Mechanics, Power Output and Efficiency of the Swimming Muskrat (Ondatra Zibethicus)

Swimming in aquatic vertebrates is accomplished either by undulations of the body and tail or by movements of the paired appendages through rowing, paddling and subaqueous flight (Robinson, 1975). Most of the research on the mechanics and energetics of swimming has focused on various piscine species employing an undulat- ory propulsive mode (see review by Webb, 1975a). This research has added much to the understanding of the dynamics of fish swimming, but has ignored the alternate modes of swimming exhibited in secondarily aquatic animals.

Recently, Blake (1979, 1980a) has formulated several models to determine the power output produced in paddling locomotion. These models were found to be applicable to the study of paddle propulsion in a small semi-aquatic mammal, the muskrat (Ondatra zibethicus). This rodent swims at the surface by alternate paddling motions of the hindfeet (Howell, 1930; Kirkwood, 1931; Svihla & Svihla, 1931; Mizelle, 1935; Dagg & Windsor, 1972).

The power input expressed as the metabolic rate of the surface swimming muskrat has been previously reported (Fish, 1982b). The ratio of the mechanical power output to metabolic power input determines the efficiency of energy utilization. Combining a biomechanical analysis of the paddling mode of the muskrat with physiological data allows an integrated approach to the study of aquatic adaptation.

Additionally, the muskrat affords the opportunity to examine the consequences of surface swimming. The forces encountered at the air–water interface for non-piscine vertebrates are complex and larger than those of submerged swimmers. Thus surface swimming may be expected to influence the energy budget of the muskrat due to the energy lost to surface waves formed by the animal (Hertel, 1966; Schmidt-Nielsen, 1972).

Ten muskrats (nine male and one female) were live-trapped in Ingham Co., Michigan, during the spring and summer of 1978 and 1979. The mean body mass of the muskrats was 649g (range 530–1604 g) over the test period. The animals were maintained outdoors in large, concrete ponds at the Limnology Research Laboratory on the campus of Michigan State University. The ponds were approximately 2 m deep, allowing unrestricted swimming and diving. Abundant aquatic vegetation, which grew in the ponds, was readily consumed by the muskrats and used for bedding material. The diet was supplemented with apples. The ponds were equipped with platforms above the water. Nest boxes were provided on the platforms and modified for the capture of a single animal when needed for testing.

Experiments on swimming were conducted in a recirculating water channel, based on a design by Vogel & LaBarbera (1978) and previously described and illustrated by Fish (1982b). A working section was provided in the channel in which a single muskrat was allowed to swim without interference. The width and depth of the muskrat relative to the dimensions of the water channel represented 30 and 29 %, respectively. The upstream end of the working section was bounded by a plastic grid (commercially termed ‘egg crate’) in conjunction with a 5 cm wide grid of plastic straws, which removed turbulence from the water flow. The downstream end of the working section was bounded by a low voltage electrified grid that stimulated swimming by the muskrat. Wires attached to the grid ran along the floor of the working section to prevent the animal from standing on the floor to rest. The voltage was controlled with a Powerstat (Superior Electric Co.). All electricity was disconnected from the grid when the muskrat maintained steady swimming. During high speed trials, a removable wall was placed in the working section to constrict its cross-sectional area and thus increase the water velocity. The top of the working section was formed by a Plexiglas metabolic chamber, which was used for the measurement of oxygen consumption as has been reported previously (Fish, 1982b).

Water velocity (U) was controlled either by a Sears 25 electric fishing motor (Model No. 217.590091) orby a Mercury electric outboard motor (Model No. 10019) situated in the return channel. Power to the motor was provided by a 12 V storage battery connected to a 6A battery charger. Motor speed was related to water speed, determined by the time a drop of ink or neutrally buoyant particle traversed a given distance. Because muskrats swimming against the water current appeared to remain stationary relative to their position in the water channel, the water velocity and swimming speed were assumed to be equivalent.

