Sp is the sperm number and de3 denotes the distance moved by the centroid over a beat cycle for the reinforced flagellum, with stiffness function e3, in figure 5, while de1 is defined analogously for the naked axoneme with stiffness function e1. Hence by examining the ratio of these distances, one has that the reinforced flagellum travels significantly further per beat cycle at a high sperm number of 25 in figure 5, relative to the naked axoneme, with the converse observation at a lower sperm number of 10.