Research on the optimal spacing resistance reduction technology for ship formation

• A multi-ship distributed resistance measurement device was designed, and a four-ship formation resistance test was carried out. • The resistance reduction mechanism of the ship formation is obtained: the wave interference of the front and rear ships. And the interference effect is related to the spacing and Froude number. • This study proposes an optimal spacing resistance reduction formula for ship formations, which can offer a convenient and efficient method for achieving energy savings during actual formation navigation. In nature, there are often numerous phenomena of collective movement, such as geese flying and fish swimming. To explore the advantages of swarm motion, this paper examines swarm motion from the perspective of energy consumption. Focusing initially on the common scenario of ducklings swimming with their mother, two ellipsoids with similar geometry were introduced to simulate the swimming motion and analyze movement resistance. The results show that within a certain distance range, the resistance of the ellipsoid in the rear is significantly reduced compared with the resistance of a single ellipsoid. The resistance reduction effect is related to the spacing of the two ellipsoids, and there is an optimal spacing for resistance reduction at different moving speeds. Subsequently, resistance calculations and energy-saving analyses were conducted for four Unmanned Surface Vessel formations, revealing that formation navigation had a significant energy-saving effect. Additionally, this paper includes an experimental study of a ship formation model, and the calculation results are compared with the experimental results, verifying the reliability of the swarm motion resistance calculation method. Finally, a formula for optimal spacing in ship formations to reduce resistance is proposed, providing a convenient and feasible energy-saving reference for actual ship formation navigation.