The determination of drag in front crawl swimming

The measurement of drag while swimming (i.e. active drag) is a controversial issue. Therefore, in a group of six elite swimmers two active drag measurement methods were compared to assess whether both measure the same retarding force during swimming. In method 1 push-off forces are measured directly using the system to measure active drag (MAD-system). In method 2 (the velocity perturbation method, VPM) drag is estimated from the difference in swimming speed when subjects swim twice at maximal effort (assuming equal power output and assuming a quadratic drag-speed relationship): once swimming free, and once swimming with a hydrodynamic body attached that created a known additional resistance. The average drag for the VPM tests (53.2 N) was statistically significant and different from the active drag for the MAD-test (66.9 N), paired Student's t-test: 2.484, 12 DF, p=0.029. A post hoc analysis was performed to assess whether the two methods measure a different phenomenon. Based on the drag speed curve obtained with the MAD-system, the VPM-data were re-examined. For diverging drag determinations the assumption of equal power output of the 'free' trial (swimming free) vs. the towing trial (swimming with hydrodynamic buoy) appeared to be violated. The regression of the relative difference in force (MAD vs. VPM) on the relative difference in power (swimming free vs. swimming with hydrodynamic body) was: %Deltadrag=1.898 x %Deltapower -4.498, r2=0.88. This suggests that the major part of the difference in active drag values is due to a non-equal power output in the 'free' relative towing trial during the VPM-test. The simulation of the violation of the equal power output assumption and the calculation of the effect of an other than quadratic drag-speed relationship corroborated the tentative conclusion that both methods measure essentially the same phenomenon and that active drag differences can be explained by a violation of test assumptions.     

Propulsion Modeling and Analysis of a Biomimetic Swimmer

<正> We have studied a biomimetic swimmer based on the motion of bacteria such as Escherichia coli (E. coli) theoretically andexperimentally. The swimmer has an ellipsoidal cell body propelled by a helical filament. The performance of this swimmer wasestimated by modeling the dynamics of a swimmer in viscous fluid. We applied the Resistive Force Theory (RFT) on this modelto calculate the linear swimming speed and the efficiency of the model. A parametric study on linear velocity and efficiency tooptimize the design of this swimmer was demonstrated. In order to validate the theoretical results, a biomimetic swimmer wasfabricated and an experiment setup was prepared to measure the swimming speed and thrust force in silicone oil. The experimentalresults agree well with the theoretical values predicted by RFT. In addition, we studied the flow patterns surrounding thefilament with a finite element simulation with different Reynolds number (Re) to understand the mechanism of propulsion. Thesimulation results provide information on the nature of flow patterns generated by swimming filament. Furthermore, the thrustforces from the simulation were compared with the thrust forces from theory. The simulation results are in good agreement withthe theoretical results.     

Is tilting behaviour at low swimming speeds unique to negatively buoyant fish? Observations on steelhead trout,Oncorhynchus mykiss,and bluegill,Lepomis macrochirus

When swimming at low speeds, steelhead trout and bluegill sunfish tilted the body at an angle to the mean swimming direction. Trout swam using continuous body/caudal fin undulation, with a positive (head-up) tilt angle ( 0 , degrees) that decreased with swimming speed ( u , cm s⁻¹) according to: 0 =(164±96).u^{(−1.14±0.41)} (regression coefficients; mean±2 s.e. ). Bluegill swimming gaits were more diverse and negative (head down) tilt angles were usual. Tilt angle was −3·0 ± 0.9° in pectoral fin swimming at speeds of approximately 0.2–1.7 body length s⁻¹ (Ls⁻¹; 3–24 cm s⁻¹), −4.5 ±2.6° during pectoral fin plus body/caudal fin swimming at 1·2–1·7 L s⁻¹ (17–24cm s⁻¹), and −5.0± 1.0° during continuous body/caudal fin swimming at 1.6 and 2.5 L s⁻¹ (22 and 35cm s⁻¹). At higher speeds, bluegill used burst-and-coast swimming for which the tilt angle was 0.1±0.6°. These observations suggest that tilting is a general phenomenon of low speed swimming at which stabilizers lose their effectiveness. Tilting is interpreted as an active compensatory mechanism associated with increased drag and concomitant increased propulsor velocities to provide better stabilizing forces. Increased drag associated with trimming also explains the well-known observation that the relationship between tail-beat frequency and swimming speed does not pass through the origin. Energy dissipated because of the drag increases at low swimming speeds is presumably smaller than that which would occur with unstable swimming.     

