Alternative Empirical Formula for Predicting the Frictional Drag Penalty due to Fouling on the Ship Hull using the Design of Experiments (DOE) Method

Biofouling is known as one of the main problems in the maritime sector because it can increase the surface roughness of the ship’s hull, which will increase the hull’s frictional resistance (ΔC_F) and consequently, the ship’s fuel consumption and emissions. It is thus important to reduce the impact of biofouling by predicting the value of ΔC_F. Such prediction using existing empirical methods is still a challenge today, however. Granville’s similarity law scaling method can predict accurately because it can be adjusted for all types of roughness using the roughness function ΔU⁺(k⁺) variable as the input, but it requires iterative calculations using a computer, which is difficult for untrained people. Other empirical methods are more practical to use but are less flexible because they use only one ΔU⁺(k⁺) input. The variance of ΔU⁺(k⁺) is very important to represent the biofouling roughness that grew randomly. This paper proposes an alternative formula for predicting the value of ΔC_F that is more practical and flexible using the modern statistical method, the Design of Experiments (DOE), particularly two-level full factorial design. For each factor, the code translation method using nonlinear regression combined with optimization of constants was utilized. The alternative formula was successfully created and subjected to a validation test. Its error, calculated against the result of the Granville method, had a coefficient of determination R²= 0.9988 and an error rate of ±7%, which can even become ±5% based on 93.9% of 1,000 random calculations.