DEVELOPMENT AND PERFORMANCE ESTIMATION OF FLAPPING FIN PROPULSION SYSTEM

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1 DEVELOPMENT AND PERFORMANCE ESTIMATION OF FLAPPING FIN PROPULSION SYSTEM Akihisa Konno a;, Koichi Hirata b and Masakuni Kawada b a Kogakuin University, Japan b National Maritime Research Institute, Japan Abstract The objective of this research was to understand the mechanism of flapping fin propulsion. Two submergence vehicles were developed. One modeled itself on a sea turtle, and the other modeled itself on a penguin. Maximum swimming velocity is :6 m=s for the turtle-like vehicle, and :48 m=s for the penguin-like one. The relationship between flapping frequency and swimming velocity seems linear in the region of the experiment. This implies that the velocity had not yet reached to the limit because of insufficient fin frequency. Swimming velocity of the turtle-like vehicle was also numerically estimated using blade element theory, and the result was faster than the experimental result. This is because of some assumptions for the estimation, and improvements of estimation should be done. Effect of fin deformation was numerically investigated, and the result implies the possibility of improvement of flapping performance using flexible fins. A flapping fin propulsion performance measurement system was developed, and will be used to investigate fundamental features of flapping fin propulsion. Keywords: Flapping Motion, Propulsion, Submergence Vehicle, Blade Element Theory, Fin Deformation NOMENCLATURE C.s/ Chord length at span position r [m] C L. / Lift coefficient of blade elements with given angle of attack C D. / Drag coefficient of blade elements with given angle of attack L b Body length of an aquatic animal or a vehicle [m] L s Fin span length [m] R Root position of fin from rotational center [m] s Span position [m] T Feathering period [s] Th Thrust [N] Tq Torque to swing a fin [N m] U Vehicle velocity (uniform flow velocity) [m=s] V.s; t/ Flow velocity relative to a wing element [m=s] y.s; t/ and z.s; t/ Fin shape [m=s].s; t/ Relative angle of attack [rad] ˇ.t/ Feathering angle [rad] ˇmax Amplitude of feathering angle [rad].s; t/ Inflow angle [rad] Phase delay from flapping angle to feathering angle [rad] Density of fluid [kg=m 3 ].t/ Flapping angle [rad] max Amplitude of flapping angle [rad] Corresponding author: Nakano-machi 2665, Hachioji-shi, Tokyo , Japan, Tel: , Fax: , E- mail: konno@researchers.jp. I. INTRODUCTION Fish swimming has become one of interesting research topics in the field of marine engineering. Both fundamental analysis of the mechanism of fish swimming and application to propulsion and/or maneuvering have been studied by many researchers [1]. We have also studied this topic, and developed several fish-like underwater vehicles [2], [3]. There may be potentially many demands of underwater vehicles so that further studies of fish swimming may well be done. For applying to underwater vehicles, a swimming style in which many parts of the body are used, like that of eels and many freshwater fish, might not be appropriate, because it is hard to realize that motion with mechanics, and because loading capacity will be limited. On this standpoint, we directed our attention to flapping motion of fins which is used by, for example, manta ray, turtles and penguins. These creatures do not, at least widely, deform the body and mainly use a pair of fins for propulsion and maneuvering. This feature fits for the development of underwater robots. The essence of fin motion of turtles and penguins is a combination of flapping (swinging) and feathering (twisting) motion, as shown in Fig. 1. We would like to understand the feature of these motion and to make use of them to underwater robots. Deformation of fins is also a considerable feature of the performance of flapping fin propulsion. In this paper we report our research work related to flapping fin propulsion. Two underwater vehicles based on different aquatic animals were developed. One is based on a sea turtle, and the other based on a penguin. We are also trying to develop a theoretical estimation method of flapping fin propulsion systems. Currently we make use of the blade element theory. Numerical