Flight kinematics of the barn swallow (Hirundo rustica) over a wide range of speeds in a wind tunnel
1 Department of Biological Sciences, University of Stirling, Stirling FK9 4LA, UK and
2 Department of Animal Ecology, Lund University, SE-223 62 Lund, Sweden
*Author for correspondence (e-mail: k.j.park{at}stir.ac.uk)
Accepted May 14, 2001
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Summary |
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Key words: flight, kinematics, wind tunnel, flap-gliding, barn swallow, Hirundo rustica.
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Introduction |
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Depending on species, i.e. size and morphology, birds flap their wings continuously or in bursts, with wingbeats interspersed by phases of glides or bounds, the latter flight mode resulting in a sinusoidal flight trajectory around the horizontal level. Species using bounding flight or intermittent flight (wings not completely folded during the non-flapping phase) include the budgerigar Melopsittacus undulatus, finches such as the zebra finch Taenopygia guttata, the starling Sturnus vulgaris and woodpeckers (Rayner, 1995; Tobalske, 1995; Tobalske, 1996; Tobalske and Dial, 1994; Tobalske et al., 1999). In birds that typically use continuous flapping flight, some characteristics of the wingbeat kinematics change with speed. For example, in some species the relation between wingbeat frequency and speed is U-shaped (Pennycuick et al., 1996), in a way similar to the mechanical power output of bird flight (Pennycuick, 1975; Pennycuick, 1989a; Rayner, 1979; Rayner, 1999). In other species, such as the starling, wingbeat frequency appears to have a more or less linear relationship with air speed (Tobalske, 1995), or there is no systematic change with speed (black-billed magpies Pica pica and pigeons Columba livia) (Tobalske and Dial, 1996). Other features of wingbeat kinematics related to force generation may also change in relation to forward air speed.
Birds tails also play an important aerodynamic role in mechanical flight power and flight performance. Conventional models of bird flight ignore the tail (e.g Pennycuick, 1989a), although it has been calculated that the tail of many birds could generate as much as a third of the total lift required to support a birds weight (Thomas, 1995).
In this paper we present data on wing and tail kinematics over a wide range of speeds in two swallows Hirundo rustica flying in a wind tunnel. We observed interesting features associated with flapping flight and we discuss these findings in relation to the theory of flight mechanics.
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Materials and methods |
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Equivalent air speed
The Lund wind tunnel uses dynamic pressure (q) to set the equivalent air speed (Ve), which can be defined as
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where 0 is the value assumed for the air density (1.23kgm-3) at sea level under International Standard Atmospheric conditions. The disparity between true and equivalent air speed varies depending on changes in air temperature and barometric pressure. Equivalent air speed is used throughout this paper, as it is this that determines the magnitudes of the aerodynamic forces acting upon the bird.
Birds and training
Four adult male barn swallows Hirundo rustica (L.) were caught near Lund, Sweden, on May 21, 1999. All were willing to fly in the wind tunnel from the beginning but two birds flew more steadily and for longer periods than the others and were therefore chosen for the experiment (for morphological details see Table1). Over the first week each of the birds was trained to fly in the wind tunnel for approximately 1h per day. After this the two birds used in this experiment were sufficiently steady in flight (maintaining their position in the horizontal and vertical planes) for data collection. All birds were released at the original capture site after the experiment was completed on June 16, 1999.
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(1) Wingbeat frequency was calculated by dividing the number of wingbeats by the number of frames and converting the value to wingbeatss-1 (Hz). To calculate the wingbeat cycle period the inverse of wingbeat frequency was taken.
(2) Wingbeat amplitude was calculated as the angle described by the pivoting of the right shoulder jointwrist line during the time between the end of an upstroke and the end of the next downstroke (see Pennycuick et al., 2000). The shoulder joint was a well-defined point easily distinguished on the posterior-view images. Wingbeat amplitude using the shoulder jointwingtip line was also calculated for direct comparison with other studies. The beginning or end of a stroke was defined as the point where the wing amplitude angle reached maximum values above or below the horizontal in the xz plane. Ensuring that the bird was in horizontal flight, a maximum of 10 wingbeat amplitudes from the right wing was calculated for each flight sequence (range 110) and the average taken. From these data, the duration of the downstroke and its angular velocity, and the up- and downstroke fractions of the wingbeat cycle period, were also calculated. Downstroke angular velocity was calculated by converting the duration of the entire downstroke, in frames, to seconds and calculating velocity as radians per second. 8ms per frame was the minimum time resolution for any instantaneous kinematic event, so the maximum error of stroke duration was 16ms, which is about 20% of the maximum downstroke duration. Note that on average the error will be 8ms for determining stroke duration, which is half that of the maximum.
