Flight Physiology of Intermediate-Sized Fruit Bats (Pteropodidae)

Wind tunnels have been used to make physiological measurements on at least six species of flying birds, but this approach has been used less extensively on bats. Physiological measurements are available from only three species of bats of two disparate sizes: Phyllostomus hastatus, body mass approximately 0-100 kg (Thomas, 1975; Thomas, Lust & Van Riper, 1984) and two species of flying foxes, of 0 ·650 –0 ·870kg body mass (Thomas, 1975, 1981; Carpenter, 1975, 1985).

As part of a study on the energetics of some West African fruit bats, I measured respiratory gas exchange, heart beat and respiratory frequencies, body temperatures and endurance from representatives of three species that are intermediate in size between the previously studied animals. In addition, I include some previously unreported data from several flying foxes (Pteropus poliocephalus) from Brisbane,

Australia. This report doubles the number of species and specimens of bats for which there are some physiological data while flying in wind tunnels. The sizes of animals involved, along with data from previous studies, permit preliminary descriptions of the allometric scaling relationships between the body masses of bats and several physiological parameters during steady flight.

Data were obtained from four animals that were captured in the vicinity of Makokou, Gabon, and shipped by air to San Diego (Table 1). I have also included at appropriate places previously unreported measurements on three Australian Pteropus poliocephalus (Table 1) that were made at the same time as those in a previous study (Carpenter, 1985).

The tunnel was the same one used previously (Carpenter, 1985), except that the fan was now powered by a 14·9 kW motor that allowed increased horizontal airspeeds (V).

Bats were trained as before, with a mild electric shock as a negative reinforcement for landing on the floor or ends of the test section, and the presentation of a landing perch as a reward for successful flights. It was essential that bats be flown daily for many weeks to develop the stamina necessary for physiological measurements. The P. poliocephalus (Pp) had generally learned to fly for brief periods with only 2 –3 days of training, but all of the African bats were more difficult to train. The two Eidolon helvum (Eh) learned to fly without masks in 4 –8 days, but only no. 3 eventually learned to fly with a mask. Rousettus aegyptiacus (Ra 3) was never successfully flown with a mask for respiratory measurements. The strong sexual dimorphism of Hypsignathus monstrosus (Hm) (Allen, Lang & Chapin, 1917; Bradbury, 1977) made the flight energetics of both sexes of special interest. But it took 2 weeks to train two females to fly for as long as 10 s, and a male never learned to fly in 6 months of training.

At the start of each day’s flight activities, including training flights or measurements of physiology or endurance, each of the African bats was given a ‘warm-up’ flight, usually of 120 –150 s, at a moderate airspeed. Gas exchange was measured in Eh 3 and Hm 11, which were trained to fly with masks using the methods described earlier for this tunnel (Carpenter, 1985). In summary, a diaphragm pump drew air in through the rear of a mask worn by a bat in flight, and sent it through a rotameter that measured total rates of air flow, usually 14 ·91 min⁻¹.

This air stream was divided into two parallel circuits, and the remainder bled off. Circuit no. 1 carried air at the rate of 0 ·251 min⁻¹ through a desiccant (Drierite) and to an oxygen analyser (model E-2, Beckman Instrument Co.) which measured fractional O₂ content to the nearest 10⁻⁵ over the sensitivity range (0·20 – 0·21) that could be used for all measurements in this study. Readings from the analyser and comments on a bat’s behaviour were voice-recorded on tape recorder for later transcription and evaluation.

