Hydrodynamic Analysis of C-start in Crucian Carp

Joumal of Bionics Engineering (2004) Vol.1 No.2, 102 - 107Article No. JBE- 2004 - 019Hydrodynamic Analysis of C-start in Crucian CarpJun Jing, Xiezhen Yin, Xiyun LuDepartment of Modern Mechanics , University of Science and Technology of China ,Hefei, Anhui 230026, P. R. China .AbstractThe kinematics of turning maneuvers of startled Crucian Carp (Carassius auratus) are presented. All escape responsesobserved are C type fast starts. The position of the center of mass and the moment of inertia of the fish are calculated.The resuts show that the position of the center of mass is always at 35% of the length of the fish from the head and theposition of the center of mass and moment of inertia can be considered unchanged during C-start of Crucian Carp. Hydro-dyamic analysis of the C-start is given based on the kinematics data from our experiments. The C start consists of threestages. In stage 1, the tail fin of fish rapidly flaps in one direction, and a large moment acts on the fish's body, which ro-tates around the center of mass with an angular acceleration. In stage 2, the tail fin flaps more slowly in the opposite di-rection at slower speed, the fish' s body rotates around the center of mass with angular deceleration and the center of massof the fish moves along an arc. In stage 3, the moment approximately equals zero, the fish' s body stops rotating and thecenter of mass the moves along a straight line.Keywords : Ctype fast start, Crucian Carp (Carassus auratus), force, moment, center of mass, moment of inertiawater vessels. Most fishes can rapidly change their di-1 Introductionrection of motion without decreasing their speed, withThe lcomotion of fish can be divided into cruiseturmning radius less than 30% body length. The maxi-and fast-start.“ Cruise” means the fish swims at amum acceleration of the northern pike ( Esox lucius )steady speed, while fast-start means the fish changes itscan excess 150m/s-. These abilities are superior todirection and speed of motion either from rest or inter-those of most existing man-made vessels2) . Therefore,spersed between periods of steady swimming'1l. Thean understanding of the mechanism of fish swimmingfast-starts include two main types, C-starts and Sshould be useful in bionics.starts, in which the fish is bent intoa' 'C' or 'S' shapeFor bionic studies, engineers are interested irat the end of the first contraction of the lateral muscula- seeking the secret of superior performance of animal'sture. Fast-starts are important for most fishes. A preylocomotion and suggesting new engineering possibilitiesfish mainly uses the Cstart for escaping from its preda-for improvement of man-made vehicles. Recently,tors, while predators use S-start in capturing theirbased on the big progress of high technology achieved,prey. Fishes have developed their superior and completethe biomimesis has attracted people' s great attentionperformance of swimming over billions of years of evo-and the robotic fish, which has ability of cruise, haslution with natural selection. The existing aquatic ani-appeared3) . Studding the fast-start of fish undoubtedlymals have a series features of low energy-consuming,can help to one' s develop new robotic fish with maneu-high efciency and maneuverable. Most of marine fishverable.and cetaceans have hydrodynamic propulsion efficiencyBut on unsteady swimming of fish, including fastof 80%，which is much higher than the existing under-starts, the mechanism is still not clearly.The main work studding the fast starts has focusedon a中国煤化工ape responses. GrayCorresponding author:Xiezhen YinfirstYHC N M H Gyprinus auratus) andE mail: xzyin@ ustc. edu. cnrudd (Scardinius erythrophthalmus) in a tank with aFax: + 86551-3606459grid drawn on the bottom. Jayne and Lauder-5J carefullyJun Jing, et al.: Hydrodynamic Analysis of C-start in Crucian Carp103studied the kinematics of escape responses of the remarks are summarized in Section 5.bluegill sunfish ( Lepomis macrochirus). Recently,2 Kinematics characteristicsmost papers report the way the muscles function in fishturming. For example, Spierts et al. 16 studied muscleExperiments were conducted on Crucian Carpfunction in the fast-start of carp. To our knowledge, (Carassius auratus) obtained from a local dealer. Thefew people have investigated the hydrodynamics of fast- protocol of the experiments was presented in ref [9].starting fish， except that Weihs-7,8] calculated the In the experiments, four fishes ( total length, L =thrust force of rudd based on the experimental resultsof 20.52+1.13 cm, mass, M= 302.5+20.5 g) wereGray[4].tested. The escape responses of all Crucian Carp areIn this paper, our purpose is to investigate the hy-‘“C start”and all the fish have similar kinematic charac-drodynamics of fast-starting fish based on our experi- teristics.ments9J . This paper is organized as follows. The kine-Fig.1 shows some typical pictures chosen from amatics characteristics of Cstarting fish are briely de- series of frames of one fish turning process reorded byscribed in Section 2. The position of the center of mass high- speed CCD camera (1000 fps). The curves of theand the moment of inertia of fish, which are variable backbone of the fish shown in Fig. 1 are presented inwith changes in the shape of the fish' s body, are given Fig.2. From a series of curves, the speed of the fishin Section 3. The force and moment imposed on fish was calculated using calculation method presented in refbody are analyzed in Section 4. Finally, concluding[9].(0.010 s)(0.040s)(0.070 s)(0.100 s)(0.150s)9。10。(0.2505)(0.450s)(0.550s)(0.750s)(0.850 s)framesFig.1 Typical pictures of C-start of Crucian CarpIn C-start, first the tail fin of the fish rapidly flaps stationary. In the second stage (frames 3- 6), theclockwise, then flaps counter-clockwise， while the center of mass moves along an arc. In the third stagefish' s body only rotates counter clockwise. The process (frames 7- 10), the center of mass moves along aof C-start consists of three stages. In the first stage straigl中国煤化工m, then at constant(frames 1 -2 in Fig. 1), the body rotates counter- speed.!YHCNMHGofmassisshownin.clockwise around the center of mass, which remains Fig. 3.104Joumal of Bionics Engineering (2004) Vol.1 No.2the position of the center of mass relative to the fishbody was considered to be almost invariable. In fact,300 rthe position of the center of mass and the moment of in-ertia can change when the backbone of fish bends to Ctypellol. In this paper, the center of mass and momentHeadof inertia were calculated for all the frames shown inFig.2. In calculation, it is assumed that the cross sec-tion of the fish is an elipse and that the density of fish150 Fis variable depending on its length.The results are shown in Table 1. Throughout the100 Fail。escape, the fish (Crucian Carp) keeps the position of10the center of mass at 35% of its length from the head,50 Fand the change in position of the center of mass is lessthan 2% of the body length in the normal direction ofthe backbone and less than 1. 5% measured along th150200x/mmdirection of backbone. The change in moment of inertiais less than 5%. Therefore, it is reasonable to say thatthe center of mass and moment of inertia are more orFig.2 The curves of fish backbone. (The numbersrefer to corresponding frame in Fig. 1)less unchanged in C-start of the Crucian Carp.Table 1 The center of mass and moment of inertia ofthe fish in the different frames of Fig. 1The position of theThe moment of inertiaFramecenterof of mass (am)"(X 106 gmm?)210 [(0. 3540,0)0.368(0. 3523,0.0116)0.362190(0.3516, 0.0115)0.357180(0. 3516, 0.0115)170(0. 3484, 0.0215)0.349160 |(0.3512, 0.0068)0.351(0. 3512, -0.0176)0.359 .(0. 3514, -0.0190)0.363(0. 3515, -0.0191)0. 364120(0. 3507, -0.0186)0.360￥The x-direction denotes the tangential direction of the backbone40(the head as origin) , y diretion is chosen to formn a right-handedpair of axes. The length unit is the length of fish body L.4 Forces and moments on the fish’s bodyFig.3 The track of the center of mass (The numberThe model based on Lighthill ’s elongated-bodyrefers to corresponding frame in Fig. 1)theory:8] is used to calculate the propulsive forces pro-duce3 Center of mass and moment of inertia中国煤花宁fish during the C-start.The center of mass and the moment of inertia areTY分CNMHGimportant in dynamic analysis. In all previous studies,. Jomaundl -.i=1(1a)Jun Jing, et al.: Hydrodynamic Analysis of C start in Crucian Carp105L;= ZpA.VCua;(1b)the fin, CL, the coefficient of lift, and a; the angle ofwhere L is the length of the body which is divided intoattack of a fin relative to its direction of motion. Fur-ther details of equation (1b) can be found in ref [7].many sections. dl is the length of longitudinal section,The added mass calculated from (2) is shown inma is the added mass in length dl, w is speed of move-Fig. 4. The distributions of the lateral velocity alongment of each section perpendicular to the backbone, L;the