Hollow Keel Section

Weight–Drag Tradeoff with Structural Constraints

This case study builds upon the methodology used in a previous keel section optimization, but introduces a new design variable: section weight. The objective is to explore the trade-off between hydrodynamic drag and structural weight, using a hollow keel section.

Context

Designing a keel section requires balancing hydrodynamic efficiency, structural performance, and now, wall thickness. A thinner structure reduces weight, but may increase drag or compromise strength. Understanding this trade-off is key to identifying a meaningful optimum.

Methodology

Input Parameters
Defined performance and cavitation conditions, along with structural and geometrical constraints (e.g. max chord, thickness).
For the particular case study:
- Upwind: 8 kn, CL·chord = 0.16
- Downwind: 12 kn, CL·chord = 0.05
Candidate Generation
A parametric model produces thousands of hollow section shapes, each with a different internal geometry.
Evaluation & Optimization
- Each section is evaluated using XFoil.
- A machine-learning surrogate model is trained on the dataset and used to generate a Pareto front of drag vs. weight, under the constraint that sections must meet structural criteria.

Results

The resulting Pareto front reveals a clear turning point around Section_3:

Attempting to go lighter than that point leads to a steep increase in drag.
Up to that threshold, weight can be reduced by ~50% with only a moderate drag penalty.
This enables informed design decisions based on project priorities — whether to favor lighter structure or lower hydrodynamic resistance.

Drag vs Weight Pareto Front

The images below show the four representative sections along the Pareto front, illustrating the design trade-offs between weight and drag.

Section 0 – Lowest drag
Solid section thath prioritizes hydrodynamic performance, resulting in higher weight.
Section 1 – Low drag, heavier structure
A compromise between weight and drag; sits well before the sharp increase on the Pareto curve.
Section 3 – On the Pareto kink
Marks the transition point on the Pareto front — just before drag increases significantly. A particularly interesting design from a trade-off perspective.
Section 5 – Very light, high drag Achieves very low weight with a large chord and thin walls, but at the cost of significantly higher drag — beyond the efficient trade-off region.

Summary

By introducing section weight as an optimization variable, this study shows how machine learning can help navigate the complex relationship between drag and structural mass.