Parallel circuit no. 2 carried air at a rate of 0·81 min⁻¹ through preweighed tubes of Drierite and then a CO₂ absorbent (Ascarite). Respiratory evaporative water loss (EWL) and rates of CO₂ production were determined by measuring, to the nearest 0 ·1 mg, the weight gain of the tubes after subtraction of background readings made in the same way with the empty mask in the tunnel. Drierite was usually introduced into this circuit at 70s after the start of flight, and the Ascarite added in series at 170 s. Determinations of response times of the system indicated that these times were sufficient to allow accurate readings of changes in steady-state gas concentrations. The rotameters were calibrated at the pressures used by introducing pure N2 into the mask or other parts of the system with a rotameter accurate to within 0 ·5% and measuring the reduction in with the analyser. Carbon dioxide introduced into the mask by syringe at rates several times the flight was recovered to within 1 % of the amount introduced. All gas volumes were corrected to STPD.

For the first ten metabolic measurements of Eh 3 and Hm 11, Ascarite was in the circuit for 170 –770 s and 800 –1500 s after the start of flight, in order to determine whether the respiratory exchange ratio (R) changed during flight duration. Rates of O₂ consumption and were determined according to equation 2 of Tucker (1968). For subsequent metabolic runs with both bats, two flights of shorter duration were made within 1 h of each other; for most of these, was measured between 170 and 770s in each flight. Two mean values for R were calculated: from the first halves of flights 1–10 and the first of each subsequent day’s shorter flights, and from the second halves of flights 1–10 and each day’s second flight. In the few flights where was not measured, the appropriate mean values for R (lines 5 and 6, Table 2) were used in Tucker’s equation 3 to calculate ⁠.

For many flights on the African bats I measured body temperatures (T_b) over a wide range of ambient temperature (T_a). These were usually measured on runs when masks and other recording apparatus were not used. I was unable to secure rectal thermocouples for the duration of a flight. Therefore, body temperatures were measured by seizing an animal as soon as it landed, and inserting a shielded 38-gauge copper-constantan thermocouple at least 5 cm into the colon. Temperatures were indicated to the nearest 0·1 °C, within 15 s of landing, on a multichannel digital readout instrument (Bailey Instrument Co., model BAT-8).

In some runs, thermocouples taped on the feet recorded foot temperatures (T_f) during the length of the flight as an index of circulatory changes through the wings or other naked membranes. These thermocouples were connected to a multichannel recording potentiometer (Leeds & Northrup, Speedomax W) that could be read to the nearest 0 ·2°C. T_a was recorded with a second thermocouple in the airstream. All thermocouples and instruments were calibrated by a mercury thermometer with accuracy traceable to the National Bureau of Standards.

I measured heart rates (fH) by attaching thin shielded recording leads from an oscillograph to the bats’ skin at various sites. When the ECG signal was masked by the EMGs from flight muscles, counts were easily made within the first 8 s of a bat’s landing. Continuous records during and after flight on some of the bats indicated that the decline in fH over the first 8 s after landing averaged 92 % of the in-flight rates (N = 15; r = 83–100%; S.E.M. = 1·5%).

Respiratory frequencies (fR) were initially determined at moderate airspeeds by using the oscillograph to record temperature changes of a thermocouple mounted in front of the animal’s nose in the mask. During some flights, simultaneous records were also made of wingbeat frequencies (fw) by recording EMGs from leads attached to skin over the pectoral muscles. Subsequent counts of fw only were made by filming bats flying at assorted airspeeds with a 1 rev. s⁻¹ timer in the field of view.

Wingspans of Eh 3 and Ra 3 were measured by gluing a 15-cm ruler on their backs and photographing them from above while in flight at their apparent speeds of lowest power input. Negatives were projected to full size, using the ruler as a scale, and span was measured directly.

There now seem to be enough data to describe the relationships between several physiological parameters and body masses of bats. However, there were unequal numbers of individuals representing the species for which data are available, and in some cases (e.g. P. poliocephalus), there was nearly a two-fold variation in size among individuals of a species. Rather than using an average value for each species, I have made the assumption that the primary factor affecting physiological parameters is body mass, and have used each individual as a separate data point in calculating least squares regression lines of log-transformed data on physiological rates and body masses.