The muskrats were tested at velocities ranging from 0·2 to 0·75 m s⁻¹. There was no sequence order of the test velocities for each muskrat. Single animals were forced to swim steadily at a given test velocity for a period of 10 to 30 min.

Plexiglas windows were installed in the side and floor of the working section to allow for observation and filming. The windows were marked with a grid of 2 cm squares to act as reference points. To film simultaneous lateral and ventral views of the muskrat, a mirror was positioned under the floor at a 45 ⁰ angle to reflect the ventral image of the animal toward the camera.

Individual muskrats swimming over the range of velocities were filmed at 24 and 50 frames s^-1 with a Bolex H-16 SB reflex ciné camera equipped with a Kern Vario-Switar 100 POE zoom lens (1: T9, f = 16–100 mm) using 16 mm film (Kodak 4-X Reversal film 7277, ASA 320). The camera was driven with an ESM 13 V d.c. motor. Lighting was supplied by three 250 W flood lamps surrounding the working section. For analysis, sequential tracings of the propulsive appendages were made from films using a stop-action projector (Lafayette Instrument Co., Model 00100).

Modifications of the models proposed by Blake (1979, 1980a,b) were used to compute the power, energy and efficiency generated by the paddling appendages of the muskrat from the kinematic data obtained from the films. The stroke cycle of the hindfeet was analysed according to the assumptions stated by Blake (1979) for dragbased paddling propulsion. Unlike in the blade-element theory used by Blake, all forces were estimated from a point on the foot, designated as the centre of action (CA), which approximated to the point where the mean force would act.

Total body drag was measured on seven dead muskrats, which were frozen into a natural swimming posture with the tail stretched out straight. The hindlegs were removed for separate drag measurements. When placed in the water each carcass was buoyed up by residual air in the lungs, air entrapped in the fur and the lowered density of the frozen tissues, so that the muskrat floated at a level similar to living animals, when compared to the films of swimming muskrats.

All drag measurements were made using a lever type balance (Fig. 1). Six metal bars were positioned orthogonally and welded to a central point. The bars in the rotational axis (Z) acted as a fulcrum and passed through two sets of bearings held in position by brackets. The ends of the bars in the horizontal axis (X) were threaded for balancing weights which could be positioned to align the vertical axis bars (Y) at with the protractors (P). The lower bar of the vertical axis was employed as the mounting bar for the attachment of the muskrat body. At the end of the mounting bar was a plastic bracket (B) shaped as an inverted U. The ends of the bracket straddled the nose of the muskrat and a large pin was passed through holes in the bracket and through the nose of the animal. This arrangement firmly attached the animal to the mounting bar while allowing rotation of the muskrat about the long axis of the pin, but prevented yawing.

When placed in the water current, a torque developed around the rotational axis due to the drag on the muskrat. The drag was countered by a sliding weight (W_b) on the horizontal axis bar. The weight was moved to a point on the bar such that the vertical axis bar was orientated at 90 ⁰ as determined by siting the vertical axis with the two protractors. By measuring the distances from the fulcrum to the pin and the weight, a standard lever equation was used to compute the drag in Newtons. Since the mounting bar was not submerged, no correction for drag was necessary.

The drag of isolated hindfeet was measured in a manner similar to that described above. However, the feet were attached directly to the mounting bar. The hindfeet had been frozen in either a fully spread or fully closed position, similar to the positions of the feet during the stroke cycle in the power and recovery phases, respectively. The feet were positioned so that the plantar surface of the power phase foot and dorsal surface of the recovery phase foot were normal to the incident water flow. Additionally, drag measurements of the power phase foot were determined with the fringe hairs removed to determine their effect on thrust. The drag on the submerged portion of the mounting bar was subtracted from the foot drag.

Frontal and plantar surface areas of the isolated hindfeet were measured from photocopies using a portable area meter (LAMBDA Instruments Corp., Model LI- 3000).

