Spectral Co-Design of Ship Rudder Geometry and Heading Autopilot for Energy Efficiency and Manoeuvring Safety
DOI:
https://doi.org/10.62051/bgsje749Keywords:
Rudder design; Ship manoeuvrability; Energy efficiency; Multi-objective optimisation; Autopilot co-design; MMG model; Steering losses; KVLCC2.Abstract
Rudders determine the manoeuvring safety of a ship and permanently consume propulsive power through profile drag, weather helm and autopilot action. Because rudder geometry and course-keeping controller are designed separately and the energy cost of steering requires long stochastic simulations, their joint trade-off between energy efficiency and safety has remained unquantified. This paper proposes a spectral co-design method that optimises rudder area, span and section thickness together with the parameters of a PID heading autopilot. A baseline-anchored, stall-aware rudder model preserves the captive-model calibration of the MMG standard method while extrapolating to new geometries with section data from a physics-informed airfoil model. A frequency-domain evaluator combines steady-sailing equilibria in wind and wave drift with closed-loop second moments under gusts, slowly varying drift and first-order wave loads, and obtains the mean steering resistance from a second-order expansion of the surge balance. The constrained three-objective problem—rudder-related power, utilisation of the IMO manoeuvring criteria and heading deviation, subject to adverse-weather course keeping, steering-gear rate, cavitation and stability—is solved for the KVLCC2 tanker over a climate derived from 194,475 NOAA buoy records. The evaluator reproduces nonlinear time-domain statistics with R2 = 0.976–0.996 at an 1100-fold speed-up. Against the original rudder with a conventionally tuned autopilot, the knee co-design reduces the rudder-related power by 15.0% while improving both safety objectives. In every run, co-design outperforms sequential design and geometry optimisation with a fixed autopilot (hypervolume +2.0% and +2.8%), and nonlinear time-domain simulation over the full climate confirms the saving of the knee design (15.4%). A quantile-based robust formulation raises the Monte Carlo reliability of the Pareto designs from 0.77 to 0.91 under hydrodynamic-coefficient uncertainty.
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