The effect of airspeed on endurance was measured for Eh 3, Hm 11 and Ra 3. Each bat was flown twice each day without mask or other encumbrance until it showed reliable symptoms of fatigue (see next section). One flight was at the speed already known from data to be the velocity of minimum power input (V_mp), or, iorRa 3, the speed (V = 5ms⁻¹) at which posture and behaviour suggested the least effort to fly. The other flight was made at a chosen test speed (V_t), with at least 4h rest between flights. V_t or V_mp were used for the first flight of the day on alternate days, and all measurements were completed at one V_t value before proceeding to the next V_t value. The duration of each flight was timed, and endurance was expressed as the ratio of the endurance at a test speed (E_t) to the endurance on the same date at the V_mp (E_mp).

Each bat flew in a somewhat distinctive manner, with occasional changes of position within the test section. However, these movements had no apparent effect on physiological measurements. Flight behaviour of Eh 3 and Hm 11 was apparently not influenced by the masks, except that Eh 3 would fly briefly at V = 5 ms⁻¹ and 9 ms⁻¹ only without the mask.

At high speeds, bats flew more consistently at the rear of the test section; at the slowest speeds they flew at the front, and oscillated from side-wall to side-wall. Airspeed had an obvious effect on the angle of flapping plane and inclination of the body, as described for P. poliocephalus (Carpenter, 1985). Thus, it was again easy to use behaviour to determine with fair accuracy the airspeed at which power input was minimum.

Each animal showed reliable symptoms of fatigue shortly before being unable to continue in a flight, after which it landed or crashed. All bats began flying again immediately if they received a shock, but would soon stop again if the front perch was not lowered for normal landing.

The four African bats showed symptoms of overheating at high T_a values (Figs 3, 4). Bats opened their mouths either intermittently or continuously, and curled their tongues upward in the manner employed by P. poliocephalus. In Eh 3 the testes descended at Tb above 39·7°C and this bat often licked its scrotum after being replaced in its cage when overheated. However, after landing, additional cooling behaviour seen in the Australian bats, such as licking of the wrists or fanning the wings, was never observed.

The mean R values for all flights of Eh 3 and Hmll were 0 ·78 and 0 ·79, respectively. Thus, the energy equivalent used in converting to power input (P,) and correcting for drag of the mask was 5·58 W when was 1·01h⁻¹. For both bats, the R values in first halves of flights 1–10 and first flights on subsequent days were significantly higher than values from second halves of runs 1–10 and second flights in a day (paired sample t-test, P< 0·005; Table 2).

The start of flight caused an abrupt increase in from preflight rates; this pattern was reversed when a bat landed. Eh 3 would fly with a mask only at V= 6 –8ms⁻¹. Its V_mp was 7ms⁻¹, but P_i differed only slightly at the other two speeds (Table 3; Fig. 1). For Hm11, the V_mp was 5 ms⁻¹; P_i increased by 11% at V= 4ms⁻¹, but increased only slightly at three higher speeds (Table 3; Fig. 1). At V= 8 ms⁻¹, was actually higher than at any speed except 4 ms⁻¹, but corrections for D_m resulted in a lower P₁ value at V = 8ms⁻¹ than at 7ms⁻¹ (Table 3).

It was not possible to determine systematically the effect of V on of Pp 1 or Pp 7, but flight posture, good endurance and absence of prolonged heavy breathing after flight suggested that was measured at speeds close to the V_mp (Table 3).

Pulmonary EWL of Eh 3 and/Arc 11 was measured during all flights in which was measured, regardless of airspeed. To compensate for variations in pulmonary ventilation at different values of ⁠, the EWL value for each flight was expressed relative to ⁠. These measurements were all made at T_a of 18–25·6°C; there was no significant correlation of EWL with T_a. However, there were significant (P< 0·001) negative correlations of EWL with ambient vapour pressure (VP) (Fig. 2). Bats did not open their mouths in the stereotyped cooling response while wearing masks and there are no data on the rates of evaporation during this behaviour.

