Optimal Flight Path of Flying Fish

Abstract

The flight path of flying fish is analyzed by two methods, a simple analytical method and a numerical method based on optimal control theory. It has been observed that flying fish fly over the sea to escape from predators. Therefore, two possible strategies are considered, flight for the maximum range and flight for the longest time.The simple analytical method is based on energy consumption during flight. Using this method, the flight distance and the flight time of unsteady level gliding flight were compared to those of steady gliding flight. The steady gliding flight achieves a longer flight distance and time than the unsteady level gliding flight when the ground effect is not considered, although the differences are small. When the ground effect is taken into consideration, the unsteady level gliding flight is superior both in the length and the duration of flight.In order to obtain detailed flight behaviors the numerical method based on optimal control theory was then used. This theory has the capability of giving the optimal solution for a given performance index. The calculated optimal flight path for the maximum flight range agrees well with the observed flight paths of the flying fish, Cypselurus agoo agoo and Cypselurus heterurus doederleini. In contrast, the calculated optimal flight path for the longest flight time is similar to that of the steady gliding flight and is different from the observed flight paths. Therefore, it is concluded that the flight of flying fish corresponds closely to the optimal solution for achieving the maximum flight range.