Estimate yacht residuary resistance before committing to a hull design
This hydrodynamic surrogate predicts residuary resistance from five hull-form coefficients and the Froude number. It provides naval architects with a fast screening model for comparing candidate geometries and speeds during early-stage design.
Residuary resistance influences the power required to reach a target speed and is therefore an important quantity during preliminary hull design. Physical towing-tank campaigns and high-fidelity simulations are valuable but costly to repeat for every candidate. A trained surrogate can provide rapid estimates inside an experimentally represented design space and help engineers decide which alternatives deserve detailed analysis.
1. Industrial challenge
This is an approximation problem: the model maps hull geometry and speed to the continuous response resistance, defined in the dataset as residuary resistance per unit weight of displacement.
Potential users include naval architects, hydrodynamicists, yacht designers, shipyards, marine engineering consultancies and research teams.
2. Data set
The Delft Yacht Hydrodynamics dataset contains 308 experiments performed at the Delft Ship Hydromechanics Laboratory. It covers 22 hull forms derived from a parent form related to the Standfast 43, with 14 Froude numbers per hull form.
| Variable | Engineering meaning | Role | Range |
|---|---|---|---|
center_of_buoyancy | Longitudinal centre of buoyancy | Input | -5.00 to 0.00 |
prismatic_coefficient | Prismatic coefficient | Input | 0.53 to 0.60 |
length_displacement | Length–displacement ratio | Input | 4.34 to 5.14 |
beam_draught_ratio | Beam–draught ratio | Input | 2.81 to 5.35 |
length_beam_ratio | Length–beam ratio | Input | 2.73 to 3.64 |
froude_number | Dimensionless speed parameter | Input | 0.125 to 0.450 |
resistance | Residuary resistance per unit weight of displacement | Target | 0.01 to 62.42 |
There are no missing values. The configured split uses 186 samples for training, 61 for selection and 61 for testing.
3. Model
The exported neural network receives six dimensionless inputs and returns one continuous resistance estimate. Mean-and-standard-deviation scaling feeds three tanh hidden neurons; a linear output is then unscaled to the resistance units used by the dataset. The resulting 6–3–1 model contains 25 trainable parameters and applies no output bounding.
4. Training strategy
The model minimizes normalized squared error with L2 regularization (weight 0.01) and the quasi-Newton method. Training stopped after 62 epochs because the loss improvement fell below the configured threshold. The final recorded training and selection errors are 0.017 NSE and 0.007 NSE.
5. Model selection
The current exported deployment model uses three hidden neurons. This is the same architecture described above, evaluated in the testing section and implemented in the browser calculator and downloadable Python model.
For production use, architecture selection should be repeated with complete hull forms held out. A random row split can reward models that interpolate the speed curve of a hull geometry already represented during training.
6. Testing analysis
The exported Python model was independently recalculated on the 61 observations marked as testing in the supplied Neural Designer project. R² measures explained variation, while MAE and RMSE express error in the resistance units used by the dataset.
| Testing samples | R² | MAE | RMSE | Maximum absolute error |
|---|---|---|---|---|
| 61 | 0.9474 | 1.881 | 3.114 | 16.849 |
The model captures the dominant speed–resistance trend, but the largest errors occur at the high-resistance end. This matters operationally because those cases can drive powering and feasibility decisions.
7. Model deployment
The surrogate can be integrated into an early-stage design workflow to screen geometries, generate speed–resistance curves and identify candidates for higher-fidelity analysis.
Try the hydrodynamic surrogate model
Enter a hull geometry and Froude number within the experimental ranges. The browser evaluates the compact analytical expression published with this example.
Demonstration surrogate — not a certified hull-design or powering tool.
Response optimization
The updated run minimizes predicted resistance while constraining the longitudinal centre of buoyancy between -3 and -2. It returns the following feasible point inside the declared bounds:
| Quantity | Optimized value |
|---|---|
| Centre of buoyancy | -2.341 |
| Prismatic coefficient | 0.564 |
| Length–displacement ratio | 4.943 |
| Beam–draught ratio | 4.902 |
| Length–beam ratio | 2.898 |
| Froude number | 0.152 |
| Predicted resistance | 0.008 |
Directional response
The updated directional output varies Froude number around a reference hull defined by centre of buoyancy -2.3, prismatic coefficient 0.53, length–displacement ratio 4.76, beam–draught ratio 3.68 and length–beam ratio 3.16.
Download and reproduce
The deployment package contains the current Python and browser models. The project package contains the Neural Designer project and its CSV dataset.
8. Scope and limitations
- The dataset represents 22 related hull forms derived from one parent family, not the full yacht design space.
- The model is valid only inside the coefficient and Froude-number ranges shown above.
- The response covers residuary resistance per unit weight of displacement; total powering also requires other resistance components and propulsion-system assumptions.
- The random row split does not prove generalization to unseen hull forms.
- Feasible design constraints, stability, seakeeping, structural requirements and regulatory criteria are outside this surrogate.
- Final decisions should be confirmed with naval-architecture analysis, CFD, model testing or full-scale evidence as appropriate.
References
- Gerritsma, J., Onnink, R., & Versluis, A. (1981). Yacht Hydrodynamics dataset, UCI Machine Learning Repository.
- Ortigosa, I., López, R., & García, J. (2007). A neural networks approach to residuary resistance of sailing yachts prediction. Proceedings of MARINE 2007.