Mean EWL from Pp 1 was 0·604 gH₂Ol ⁻¹ O₂ (N=3, S.E.M. = 0 ·05), or 6 ·92g H₂Okg⁻¹ h⁻¹ (N = 3, S.E.M. = 0·58) at a mean VP of 5·3 Torr (s.E.M. = 0 ·07). For Pp7, EWL was 0·375gH₂O1⁻¹O₂ (N = 4, s.E.M. = 0·07), or 3·75gH₂Okg⁻¹h⁻¹ (N = 4, s.E.M. = 0 ·06) at a mean VP of 13·2Torr (s.E.M. = 0·6).

Body temperatures of three African bats after flights of 200 s or longer are shown in Figs 3 and 4. Eh 4 would rarely fly this long; therefore, data are reported for all flights of this bat lasting 120 s or longer. For all four bats the correlation of T_b with T_a was significantly different from zero (P< 0·001).

Low T_a had a dramatic effect on Ra 3 and Hm 11. During three flights at T_a between 2·7 and 5·3°C, Ra3 landed repeatedly in flights lasting less than 170s, despite being able to fly for 600 –640 s later on each morning, when T_a had increased to about 11–15 °C.

Hm 11 was especially affected by low T_a. On very cold mornings, this bat started each flight normally but soon appeared to lose wing coordination. Shortly afterwards, it crashed against the side or floor of the tunnel, even though the wings were pumping vigorously. In each instance, the bat was able to fly normally and for its characteristic duration (800 –1000 s) at warmer T_a later in the morning. Review of data and comments in the notebooks used to record training flights showed a striking pattern of drastically reduced endurance at T_a< 11 °C (Fig. 5). Body temperatures measured immediately after these abbreviated flights were often as high or higher than those recorded at the ends of flights at T_a of 12 –20°C (Fig. 4). T_a as low as 3·5 °C had no apparent effect on Eh 3, and Eh 4 was not flown at T_a below 13·5°C.

Temperatures of the feet (T_f) were usually high at the time of thermocouple attachment (Fig. 6). Prior to, or at the start of, flight, T_f usually dropped to low levels. At T_a < 15 °C, T_f declined (Fig. 6C,D,G) until there was almost no difference between T_f and T_a (Fig. 7). At warmer T_a, T_f usually increased after the start of flight to a nearly constant high level (Fig. 6B,E), but sometimes cycled (Fig. 6F). T_f typically declined promptly after a bat landed. However, when a bat was clearly overheated, T_f remained at high levels after landing (Fig. 6A). The highest T_f values were at the warmest T_a, but the greatest (T_f –T_a) differences occurred around T_a = 20°C (Fig. 7).

Heart rates increased abruptly with the start of flight, and dropped quickly to below pre-flight levels soon after landing (see Table 4).

In both Eh 3 and Hm 11, the fw and fR were coupled 1:1 at or near the V_mp of these bats. For Pp 1, the respiratory frequencies measured with a mask thermocouple matched almost exactly the visual counts of wingbeats over the same time intervals. Although measurements of fR were not feasible over a wide range of airspeeds for any of these bats, it was easy to use fw, measured from films, as an index of the probable relationship between V and fR (Table 5).

The fw values determined from films were close to their minimum values at the measured V_mp of Eh 3 and Hm 11; for all bats, these frequencies were maximal at the lowest flight speeds (Table 5).

The mean wingspan of Eh 3 at 7ms⁻¹ was 0·777 m (N = 14, S.E.M. = 0 ·007), and the wingspan of Ra 3 at V = 5ms⁻¹ was 0·646m (N = 4, S.E.M. = 0·008).