(3) Wingspan. For each speed the lengths of the mid-downstroke and mid-upstroke wingspan (wingtip to wingtip) were measured and the span ratio expressed as the upstroke span divided by the downstroke span. Lengths were obtained using Mapinfo and a reference length of a known distance on the bird was used to calibrate the values (see Table1). Three downstroke and upstroke spans were calculated and averaged for each flight sequence.
(4) Upstroke pauses. It was observed that in steady level flight swallows would occasionally pause for a fraction of a second in the middle of the upstroke. The duration of these pauses was measured and averaged per wingbeat with pauses across the entire flight sequence. Not all wingbeats exhibited such pauses and so we also noted the proportion of wingbeats with upstroke pauses. Due to the frame frequency (125Hz) of the cameras, the minimum pause length that could be detected was if the wing remained in the same position on two consecutive frames, representing a minimum time of 8ms. Our measurements hence underestimate the duration of the pauses by a maximum of 16ms and on average 8ms.
(5) Body-tilt angle was calculated from lateral flight sequences by drawing a line between the sharp angle of the inner dorsal bill and the feathering and the tip of the central tail feather, and measuring the angle of this line relative to the direction of airflow, given by the metal frame of the tunnel test section. Body-tilt angles at the end of the downstroke, mid-upstroke and the end of the upstroke were calculated and averaged for each flight sequence.
(6) Tail-spread angle and angle of attack were calculated from ventral and lateral flight sequences, respectively. Tail-spread angle was calculated by drawing two lines out from the centre of the tail (where it meets the body) to the tips of the tail streamers. Care was taken to use only those images where the bird was in steady forward flight (not moving side to side) and the streamers were straight-sided. Three tail-spread angles at mid-downstroke were measured and averaged for each flight sequence. Tail angle of attack was measured in a similar way to body tilt, measuring the angle of the line between the proximal and distal ends of the central tail feathers to the direction of airflow. One measurement at mid-downstroke was made for each flight sequence.
Statistics
Analyses were carried out using General Linear Models in MINITAB release 12.1 (Ryan et al., 1985). Mean values were calculated for the flight variables at each air speed. A model was constructed for each of the flight variables (dependent variable), with air speed (covariate) included initially as a linear, quadratic and up to quartic term, then sequentially removing the highest level non-significant terms. Residuals from the analyses were tested for normality (AndersonDarling) and homoscedascity, and descriptive data are presented as means ± S.E.M. The bootstrapping procedure was carried out using S-PLUS 4.5 (MathSoft Inc. 2000).
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Results |
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Data are presented graphically for the two swallows separately. Statistics are given in the figure legends, and equations for the fitted lines are provided in Table2.
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Discussion |
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Wingbeat frequency and body drag
The range of wingbeat frequencies observed during this study (79Hz) corresponds closely to the 8.2Hz calculated by Pennycuick using a formula based on a barn swallows size and morphology (Pennycuick, 1996). Danielsen (Danielsen, 1988) measured 9.0 and 9.3Hz in two barn swallows on migration, i.e. showing a similar wingbeat frequency to our swallows when flying in the higher speed range. Compared with other species of similar size, the swallow has quite low wingbeat frequency and relatively long wings that increase the wing moment of inertia. Wingbeat frequency showed a clear U-shaped relationship with air speed, with minima at 8.9ms-1 and 8.7ms-1 for bird 1 and bird 2, respectively. A measure of the drag caused by the body (body drag coefficient CD,par) is required to calculate the mechanical power requirements of flight in relation to air speed in birds (Pennycuick, 1989a). The speed of minimum wingbeat frequency is believed to be identical with the speed associated with minimum power (Vmp) (e.g. Pennycuick et al., 1996). Agreement between calculated Vmp (using CD,par) and observed wingbeat frequency can be obtained by adjusting the value of CD,par, allowing a more realistic estimate of CD,par to be calculated. Pennycuick et al. (Pennycuick et al., 1996) found that, to get a match between calculated Vmp and minimum wingbeat frequency in a thrush nightingale Luscinia luscinia and a teal Anas crecca, CD,par had to be set at 0.08 rather than the old default value of 0.4 (cf. Pennycuick, 1989a). Using the same technique for the two swallows, we found that CD,par must be reduced even more to 0.03. However, on considering the plots of wingbeat frequency in relation to speed (Fig.1), one will note two minima, at 78ms-1 and 10ms-1, with slightly elevated values inbetween. This pattern is present in both birds and can be attributed to the upstroke pauses observed at speeds above about 79ms-1, which causes the apparent wingbeat frequency to decline and shifts the speed of minimum wingbeat frequency upwards. Hence, the continuous flapping flight speed of minimum wingbeat frequency should be lower, and closer to the speed of minimum power than the apparent values estimated from Fig.1. Hence, if the lower ends of the 95% confidence limits around the estimated minima are used for speeds of minimum wingbeat frequency (7.88 and 8.00ms-1 for bird 1 and bird 2, respectively), we get CD,par=0.05 and 0.04 for the two birds, respectively. Although swallows are streamlined birds, these values seem extremely low.
