Propulsive force calculations in swimming frogs. I. A momentum-impulse approach

Frogs are animals that are capable of locomotion in two physically different media, aquatic and terrestrial. A comparison of the kinematics of swimming frogs in a previous study revealed a difference in propulsive impulse between jumping and swimming. To explore this difference further, we determined the instantaneous forces during propulsion in swimming using an impulse-momentum approach based on DPIV flow data. The force profile obtained was compared with force profiles obtained from drag-thrust equilibrium of the centre of mass and with the force profiles generated during jumping. The new approach to quantifying the instantaneous forces during swimming was tested and proved to be a valid method for determining the external forces on the feet of swimming frogs. On the kinematic profiles of swimming, leg extension precedes propulsion. This means that it is not only the acceleration of water backwards that provides thrust, but also that the deceleration of water flowing towards the frog as a result of recovery accelerates the centre of mass prior to leg extension. The force profile obtained from the impulse-momentum approach exposed an overestimation of drag by 30% in the drag-thrust calculations. This means that the difference in impulse between jumping and swimming in frogs is even larger than previously stated. The difference between the force profiles, apart from a slightly higher peak force during jumping, lies mainly in a difference in shape. During swimming, maximal force is reached early in the extension phase, 20% into it, while during jumping, peak force is attained at 80% of the extension phase. This difference is caused by a difference in inter-limb coordination.