Hm 11 died abruptly of unknown causes after endurance measurements were completed only for the test speed of 8ms⁻¹, for which mean endurance was significantly less (one-tailed paired sample t-test, P< 0·001) than that at V_mp = 5ms⁻¹ (Table 6). The endurance of Ra3 was significantly greater at V_t = 5ms⁻¹ than at any other V_t except 6 ms⁻¹ (P<0·01). Although the mean value at this velocity was less than at 5 ms⁻¹, the bat’s endurance was significantly greater for the first flight of each day than for the second one of each pair, whichever airspeed was the first used (P<0·05).

For Eh 3, endurance at 7ms⁻¹ was significantly greater than at 5 or 9ms⁻¹ (P<0·001) or 6ms⁻¹ (P<·05), but the difference between endurance at 8ms⁻¹ and the V_mp was insignificant. Like the pattern for Rah at 5 and 6ms⁻¹, when endurance of Eh 3 was measured at 8ms⁻¹, the duration of the day’s first flight averaged 45 % greater (P< 0·01) than that in the second flight, whichever of the two airspeeds was the first used.

The pattern in which R declines during the course of a flight, or is lower in a second flight on a given day, has been reported in all metabolic measurements in bats (Thomas, 1975; Carpenter, 1985), and for at least one species of bird (Hudson & Bernstein, 1983). The minimum R values for Eh 3 andifm 11 are the lowest reported thus far for any bat, and indicate that fat accounts for as much as 77 –92% of the energy required for flight. However, it is not clear that steady R values have been reached in any previous measurements on bats. If flights are sufficiently long, R might decline to the minimum value of 0·70 –0·72 measured in birds (Tucker, 1972; Torre-Bueno & Larochelle, 1978), which would indicate that fat is the exclusive energy source.

There are no data from other bats similar in size to Eh 3 and Hm 11. However, Thomas (1975) presented a scaling formula fitted to the minimum mass-specific power input values (P_i,min) of the five flying birds and bats that had been measured to date (Table 7). The P_1,minin of Eh 3 was only 2 % greater than the value predicted from body mass, but the data for Hm 11 were 22 % above the expected value. Even greater variation is known among birds of equal size; the P_{1, min} of fish crows was 48 % greater than that of a laughing gull of the same mass (Bernstein et al. 1973). This may have resulted from the lower aspect ratio and higher fw of the crow. The fw of Hm 11 and Eh 3 were similar at their V_mp (Table 5), but Hm 11 died before wing measurements could be made in flight.

The number of individual fliers for which has been measured in wind tunnels has now tripled since Thomas’s (1975) formula was published. New regression lines (Fig. 8) fitted to data for bats only and from all eleven animals for which P_i.min values are known are very similar to his original line (Table 7). The inclusion of P, values from Ppi, Ppi and from pigeons flying at 10ms⁻¹, which may not have been their V_mp (Butler, West & Jones, 1977), affects the regression only slightly (equation 4, Table 7).

The inverse relationship between evaporative water loss and vapour pressure (Fig. 2) conforms to the pattern reported in two P. poliocephalus in flights over a wider range of vapour pressure (Carpenter, 1985). The wide scatter in these data is presumably the result of non-respiratory water loss such as nasal secretion or salivation, although data were omitted from flights when these were apparent in the mask. The EWL of Eh 3 and Hm 11 was about the same per litre of consumed O₂, but the greater of Hm 11 resulted in a higher mass-specific EWL (Fig. 9, points 8, 9).

To compare mass-specific values with other species, I used the closely grouped data within a small range of VP (Fig. 2). Available data from other species in flight (Fig. 9) were obtained over a wide range of ambient VP, both by total weight loss during short flights, or by collection of only respiratory water loss through masks. Despite the nearly two-fold variation in EWL among bats within a narrow size range, the least squares regression line fitted to these data (equation 5, Table 7) may have crude predictive value in estimating water budgets of bats.

