Algebraic expressions for the waveforms of sea urchin sperm flagella

The waveforms of live sea urchin sperm flagella were digitized with video-digitizing apparatus. The flagellar waveforms were expressed by the coordinates of 20 points spaced 2 micron apart along the flagella. The waveforms were condensed into simple algebraic expression with four parameters. Each of these parameters showed a systematic variation with the flagellar frequency. These average trends of the parameters made it possible to define an average, idealized, waveshape as a function of the flagella frequency, in the range 8-80 Hz.