Review of Fish Swimming Modes for Aquatic Locomotion Michael Sfakiotakis,David M.Lane,and J.Bruce C.Davies
Abstract—Several physico-mechanical designs evolved infish are currently inspiring robotic devices for propulsion and maneu-vering purpos in underwater vehicles.Considering the potential benefits involved,this paper prents an overview of the swim-ming mechanisms employed byfish.The motivation is to provide a relevant and uful introduction to the existing literature for engineers with an interest in the emerging area of aquatic biomechanisms.Thefish swimming types are prented,follow-ing the well-established classification scheme and nomenclature originally propod by Breder.Fish swim either by body and/or caudalfin(BCF)movements or using median and/or paired fin(MPF)propulsion.The latter is generally employed at slow speeds,offering greater maneuverability and better propulsive efficiency,while BCF movements can achieve greater thrust and accelerations.For both BCF and MPF locomotion,specific swimming modes are identified,bad on the propulsor and the type of movements(oscillatory or undulatory)employed for thrust generation.Along with general descriptions and kinematic data,the analytical approaches developed to study each swim-ming mode are also introduced.Particular reference is made to lunate tail propulsion,undulatingfins,and labriform(oscillatory pectoralfin)swimming mechanisms,identified as having the greatest potential for exploitation in artificial systems.老师用英语怎么读
Index Terms—Hydrodynamics,kinematics,marine animals, mobile robots,underwater vehicle propulsion.
I.I NTRODUCTION
T HIS PAPER prents an overview offish swimming and the analytical methods that have been applied to some of their propulsive mechanisms.The motivation is to provide a relevant and uful introduction to the existing literature on the subject for engineers involved in underwater vehicle design and control and for tho with an interest in the fast-growing area of biomimetic swimming robots.
Natural lection has ensured that the mechanical systems evolved infish,although not necessarily optimal,are highly efficient with regard to the habitat and mode of life for each species.Their often remarkable abilities could inspire innovative designs to improve the ways that man-made sys-tems operate in and interact with the aquatic environment. An example application that could substantially benefit are Manuscript received April3,1998;revid December10,1998.This work was supported by the U.K.Engineering and Physical Sciences Rearch Council(EPSRC),through the Centre for Marine and Petroleum Technology (CMPT),as the project FLAPS(FLexible Appendages for Positioning and Stabilization)1997–99,under rearch Grant Reference GR/L29217.
M.Sfakiotakis and D.M.Lane are with the Ocean Systems Laboratory, Department of Computing&Electrical Engineering,Heriot-Watt University, Riccarton,Edinburgh EH144AS,Scotland,U.K.
J.B.C.Davies is with the Department of Mechanical&Chemical Engi-neering,Heriot-Watt University,Riccarton,Edinburgh EH144AS,Scotland, U.K.
Publisher Item Identifier S0364-9059(99)03032-0.autonomous underwater vehicles(AUV’s).As rearch and u of AUV’s are expanding,there is incread demand for improved efficiency to allow for longer missions to be undertaken.The highly efficient swimming mechanisms of some pelagicfish can potentially provide inspiration for a design of propulsors that will outperform the thrusters cur-rently in u.For maneuvering or hovering purpos,the existing systems are insufficient when it comes to demand-ing applications,such as dextrous manipulation,and coar compared to the abilities offish.The advantages of noiless propulsion and a less conspicuous wake could be of additional significance,particularly for military applications.Robotic devices are currently being developed to asss the benefits and study the ways of“porting”mechanisms utilized byfish and other aquatic animals to artificial systems(for examples, e[1]–[9]).Under this perspective,engineers working in this area should have a background knowledge of the swimming abilities and performanc
e offish that provide benchmarks for evaluating our own designs and drive further theoretical developments.Biologists have shown a much renewed interest in the area over the lastfive years,owing largely to the advent of improved experimental techniques that have shed new light on a number of thefish swimming mechanisms.
After an introduction to the classification of the variousfish swimming types(Section II),the latter are prented in more detail covering general characteristics as well as kinematic data and mathematical models(Sections III–V).Section VI concludes with some discussion on the relevance to underwater vehicle design.
II.F ISH S WIMMING M ODES
A.Forces Acting on a Swimming Fish
The main properties of water as a locomotion medium that have played an important role in the evolution offish are its incompressibility and its high density.Since water is an incompressiblefluid,any movement executed by an aquatic animal will t the water surrounding it in motion and vice versa.Its density(about800times that of air)is sufficiently clo to that of the body of marine animals to nearly counterbalance the force of gravity.This has allowed the development of a
softstarter
great variety of swimming propulsors, as weight support is not of primary importance[10].
