The kinematics, aerodynamics and energetics of vertical flight in Rhinolophus ferrumequinum (Schreber) are described. During the downstroke the resultant force generated by the wings tends to accelerate the animal upwards and forwards. Towards the end of the downstroke the wings generate negative thrust and, consequently, the animal accelerates backwards. When, during the upstroke, the wings are accelerated backwards (the ‘flick’) a significant thrust is generated. Total specific mechanical power is approximately 11.92Wkg-1, of which 84% is required during the downstroke.
Hovering can be defined as flight in which no net thrust is generated. Normally animals use it to remain stationary in the air as they sip nectar or glean resting prey. It can, however, be used to make vertical manoeuvres; i.e. although there is no net horizontal force the net vertical force is greater than the animal’s weight, thus tending to accelerate the animal vertically upwards. This behaviour has been observed in a number of bat species, such as the common slit-faced bat Nycteris thebaica, which roosts in hollow trees, the internal diameters of which are often no greater than the bats’ wing spans. When returning to roost, the animals are forced to ‘hover’ vertically up these trees (Aldridge et al. 1990). Similarly, Rhinolophus ferrumequinum sometimes roosts in narrow and derelict chimneys and has been observed hovering up these structures (R. E. Stebbings, personal communication).
When hovering and flying slowly, many vertebrates use a ‘tip-reversal’ upstroke, in which the ‘arm’ wings (the portion of the wings between the wrist and the shoulder; the pro- and plagiopatagia in bats, the secondary feathers in birds) are highly flexed and aerodynamically inactive, but the ‘hand’ wings (the chiropata-gia in bats, the primary feathers in birds) are fully extended and moved backwards and upwards (relative to the animal’s centre of mass), with their ventral surfaces facing upwards and forwards (Eisentraut, 1936; Brown, 1948; Norberg, 1970, 1976a,EXBIO_157_1_183C14b;,Altenbach, 1979; Aldridge, 1986, 1987a; von Helversen, 1986).
Some authors (e.g. Norberg, 1970, 1976a,EXBIO_157_1_183C14b; von Helversen, 1986; Aldridge, 1987a) are agreed that this movement produces thrust during slow forward flight. Two mechanisms of upstroke thrust generation have been suggested. First, thrust is generated because the incidence angles of the chiropatagia are higher than the zero-lift angle but lower than the steady-state stall angle (Fig. 1A). Second, because at the end of the upstroke the wings are accelerated backwards (the ‘flick’), a large drag force is generated. This force is directed forwards and acts as thrust (Fig. 1B; Eisentraut, 1936; Norberg, 1976a; Altenbach, 1979; Aldridge, 1987a). Similar mechanisms might also operate during the hovering upstroke, although Norberg (1976b) did not find significant upstroke thrust in a hovering brown long-eared bat, Plecotus auritus, and concluded that the upstroke was mainly a recovery stroke.
It has proved difficult to verify, experimentally, that during the ‘tip-reversal’ upstroke the wings generate weight support or thrust. For example Rayner et al. (1986) were unable to visualise upstroke circulations in the wake of slow-flying bats, although they did acknowledge that these might have been eliminated by the much larger air movements produced during the downstroke. In a previous study, I measured horizontal accelerations during the wingbeat in a number of bats belonging to six species (Aldridge, 1987a). I found that the bat’s forward velocities tended to increase during or immediately after the ‘tip-reversal’ upstroke where their wings were accelerated upwards and backwards (relative to the animal), indicating that thrust was being generated.
I showed in that paper that the accelerations and decelerations during a wingbeat could be used as independent measures of upstroke function. This should also be feasible for hovering animals. In hovering, the vertical force generated by the wings during the downstroke is opposite in direction, but equal in magnitude, to the animal’s weight. Therefore, hovering animals do not accelerate vertically during the downstroke. If the wings do not generate any significant forces during the upstroke, we can predict that, owing to the force of gravity, the animal should decelerate and, eventually, start to accelerate downwards at about 9.81ms-2. Consequently, each hovering wingbeat should be characterized by vertical accelerations and decelerations.