The metabolic demands of flight result not only in high rates of water loss, but in a proportional production of metabolic water. Since the overall average value of R was about 0·78 for both Eh 3 andHm 11 (Table 2), the mean rate of metabolic water production (MWP) would be 0·57gl⁻¹ O₂ consumed. The horizontal dashed lines in Fig. 2 indicate this ratio; the mean respiratory EWL of the two animals would apparently exceed MWP at any vapour pressure below 12–14 Torr. However, even in the ‘dry’ season in the rain forests of Gabon, the atmospheric humidity is frequently high enough to result in heavy ground fog, and a high water intake is provided by the bats’ soft fruit diet.

The EWL data in Fig. 2 can also be used to calculate the fraction of heat lost by pulmonary evaporation. I have again assumed that heat production is 75 % of metabolic rate, as in other fliers (Tucker, 1972; Bernstein, 1976; Thomas, 1975), and that evaporation of lgH₂O dissipates 2 ·44kJ (0·58kcal). Thus, when EWL is lgH₂O 1⁻¹O₂, the ratio of evaporative heat loss to metabolic heat production (H_e/H_p) is 0-161 (Fig. 2). These data show that about 10% of the heat produced was lost by respiratory evaporation, a fraction similar to that measured for P. poliocephalus (Carpenter, 1985) andP. hastatus (14%; Thomas & Suthers, 1972).

In flying birds, cutaneous water loss may account for 10% of heat production (Hudson & Bernstein, 1981), but there have been no attempts to measure this in flying bats. In the few measurements on non-respiratory water loss in caged bats, the experimental conditions and assumptions do not permit application of those data to consideration of thermoregulation during flight (Chew & White, 1960; Laburn & Mitchell, 1975). However, the sweat glands of bats are generally considered to be of little significance in thermoregulation (Quay, 1970), and the typical responses to heat stress are panting, wing fanning and licking the wings, without observable sweating (Bartholomew, Leitner & Nelson, 1964; Carpenter & Graham, 1967; Laburn & Mitchell, 1975). Thus, the respiratory system is probably the only significant avenue for evaporative heat loss in flight.

The resulting C_f values of 3 ·2, 6 ·1 and 3’5Wkg^−loC⁻¹ for Eh3, Hm11 and Ra3, respectively, are greater than the value of 2·5Wkg^−l°C⁻¹ calculated for P. poliocephalus (Carpenter, 1985), reflecting the greater mass-specific metabolic rates of these smaller species at about the same T_a. The high Cf of Hm 11 is associated with its ability to fly at a higher T_a than any of the other bats, despite losing an equal fraction of its heat production by pulmonary evaporation (Fig. 2).

Van Cleave (1975) showed that changes in patterns of blood flow could be detected in flying P. poliocephalus by changes in skin temperature, and that the patterns of change were the same on wing surfaces and the feet (although the magnitudes of temperature changes differed). Thus, the measurements of T_f for these African species indicate the conditions under which blood flow to the feet, and presumably the wings as well, increased or decreased in response to heat loads imposed by flight.

At T_a< 15 °C, the small (T_f–T_a) differences (Fig. 7) show that blood flow to naked surfaces was minimal, which results in heat conservation at low T_a. At T_a> 15°C, blood flow to the feet was high; if the bat showed behavioural signs of hyperthermia, blood flow remained high after landing, presumably until T_b declined to some (unmeasured) set point (Fig. 6A).

There are obvious theoretical limitations to the usefulness of this mechanism. The rate of heat loss from wings and feet should be proportional to the magnitude of the (T_f –T_a) differences and the rate at which blood flow can carry heat to these surfaces. However, as T_a increases, the maximum (T_f –T_a) difference must become smaller, even though T_b increases slightly. The maximum differences possible are shown in Fig. 7 by diagonal lines representing (T_f –T_a) when T_f = T_b, with T_b derived from the regression lines in Figs 3 and 4. The differences in (T_f –T_a) never reached this limit, although at higher T_a, the (T_f –T.) values of Hm 11 seemed to parallel the decline in theoretical maxima.