estimations were carried out using the above theory with deformable fins, and as a result, flexible fin flapping sometimes causes better performance than rigid fin flapping. This method, however, does not consider dynamic effects and induced drag so that there is still a room to improve. To improve the above theoretical estimation, we need to know flow structure of the wake of flapping fins, especially the structure of vortices that shed from flapping fins periodically. To obtain the flow structure and fundamental knowledge of flapping propulsion, we developed a flapping fin propulsion performance measurement system. This system is installed on a water basin, performs flap-

2 ping motion with changing feathering angle and phase arbitrarily, and measures thrust force produced by that motion. II. DEVELOPMENT OF SUBMERGENCE VEHICLE BASED ON SEA TURTLE We developed two underwater vehicles based on different aquatic animals. One is a submergence vehicle based on a sea turtle, and the other based on a penguin. In this section we will report the vehicle based on a sea turtle. The vehicle based on a penguin will be reported in the next section. Sea turtles live in the ocean in nearly all their lifetime, except when they are born or they spawn eggs. For this reason, sea turtles have features that fit for the underwater life. A sea turtle has two pairs of fins. One is fore fins, which are large and elastic, and has two joints which correspond to shoulder and elbow. The other is hind fins which are small. It mainly uses the fore fins for propulsion and maneuvering, and uses the hind fins as a rudder or for support of maneuvering. The body is covered by a hard shell, and it deforms little or nothing. This feature is good for applying to underwater vehicles. A. Modeling of Flapping and Feathering Motion Fore fins are both the main thruster and rudder of sea turtles. To model these swimming for our submergence vehicle, it is important to realize the essence of their fore fin motion. In our underwater robots, the fin motion of sea turtles is simplified. A sea turtle has two joints on each fore fin, while our vehicle has only one. This joint has two degree of freedom: swing and twisting motion. Swing motion realizes flapping of the fin. Twisting motion realizes socalled feathering motion, which dynamically changes angle of attack of the fin. As a result of observing swimming of a few sea turtles in an aquarium, we thought that these two motions were essence of movement of fore fins of sea turtles. B. Structure of Turtle-like Submergence Vehicle Fig. 2 shows a photograph of a turtle-like submergence vehicle we developed, named Turtle 25 [5]. Fig. 3 shows its general structure. The backbone part of the vehicle is made of three boxes, hereafter called Box 1, 2 and 3, which are made of acrylic resin and are watertight using silicon gasket packing. In Box 1 a battery is installed. Mechanisms of motion of fore fins and control circuits are installed in Box 2. In Box 3 the R/C servomotors for hind fins, another battery and an R/C receiver is installed. The position of gravity center can be controlled by arranging placements of these boxes. These boxes are connected each other with silicon tubes through which electric cables are laced, and are installed inside of an outer cover made of FRP. The outer cover is shaped as teardrop form to suppress fluid drag. Fig. 4 shows the structure of the joint part of the fore fins. As is explained in Section II-A, we decided to make each fore fin to have two degrees of freedom; swinging (flapping) and twisting (feathering) motions. For swinging motion, we made use of a stepping motor, a crank mechanism and a universal joint for each fin. These fore fins are designed to swing around 45 deg. To make this motion possible, a linear shaft is connected on each crank and the shaft is installed with a solid linear bearing on the shelf of Box 2 for waterproof. As the stroke of linear shafts is large, it is not appropriate to adopt rubber bellows that is often used for R/C boats. To suppress friction force inside these linear bearings, it is necessary to reduce side-way movement of the shaft. For this purpose, guide shafts are installed both inside and outside of Box 2. For