I found that captive R. ferrumequinum would not hover willingly, and would do so only for very short periods. The bats would, however, ‘hover’ vertically up a narrow flight tunnel, thus offering me the opportunity to study the kinematics and aerodynamics of this flight behaviour. Indeed vertical flight has certain advantages over hovering flight, because the hovering wingbeats are separated spatially and are therefore amenable to analysis using a multi-flash photographic technique (e.g. Rayner and Aldridge, 1985).
The primary aim of this study was to establish whether the wings are active during the ‘tip-reversal’ upstroke. I was also interested in estimating the power required by R. ferrumequinum for this expensive flight behaviour.
Materials and methods
The individual R. ferrumequinum used in this study was the same as that used in my previous studies (Aldridge, 1986, 1987a,EXBIO_157_1_183C3b). Descriptions of husbandry and training can be found in those papers and details of the bat’s morphology are given in Table 1.
The bat was photographed as it flew vertically through a 2 m high plywood flight tunnel (width 0.4 m, breadth 0.4 m). The working section was situated midway along the tunnel and consisted of four 0.5 m sheets of 3 mm Perspex (Fig. 2), which could be removed between experiments. By the time the experiments described here were performed, the bat was hand-tame and would respond to an auditory signal by landing on a perch or on my hand. Once held, the bat could be placed upon a perch situated at the bottom of the flight tunnel. Normally it would remain on the perch until I clicked my fingers, when it would fly up the tunnel and land on another perch, to be rewarded with a small piece of a mealworm (Tenebrio molitor).
As it flew up the tunnel the bat interrupted an infrared beam, activating a dark-sensitive switch and triggering the two Nikon SLRFM and FM2 cameras (fitted with Nikkor 55 mm f2.8 and f3.5 lenses, respectively). The cameras were arranged on mutually perpendicular axes with their film-planes parallel to the sides of the flight tunnel (Fig. 2). As it flew up the tunnel the bat was illuminated by a stroboscope (Dawe Instruments 1203C ‘Strobosun’) flashing at 100 Hz.
Before each series of experimental flights I took photographs of a 0.15 m reference cube which was suspended within the tunnel. For each flight two photographs were taken showing multiple images of the bat from the front and the side. Of these two photographs only the lateral view was analyzed. The frontal view was used to check that the bat had flown up the centre of the tunnel.
The data were transcribed by projecting the images onto paper on which the positions of the nose-leaf, the base of the tail, the wrist and the wingtip were marked. Positional data were used to calculate wing positive elevation, θU, wing negative elevation, θd, wingbeat amplitude (twice the angular excursion of one wing), θ, and wrist strokeplane angle, β which is defined as the angle between the horizontal and a line drawn between the position of the wrist at the beginning and end of the downstroke (Fig. 3). Wingbeat frequency, n, was also recorded for each flight. The angle of the bat to the horizontal (body angle, α) was calculated as being the angle made with the horizontal by a line drawn between the nose-leaf and the base of the tail (Fig. 3).
Image coordinates were converted into estimates of actual distances using magnification factors calculated using the dimensions of the photographic images of the 0.15 m cube. For each data point, I calculated the bat’s vertical and horizontal accelerations (az and ax, respectively) using Lanczos’ (1957) method, as described in Rayner and Aldridge (1985).
As described in Aldridge (1988), there are two important sources of positional error in this technique: parallax errors and errors due to the fact that at any instant the precise distance between the camera and the bat is unknown. Maximum parallax error will occur at the edges of the frame and I estimated it to be approximately 10 % (with a bat-to-camera distance of about 1 m; Aldridge, 1988). Towards the middle of the frame, parallax error will be negligible, and for this reason I only analyzed those images that fell within the central two-thirds of the frame. I estimated that the maximum error due to variation in the distance of the bat from the camera was 4 % (Aldridge, 1988). Errors in θu, θd and θ are likely to be greater than those in position, because it is difficult to determine accurately the beginning and end of the downstroke.
