Panel methods remain one of the most efficient tools for predicting pressures and forces on hulls, keels, rudders and appendages, yet their results are only as trustworthy as the user’s understanding of the assumptions behind them. This master’s-level course offers a structured, design-ready study of panel-method hydrodynamics for ships and yachts. It explains how a three-dimensional lifting-surface panel formulation turns potential-flow theory into pressure and force predictions, how geometry and command files are configured for structured and unstructured models, and how solutions are verified, tested for convergence and compared with experiment. Through sphere and rudder investigations and a keel-bulb interaction design problem, it shows how to interpret results from pressure, force and drag evidence rather than colour plots alone, and how to turn analysis into justified design recommendations.
Course at a glance: Duration 20 hours · Self-paced online · 7 sections, 25 lessons, a 107-page downloadable course book
What you will learn
- Explain the assumptions and numerical formulation behind a 3-D lifting-surface panel method.
- Describe the Morino formulation, the Kutta condition and how forces are obtained from surface pressure.
- Configure and interpret geometry and command files for structured and unstructured panel models.
- Plan staged validation and mesh-convergence studies, and compare solutions with experimental data.
- Interpret sphere and rudder investigations using pressure, force and drag evidence.
- Report results in a defensible, reproducible way.
- Propose justified design changes for a keel-bulb interaction problem using panel-method analysis.
Inside the course: a high-level summary, section by section.
Panel method theory
The course starts with the governing assumptions. Panel methods model the flow as inviscid, incompressible and irrotational, so it can be described by a velocity potential that satisfies Laplace’s equation. The continuous body surface is replaced by a set of panels, a flow boundary condition is enforced on each panel and the unknown surface potential or singularity strength is solved in a way that is computationally manageable. The course explains clearly what these simplifications include and exclude, particularly the absence of viscous effects, which must be added through boundary-layer coupling if drag is to be estimated.
Morino’s formulation, a widely used approach based on Green’s theorem, expresses the potential on the surface in terms of source and doublet distributions. For lifting bodies such as keels and rudders, a wake sheet is shed from the trailing edge and the Kutta condition is imposed so that the flow leaves the trailing edge smoothly. Forces and moments are then obtained by integrating the surface pressure, and the course discusses how lift and induced drag follow from the circulation and wake.
Geometry and input files
The second section treats the practical setup of a panel solver. Structured models are generated from ordered sections, with a parametric spline fitted through each section and user-controlled numbers of panels around and between sections, which makes it easy to rescale discretisation for convergence studies. The course explains the hierarchy of input files, separating parameters that apply to the whole model, to individual bodies and to mesh layout and body connections, and why that hierarchy supports systematic mesh refinement. Good file discipline, with clear naming, documented parameters and controlled changes between runs, is presented as an essential part of credible analysis rather than an administrative chore.
Unstructured models are introduced for intricate or CAD-derived geometry that is difficult to represent with structured meshes, reflecting modern design workflows. Command files and debugging techniques complete the section, teaching you to diagnose common geometry and setup errors as a practising engineer would.
Verification and validation
Validation is presented as a question of credibility, not merely whether the code runs. The course distinguishes verification, which checks that equations are solved correctly, from validation, which checks that the solution represents the physical problem. A staged approach is described, from simple analytical cases to experimental comparisons.
A rudder test case provides a detailed example. The reference geometry must be defined precisely, including planform, stock position and a reflection plane at the root to represent the effect of the hull or tunnel wall. Convergence strategy explains how to refine panel numbers systematically until results stop changing significantly. Experimental data, such as balance measurements of forces and integrated surface pressure tappings, allows the converged numerical solution to be judged as physically meaningful as well as numerically stable. Diagnostics help explain differences between prediction and experiment, for example viscous effects near stall.
