Three-dimensional Hydrodynamic Analysis of Forelimb Propulsion of Sea Turtle With Prosthetic Flippers Xiaoqian Sun a*, Naomi Kato a Yasushi Matsuda b, Kazunori Kanda b, Yusuke Kosaka b Naoki Kamezaki c, Mari Taniguchi c a Osaka University, Suita, Osaka, Japan b Kawamura Gishi Co. Ltd, Daito, Osaka, Japan c Sea Turtle Association of Japan, Hirakata, Osaka, Japan Abstract—This study is to develop prosthetic flippers strokes are usually used by most freshwater turtles, for an injured sea turtle named “Yu” from the view- which have been documented in an extensive range of point of 3D (three-dimensional) hydrodynamic analysis previous studies [e.g. 1, 2, 3, 4, 5]. Flapping strokes are of sea turtles’ forelimb propulsion. Firstly template characterized by predominantly drosoventral forelimb matching method is used to compare the 3D movements movements, whereas rowing strokes are characterized of fore flippers in three cases respectively: those of a by predominantly anteroposterior forelimb movements healthy turtle, those of Yu with and without prosthetic combined with rotation of the foot (perpendicular to flippers. Secondly 3D hydrodynamic analyses for three flow during thrust and feathered during recovery) [6]. cases based on quasi-steady wing element theory are But specifically speaking, turtle species display carried out to investigate the hydrodynamic effects of considerable diversity in their styles of forelimb prosthetic flippers on the swimming performance of sea flapping or rowing. So quantifying the exact forelimb turtles. Finally the hydrodynamic effects are clarified kinematics and the corresponding thrust forces during and some remarks for designing new prosthetic flippers turtles’ swimming is a key, which is a significant in future are given. challenge because direct measurements of force generated by the free turtles’ swimming are not feasible. Index Terms—forelimb propulsion of sea turtle, Davenport et al. estimated the thrust force by prosthetic flipper, template matching method, wing attaching a force transducer to the shells of turtles [2]. element theory But this still puts some restriction on the free swimming of turtles. Walker et al. documented the changes in I. INTRODUCTION velocity and acceleration in aquatic locomotion by tracking the center of mass of an animal through an An injured female loggerhead sea turtle (Caretta artificial locomotor cycle [7]. Some other researchers caretta) named Yu was found and rescued by Sea Turtle tried to obtain the thrust force by examining the Association of Japan at Kiisuido in the summer of 2008. properties of the flow field around the aquatic animals. Her swimming speed was just 60% of that of healthy For example Drucker et al. employed digital particle adult sea turtle because only a half of the left forelimb image velocimetry (DPIV) to examine the vortex wake and two thirds of the right forelimb were left after being shed by freely swimming fish and then evaluated the attacked by a shark. Realizing that we could not put her thrust forces [8]. Our team concentrated on directly back into the sea under such a condition, “Yu Project” observing the forelimb movements of sea turtles and has begun since 2009 to develop prosthetic flippers in calculating the corresponding hydrodynamic forces. cooperation with veterinarians, a prosthetic company, Previously Isobe et al. [9] compared the 2D and 3D aquariums, universities and a public administration for motions of fore flippers between Yu itself, Yu equipped Yu. During this process studying the kinematics of sea with prosthetic flippers and “Sho” (a healthy sea turtle) turtles and evaluating the effects of prosthetic flippers in a pool of an aquarium, an artificial lagoon and a on the swimming performance of Yu become an water circulating tank. At the same time assuming the important job. flipper consist of a rigid wing and uniform flapping, Turtle species exhibit a diversity of kinematic rowing and feathering motion from root to tip, they patterns in their forelimbs during swimming. Generally analyzed 2D hydrodynamic characteristics of different speaking, the flapping forelimb strokes are usually used flippers under uniform flow. But taking into account the by swimming marine turtles and the rowing forelimb 3D motion of fore flippers, we thought 2D analysis cannot accurately evaluate the swimming performance * Department of Naval Architecture and Ocean Engineering, School of sea turtles. In our following 3D analyses of forelimb of Engineering, Osaka University, 2-1 Yamadaoka, Suita, Osaka, 565-0871, Japan. motions, the flipper is treated as flexible in spanwise E-mail: [email protected] direction and consists of several wing segments with – 36 – JOURNAL OF AERO AQUA BIO-MECHANISMS, VOL.3, NO.1 different flapping, rowing and feathering motion from C. Background of Motion Analysis root to