During a wingbeat an animal flying vertically experiences six forces; its weight, Mg (where M is body mass and g is the acceleration due to gravity); induced drag, Di; parasite drag, Dpar; profile drag, Dpro; inertial forces, Fb; and lift, L (Fig. 4). During the downstroke the wings move forwards and downwards generating L, Fb, Di and Dpro, the consequent upward movement of the body generating Dpar. Of these forces L, Di and Fb will tend to accelerate the animal upwards, while Mg, Dpro and Dpar will retard its upward movement. Similarly, Fb, Di and Dpro will tend to accelerate the animal backwards, although L should counteract this. During the upstroke, Fb, Di and Dpro will tend to accelerate the animal downwards and forwards. If lift is generated during the upstroke then it is likely to be directed forwards. The instantaneous vertical, Fvert(t), and horizontal, Fhor(t), forces acting on the bat are, therefore:
Unfortunately, soon after the experiments described here were performed the bat died of an undiagnosed infection. When it was dead I removed its right wing at the shoulder joint (the right leg and the right side of the uropatagium were not included) and, after fully extending it, I attached it to a small card. I suspended the card plus wing sequentially from three points, thus locating its centre of mass. I knew the position of the centre of mass of the card and was therefore able to estimate r.
In calculating the inertial forces acting on the bat, I assumed that the wings were either accelerating or decelerating throughout the wingbeat and thus included mv as a constant. This probably overestimates the apparent mass of the wings, but I do not believe this to be significant.
SbCD.par can be replaced by Ae, which is the area of a flat plate with a parasite drag coefficient equal to 1, which gives the same drag as the body. Pennycuick (1975) developed an equation by which Ae for an untilted body can be calculated, assuming a drag coefficient of 0.43. Pennycuick et al. (1988), however, recommend a CD,par value of 0.40.
The virtual mass of each strip was calculated and added to the masses of each strip before I was calculated.
I analyzed six flights in detail and a summary of these data is in Table 2. The details of one flight are illustrated in Figs 5–10 and the description that follows is of this flight.
Fig. 5 shows clearly that the animal ‘zig-zags’ its way up the flight tunnel. Its body is maintained at a tilt angle of approximately 30° and its stroke plane angle is relatively low at about 46° (Fig. 6; Table 2). The resultant force generated by the wings is likely to reach a maximum when the wings are moving fastest, i.e. during the middle third of the downstroke (Fig. 7). We would expect, therefore, that the animal’s maximum vertical and horizontal accelerations would occur simultaneously with each other and with maximum wing velocity. However, because of body inertia, these maximum accelerations occur half and one-quarter of a cycle, respectively, after the wings have reached their maximum downstroke velocity (Figs 7 and 8).
During the downstroke, the wings generate weight support and thrust. Towards the end of the downstroke, however, negative thrust is produced (Fig. 9). As a result, the animal accelerates, initially forwards and upwards, but then backwards and upwards (Fig. 8). At the beginning of the upstroke, the wings are generating negative thrust and negative weight support (Fig. 9). As the upstroke proceeds, the ‘arm’ wings are flexed (thus reducing wing span by an average of 65.5 %), but the chiropatagia are accelerated backwards and upwards (relative to the animal) and thrust is therefore generated (Fig. 9). It is clear from Fig. 9 that little or no weight support is generated during the upstroke, although the animal’s deceleration exceeds that which would have been expected if the wings were generating no vertical force, indicating that the wings are generating ‘negative’ weight support (Fig. 8). Towards the end of the upstroke, the animal rapidly extends its wings in preparation for the subsequent downstroke (the ‘flick’). This movement also generates thrust.
The most important power component is induced power, net profile, parasite and inertial powers being, respectively, 0.9%, 1.7% and 0.2% of net Pi (0.2564W; Table 3). The total mechanical power of the complete wingstroke is 0.2645W, i.e. 11.92 Wkg-1, of which 84% is required during the downstroke.
It is clear from Fig. 10 that muscle power output does not remain constant throughout the wingbeat. At the beginning of the downstroke, power output is low, as the wings are supinated and no aerodynamic work is done. It increases as the downstroke proceeds and the wings are accelerated downwards and forwards. Power output reaches a maximum as the wings attain their maximum downstroke velocity. During the second half of the downstroke, the wings decelerate and power output falls, reaching a minimum at the beginning of the upstroke. Power output rises again during the upstroke, as the wings are accelerated backwards and upwards and thrust is generated. Towards the end of the upstroke, power output falls (as the wings decelerate), only to increase again as the wings are flicked backwards in preparation for the subsequent downstroke.