Upstroke Thrust, Drag Effects, and Stroke-glide Cycles in Wing-propelled Swimming by Birds

A number of bird species swim underwater by wing propulsion.Both among and within species, thrust generated during the recoveryphase (upstroke) varies from almost none to more than duringthe power phase (downstroke). More uneven thrust and unsteadyspeed may increase swimming costs because of greater inertialwork to accelerate the body fuselage (head and trunk), especiallywhen buoyant resistance is high during descent. I investigatedthese effects by varying relative fuselage speed during upstrokevs. downstroke in a model for wing-propelled murres which descendat relatively constant mean speed. As buoyant resistance declinedwith depth, the model varied stroke frequency and glide durationto maintain constant mean descent speed, stroke duration, andwork per stroke. When mean fuselage speed during the upstrokewas only 18% of that during the downstroke, stroke frequencywas constant with no gliding, so that power output was unchangedthroughout descent. When mean upstroke speed of the fuselagewas raised to 40% and 73% of mean downstroke speed, stroke frequencydeclined and gliding increased, so that power output decreasedrapidly with increasing depth. Greater inertial work with moreunequal fuselage speeds was a minor contributor to differencesin swimming costs. Instead, lower speeds during upstrokes requiredhigher speeds during downstrokes to maintain the same mean speed,resulting in nonlinear increases in drag at greater fuselagespeeds during the power phase. When fuselage speed was relativelyhigher during upstrokes, lower net drag at the same mean speedincreased the ability to glide between strokes, thereby decreasingthe cost of swimming.     

Power requirements of swimming: do new methods resolve old questions?

A recurring question in the study of fish biomechanics and energeticsis the mechanical power required for tail-swimming at the highspeeds seen among aquatic vertebrates. The quest for answershas been driven by conceptual advances in fluid dynamics, startingwith ideas on the boundary layer and drag initiated by Prandtl,and in measurement techniques starting with force balances focussingon drag and thrust. Drag (=thrust) from measurements on physicalmodels, carcasses, kinematics as inputs to hydromechanical models,and physiological power sources vary from less than that expectedfor an equivalent rigid reference to over an order of magnitudegreater. Estimates of drag and thrust using recent advanceslargely made possible by increased computing power have notresolved the discrepancy. Sources of drag and thrust are notseparable in axial undulatory self propulsion, are open to interpretationand Froude efficiency is zero. Wakes are not easily interpreted,especially for thrust evaluation. We suggest the best measuresof swimming performance are velocity and power consumption forwhich 2D inviscid simulations can give realistic predictions.Steady swimming power is several times that required for towingan equivalent flat plate at the same speed.     

A Forced Damped Oscillation Framework for Undulatory Swimming Provides New Insights into How Propulsion Arises in Active and Passive Swimming

A fundamental issue in locomotion is to understand how muscle forcing produces apparently complex deformation kinematics leading to movement of animals like undulatory swimmers. The question of whether complicated muscle forcing is required to create the observed deformation kinematics is central to the understanding of how animals control movement. In this work, a forced damped oscillation framework is applied to a chain-link model for undulatory swimming to understand how forcing leads to deformation and movement. A unified understanding of swimming, caused by muscle contractions (“active” swimming) or by forces imparted by the surrounding fluid (“passive” swimming), is obtained. We show that the forcing triggers the first few deformation modes of the body, which in turn cause the translational motion. We show that relatively simple forcing patterns can trigger seemingly complex deformation kinematics that lead to movement. For given muscle activation, the forcing frequency relative to the natural frequency of the damped oscillator is important for the emergent deformation characteristics of the body. The proposed approach also leads to a qualitative understanding of optimal deformation kinematics for fast swimming. These results, based on a chain-link model of swimming, are confirmed by fully resolved computational fluid dynamics (CFD) simulations. Prior results from the literature on the optimal value of stiffness for maximum speed are explained.     