The water flow around the body of a single dead muskrat at 0·3 and 0·6 m s⁻¹ was observed by the injection of a water-soluble ink into the flow through five small diameter tubes (0·7 mm, i.d.). The tubes were positioned in front of the muskrat and along its sides and posterior end.

Statistical analyses were made with reference to Steele & Torrie (1960). In order to perform the statistical analyses for the various data sets, trials on muskrats were assumed to be independent of one another. Variation about means was expressed as ± one standard error (s.E.). Non-linear data were logarithmically transformed for statistical analysis.

Kinematics were analysed on muskrats swimming steadily at velocities from 0·25 to 0·75 m s⁻¹. At 0·2 m s⁻¹, the experimental animals did not swim steadily. Instead, they accelerated toward the front of the working section and then drifted in the current toward the downstream end. Although this motion was sufficient for metabolic determinations (Fish, 1982b), motion analysis was confined to the higher velocities.

Muskrats swam as in the description of Mizelle (1935). They at the water surface surface maintaining a slightly lordotic posture. However, some muskrats were observed to flex their backs, although this was never observed in animals swimming unrestricted in ponds. The forelegs of the muskrats were held under the chin with the feet flexed, so that the plantar surfaces were directed dorsally under the antebrachium. Short pawing motions, which did not generate thrust, were sometimes observed, but were highly irregular.

The hindfeet moved in a paddling mode as has been observed by others (Howell, 1930; Kirkwood, 1931; Svihla & Svihla, 1931; Mizelle, 1935; Dagg & Windsor, 1972). Robinson (1975) has defined paddling as the movement of a paddle antero-posteriorly in a vertical plane parallel to the direction of motion of the craft. For the muskrat, the paddling mode is facilitated by alternating strokes of the hindfeet. The paddling cycle consisted of power and recovery phases (Fig. 2).

During the power phase (Fig. 2; frames 15–21), the hindfoot was accelerated posteriorly through an arc by plantarflexion of the foot, flexion of the shank and retraction of the femur. Although the major paddling motion occurred at the ankle joint, movement of the femur by retraction increased the posterior velocity of the foot by as much as 0·18 ms⁻¹. Maximum velocity of the hindfoot was attained when orientated at approximately 90 ⁰ to the horizontal. At the end of the power phase, rapid deceleration of the hindfoot approximated the rate of acceleration at the beginning of the phase (Fig. 3).

During the power phase, the digits were extended and maximally abducted so that they were fully spread and the foot was slightly pronated. Although there is only a slight webbing between the bases of the digits, it appears that the lateral fringe of stiff each 3-7 mm long, is passively erected by the resistance of the water as the foot is swept posteriorly. The effective plantar surface area including fringe hairs (mean = 15·7cm²; N = 7) was 21 % higher than the same feet with the fringe hairs removed (mean: 12·5 cm²; N = 7).

The recovery phase of the stroke cycle (Fig. 2; frames 5–13) was characterized by dorsiflexion and supination of the hindfoot, plantarflexion of the digits, protraction of the femur and extension of the shank. The angular velocity of the recovery phase foot showed an acceleration to a maximum at 90 ⁰ to the long axis of the body and then a deceleration at the end of the phase (Fig. 3). The maximum angular velocity of the recovery phase was on average 9 % lower than that of the power phase.

The frontal surface area of the hindfoot during the recovery phase was reduced to a mean value of 7·1 cm² (N = 7) by adduction and flexion of the digits and supination of the foot. A similar motion has been observed in grebes (Peterson, 1968).

Fig. 4 illustrates the frequency of the stroke with respect to U. The frequency remained relatively constant over all velocities at 2·5 ± 0·06 Hz. This was similar to the constant stroke frequency seen in swimming ducks (Prange & Schmidt-Nielsen, 1970), minks (Williams, 1983) and competitive human swimmers (Nadel, 1977). However, this differs from previous observations on the muskrat, beaver, nutria and mink (Mordvinov, 1976), sea lion (Kruse, 1975) and fish (Bainbridge, 1958; Hunter & Zweifel, 1971; Videler, 1981), in which the frequency of the propulsive appendages increased with swimming speed.