twisting motion, an R/C servomotor is directly connected to the shaft for each fin. Fins can be exchanged. Each hind fin is directly connected to an R/C servomotor. All of the motors can be independently controlled. To produce thrust force by flapping fore fins, flapping and feathering motion must be operated in cooperation each other. In our vehicle, two controllers are installed; one is for flapping motion and the other for feathering. A one-chip microprocessor (Atmel AVR AT9S2313-1PC) is installed on each controller. These can be operated either independently or in cooperation. On the shaft of stepping motor of a fore fin, two pairs of a cam disk and a micro switch are installed. By monitoring conditions of these switches, angle of flapping is roughly obtained. The controller for feathering angle monitors these switches, and controls the angle of the corresponding servomotor. The hind fins are also controlled by controllers with microprocessors, one for each fin. These are intended to support maneuvering operation. C. Experiments Experiments are held at Fish Robot Experiment Basin at National Maritime Research Institute. In the experiments the submergence vehicle swam near water surface, varying frequencies of feathering motion of fore fins. In these experiments simple two-dimensional hydrofoils were adopted for fore fins. Cross sections of the fore fins were NACA15 hydrofoil and were uniform to span direction. Span and chord length of each fin are 18 mm and 7 mm, respectively. Fig. 5 shows swimming velocities of the vehicle against the flapping frequencies. It is shown that the velocity was increased when the frequency was increased, and at the highest frequency of :53 Hz the maximum velocity, :6 m=s, was obtained. Fig. 5 also shows the swimming number, Sw. The swimming number was a non-dimensional parameter to estimate swimming performances of aquatic animals, and is defined as Sw D U L b f ; (1) where U is swimming velocity, L b is body length and f is the frequency of a fin. This number is often used

3 to evaluate the performance of fish that swim with tail fins. The swimming number of the turtle-like vehicle was around :24 at the maximum when the frequency of fins is :35 Hz. This is roughly same as those of fish-like robots made by our group. This vehicle cannot dive into underwater because of the absence of a buoyancy controller (and its weight), so that it could only swim near water surface. For this reason, the fore fins periodically came out on water and did not always paddle water; that decreased the performance. In addition, the motion of fins was not optimized. Therefore there is still room of improvements on this vehicle. III. DEVELOPMENT OF SUBMERGENCE VEHICLE BASED ON PENGUIN A. Motivation The turtle-like vehicle we mentioned above was not so fast and we considered to develop a faster one. To realize the faster swimming, we focused on swimming of penguins, and developed a submergence vehicle based on that. A penguin swims faster, compared to its body length, than the other aquatic animals that flap to swim. B. Mechanism and Motion of Fins To achieve the faster flapping, we designed a new mechanism of flapping motion that was rather simpler than that of turtle-like vehicle. Fig. 6 shows the penguin-like submergence vehicle named Penguin 26. Fig. 7 shows the flapping mechanism of penguin-like submergence vehicle. Flapping motion is realized by four Scotch yoke mechanisms, two for each fin, and all of that are driven by a single DC motor. A fin is connected to a Scotch yoke at the fore part, and the other at the aft part. By setting appropriate phase delay of Scotch yoke of the aft part with that of fore part, the connected fin flaps with varying its feathering angle. Phase delay is realized by changing the pin position of the aft Scotch yoke so that it cannot be controlled on the fly. Flapping frequency is controlled by changing the voltage of the DC motor. C. Experiments Experiments were held at Wake Observation Tunnel at National Maritime Research Institute. In these experiments simple two-dimensional hydrofoils were adopted for fins. Cross sections of the fore fins were NACA15 hydrofoil and were uniform to span direction. Span and chord length of each fin are 12 mm and 8 mm, respectively. Fig. 8 shows the swimming velocity of penguin-like submergence vehicle as a function of flapping frequency. The following results were obtained. 