Locomotion of Gymnarchus Niloticus： Experiment and Kinematics

In addition to forward undulatory swimming, Gymnarchus niloticus can swim via undulations of the dorsal fin while the body axis remains straight; furthermore, it swims forward and backward in a similar way, which indicates that the undulation of the dorsal fin can simultaneously provide bidirectional propulsive and maneuvering forces with the help of the tail fin. A high-resolution Charge-Coupled Device （CCD） imaging camera system is used to record kinematics of steady swimming as well as maneuvering in G. niloticus. Based on experimental data, this paper discusses the kinematics （cruising speed, wave speed, cycle frequency, amplitude, lateral displacement） of forward as well as backward swimming and maneuvering. During forward swimming, the propulsive force is generated mainly by undulations of the dorsal fin while the body axis remains straight. The kinematic parameters （wave speed, wavelength, cycle frequency, amplitude） have statistically significant correlations with cruising speed. In addition, the yaw at the head is minimal during steady swimming. From experimental data, the maximal lateral displacement of head is not more than 1% of the body length, while the maximal lateral displacement of the whole body is not more than 5% of the body length. Another important feature is that G. niloticus swims backwards using an undulatory mechanism that resembles the forward undulatory swimming mechanism. In backward swimming, the increase of lateral displacement of the head is comparatively significant; the amplitude profiles of the propulsive wave along the dorsal fin are significantly different from those in forward swimming. When G. niloticus does fast maneuvering, its body is first bent into either a C shape or an S shape, then it is rapidly unwound in a travelling wave fashion. It rarely maneuvers without the help of the tail fin and body bending.     

A hydro-mechanical approach to the scaling of swimming performance in the sand flathead Platycephalus bassensis Cuvier: effects of changes in morphological features based on fish size

The swimming performance of Platycephalus bassensis at steady speed was assessed with an emphasis on hydrodynamics. The minimum swimming speed to maintain hydrostatic equilibrium for P. bassensis of 0·271 m total length ( L _T) was calculated to be 1·06 L _T s⁻¹. At this speed, the required lift to support the mass of the fish was equivalent to 6·6% of the fish mass; 82·7% of which was created by the body as a hydrofoil, and the rest of which was created by the pelvic fins as hydrofoils. The minimum swimming speed decreased with the L _T of the fish and ranged from 1·15 L _T s⁻¹ for a fish of 0·209 m to 0·89 L _T s⁻¹ for a fish of 0·407 m. The forward movement per tail-beat cycle ( i.e. stride length) was described with an equation including quantities of morphological and hydro-mechanical relevance. This equation explained that stride length was increased by the effect of turbulence characterized by the Reynolds number and demonstrated the morphological and hydro-mechanical functional design of the fish for maximizing thrust and minimizing drag. The larger span of the caudal fin and caudal tail-beat amplitude was associated with larger stride length, whereas greater frictional drag was associated with smaller stride length.     