fish body calculated from the displacement of fishis the force caused by the momentum shedding from finbody are shown in Fig. 5. The force generated by eachi, n isa unit vector perpendicular to the backbone. longitudinal setion along the backbone of fish can beThe added mass is calculated ascalculated from equation (1). The total force and mo-ma =→prd2β2)ment applied on the center of mass are shown in Tablewhere d is the depth of longitudinal section and β is an2.We can calculate the angular aceleration of theadded mass cofficient'l11. In the equation (1), k isfish' s body from the moment and the moment of inertiathe number of fin with sharp-edge, p is the density ofwater, A; the surface area of ith fin, V; the velocity ofφ=M(3)0r0f40-2010- HeadTail40608010120 140 160 180 200The lengh of fish body (mm)Fig.4 The added mass of Crucian Carp00 t0←6-7→7-8包-200-★- 9-10-400t0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0The length of fish (L)中国煤化工Fig.5 Local velocities perpendicular to the backb.MYHCNMHG(A positive value shows that the direction of velocity points to the right side of the fish)106Journal of Bionics Engineering (2004) Vol. 1 No.2Table 2 Forces and moments in the C-start ofwhere φ is the turming angular acceleration, M isthe Crucian Carp (Carassius auratus)the moment and I is the moment of inertia. The calcu-Framel()Total Force (N)Moment(3)lated angular aceleration is shown in Fig.6 (a). In or-F(x 10-3 N.m)der to compare, the measured angular speed from Fig.22-0.13600.295030.3is shown in Fig.6 (b). It is obvious that the calculated0.06300.3030.12.4angular acceleration agrees with the changing tendency-0. 15700.0044-2.41of the measured angular velocity. We can see from Fig.- 0.08100.2520-11.36 (a) that during the Cstart, the rotation of fish'sbody undergoes acceleration ( stage 1)，deceleration-0.02100.0680-6.54(stage 2) and no rotation (stage 3).- 0.0292-1 0.0250-2.00If we take the integrating of the calculated angular80.02300.0030-3.46acceleration, we can get the turning angular velocity.-0.07100.0240-2.9CThe angular velocity at 0. 04 s calculated from the inte-(1) The forces and moments are calculated from the time derivativesgral is φ= 8.16 rad/s, while the measured angular ve-of the lateral velocitis. These derivatives are approximated by dividing thedifference in velocities obtained in two sccessive frames by the time inter-locity in Fig.6 (b) is 7.44 rad/s. The agreement isval between them, and express the forces at an instant midway betweensatisfactory.the two frames.Next we analyze the force on fish's body. In the(2) The x-y cordinate is laboratory cordinates, x direction is thefirst stage, the total force acted on the center of mass istangential diretion of the backbone (from mass center to head ) in the ini-tial time, while y is chosen to form a right- handed pair of axes.bigger than in the other stages. The center of mass of(3) Moments are positive in the counter-clockwise.the fish should have bigger acceleration in stage 1, but1008r 48Cstage2stage3+; 80604C20-20-40.0 0.10.20.30.4 0.5 0.6 0.7 0.8(a) The calculated angular aceleration(b) The measured angular velocty .Fig.6 The calculated angular acceleration and measured angular velocitythe center of mass of the fish remains stationary inble. In frame 2 of Fig. 1, the acceleration calculatedstage 1 in experiment. This can be explained as fol-from the force is 1.07 m/s2，the interval time betweenlows. The time interval of stage 1 is so short that thethe中国煤化工s, the movement dis-distance of movement of the center of mass is very small tance|Y台CNMHGestimatedtobeaboutrelative to the length of fish's body and can be negligi-0.48 mm, which agrees with the above conclusion.Jun Jing, et al. : Hydrodynamic Analysis of C-start in Crucian Carp107In stage 2, the center of mass of the fish moves al- Science Foundation( No.10332040, 10072063) and themost along a circular arc and the movement of the cen- Innovation Project of the Chinese Academy of Sciencester mass can be expressed as(No. KJCX-SW-L04)F= ms(出+别(4) Referenceswhere V is the speed of the center of mass, s is the tan-[ 1 ] Domenici P, Blake R. Review: the kinematics and perfor-gential unit vector of track of center of mass, n is themance of fish fast-start swimming. 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Large anplitude elongated-body theory of fishlcomotion. Proeedings of the Royal Society of London ,Acknowledgements1971, B 179: 125- 138.This work was supported by the National Natural中国煤化工MYHCNMHG