To aid in the description of thefish swimming mechanisms, Fig.1illustrates the terminology ud to identify morpho-logical features offish,as it is most commonly found in literature and ud throughout this text.Median and paired
million years ago0364–9059/99$10.00©1999IEEE
Fig.1.Terminology ud in the text to identify thefins and other features offish.
fins can also be characterized as either short-bad or long-bad,depending on the length of theirfin ba relative to the overallfish length.Thefin dimensions normal and parallel to the waterflow are called span and chord,respectively. Swimming involves the transfer of momentum from thefish to the surrounding water(and vice versa).The main momen-tum transfer mechanisms are via drag,lift,and acceleration reaction forces.Swimming drag consists of the following components:
1)skin friction between thefish and the boundary layer of
water(viscous or friction drag):Friction drag aris as
a result of the viscosity of water in areas offlow with
large velocity gradients.Friction drag depends on the
wetted area and swimming speed of thefish,as well as
the nature of the boundary layerflow.
2)pressures formed in pushing water aside for thefish to
pass(form drag).Form drag is caud by the distortion
offlow around solid bodies and depends on their shape.
Most of the fast-cruisingfish have well streamlined
bodies to significantly reduce form drag.
3)energy lost in the vortices formed by the caudal and
pectoralfins as they generate lift or thrust(vortex or
induced drag):Induced drag depends largely on the
shape of thefins.
The latter two components are jointly described as pressure drag.Comprehensive overviews of swimming drag(including calculations for the relative importance of individual drag components)and the adaptations thatfish have developed to minimize it can be found in[11]and[12].
Like pressure drag,lift forces originate from water viscosity and are caud by assymetries in theflow.
Asfluid moves past an object,the pattern offlow may be such that the pressure on one lateral side is greater than that on the opposite.Lift is then exerted on the object in a direction perpendicular to theflow direction.
Acceleration reaction is an inertial force,generated by the resistance of the water surrounding a body or an appendage when the velocity of the latter relative to the water is changing. Different formulas are ud to estimate acceleration reaction depending on whether the water is accelerating and the object is stationary,or whether the rever is true[13].Acceleration reaction is more nsitive to size than is lift or drag velocity and is especially important during periods of unsteadyflow and for time-dependent movements[14],
[15].
(a)
(b)
Fig.2.(a)The forces acting on a swimmingfish.(b)Pitch,yaw,and roll definitions.(Adapted from Magnuson[11].)
The forces acting on a swimmingfish are weight,buoyancy, and hydrodynamic lift in the vertical direction,along with thrust and resistance in the horizontal direction[Fig.2(a)]. For negatively buoyantfish,hydrodynamic lift must be generated to supplement buoyancy and balance the vertical forces,ensuring that they do not sink.Manyfish achieve this by continually swimming with their pectoralfins extended. However,since induced drag is generated as a side effect of this technique,the balance between horizontal forces will be disturbed,calling for further adjustments for thefish to maintain a steady swimming speed.For a discussion on this coupling of the forces acting on a swimmingfish,e[11].The hydrodynamic stability and direction of movement are often considered in terms of pitch,roll,and yaw[Fig.2(b)].The swimming speed offish is often measured in body lengths per cond(BL/s).health and wealth
For afish propelling itlf at a constant speed,the mo-mentum conrvation principle requires that the forces and moments acting on it are balanced.Therefore,the total thrust it exerts against the water has to equal the total resistance it encounters moving forward.Pressure drag,lift,and accelera-tion reaction can all contribute to both thrust and resistance. However,since lift generation is associat
ed with the inten-tional movement of propulsors byfish,it only contributes to resistance for actions such as braking and stabilization rather then for steady swimming.Additionally,viscous drag always contributes to resistance forces.Finally,body inertia,although not a momentum transfer mechanism,contributes to the water resistance as it oppos acceleration from rest and tends to maintain motion once begun.The main factors determining the relative contributions of the momentum transfer mechanisms to thrust and resistance are:1)Reynolds number;2)reduced frequency;and3)shape[15].
The Reynolds number(Re)is the ratio of inertial over viscous forces,defined
as
SFAKIOTAKIS et al.:REVIEW OF FISH SWIMMING MODES FOR AQUATIC LOCOMOTION239
Fig.3.Diagram showing the relative contribution of the momentum transfer
mechanisms for swimming vertebrates,as a function of Re.The shaded area
corresponds to the range of adultfish swimming.(Adapted from Webb[15].)
where
shhh
is the swimming velocity,and
indicates the importance of un-
steady(time-dependent)effects in theflow and is defined
as
新年快乐的英语where is the characteristic
length,and
,all three mechanisms of
force generation are important,while for larger values of
,defined as
is the mean forward velocity of thefish,
240IEEE JOURNAL OF OCEANIC ENGINEERING,VOL.24,NO.2,APRIL
1999
Fig.4.Diagram showing the relation between swimming propulsors and swimming functions.(Adapted from Webb[20].)
result from the coupled oscillations of smaller elements that constitute the ,muscle gments andfin rays for BCF and MPF propulsion,respectively).