Meandering worms: mechanics of undulatory burrowing in muds

Recent work has shown that muddy sediments are elastic solids through which animals extend burrows by fracture, whereas non-cohesive granular sands fluidize around some burrowers. These different mechanical responses are reflected in the morphologies and behaviours of their respective inhabitants. However, Armandia brevis, a mud-burrowing opheliid polychaete, lacks an expansible anterior consistent with fracturing mud, and instead uses undulatory movements similar to those of sandfish lizards that fluidize desert sands. Here, we show that A. brevis neither fractures nor fluidizes sediments, but instead uses a third mechanism, plastically rearranging sediment grains to create a burrow. The curvature of the undulating body fits meander geometry used to describe rivers, and changes in curvature driven by muscle contraction are similar for swimming and burrowing worms, indicating that the same gait is used in both sediments and water. Large calculated friction forces for undulatory burrowers suggest that sediment mechanics affect undulatory and peristaltic burrowers differently; undulatory burrowing may be more effective for small worms that live in sediments not compacted or cohesive enough to extend burrows by fracture.     

Numerical simulation of cross-country skiing

A program for numerical simulation of a whole ski race, from start to finish, is developed in MATLAB. The track is modelled by a set of cubical splines in two dimensions and can be used to simulate a track in a closed loop or with the start and finish at different locations. The forces considered in the simulations are gravitational force, normal force between snow and skis, drag force from the wind, frictional force between snow and ski and driving force from the skier. The differential equations of motion are solved from start to finish with the Runge-Kutta method. Different wind situations during the race can be modelled, as well as different glide conditions on different parts of the track. It is also possible to vary the available power during the race. The simulation program's output is the total time of the race, together with the forces and speed during different parts of the race and intermediate times at selected points. Some preliminary simulations are also presented.     

Numerical simulation of cross-country skiing

A program for numerical simulation of a whole ski race, from start to finish, is developed in MATLAB. The track is modelled by a set of cubical splines in two dimensions and can be used to simulate a track in a closed loop or with the start and finish at different locations. The forces considered in the simulations are gravitational force, normal force between snow and skis, drag force from the wind, frictional force between snow and ski and driving force from the skier. The differential equations of motion are solved from start to finish with the Runge–Kutta method. Different wind situations during the race can be modelled, as well as different glide conditions on different parts of the track. It is also possible to vary the available power during the race. The simulation program's output is the total time of the race, together with the forces and speed during different parts of the race and intermediate times at selected points. Some preliminary simulations are also presented.     

Investigating the locomotion of the sandfish in desert sand using NMR-imaging

The sandfish (Scincus scincus) is a lizard having the remarkable ability to move through desert sand for significant distances. It is well adapted to living in loose sand by virtue of a combination of morphological and behavioural specializations. We investigated the bodyform of the sandfish using 3D-laserscanning and explored its locomotion in loose desert sand using fast nuclear magnetic resonance (NMR) imaging. The sandfish exhibits an in-plane meandering motion with a frequency of about 3 Hz and an amplitude of about half its body length accompanied by swimming-like (or trotting) movements of its limbs. No torsion of the body was observed, a movement required for a digging-behaviour. Simple calculations based on the Janssen model for granular material related to our findings on bodyform and locomotor behaviour render a local decompaction of the sand surrounding the moving sandfish very likely. Thus the sand locally behaves as a viscous fluid and not as a solid material. In this fluidised sand the sandfish is able to "swim" using its limbs.     

Optimal swimming speed in head currents and effects on distance movement of winter-migrating fish

Migration is a commonly described phenomenon in nature that is often caused by spatial and temporal differences in habitat quality. However, as migration requires energy, the timing of migration may depend not only on differences in habitat quality, but also on temporal variation in migration costs. Such variation can, for instance, arise from changes in wind or current velocity for migrating birds and fish, respectively. Whereas behavioural responses of birds to such changing environmental conditions have been relatively well described, this is not the case for fish, although fish migrations are both ecologically and economically important. We here use passive and active telemetry to study how winter migrating roach regulate swimming speed and distance travelled per day in response to variations in head current velocity. Furthermore, we provide theoretical predictions on optimal swimming speeds in head currents and relate these to our empirical results. We show that fish migrate farther on days with low current velocity, but travel at a greater ground speed on days with high current velocity. The latter result agrees with our predictions on optimal swimming speed in head currents, but disagrees with previously reported predictions suggesting that fish ground speed should not change with head current velocity. We suggest that this difference is due to different assumptions on fish swimming energetics. We conclude that fish are able to adjust both swimming speed and timing of swimming activity during migration to changes in head current velocity in order to minimize energy use.     