When flying horizontally, animals flap their wings in order to generate thrust while maintaining weight support, and they ensure net positive thrust by altering the wing configuration during the upstroke (Rayner, 1986). At low speeds, bats use a ‘tip-reversal’ upstroke during which the chiropatagia are accelerated backwards and upwards, thereby generating thrust (Eisentraut, 1936; Norberg, 1976a; Altenbach, 1979; Aldridge, 1986, 1987a). Hovering bats also use the ‘tipreversal’ upstroke (Norberg, 1970,1976b; von Helversen, 1986), and the results of this study suggest that the wings are active during this phase of the hovering wingbeat. During the downstroke, weight support and negative thrust are generated, while during the upstroke, the wings generate thrust. In the Introduction I described two possible mechanisms by which the wings could generate thrust during the ‘tip-reversal’ upstroke (Fig. 1). In the first, the chiropatagia are moved upwards and backwards, with the resultant airflow striking their dorsal surfaces and in this manner generating lift. This lift is directed forwards and therefore acts as thrust. In the second mechanism, the wings are ‘flicked’ rapidly backwards so that the resultant airflow strikes the dorsal surfaces of the chiropatagia at high incidence angles. Lift is not generated, but the resultant drag acts as thrust. I would suggest that when flying vertically R. ferrumequinum uses both mechanisms to generate thrust during the upstroke. The results indicate that at the beginning of the upstroke no thrust is generated but, as the wings are accelerated backwards, thrust increases and reaches a maximum just after the middle of the upstroke. It then falls, but rises again as the wings are rapidly extended in preparation for the subsequent downstroke. During the first phase the wings may generate lift, while during the flick no lift is generated, but drag acts as thrust.
I have argued in this paper that the vertical flight of R. ferrumequinum is equivalent to hovering flight. It is clear that the kinematics of both flight styles are similar; in both R. ferrumequinum, climbing vertically, and P. auritus, whilst hovering (Norberg, 1970, 1976 b), wingbeat amplitude is between 100° and 120° and the angle of the body to the horizontal is about 30°. There are differences in wingbeat frequency (between 9 and 11 Hz in R. ferrumequinum and between 11 and 12Hz in P. auritus), but these can be explained by the differences in the size of the two species, maximum wingbeat frequency being inversely proportional to M1/3 (Pennycuick, 1975). Strokeplane angle in the two species differs by about 15 – 20°, a difference that cannot be explained as a result of differences in size. The higher strokeplane angles observed in R. ferrumequinum result in this species experiencing larger horizontal forces throughout the wingbeat, although net thrust is zero. Ideally, a hovering animal should only generate vertical forces; it is therefore clear that R. ferrumequinum is not hovering ‘ideally’. It is possible that P. auritus is able to rotate its wings at the humeral joint through a greater angle than is R. ferrumequinum, thus enabling this species to have a smaller strokeplane angle and therefore ensuring smaller horizontal forces. This could explain why Norberg (1976 b) found that upstroke thrust in hovering P. auritus was very slight.
As described above, the wingstroke can be divided into three functionally distinct phases: the downstroke, the upstroke and the flick. These phases are powered by different muscle groups and, therefore, it is appropriate for power output to be considered separately for each phase. The downstroke is primarily powered by Mm. pectoralis, serratus anterior, subscapularis, clavodeltoides and latissimus dorsi (Hermanson and Altenbach, 1983), which are required to generate approximately 84 % of total mechanical power, i.e. 10.01 W kg-1. In the past it has been assumed that the upstroke in hovering flight is essentially a recovery stroke and, therefore, that the muscles that power it are only required to work against wing inertia, i.e. in this example, to generate about 1.33 × 10−3 Wkg-1. However, the results of this study make it clear that the animal’s wings are active during the upstroke, generating thrust. Hermanson and Altenbach (1983) have shown that the abductor muscles (Mm. spinodeltoideus, acromiodeltoideus, the trapezius group and M. triceps brachii) are active throughout the upstroke, but that towards the end the adductors become active and are probably responsible for powering the flick. If this is the case in R. ferrumequinum, the abductor muscles are responsible for approximately 50% of the total mechanical power during the upstroke (i.e. 0.69Wkg-1). During the flick, the adductor muscles generate approximately 0.69Wkg-1. Overall, the adductor muscles are responsible for generating about 90% of the power required for vertical flight in R. ferrumequinum.