Generally,fish that routinely u the same propulsion method display similar morphology.However,form differ-ences do exist and the relate to the specific mode of life of each species.Webb[20]identified three basic optimum designs forfish morphology,derived from specializations for accelerating,cruising,and maneuvering.Although describing the designs is beyond the scope of this paper, it should be pointed out that they are cloly linked to the locomotion method employed(Fig.4).Also,since they are largely mutually exclusive,no singlefish exhibits an optimal performance in all three functions.But neither are allfish specialists in a single activity;they are rather locomotor generalists combining design elements from all three specialists in a varying degree.Further details on the relation between function and morphology infish swimming can be found in[19]and[20].
Within the basic grouping into MPF and BCF propulsion, further types of swimming(often referred to as modes)can be identified for each group,bad on Breder’s[17]original clas-sification and using his nomenclature(Fig.5).The modes should be thought of as pronounced points within a continuum, rather than discrete ts.Fish may exhibit more than one swimming mode,either at the same time or at different speeds. Median and pairedfins are routinely ud in conjunction to provide thrust with varying contributions from each,achieving smooth trajectories.Also,manyfish typically utilize MPF modes for foraging,as the offer greater maneuverability, the ability to switch to BCF modes at higher speeds,and high acceleration rates.
The following ctions prent the modes of Fig.5in more detail,along with some of the mathematical models developed to describe them.Additional biological characteristics and literature references can be found in[10].
III.BCF P ROPULSION
A.General
In undulatory BCF modes,the propulsive wave travers thefish body in a direction opposite to the overall movement and at a speed greater than the overall swimming speed.The four undulatory BCF
locomotion modes identified in Fig.5(a)reflect changes mainly in the wavelength and the amplitude envelope of the propulsive wave,but also in the way thrust is generated.Two main methods have been identified: an added-mass method and a lift-bad(vorticity)method. The latter is primarily ud in thunniform swimming,while anguilliform,subcarangiform,and carangiform modes have long been associated with the added-mass method.However, recent studies suggest that vorticity mechanisms are also important for subcarangiform and carangiform swimming(e text below).
A qualitative description of the added-mass method is given by Webb in[20](e also[21]for a more mathematical description)and is summarized here.As the propulsive wave pass backward along thefish,each small body gment (called propulsion element)generates a force that increas the momentum of the water passing backward.An equal opposing force(the reaction
mick jagger
force
jeans怎么读has a larger thrust
component
is the overallfish swimming speed
西安电脑学校and
SFAKIOTAKIS et al.:REVIEW OF FISH SWIMMING MODES FOR AQUATIC LOCOMOTION
241
(a)
(b)
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Fig.5.Swimming modes associated with (a)BCF propulsion and (b)MPF propulsion.Shaded areas contribute to thrust generation.(Adapted from Lindy
[10].)
Fig.6.Thrust generation by the added-mass method in BCF propulsion.(Adapted from Webb
[20].)
(a)(b)(c)(d)
Fig.7.Gradation of BCF swimming movements from (a)anguilliform,through (b)subcarangiform and (c)carangiform to (d)thunniform mode.(Taken from Lindy [10].)
locomotion.Similar movements are obrved in the sub-carangiform mode (e.g.,trout),but the amplitude of the undulations is limited anteriorly,and increas only in the posterior half of the body [Fig.7(b)].For carangiform swim-ming,this is even more pronounced,as the body undulations
are further confined to the last third of the body length [Fig.7(c)],and thrust is provided by a rather stiff caudal fin.Carangiform swimmers are generally faster than anguilliform or subcarangiform swimmers.However,their turning and accelerating abilities are compromid,due to the relative rigidity of their bodies.Furthermore,there is an incread tendency for the body to recoil,becau the lateral forces are concentrated at the posterior.Lighthill [24]identified two main morphological adaptations that increa anterior resistance in order to minimize the recoil forces:1)a reduced depth of the fish body at the point where the caudal fin attaches to the trunk (referred to as the peduncle ,e Fig.1)and 2)the concentration of the body depth and mass toward the anterior part of the fish.
Thunniform mode is the most efficient locomotion mode evolved in the aquatic environment,where thrust is generated by the lift-bad method,allowing high cruising speeds to be maintained for long
periods.It is considered a culminating point in the evolution of swimming designs,as it is found among varied groups of vertebrates (teleost fish,sharks,and marine mammals)that have each evolved under different circumstances.In teleost fish,thunniform mode is encountered in scombrids,such as the tuna and the mackerel.Significant lateral movements occur only at the caudal fin (that produces more than 90%of the thrust)and at the area near the narrow peduncle.The body is well streamlined to significantly reduce pressure drag,while the caudal fin is stiff and high,with a crescent-moon shape often referred to as lunate [Fig.7(d)].Despite the power of the caudal thrusts,the body shape and mass distribution ensure that the recoil forces are effectively minimized and very little sideslipping is induced.The design of thunniform swimmers is optimized for high-speed swim-ming in calm waters and is not well-suited to other actions such as slow swimming,turning maneuvers,and rapid acceleration from stationary and turbulent water (streams,tidal rips,etc.).