Pennycuick et al. (Pennycuick et al., 2000) developed a new technique for directly estimating the mechanical power required to fly in birds. This method is based on the observation that the birds body exhibits vertical movements, such that it raises its position in relation to the horizontal during the downstroke, when most of the lift force is generated, and lowers its position during the upstroke. By measuring the amplitude of the humeral excursion and angular velocity of the wings, Pennycuick et al. (Pennycuick et al., 2000) were able to calculate the mechanical power output of a swallow (swallow 1 of this study). The mechanical power was only calculated for speeds of 611ms-1; CD,par was set to 0.26 and the profile power ratio X1 to 2.25. These values achieved the best fit between calculations of the mechanical power using the body drag coefficient and profile power ratio (Pennycuick, 1989a) and the average mechanical power derived from wind-tunnel observations (see Pennycuick et al., 2000 for details). The Vmp was estimated at 5.3ms-1 for this swallow and these parameter settings, which is clearly outside the 95% confidence interval for the speed of minimum wingbeat frequency (7.99.9ms-1, see Results). Estimating CD,par on the basis of wingbeat frequency, therefore, may not be valid in this species.
Flight mode and kinematics of wings and tail
Many smaller bird species exhibit bounding or intermittent flight, in which bursts of wingbeats are followed by periods without wingbeats (e.g. Rayner, 1985; Tobalske et al., 1999). There are two main explanations for the function of bounding flight; the first postulates that the total drag taken over an entire bounding cycle is lower than if the bird flapped its wings continuously because the profile drag is reduced by folding the wings for a fraction of the cycle (Lighthill, 1977). The second explanation, the fixed-gear hypothesis, assumes that the fibres of the pectoralis muscle restrict small birds to a narrow range of frequencies where the efficiency of the muscle is maximum (Rayner, 1985). This second hypothesis implies that bounding is a means of adjusting the power output to the level required for a certain flight speed. In zebra finches, the wingbeat frequency increased from 25Hz at 0ms-1 (hovering) to 27Hz at 14ms-1 (Tobalske et al., 1999), a 12% increase compared with the 19% and 29% increase from minimum to maximum wingbeat frequency in the two swallows in the present study. It is possible that differences in the relative ranges of wingbeat frequencies used over the same range of speeds in zebra finch and barn swallow represent the variation between a typical bounding species using continuous flapping and flap-gliding. The upstroke pauses seen in the swallows may be a way to adjust the force generation to the required level at medium and high speeds, and may perhaps be regarded as intermittent flap-gliding (cf. Danielsen, 1988).
Amplitude increased with speed which, combined with downstroke duration, yielded a nearly constant downstroke angular velocity between 4 and 7ms-1, which then increased with further increases in air speed. Changes of these parameters are closely linked to the force generation of the wings and the power output (cf. Pennycuick et al., 2000). The wingtip showed an elliptical path when viewed laterally, with the centre of the ellipse moving back along the horizontal axis of the bird with increasing air speed. This is similar to observations of pigeons at speeds of 10ms-1 and above, but not magpies, which show no apparent differences in relation to speed (Tobalske and Dial, 1996). It is perhaps due to this that the pigeon and the swallow are more similar with respect to wing morphology than the swallow and magpie.