1) Maximum swimming velocity was :48 m=s when the amplitude of flapping and feathering angle were both 3 deg: and flapping frequency was 3:13 Hz. 2) The relationship between flapping frequency and swimming velocity seems linear in the region of this experiment. Swimming velocity must reach the highest limit with increasing flapping frequency so that, although the flapping frequency is larger than that of the turtle-like vehicle, it is still not enough to reach the limit. 3) Swimming velocity depends on the amplitude of flapping angle, but seems not depend on that of feathering angle. Experimental results of the turtle-like submergence vehicle are also plotted in Fig. 8. These results seems on the line of, or a little lower than, the extended line of the results of the penguin-like vehicle when flapping angle was 3 deg to the origin. Note that, as is mentioned in Section II-C, the fin size of the turtle-like submergence vehicle is 7 mm 18 mm. This is 1:3 times as large as that of the penguin-like one. For these reasons it can be said that the penguin-like vehicle performs better than the turtle-like vehicle with the viewpoint of frequencyvelocity relationship. This does not mean that the flapping motion of the penguin-like vehicle was optimal. As is mentioned in the end of Section II-C, the fore fins of the turtle-like vehicle periodically came out on water and did not always paddle water; that decreased the performance. Further investigation is required; for example, effect of fin shape is not considered. IV. PERFORMANCE ESTIMATION OF FLAPPING FIN PROPULSION SYSTEM A. Blade Element Theory for Flapping Fins To estimate the performance of a flapping fin propulsion system, blade element theory was adopted to the flapping and feathering motion of fins. In blade element theory, a fin is divided into wing blade elements with infinitesimal span width, and fluid force affecting on each element is considered. In our analysis the following things are assumed. 1) Performance of a wing element, which is represented as a combination of lift and drag coefficients, is same as that in stable condition. Dynamic effect is not considered. 2) Wing-tip loss can be ignored. 3) Fins can be flexible. Deformation of fins are given, and are limited to a certain plane perpendicular to the swimming direction. Under these assumptions, and under definitions of variables as shown in Fig. 9, the thrust produced by a flapping wing is expressed by the following equations, respectively. Th D Z Ls R.C L sin C D cos / 1 2 V 2 C.s/ ds (2) Here C L and C D are not constant, but functions of angle of attack. V is the flow velocity relative to the wing element, and is calculated as follows: V.s; t/ D s U 2 C dy 2 C dt dz 2 ; (3) dt

4 here y and z represent the fin shape. Inflow angle is calculated as follows: p.s; t/ D tan 1.dy=dt/2 C.dz=dt/ 2 (4) U As flapping motion is periodic, flapping angle,.t/ are given by the following equation..t/ D max sin 2 T t (5) Feathering angle ˇ is given as follows: 2 ˇ.t/ D ˇmax sin T Here represents phase delay of the feathering angle against the flapping motion, and is assumed constant. The angle of attack is given as.s; t/ D.s; t/ ˇ.t/. B. Estimation of Fluid Force and Comparison with Experimental Results Using the above theory, velocity of the turtle-like vehicle was estimated under the condition same as that in the experiments explained in Section II-C. In the following calculation, fins were assumed rigid so that the flow velocity relative to the wing element and the inflow angle were calculated as follows, respectively: V.s; t/ D r U 2 C (6) s P.t/ 2; (7).s; t/ D tan 1 s P.t/ U : (8) To evaluate fin performance, we made use of lift and drag coefficients of NACA15 airfoil under condition that Reynolds number is 8; that data were given by Sheldahl and Klimas [6]. Reynolds number of the experiments was around 4, but appropriate data for this condition is not obtained so that the above data were used. The amplitude of flapping angle was =4 and was constant. The thrust calculated by Eq. (2) should balance with drag force