Abstract: The averaged equation of motion for linear acceleration in the BCF swimming mode was derived using the Elongated Body Theory (EBT) through time averaging. An analytical solution for the linear acceleration swimming velocity was obtained, revealing that the average velocity follows a hyperbolic tangent function of time, which can be considered a semi-empirical formula for linear acceleration swimming. The formula’s parameters, such as the steady swimming velocity and the acceleration time constant, can be determined by conducting experiments on linear acceleration, enabling the estimation of drag coefficient, effective added mass, thrust, and drag force. We developed a tensegrity robotic tuna and conducted a linear acceleration experiment. The results confirmed both the averaged equation of motion and its empirical formula, indicating that the formula is not limited by EBT and can be extended to large amplitude swimming and thunniform swimmers with large aspect ratio caudal fins. This provides researchers with an efficient and easy-to-implement method to estimate the swimming thrust and drag forces through linear acceleration experiments, without the need for complex and expensive flow field and force measurement equipment.

Key words: Body and/or caudal fin · Linear acceleration swimming · Robotic fish · Tensegrity · Thrust · Drag