The stroke cycle of the muskrat was asymmetrical in time. The mean durations of power and recovery phases were 0·18 ± 0·01 and 0·22 ± 0·01 s, respectively, over the range of U. The duration of the power phase was significantly shorter than the recovery phase (P < 0·0005 ; paired t-test; df = 28).

The arc through which the hindfeet were swept during the power phase measured as the angle between the metatarsals and horizontal plane is shown as a function of U in Fig. 5. The arc varied linearly with U, so that the muskrat increased swimming speed by increasing the distance the hindfeet were swept in a constant time period. the arc was only increased at the end of the phase, while at the beginning the foot initiated the stroke at a relatively constant angle of 24° from 0·25 to 0·55 ms⁻¹, which decreased slightly at higher velocities.

The energy and power generated for both power and recovery phases were computed from the equations by Blake (1979). For the recovery phase, the sign was changed to positive in equation (1) (Blake, 1979) to calculate the resultant relative velocity to adjust for the direction change of the foot.

CA was represented for the power and recovery phases by the distal end of the second metatarsal of the foot. The CA, which could be easily observed from the films, averaged 5·2 % and never more than 28 % of the true centre of thrust determined by blade-element analysis.

The effective radius of rotation for the paddle was estimated by the method utilized by Youm, McMurtry, Flatt & Gillespie (1978) and outlined by Alexander (1983).

Using the model presented by Blake (1979), the power and recovery phases of a single hindfoot was calculated (Fig. 6). A curvilinear increase of the mean power expended over the range of test velocities was noted for both power and recovery phases. Regressions of the data for the power and recovery phases (Fig. 6) were highly significant (P< 0·001) with correlation coefficients of 0·85 and 0·80 (df = 27), respectively. The mean power expended during the recovery phase represented 20–39 % of the power expended in the power phase over the range of U.

The drag experienced by the muskrat body over the range of U is shown in Fig. 7. The drag increased curvilinearly with increasing U with the larger animals having higher drag. This was expressed by the equation:

The importance of increased surface area from the fringe hairs is illustrated in Fig. 8. At the same water flow velocities, U, the normal force which was measure in the drag balance for the isolated hindfeet with the fringe hairs intact, was 20 % higher than without the hairs. During the recovery phase, the configuration change of the hindfoot represented a reduction of 55 % from the frontal surface area of the hindfoot (including the fringe hairs) during the power phase. As a consequence of the reduced frontal surface area, the drag for the recovery phase of the hindfoot represented only 33 % of the drag experienced by the foot in the power phase position (Fig. 8).

Ink injected into the water flow just anterior to the muskrat accumulated under the nose, indicating a large stagnation point with a high pressure (Potter & Foss, 1975). The presence of a bow wave anterior to the muskrat indicated the same phenomenon. Much of the ink was swept under the body and encountered large turbulence due to the flow separation which occurred posterior to the deepest part of the body at speeds greater than 0·6 m s⁻¹.

Turbulence along the side of the muskrat was observed at 0·3 and ·6 ms⁻¹. Turbulence with the development of vortices occurred approximately midway along the body.

The greatest turbulence appeared just downstream of the posterior end of the muskrat at both velocities. Similar data have been gathered on live muskrats by Mordvinov (1974). The observed turbulence allowed water to cross over the tail. Both in the region of the tail and further downstream, the wake of the muskrat showed a considerable amount of turbulence and vorticity.

Water flow about isolated hindfeet in the power phase showed large amounts of turbulence directly downstream. Similar results were observed for feet positioned in the recovery phase.

Blake (1979, 1980a) was able to calculate the energy utilized for propulsion by the paddling movements of the pectoral fins of an angelfish (Pterophyllum eimekei). The energy was determined as the difference between work done in the power and recovery phases of both fins through the stroke cycle.