affecting on the vehicle. The drag is calculated using the following equation. D D C D A 1 2 U 2 (9) Here C D is the drag coefficient of the vehicle and A is the projection area of the body: A D :6 m 2. As it is difficult to accurately estimate the drag force, we roughly assumed that the body drag is dominant, and that its drag coefficient is equal to that of a teardrop: C D D :5. Fig. 1 shows calculated thrust and drag forces under conditions that the flapping frequency is :53 Hz. Thrust forces are calculated varying the feathering angle. A certain point where a thrust line (thick) and the drag line (thin) cross corresponds to estimated velocity the vehicle will swim under given condition. In the experiment, the feathering angle was =4 and at that condition the vehicle velocity was estimated around :26 m=s. This is around four times as fast as the experimental result, :6 m=s. This may be because of the following reasons. 1) As the wing-tip loss is not considered, the numerical estimation gives higher thrust than that in the real situation. 2) As is mentioned in Section II-C, the experimental condition was not ideal; especially the fins did not always paddle water. 3) Drag coefficient of the body may not be appropriate. For the above-mentioned reasons this estimation cannot be trusted yet, and improvements are required. V. DEFORMATION OF FINS Our turtle-like and the penguin-like vehicles used rigid fins in the experiments reported above. Aquatic animals, however, do not have rigid fins; they have flexible fins. Some animals deform their fins by their muscles, but some do not deform their fins by their own power but passively deform (at least a part of) their fins by fluid force. It might be essential to the performance of aquatic animals. For the first step of this research, we tried to estimate the performance of flexible fins by the blade element theory explained in Section IV, and compared the performance against that of a rigid fin. A. Definition of Motion and Estimation Method Motion of the flexible fin was given as follows: 2.s; t/ D max.s/ sin t ı.s/ ; (1) T y.s; t/ D z.s; t/ D Z Ls R cos.s; t/ ds; (11) Z Ls R sin.s; t/ ds (12) where.s; t/ is the tangential angle of the fin against the horizontal plane, max.s/ the maximum angle of fin gradient at span position s, and ı.s/ the phase difference between the fin root and position s. Thrust of the flapping fin is estimated by the blade element theory explained in Section IV. B. Calculation Conditions and Results Fig. 11 shows the flexible fin motion defined as Eq. (1) with following parameters: max.s/ D.2 C :1s/ deg: and ı.s/ D 36=7 deg. The following calculation was based on this motion. Feathering angle was assumed uniform over the span. The thrust was calculated by Eq. (2), and should balance with drag force affecting on the vehicle. The drag was calculated using Eq. (9), where C D A was assumed :312. Fig. 12 shows estimated velocity of a submergence vehicle as a function of the amplitude of feathering angle. Results of both flexible and rigid fins are plotted. This figure shows that the flexible fin will perform better than the rigid fin for all region of feathering angle.

5 This estimation should be verified by the experiments, and we are planned to do so. After that, we would like to make use of flexible fins to develop an efficient flapping system. VI. DEVELOPMENT OF FLAPPING FIN PROPULSION PERFORMANCE MEASUREMENT SYSTEM To investigate fundamental features of flapping propulsion such as flow field and fluid force, performance measurement system of flapping propulsion was developed. This system realizes the flapping propulsion and measures forces due to the propulsion in flow direction and oscillatory direction. A. Structure of Measurement System Fig. 13 shows structure of the flapping fin propulsion performance measurement system. Flapping motion was realized by an AC motor with crank mechanism. This AC motor has a continuously variable transmission built in, so that arbitrary flapping frequency can be obtained. Feathering motion was realized by a stepping motor and a set of gears that are installed on the shaft of flapping fin. Phase delay of feathering motion against flapping motion can be set arbitrarily. For measurements, the