Drag of suction cup tags on swimming animals: Modeling and measurement

Bio‐logging tags are widely used to study the behavior and movements of marine mammals with the tacit assumption of little impact to the animal. However, tags on fast‐swimming animals generate substantial hydrodynamic forces potentially affecting behavior and energetics adversely, or promoting early removal of the tag. In this work, hydrodynamic loading of three novel tag housing designs are compared over a range of swimming speeds using computational fluid dynamics (CFD). Results from CFD simulation were verified using tag models in a water flume with close agreement. Drag forces were reduced by minimizing geometric disruptions to the flow around the housing, while lift forces were reduced by minimizing the frontal cross‐sectional area of the housing and holding the tag close to the attachment surface. Hydrodynamic tag design resulted in an experimentally measured 60% drag force reduction in 5.6 m/s flow. For all housing designs, off‐axis flow increased the magnitude of the force on the tag. Experimental work with a common dolphin (Delphinus delphis) cadaver indicates that the suction cups used to attach the types of tags described here provide sufficient attachment force to resist failure to predicted forces at swimming speeds of up to 10 m/s.     

STABILIZATION MECHANISM IN SWIMMING ODONTOCETE CETACEANS BY PHASED MOVEMENTS

Propulsive movements of the caudal oscillating flukes produce large forces that could induce equally large recoil forces at the cranial end of the animal, and, thus, affect stability. To examine these vertical oscillations, video analysis was used to measure the motions of the rostrum, pectoral flipper, caudal peduncle, and fluke tip for seven odontocete cetaceans: Delphinapterus leucas, Globicephala melaena, Lagenorhynchus obliquidens, Orcinus orca, Pseudorca crassidens, Stenella plagiodon , and Tursiops truncatus. Animals swam over a range of speeds of 1.4–7.30 m/sec. For each species, oscillatory frequency of the fluke tip increased linearly with swimming speed. Peak-to-peak amplitude at each body position remained constant with respect to swimming speed for all species. Mean peak-to-peak amplitude ranged from 0.02 to 0.06 body length at the rostrum and from 0.17 to 0.25 body length at the fluke tip. The phase relationships between the various body components remain constant with respect to swimming speed. Oscillations of the rostrum were nearly in phase with the fluke tip with phase differences out of—9.4°-33.0° of a cycle period of 360°. Pectoral flipper oscillations trailed fluke oscillations by 60.9°-123.4°. The lower range in amplitude at the rostrum compared to the fluke tip reflects increased resistance to vertical oscillation at the cranial end, which enhances the animal's stability. This resistance is likely due to both active and passive increased body stiffness, resistance on the flippers, phased movements of body components, and use of a lift-based propulsion. Collectively, these mechanisms stabilize the body of cetaceans during active swimming, which can reduce locomotor energy expenditure and reduce excessive motions of the head affecting sensory capabilities.     

Active drag related to velocity in male and female swimmers

Propulsive arm forces of 32 male and 9 female swimmers were measured during front crawl swimming using arms only, in a velocity range between 1.0 m s-1 and 1.8 m s-1. At constant velocity, the measured mean propulsive force Fp equals the mean active drag force (Fd). It was found that Fd is related to the swimming velocity v raised to the power 2.12 +/- 0.20 (males) or 2.28 +/- 0.35 (females). Although many subjects showed rather constant values of Fd/v2, 12 subjects gave significantly (p less than 0.01) stronger or weaker quadratic relationships. Differences in drag force and coefficient of drag between males and females (drag: 28.9 +/- 5.1 N, 20.4 +/- 1.9 N, drag coefficient: 0.64 +/- 0.09, 0.54 +/- 0.07 respectively) are especially apparent at the lowest swimming velocity (1 m s-1), which become less at higher swimming velocities. Possible explanations for the deviation of the power of the velocity from the ideal quadratic dependency are discussed.     

