VOGEL, S; Duke University: Bioballistics: The Scaling of Prelaunch Acceleration and Subsequent Trajectories

Biological projectiles, from spores to leaping mammals, range over 100,000-fold in length. If force available varies with length squared and projectile mass with length cubed, then acceleration should scale inversely with length. Thus the prodigious accelerations of small ones (approaching 1,000,000 g) come as no surprise. The scaling of acceleration suggests constant stress and a limit on performance based on the strength of available materials, not on the outputs of biological motors. The smaller the projectile, the more its trajectory reflects a drag-dominated rather than a gravity-dominated world; a scaling index based on that shift can predict ranges and optimal launch angles. Borelli�s adage that (drag aside) animals of any size should jump to about the same height ignores prelaunch energy storage. While the rule turns out to be remarkably general, its applicability has quite a different basis.