        Type: general
      – SubjectFull: Free surfaces
        Type: general
      – SubjectFull: Hydrostatic pressure
        Type: general
      – SubjectFull: Empirical research
        Type: general
      – SubjectFull: Numerical integration
        Type: general
      – SubjectFull: Lift (Aerodynamics)
        Type: general
      – SubjectFull: Surface dynamics
        Type: general
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      – TitleFull: Linearized Three‐Dimensional Planing in Deep and Shallow Water.
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              Text: 12/15/2025
              Type: published
              Y: 2025
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