Burst swimming speeds of mackerel, Scomber scombrus L.

Burst swimming speeds were measured in mackerel 0.275–0.380 m long by filming newly caught fish, first released into a large shore-sited tank, using a high-speed cine camera and real time TV camera. The highest speed was 5.50 m s⁻¹ or 18 body length per second ( b.l . s⁻¹) in a 0.305 m long mackerel at 12° C. The recorded maximum tail beat frequency of 18 Hz agrees well with 19 Hz predicted from the measured contraction time of 0.026 s for the anterior lateral swimming muscle. The stride length was close to 1 B.L.; the power, calculated from the drag, was 4.53 W, and, calculated from the muscle used, was 5.07 W; all suggesting that the mackerel is swimming close to its physiological limit.     

Mechanical and propelling efficiency in swimming derived from exercise using a laboratory-based whole-body swimming ergometer

Determining the efficiency of a swimming stroke is difficult because different "efficiencies" can be computed based on the partitioning of mechanical power output (W) into its useful and nonuseful components, as well as because of the difficulties in measuring the forces that a swimmer can exert in water. In this paper, overall efficiency (η(O) = W(TOT)/?, where W(TOT) is total mechanical power output, and ? is overall metabolic power input) was calculated in 10 swimmers by means of a laboratory-based whole-body swimming ergometer, whereas propelling efficiency (η(P) = W(D)/W(TOT), where W(D) is the power to overcome drag) was estimated based on these values and on values of drag efficiency (η(D) = W(D)/?): η(P) = η(D)/η(O). The values of η(D) reported in the literature range from 0.03 to 0.09 (based on data for passive and active drag, respectively). η(O) was 0.28 ± 0.01, and η(P) was estimated to range from ～0.10 (η(D) = 0.03) to 0.35 (η(D) = 0.09). Even if there are obvious limitations to exact simulation of the whole swimming stroke within the laboratory, these calculations suggest that the data reported in the literature for η(O) are probably underestimated, because not all components of W(TOT) can be measured accurately in this environment. Similarly, our estimations of η(P) suggest that the data reported in the literature are probably overestimated.     

The muscle twitch and the maximum swimming speed of giant bluefin tuna, Thunnus thynnus L.

Sustained swimming of bluefin tuna was analysed from video recordings made of a captive patrolling fish school [lengths (L) 1.7–3.3 m, body mass (M) 54–433 kg]. Speeds ranged from 0.6 to 1.2 L s⁻¹ (86–260 km day⁻¹) while stride length during steady speed swimming varied between 0.54 and 0.93 L. Maximum swimming speed was estimated by measuring twitch contraction of the anaerobic swimming muscle in pithed fish 5 min after death. Muscle contraction time increased from the shortest just behind the head (30–50 ms at 20% L) to the longest at the tail peduncle (80–90 ms at 80% L) (all at 28°C). A fish (L = 2.26 m) with a muscle contraction time of 50 ms at 25% L can have a maximum tail beat frequency of 10 Hz and maximum swimming speed of 15m s⁻¹ (54km h⁻¹) with a stride length of 0.65L. With a stride length of 1 L a speed of 22.6 m s⁻¹ (81.4 km h⁻¹) is possible. Power used at maximum speed was estimated for this fish at between 10 and 40 kW, with corresponding values for the drag coefficient at a Reynolds number of 4.43 × 10⁷ of 0.0007 and 0.0027.     

The effect of external dummy transmitters on oxygen consumption and performance of swimming Atlantic cod

Decreased critical swimming speed and increased oxygen consumption (     ) was found for externally tagged Atlantic cod Gadus morhua swimming at a high speed of 0·9 body length (total length, L _T) s⁻¹. No difference was found in the standard metabolic rate, indicating that the higher     for tagged cod was due to drag force rather than increased costs to keep buoyancy.