Lift and drag performance of odontocete cetacean flippers

Abstract

SUMMARYCetaceans (whales, dolphins and porpoises) have evolved flippers that aid in effective locomotion through their aquatic environments. Differing evolutionary pressures upon cetaceans, including hunting and feeding requirements, and other factors such as animal mass and size have resulted in flippers that are unique among each species. Cetacean flippers may be viewed as being analogous to modern engineered hydrofoils, which have hydrodynamic properties such as lift coefficient, drag coefficient and associated efficiency. Field observations and the collection of biological samples have resulted in flipper geometry being known for most cetacean species. However, the hydrodynamic properties of cetacean flippers have not been rigorously examined and thus their performance properties are unknown. By conducting water tunnel testing using scale models of cetacean flippers derived via computed tomography (CT) scans, as well as computational fluid dynamic (CFD) simulations, we present a baseline work to describe the hydrodynamic properties of several cetacean flippers. We found that flippers of similar planform shape had similar hydrodynamic performance properties. Furthermore, one group of flippers of planform shape similar to modern swept wings was found to have lift coefficients that increased with angle of attack nonlinearly, which was caused by the onset of vortexdominated lift. Drag coefficient versus angle of attack curves were found to be less dependent on planform shape. Our work represents a step towards the understanding of the association between performance, ecology, morphology and fluid mechanics based on the three-dimensional geometry of cetacean flippers.

Hydrodynamic properties of fin whale flippers predict maximum rolling performance

“…Similar to engineered wings, flippers have a fusiform crosssection and a swept-back planform, and this morphological design enables enhanced lift generation relative to drag (Weber et al, 2009). The highly tapered, high aspect ratio flippers of fin whales yield greater lift-to-drag characteristics and a greater coefficient of lift compared with other large cetaceans that have more paddle-like flippers (Weber et al, 2014).…”

“…In whales and dolphins (Cetacea), these control surfaces include flukes and flippers with geometries and hydrodynamic properties similar to those of engineered wings (Fish, 2004;Weber et al, 2014). A central paradigm of cetacean locomotion is that posteriorly positioned flukes are oscillated to generate thrust , while the anteriorly located flippers create lift used for maneuvers, stability and the maintenance of body trim (Fish, 2002;Fish et al, 2003b;Weber et al, 2009). Given that their locomotion relies on separate propulsion and control surfaces (Fish, 2002), and the evidence that their vertebral design may limit flexibility (Long et al, 1997;Woodward et al, 2006), large cetaceans may behave more like rigid-hulled objects, and their maneuvering performance can be modeled as such.…”

Effects of added drag on cetaceans : fishing gear entanglement and external tag attachment

“…Drag loading sometimes results in reduction in speed (Lang and Daybell, 1963;Boyd et al, 1997;Elliott et al, 2007;van der Hoop et al, 2014a); however, there are instances where speed is maintained and additional energy consumption occurs (Williams et al, 1993). Swimming speeds are often maintained in migratory species, where enough time must be left for essential activities such as feeding and reproduction (Weber et al, 2009). Our assumption that whales maintain speed likely provides an upper bound of power requirements.…”

“…Our propulsive model suggests that drag from entanglement in fishing gear can incur energetic demands similar to costly life-history stages. Daily additional costs of swimming while entangled (7.24 ⇥ 10 7 7.52 ⇥ 10 8 J/day) are comparable to pregnancy (1.84 ⇥ 10 8 J/day; Fortune et al, 2013) Figure 3; Cherel et al, 1988;Miller et al, 2011;Christiansen et al, 2013) and organ function (Weber et al, 2009), entanglement is unanticipated and is not necessarily associated with any particular seasonal cue; whether an individual animal has laid down fat reserves to cope with the energetic costs of entanglement is a matter of chance.…”

“…The economical approach is to perform a task while expending the least amount of energy as possible (Alexander, 1989;Sparrow and Newell, 1998): for example, humans adjust their step length or stride frequency when carrying loads to minimize energy expenditure, and horses change from trot to canter to gallop because these gaits require less energy than their intermediates. By moving at speeds where transport costs are minimized (Williams, 1999;Wickler et al, 2000;Rosen and Trites, 2002a;Weber et al, 2009;Halsey, 2016), or by taking advantage of environmental factors such as winds (Hedenstrom, 1993;Weimerskirch et al, 2000), tides (Weihs, 1978;Metcalfe et al, 1990;Forward and Tankersley, 2001), or buoyancy (Webb et al, 1998;Fahlman, 2008;Aoki et al, 2011;Miller et al, 2012b;Adachi et al, 2014), animals can improve their energy economy.…”