The work done by the paddling of the muskrat for forward propulsion was calculated as the sums of differences of the energies in Joules generated by power and recovery phases of the stroke cycle of both hindfeet. Added to this quantity was the small energetic contribution generated by the lateral undulations of the tail (Fish, 1982a, Fig. 3). Empirically, the sum of energies producing the muskrat’s forward motion (E_th) was found to correspond to the regression equation (Fig. 9):

Over the range of U, Eth was 2·2–3·2 times greater than E_D, where E_D represents the propulsive energy expended due to body drag. E_D was calculated as the product of the drag, U, and the time of the stroke cycle. Such a difference between these two independent estimations was probably due to the movements of the propulsive appendages and acceleration of the body, which were not taken account of in the estimation of E_D This has also been a primary problem preventing correspondence between similar measures in fish (Webb, 1975a).

The energy utilized for forward propulsion (E_th) does not represent the total energy expended in paddling. The total energy required for power and recovery phases to produce the hydrodynamic thrust force (E_p and E_r, respectively) was calculated from the integration of equation (13) in Blake (1979).

Additionally, the energy losses required for the inertia and added mass of the hindfeet, and undulations of the tail were calculated. The energy required to move the mass of the hindfoot (9 ·36 g) during the power (E_f) and recovery (E_f′) phases was computed from the integration of equation (17) of Blake (1979). The energy needed to accelerate and decelerate the added mass (power, E_a; recovery, E_a′) was calculated from equation (22) of Blake (1979), using the maximum chord of the foot for each phase (power, 0·04 m; recovery, 0·01 m). The total energy produced by the tail over the stroke cycle (Eu) was calculated from Fish (1982a).

The efficiency of energy utilization for the swimming muskrat may be analysed from three perspectives. These are the metabolic thrust efficiency (η_aerob), overall energetic efficiency (η_c) and mechanical efficiency (η_me).

As illustrated in Fig. 10, the value of T]_e was found to increase steadily with increasing U. With regard to the metabolic thrust efficiency, the overall energetic efficiency was 2·5–3·9 times larger. This difference was due to the additional energy needed during the stroke for the recovery phase and the acceleration and deceleration of the hindfeet which is not taken into account in the computation of the η_aerob.

Webb (1975b) calculated η_aerob for rainbow trout and sockeye salmon as 0·15 and 0·22, respectively. Unlike organisms that propel themselves by lateral undulations, paddle-propulsive organisms, such as the muskrat, are not as efficient in the conversion of metabolic energy to propulsive power. For paddlers such as the duck (Prange & Schmidt-Nielsen, 1970), minks (Williams, 1983) and humans (DiPrampero, Pendergast, Wilson & Hennie, 1974) maximum values for η_aerob were 0·047, 0·014 and 0·052, respectively.

Prange (1976) found that η_aerob for green sea turtles reached a maximum value of 0·09. This high value is not too surprising since the sea turtle derives thrust in power and recovery phases of the forelimb stroke (Walker, 1971). Comparable efficiencies of 0·12 and 0·13 were found for the fish Cymatogaster, which utilizes a lift-based propulsive mechanism (Webb, 1975b). These values are believed to be lower than efficiencies of caudal fin propulsora due to the energy necessary for rotating and accelerating the pectoral appendages (Webb, 1975b).

In contrast to fish which swim in the carangiform mode, the muskrat is inefficient in the generation of propulsive power. The mechanical efficiency of the rainbow trout and sockeye salmon were 0·7 and 0·9, respectively (Webb, 1975b). Wu (1971) has suggested that under optimal conditions the propulsive efficiency for this type of final maay be as high as 97 %. It thus appears that the paddling mode with its recovery phase and associated energy loss is a liability in the attainment of high propulsive efficiency.

The muskrat’s morphology is little different from that of a terrestrial form. The most significant morphological change in terms of propulsion has been the development of large, fan-shaped hindfeet with lateral fringe hairs and a laterally compressed tail.