The reduction in the degree of body tilt and tail spread with increasing speed is similar to that reported for magpies and pigeons by Tobalske and Dial (Tobalske and Dial, 1996). In addition, our data show that the tail angle of attack exceeds body tilt at low air speeds, and decreases with increasing speed. These observations suggest that there is an aerodynamic function of the tail at low speeds. Thomas (Thomas, 1996) used a simple aerodynamic model to argue that the power required for flight at low speeds can be reduced by increasing both the degree of tail spread and the angle of attack. While there are broad similarities in the direction of change predicted by the model and that observed in this study, there are both qualitative and quantitative differences which indicate that modifications to the model are required (M. R. Evans, M. Rosén, K. J. Park and A. Hedenström, in preparation).
Variable wing span
Pennycuick (Pennycuick, 1989b) developed a method for calculating the lift:drag ratio based on the span ratio, i.e. the ratio of the wingspan during the upstroke to that during the downstroke, assuming that the circulation of the wingtip vortices and the lift distribution remains constant throughout the cycle. A concertina wake concomitant with these properties was observed in a kestrel Falco tinnunculus (Spedding, 1987). A requirement for applying the simplified span ratio method to calculations of effective lift:drag ratios is that the durations of the up- and downstrokes are the same (Pennycuick, 1989b), which was obviously violated in our swallows (see Fig.2). The span ratio declined with increasing speed from 0.5 at 5ms-1 to about 0.2 or less at 1011ms-1, but it was 0.4 at 4ms-1. The lower value at 4ms-1 indicates that the upstroke is feathered at this speed and provides no lift, although the upstroke does provide small lift forces at higher speeds (6ms-1), as indicated by the observations of vertical accelerations of the body (Pennycuick et al., 2000). The swallow body accelerated downwards during the wing upstroke, although not as much as during a free fall, which is evidence of an upward lift force. An interesting observation regarding the span ratio was that the wingspan at mid-downstroke declined from the maximum possible at 4ms-1, with a 35cm reduction in wingspan at higher speeds. We did not observe any drastic changes in either the upstroke or the downstroke kinematics, suggesting that the wingbeat kinematics change in a continuous manner in relation to air speed. Such changes of kinematics differ from those predicted by the gait theory of flapping forward flight, but as yet we have no data on the actual vortex wakes of these birds. The span during the upstroke declined even more than during the downstroke, resulting in the overall decline in span ratio. Even if the span reduction during downstrokes was quite small, it may be analogous to the wingspan adjustments in gliding flight (Tucker, 1987). In gliding flight, reducing the span with increasing speed increases the overall lift:drag ratio of the bird, by trading profile drag against required lift production. We propose that by reducing the span at high speeds the swallow will reduce the profile drag and yet produce enough lift to overcome induced and parasite drag. This analogy does not, however, apply to Pennycuicks (Pennycuick, 1989a) method of calculating the profile power as a multiple of the absolute minimum power a quantity that is proportional to b-3/2, where b is wingspan. Then profile power is always minimum with maximum wingspan and there is no trade-off with induced power. In pigeons and magpies, also studied in a wind tunnel, the span during mid-downstroke was constant across a wide speed range (Tobalske and Dial, 1996). Other bird species with high aspect ratio wings, such as the arctic tern Sterna paradisaea and skuas Stercorarius spp., likewise flex their wings and reduce their wingspan during downstroke when observed in fast cruising or chasing flights (A. Hedenström and M. Rosén, personal observations).
Depending on size and structure there are many ways that birds can adjust the lift and power output required in relation to speed, including changing wingbeat frequency, wingbeat amplitude, span and span ratio, body-tilt angle, tail-angle of attack, etc. Considering the plasticity in this system, some caution may be warranted when equating speeds of minimum wingbeat frequency and minimum power (cf. Pennycuick et al., 2000). There is a continuum with respect to flight kinematics between continuous flapping flight and bounding flight, including the intermittent flap-gliding represented by the upstroke pauses seen in the swallows, and where a particular species falls on this continuum is determined by its size, and wing and muscle morphology. These characters are, in turn, the products of evolutionary adaptations moulded by a species flight requirements.
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Acknowledgments |
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References |
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