tip. A motion capturing software using template matching method was utilized to observe forelimb movements in II. MOVEMENTS ANALYSIS the form of time variation of the prescribed points on the forelimbs. As Sho is healthy and possesses A. Sea Turtles symmetric fore flippers, we will only analyze the Table.1 and Fig.1 show the details of the sea turtle movements of its left fore flipper during swimming. But “Yu” and “Sho”. as for the case of Yu, because its actual left flipper and actual right flipper show different shapes, we have to Table.1 Specifications of sea turtles for motion analysis analyze the movements of both flippers in the following Carapace Body Area (left Area (right context. Locations of the targeted points on Sho’s left Name length mass flipper) flipper) flipper, Yu’s flippers and the prosthetic flippers are Yu 0.797 [m] 100.5[kg] 0.039[m2] 0.026[m2] shown in Fig.4, Fig.5 and Fig.6 respectively. Two Sho 0.751 [m] 84.8[kg] 0.063[m2] 0.067[m2] targeted points located in the spanwise middle of the flipper are used to obtain the feathering motion of the flipper. The body fixed coordinate during motion analysis is defined as O-XYZ in Fig.17. Fig.1 Photographs of “Yu” (left) and “Sho” (right) B. Prosthetic Flippers The prosthetic flippers are made of a kind of copolymers by Kawamura Gishi Co. Ltd. The left and Fig.4 Motion captured points on Sho’s left flipper right flippers for “Yu” are shown in Fig.2. At first we (In the following context Lroot, LM and Ltip denote the let Yu put on the specially designed jacket (Fig.3). And root, the middle, and the tip of left flipper, respectively. then the prosthetic flippers are installed onto the Rroot, RM and Rtip denote the root, the middle and the corresponding forelimb of Yu. Finally Velcro tape is tip of right flipper respectively) used to tighten the prosthetic flippers around each sleeve of the jacket. Honestly speaking, the present shape of flippers and the procedure of installing prosthetic flippers onto the forelimb are the results of many trials and errors in the past. The specially designed jacket has the function of avoiding the prosthetic flippers coming off the forelimb. Fig.5 Motion captured points on Yu’s fore flippers Fig.2 Left and right prosthetic flippers for “Yu” Fig.6 Motion captured points on the prosthetic flippers Fig.3 Specially designed jacket for “Yu” equipped with D. Experimental Condition both prosthetic flippers – 37 – JOURNAL OF AERO AQUA BIO-MECHANISMS, VOL.3, NO.1 Three videos were taken simultaneously from the left side, the right side and the upper side of Sho, Yu with and without prosthetic flippers at the water tank of Suma Aqualife Park KOBE. E. Results of Movement Analysis Fig.7 shows the trajectories of the motion captured points on the left flipper of Sho in x-y plane of the body fixed coordinate. The period of motion is 3.0s. Fig.8 and Fig.9 show the trajectories of the motion captured Fig.8 Trajectories of motion captured points on the left points on the left and right flippers of Yu without flipper of Yu in x-y plane (period:2.4s) prosthetic flippers in x-y plane of the body fixed coordinate separately. Fig.10 and Fig.11 show the trajectories of the motion captured points on the left and right prosthetic flippers of Yu in x-y plane of the body fixed coordinate separately. First of all it is observed that Yu swims with a bigger frequency of flipper movements than Sho does, but if the prosthetic flippers are installed, the flipper movement frequency of Yu decreases. From the five figures we can see that the flippers of Sho and Yu describe a circular arc with large curvature in both the power stroke (from anterior Fig.9 Trajectories of motion captured points on the right position to posterior position) and the recovery stroke flipper of Yu in x-y plane (period:2.3s) (from posterior position to anterior position). On the other hand, in the case of Yu equipped with prosthetic flippers, the trajectory of the flippers in x-y plane is a circular arc with small curvature. Fig.12 shows the trajectories of the motion captured points on the left flipper of Sho in x-z plane of the body fixed coordinate. Fig.13 and Fig.14 show the trajectories of the motion captured points on the left and right flippers of Yu in x-z plane of the body fixed coordinate. Fig.15 and Fig.16 show the trajectories of Fig.10 Trajectories of motion captured points on the left the motion captured points on the left and right prosthetic flipper of Yu in x-y plane (period: 2.93s) prosthetic flippers of Yu in x-z plane of the body fixed coordinate. The trajectories of the flippers of Sho and Yu are ovals but in the case of Yu equipped with prosthetic flippers the trajectory of the flippers is similar to an oval with twist at the posterior position for the left prosthetic flipper and at the middle position for the right prosthetic flipper.