Fig. 2. Quantitative model of force balance between the force F_M produced by medusan muscle contraction and the forces F_J or F_L required for locomotion. Solid line, 0.5 Hz swimming frequency model; broken line, 1 Hz model; dotted line, 2 Hz model. The constraint on morphological diversity becomes more severe with increasing swimming frequency due to the increased flow accelerations and required locomotive forces. (A) Limiting curve corresponding to force balance F_M=F_J, i.e. Eqn 11 plotted with the first term in parenthesis neglected. The model predicts that jet-propelled medusae are limited to the morphospace below this curve, i.e. medusae with bell shape and size combinations above the curve are not capable of swimming via jet propulsion. (B) Limiting curve corresponding to force balance F_M=F_L, i.e. Eqn 11. The new model predicts that all medusae are limited to the morphospace below this curve. At high fineness ratios the force constraints for jet-paddling and jet propulsion do not differ significantly because magnitude of the stopping vortex during the recovery stroke of jet-paddling is inversely related to fineness ratio. At low fineness ratios the stopping vortex sufficiently reduces F_L such that it is never greater than F_M; therefore, medusan sizes are not constrained below the critical fineness ratio f_CRIT=0.265. This is the key difference between A and B.