above mechanisms were installed on a flat plate; the plate was installed on a cross guide, which was installed on the plate that was fixed to a water basin. These plates above and below were fixed with small flat aluminum plates, and by measuring the strain of the aluminum plates with strain gages, net fluid forces for x and y directions are obtained. B. Calibration and Experiments The system explained above was installed on the Wake Observation Tunnel at National Maritime Research Institute (the same water tunnel used in Section III-C), and after static calibration, thrust due to flapping motion was measured. By static calibration it was found that the error of force measurement is around 5 and 6 percent for x and y direction, respectively. The main cause of error seems friction of the cross guide. In the experiment, maximum frequency for experiment is around 1 Hz, amplitude of flapping angle 3 deg:. The amplitude of feathering angle is limited to less than 3 deg: when flapping frequency is 1 Hz; with larger amplitude, feathering motion cannot be synchronized with flapping motion. Fig. 14 shows the measured thrust produced by the above system. Results of :65 Hz and :83 Hz show similar tendencies each other. Results of :73 Hz and :91 Hz also show similar tendencies. In addition, the order of magnitude does not correspond to the frequencies in low flow velocity region, although it agrees with that of frequencies in high velocity region. It seems because, in case flow velocity is low, the effect of secondary flow due to flapping motion itself became dominant. We must figure out the region where the measured results are reliable. Fig. 15 shows the thrust estimated by the blade element theory in the same condition of experiments. In the region the flow velocity is larger than :3 m=s, the tendencies of thrust agrees qualitatively with those of measured results. However, the magnitude of thrust is around one tenth smaller than that of measured thrust. This seems due to the lack of consideration of dynamic effect. In the above experiments, it is observed that two large vortices are shed from the fin for each flapping motion, one for motion from left to right, and the other for opposite motion. Further investigation is required for both measurement and theoretical estimation. VII. CONCLUSIONS The objective of this research was to understand the mechanism of flapping fin propulsion. Two submergence vehicles were developed. One modeled itself on a sea turtle, and the other modeled itself on a penguin. Performance of these vehicles were experimentally measured, and the performance of the turtle-like vehicle was also estimated by blade element theory. Effect of fin deformation was numerically investigated. A flapping fin propulsion performance measurement system was developed. The following conclusions were obtained. 1) Flapping mechanism of the vehicles can perform essential motion of that of aquatic animals that flap to swim, such as sea turtles and penguins. 2) Maximum swimming velocity is :6 m=s for the turtle-like vehicle, and :48 m=s for the penguin-like one. The relationship between flapping frequency and swimming velocity seems linear in the region of the experiment. This implies that the velocity had not yet reached to the limit because of insufficient fin frequency. 3) Swimming velocity of the turtle-like vehicle was estimated using the blade element theory. The result was faster than the experimental result. This is because of some assumptions for the estimation, and improvements of estimation should be done. 4) In the estimation with blade element theory, a flexible fin shows better performance than a rigid fin. This implies the possibility of improvement of flapping performance using flexible fins. 5) Performance of the flapping fin propulsion was measured by the flapping fin propulsion performance measurement system we had developed, and also estimated with the blade element theory. As a result, in the region the flow velocity is larger than :3 m=s, the tendencies of thrust agrees qualitatively with those of measured results. However, the magnitude of thrust is around one tenth smaller than that of measured thrust. This seems due to the lack of consideration of dynamic effect in the blade element theory. Further investigations are required for vehicles, measurement systems and theoretical estimation methods, and