Surface panel investigation
The fourth section is built around an assignment-style investigation that illustrates professional practice. The broader aims are to understand how mesh quality affects accuracy, to evaluate coupled potential-flow and boundary-layer methods, to predict physical performance from numerical results and to comment on usability and improvements. A sphere provides a non-lifting validation case, where computed pressures can be compared with exact theory and drag estimated through boundary-layer methods at a given Reynolds number. A rudder provides a lifting case for exploring panel sensitivity, loading and drag-polar behaviour. The course stresses clear presentation, reproducible assumptions and defensible conclusions as the hallmarks of good reporting.
Keel-bulb design application
The final section applies the method to a practical yacht design problem: the interaction between a keel and its bulb. The design problem is framed by identifying the performance objectives, such as lift, induced drag and righting moment, and the geometric variables that can be changed. A modelling strategy sets out how to represent the keel, bulb and junction with appropriate panelling and wake modelling. Design recommendations are then developed from evidence, showing how panel-method results can guide decisions on bulb shape, position and junction geometry while recognising the limits of inviscid analysis.
Why this matters in practice
Panel methods are fast enough to explore many design variants, making them valuable in early-stage hull and appendage design and as a check on more expensive CFD. Their value depends entirely on disciplined setup, convergence and validation, which are skills transferable to all numerical hydrodynamics. Engineers who understand what a panel code can and cannot represent are better placed to choose the right tool for each design question, to interpret results from colleagues or consultants, and to explain the confidence that can be placed in a prediction. Those are increasingly important skills as simulation replaces or supplements model testing in ship and yacht design. A sound grasp of the underlying potential-flow theory also makes it easier to recognise when a result is physically implausible.
Key takeaways
You leave able to explain the theory of lifting-surface panel methods, set up and debug structured and unstructured models, verify and validate results, report them defensibly and use panel analysis to support practical design decisions.
How you study
The course is delivered fully online and is self-paced, so you can fit roughly 20 hours of study around professional commitments. Lessons combine clear explanation with examples, diagrams and short interactive checks, and the main sections end with graded quizzes (5 in total) so you can confirm you can apply each method before moving on. A 107-page course book can be downloaded and printed for offline reading and later reference.
Course contents
- Potential Flow & Panel Theory: Governing Assumptions; Morino’s Formulation; Kutta and Forces
- Geometry & Command Files: Input Architecture; Reading .pan Files; Reading .uns Files; Command Files and Debugging
- Validation & Rudder Exercise: Validation Stages; Rudder Test Case; Convergence Strategy; Experiment and Diagnostics
- Surface Panel Investigation: Brief and Marking Scheme; Sphere Investigation; Rudder Investigation; Reporting Defensible Results
- Keel-Bulb Design Application: Design Problem Framing; Modeling Strategy; Design Recommendations
- Summary: Key Takeaways
Who this course is for
This master’s-level course is for engineering graduates and practising engineers in naval architecture, yacht design, hydrodynamics and CFD who want a rigorous grounding in panel methods. It also suits engineers who use commercial or in-house panel codes and want to understand their assumptions and limitations. A background in fluid mechanics and potential-flow theory is helpful.
Frequently asked questions
How long does Advanced Hydrodynamics for Ship-Yacht Design take?
The course is designed for about 20 hours of study. It is self-paced and fully online, so you can spread it over a few weeks or complete it more quickly.
What is covered?
The course is organised into 7 sections with 25 lessons, moving from foundations to applied methods, as summarised above.
Is there material to keep after the course?
Yes. A downloadable 107-page course book accompanies the lessons for offline reading and later reference.
How is progress checked?
Each main section closes with a graded quiz (5 in total). The quizzes test understanding of the concepts and methods explained in the lessons rather than memorisation, and you can review the relevant lessons before attempting them.
Can I record this study for my own professional development?
Yes. The course notebook includes a self-assessment of the course objectives before and after study, a reflection page and a learning log, which you can use to keep your own record of professional development.
Duration: 20 hours
Related courses: A14 – Design of Advanced Marine Vehicles; A17 – Advanced Structural Design and Analysis; A04 – Project Introduction to Hydromechanics; A18 – Naval Architecture Fundamentals
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Study at your own pace and work through the full course material, worked examples and section quizzes. Enrol in A16 – Advanced Hydrodynamics for Ship-Yacht Design →
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