During paddling locomotion, the paddle must be shaped so as to maximize its drag as it is swept posteriorly in order to maximize thrust and efficiency. The optimum paddle shape is similar to a flat plate orientated normal to the direction of movement so that the water striking the paddle surface produces drag (Robinson, 1975). Blake (1981) found that fish which employ drag-based propulsion are more likely to have triangular fins which generate large pressure drag.

In mammals, the surface areas of the hindfeet, which are used as paddles, is increased by interdigital webbing (e.g. otter, beaver) or fringe hairs (e.g. muskrat), in conjunction with a general lengthening of the foot. Howell (1930) stated that the percentage of hindfoot length to body length for terrestrial rodents is usually less than 20%, while a value of 38·5 % was reported for the muskrat.

Howell (1930) believed that fringe hairs were not as efficient as webbing, but were undoubtedly adequate to propel a small body. In comparison to webbing, fringe hairs would not serve as an effective barrier in preventing water from passing between the digits, thereby reducing the effective surface area of the foot. However, Counsilman (1968) reported that a human hand with the fingers spread slightly produced more drag than a closed hand. Such results may be induced by an increase in turbulence between the digits increasing pressure drag (Counsilman, 1968). The muskrat may therefore utilize the fringe hairs to generate turbulence for more effective propulsion. The significance of the fringe hairs was illustrated in the present study by a large decrease of the drag on isolated hindfeet in which the hairs were removed.

Alexander (1983) has argued that generation of thrust is most economical when the mass of water being worked on is large. The effective increase in surface area by modifications of the muskrat foot would therefore accelerate a large mass of water posteriorly, providing momentum to the animal.

In contrast to the power phase, in which the drag on the hindfoot should be maximized, the recovery phase should reduce the drag on the foot as much as possible. In this manner, the thrust generated during the power phase will not be cancelled during the recovery phase. Observations on the recovery phase of the muskrat showed an adduction and plantarflexion of the digits, and supination of the entire foot. These actions tended to minimize the frontal surface area of the foot, thus reducing drag.

Although the muskrat has evolved a foot morphology which allows it to move in an aquatic environment while maintaining terrestrial capabilities, it has been necessary to change in gait from a terrestrial type to one which is more effective for swimming. In contrast to terrestrial vertebrates, in which the recovery phase is shorter than the power phase (Goslow, Reinking & Stuart, 1973; Edwards, 1976), the muskrat has a relatively longer recovery phase. The recovery phase for terrestrial locomotion is ‘wasted’ time, and a shorter recovery would maximize the time that the limb contacts Éhe substrate for more effective propulsion (Edwards, 1976). Because the muskrat not during recovery has a large pressure drag and relative velocity, a long recovery would reduce the resultant velocity and decrease the negative thrust force. The negative thrust would also be minimized by a decrease in the radius of the recovery phase through a shift of CA due to plantarflexion of the digits and retraction of the femur to bring CA closer to the rotation point.

Because of the metabolic and mechanical inefficiencies of the paddling mode and substantial energy loss to the wake for surface swimming, aquatic locomotion is more costly for the muskrat than for more highly adapted organisms. However, in that the muskrat is semi-aquatic and is thus highly mobile on both land and water, the morphology of this animal should be viewed as a compromise of both form and function between vastly different environments.

I wish to express my sincere appreciation to Dr J. L. Edwards, Dr P. W. Webb, Dr R. W. Hill and Dr R. H. Baker for their advice and constructive criticism during the course of this study. I also wish to thank especially Dr R. W. Blake for assistance with his model and E. Rybak for programming assistance. Dr C. D. McNabb, Dr R. A. Pax, Dr G. W. Bird and J. L. Erwin are gratefully acknowledged for use of facilities and M. Flanders for assistance with figures. I am grateful to the Department of Zoology, Michigan State University for financial support and to the American Society of Mammalogists and Sigma Xi for funding through student grants-in-aid. The State of Michigan, Department of Natural Resources is acknowledged for allowing the collection of muskrats.