6 fore fin flapping Box 2 buoyancy controller hind fin fore fin joint feathering swimming direction servomotor for hind fin Box 1 Box 3 Flapping and feathering motion 438 Fig. 1. battery outer cover stepping motor for fore fin battery controller circuit servomotor for fore fin Submergence vehicle Turtle Fig. 2. we will cope with them. 57 ACKNOWLEDGMENTS Fig. 3. This research was partially supported by the Ministry of Education, Science, Sports and Culture, Grant-in-Aid for Young Scientists, , 25. This research is partially based on graduation theses of Kogakuin University by Mr. Takuro Furuya (Section II), Mr. Tomohiko Matsuda (Section III) and Mr. Takeshi Kawano (Section VI). It is also partially based on a master s thesis of Kogakuin University by Mr. Kazuhisa Hishinuma (Sections IV and V). Structure of turtle-like submergence vehicle fore fin slider linear bearing crank R EFERENCES [1] Triantafyllou, M. S., Triantafyllou, G. S. and Yue, D. K. P., Hydrodynamics of Fishlike Swimming, Ann. Rev. Fluid Mech. vol. 32, pp , 2. [2] Hirata, K., Takimoto, T. and Tamura, K., Study on Turning Performance of a Fish Robot, Proc. 1st Int. Symp. on Aqua Bio-Mechanisms, pp , 2. [3] Hirata, K., Development of Experimental Fish Robot, Proc. 6th Int. Symp. on Marine Eng., pp , 2. [4] Hishinuma, K. et al., Analysis Method of Flapping Fin Motion for Manta-like Underwater Robot, Proc. 7th Int. Symp. Marine Eng., CD-ROM, October 25. [5] Konno, K. et al., Development of Turtle-like Submergence Vehicle, Proc. 7th Int. Symp. Marine Eng., CD-ROM, October 25. [6] Sheldahl, R. E., and Klimas, P. C., Aerodynamic Characteristics of Seven Symmetrical Airfoil Sections Through 18-Degree Angle of Attack For Use In Aerodynamic Analysis of Vertical Axis Wind Turbines, SANDIA REPORT SAND8-2114, Sandia National Laboratories, universal joint controller stepping motor (a) Appearance rod end slider linear shaft radial shaft universal joint (b) Illustration of structure Fig. 4. Structure of fore fin joint of turtle-like submergence vehicle

7 .25.5 Velocity [m/s] Vehicle Velocity Swimming Number Fin Frequency [Hz].5.5 Swimming Velocity [m/s].2.6 Swimming Number.7 Penguin-26 Flapping: ±19deg., Feathering: ±1deg. Flapping: ±3deg., Feathering: ±1deg. Flapping: ±3deg., Feathering: ±2deg..4 Flapping: ±3deg., Feathering: ±3deg. Turtle Fig. 5. Swimming velocities and swimming numbers as functions of flapping frequencies Fig Flapping Frequency [Hz] 3.5 Velocity of vehicles as functions of flapping frequencies Uniform flow U Inflow angle ttac kα γ Featheri ng angle β Ang le of a Dra gd Lift L Relative flow velocity V Flapping velocity (Vy, Vz) z s fin tip ψ(s,t) Fig. 6. body Submergence vehicle Penguin 26 fin root fin y x Motor Fig. 9. Definition of variables.7 Thrust, βmax = π/3 Thrust, βmax = π/4 Thrust, βmax = π/8 Thrust, βmax = π/16 Drag β m.6 ax Fin π/ 4 (e xp.c on d.).4 βmax = π/8 β ma x.3 =π /3 Crank Thrust / Drag [N].5 = βmax = π/16.2 g Dra.1 Scotch Yoke Mechanisms Fig. 7. Flapping mechanism of Penguin-like submergence vehicle Vehicle Velocity [m/s] Fig. 1. Thrust and drag forces as functions of vehicle velocities. Flapping frequency is :53 Hz.

8 Z [m] Fig. 11. Y [m] deg. 36 deg. 72 deg. 18 deg. 144 deg. 18 deg. 216 deg. 252 deg. 288 deg. 324 deg. Predefined fin deformation Time-Averaged Thrust [N] Flow Velocity [m/s] Freq.:.65 Hz.73 Hz.83 Hz.91 Hz Fig. 14. Thrust of flapping propulsion measured by flapping propulsion performance measurement system. Results of four different flapping frequencies are shown. Swimming Velocity [m/s] Elastic Fin Rigid Fin Feathering Angle Amplitude [deg.] Fig. 12. Estimated swimming velocities with flexible and rigid fins AC motor for flapping motion stepping motor for twisting motion, placed above the gear box. Time-Averaged Thrust [N] Freq.:.65 Hz.73 Hz.83 Hz.91 Hz rotational bearings are placed at this height cross guide Flow Velocity [m/s] Fig. 15. Thrust of flapping propulsion estimated by blade element theory. Results of four different flapping frequencies are shown. fin flow Fig. 13. Schematic of performance measurement system of flapping propulsion