It is interesting to compare the power required by R. ferrumequinum for vertical flight with the power required by this species for other characteristic flight behaviours. The relationship between power and flight speed for a particular individual can be defined by the required powers for three flight behaviours: (1) stationary hovering flight, Pih, (2) horizontal flight at the speed at which required power is at a minimum (minimum power speed, Vmp), Pam, and (3) horizontal flight at the speed at which the power/speed ratio reaches a minimum (i.e. maximum range speed, Vmr), Pmr. For the individual R. ferrumequinum used in this study Pih, Pam and Pmr are, respectively, 11.02Wkg-1, 4.72Wkg-1 (Vmp=4.84ms-1) and 5.39Wkg-1 (Vmr=6.39ms-1). Vertical flight therefore requires 8%, 150% and 120% more power than is required for stationary hovering flight and flight at Vmp and Vmr, respectively.
Finally, it is necessary to consider how reliable is my estimate of the power required for vertical flight in R. ferrumequinum. When compared with estimates of the power required by R. ferrumequinum for level flight using Pennycuick’s (1989) and Rayner’s (Norberg and Rayner, 1987) models, my estimate seems reasonable, being approximately 50% higher than both. However, Norberg (1976a) estimated that the metabolic flight cost for level flight in a 0.009 kg P. auritus was approximately 17 times basal metabolic rate (BMR). For a 0.0222 kg R. ferrum-equinum in level flight, this would mean a metabolic flight cost of approximately 165 W kg-1 [using Stahl’s (1967) equation for resting metabolic rate to estimate BMR], The comparable value for a vertically flying R. ferrumequinum is approximately 60 W kg-1 (calculated using the estimate of mechanical power given above), i.e. at least 60 % lower than one would have expected. Similarly this value is significantly lower than equivalent estimates for level flight calculated from respiratory and doubly labelled water data (Racey and Speakman, 1987; Norberg, 1990), which, like Norberg’s estimates (1976a), suggest that flight costs are approximately 15 – 20 times BMR.
There are no clear reasons for these discrepancies, although a number of suggestions can be made. For example, to estimate metabolic flight costs for vertical flight I assumed that mechanical efficiency (i.e. the efficiency by which chemical power is converted into mechanical power) was 0.20. Measured values of mechanical efficiency in bats can be as low as 0.12 (Thomas, 1975), a value that would almost double my estimate of metabolic flight costs for vertical flight. Similarly, the physiological methods may overestimate flight costs (e.g. Tucker, 1972).
Clearly, we need to know a great deal more about the mechanism by which flying animals convert chemical power into mechanical power before we will be able to explain the discrepancies in the results obtained by different techniques.
List of symbols
Acceleration of the body due to wing inertia
Acceleration of the centre of mass of a wing
Vertical acceleration of the body
Horizontal acceleration of the body
Equivalent flat-plate area
Parasite drag coefficient
Profile drag coefficient
Distance, within the strokeplane, between the wrist and the longitudinal axis of the body at the end of the downstroke
Distance, within the strokeplane, between the wrist and the longitudinal axis of the body at the beginning of the downstroke
Resultant force acting on the bat
Inertial forces on the animal due to wing oscillation
Total inertial force acting on the body due to the acceleration of one wing
Acceleration due to gravity
Wing moment of inertia
Induced power factor
Distance of a wing element from the humeral joint
p Distance between a point midway between the two humeral joints and the wrist when the wing is fully extended
w Wing length
Wing virtual mass
′ Virtual mass of a wing element
w Wing mass
′ Mass of a wing element
Total mechanical power
Induced power of hovering
Maximum range speed power
Distance between the centres of mass of the wing and body
Projected area of the body perpendicular to the airflow
Wing disk area
Resultant velocity of the body
Minimum power speed
Maximum range speed
Flapping velocity of the wing
Resultant velocity of the wing
Angle of body to the horizontal
Positive elevation of the wing
Negative elevation of the wing
This research was funded by the Natural Environment Research Council and the Science and Engineering Research Council. I am grateful to Drs C. J. Pennycuick, J. M. V. Rayner, K. D. Scholey, S. Dow and S. S. Burtles for their assistance and support during the course of the work. Drs U. M. Norberg, Å. Norberg and J. W. Hermanson read an earlier version of the manuscript and I am grateful for their comments.