The comparative hydrodynamics of rapid rotation by predatory appendages

Abstract

Countless aquatic animals rotate appendages through the water, yet fluid forces are typically modeled with translational motion. To elucidate the hydrodynamics of rotation, we analyzed the raptorial appendages of mantis shrimp (Stomatopoda) using a combination of flume experiments, mathematical modeling and phylogenetic comparative analyses. We found that computationally efficient blade-element models offered an accurate first-order approximation of drag, when compared with a more elaborate computational fluid-dynamic model. Taking advantage of this efficiency, we compared the hydrodynamics of the raptorial appendage in different species, including a newly measured spearing species, Coronis scolopendra. The ultrafast appendages of a smasher species (Odontodactylus scyllarus) were an order of magnitude smaller, yet experienced values of drag-induced torque similar to those of a spearing species (Lysiosquillina maculata). The dactyl, a stabbing segment that can be opened at the distal end of the appendage, generated substantial additional drag in the smasher, but not in the spearer, which uses the segment to capture evasive prey. Phylogenetic comparative analyses revealed that larger mantis shrimp species strike more slowly, regardless of whether they smash or spear their prey. In summary, drag was minimally affected by shape, whereas size, speed and dactyl orientation dominated and differentiated the hydrodynamic forces across species and sizes. This study demonstrates the utility of simple mathematical modeling for comparative analyses and illustrates the multi-faceted consequences of drag during the evolutionary diversification of rotating appendages.

Beyond power amplification: latch-mediated spring actuation is an emerging framework for the study of diverse elastic systems

“…These sampling and acquisition rates are not sufficient to resolve a single meral-V unloading event. Such tests are also challenged by imposing realistic forces on the elastic mechanism that would occur in the natural contexts for the movement, such as fluid dynamic forces on rotating appendages of mantis shrimp (McHenry et al, 2012(McHenry et al, , 2016.…”

Context-dependent scaling of kinematics and energetics during contests and feeding in mantis shrimp

“…We measured strike energy during contests and feeding through a combination of kinematic measurements and a previously published mathematical model of the mantis shrimp strikes (McHenry et al, 2012). This model equates the elastic potential energy of the raptorial appendage prior to a strike (as determined by spring energy storage and linkage mechanics; McHenry et al, 2012;Patek et al, 2013;Zack et al, 2009) with the kinetic energy of the strike (determined by fluid mechanics; McHenry et al, 2016). We begin this section with a brief overview of the mathematical model (see also Fig.…”

“…We begin this section with a brief overview of the mathematical model (see also Fig. 3) and advise the reader to consult McHenry et al (2012McHenry et al ( , 2016 for the full expression of and rationale for the mathematical model.…”

“…Simultaneously, merus flexor muscles engage latches (modified apodemes) that prevent distal rotation of the striking body (defined as the combined propodus and dactyl segments that serve as a hammer) while the spring is loaded. Upon latch release, the spring's elastic potential energy transitions to kinetic energy, such that work is performed to rotate the striking body toward its target and to resist drag forces (for detailed descriptions of the strike mechanism, see Burrows, 1969;Burrows and Hoyle, 1972;Cox et al, 2014;McHenry et al, 2012McHenry et al, , 2016McNeill et al, 1972;Patek et al, 2004Patek et al, , 2007Patek et al, , 2013Rosario and Patek, 2015;Zack et al, 2009). Strike duration is so short that smashing mantis shrimp must use open loop control: in order to vary kinematic output, they adjust elastic energy storage prior to striking by compressing the spring to different displacements (Kagaya and Patek, 2016).…”

“…Increased extensor muscle activity causes greater shortening of the compression spring, thereby storing more elastic energy and resulting in a higher angular velocity of the strike (Kagaya and Patek, 2016). These studies, along with the development of a vetted mathematical model of strike energetics (McHenry et al, 2016(McHenry et al, , 2012, allow for measurements of strike kinematics to be connected with two types of energy: elastic energy storage (input) and combined strike kinetic and drag energy (output).…”