The second limitation of this mechanism is the amount of blood that can be sent to wings and feet, since blood used for cooling is presumably less available for O₂ transport to the muscles. Ever increasing amounts of blood would be required to dissipate heat as T_f approaches T_a. Thus, as useful as this system might be at moderate temperatures, its effectiveness actually diminishes as increasing T_a reduces the (T_f –T_a) differential. Elevated pulmonary ventilation and evaporative cooling, which birds employ at high T_a (Torre-Bueno, 1978a; Hudson & Bernstein, 1981), is free of both of these limitations. However, the 1:1 coupling of fw and fR in all bats studied thus far (Suthers, Thomas & Suthers, 1972; Thomas, 1981; Carpenter, 1985) apparently precludes major increases in pulmonary ventilation necessary to achieve this effect. The rates of evaporative heat loss caused by opening the mouth in flight have not been measured, but all bats have usually been unable to continue flights at T_a that caused this behaviour.

The limited thermoregulatory capabilities of flying bats appears to be one factor associated with flight activity primarily during cooler nocturnal temperatures in the tropical and subtropical habitats where they are most abundant (Carpenter, 1985). However, all measurements on metabolic rate, body temperature and evaporative heat loss on bats in sustained flight have been made in wind tunnels. Under these circumstances, the opportunity for radiative heat losses to the night sky is absent, and the apparent limitations to flight of bats at high T_a may be artificially exaggerated by this situation.

The dramatic effect of low T_a on Hm 11 and Ra 3 suggests that wing structure imposes another climatic limitation on bats. Convective heat losses to cold air may be so great that wing muscles are chilled to a degree prohibiting the precise coordination necessary for flight. Indeed, in isolated forearm muscles from several species of temperate zone bats, the durations of contractions at temperatures below 8°C were 8–10 times those at 32°C (Nelson, Hirshfield, Schreiweis & O’Farrell, 1977). Even if non-tropical species are less sensitive to cold, there must be an absolute minimum T_a at which bats can fly, set by the freezing point of tissues in the wings.

The wings might be warmed through vasodilation, but at T_a near 0°C the resulting rate of heat loss from the body must be enormous. Even at warm T_a, the smallest differences between T_b and T_f in the African bats were 8-10°C, which indicates how ‘rapidly heat was lost from the (relatively) thick feet when T_a was as high as 27°C.

The reports of small bats in flight at T_a as low as –5°C (O’Farrell & Bradley, 1977) suggest a need for very careful environmental measurement or further physiological study, especially in light of the data on lengthened contraction times in the same species. Hibernation or autumn migration to warmer climates may be as important in enabling temperate zone bats to avoid the difficulties of flight at low temperatures as they are to alleviating the energy imbalances when food is scarce. Birds are presumably relatively immune to the control problems in flight owing to the insulation on their wings, and the absence of muscles in the wing surface.

Data are now available for fH during, or immediately after, flight for nine bats over a range of body masses from about 0 ·020 to 0 ·80 kg (Thomas & Suthers, 1972; Carpenter, 1985; Table 4). Separate least squares regression lines were fitted to log-transformed data on fH and body masses of bats and birds; the resulting slopes (equations 8, 9, Table 7) were both significantly different from zero (P < 0 ·01), and were also different from each other (analysis of covariance; Zar, 1974). However, values along the two lines were identical at a body mass of about O il kg, and did not differ by more than 15 % at any body mass within the size range of the bats (Fig. 10).

In this study fw and fR have been measured in several ways. In some cases, such as Eh 3 at V = 7 m s⁻¹, there was good agreement between values obtained with a thermocouple in a mask (Table 4) and counts from films of bats flying without any encumbrance (Table 5). However, in other instances, the fw values from mask thermocouples were up to 20% greater than values determined by film or EMG records. The difference may reflect the added work to overcome drag of the mask and tubing; if so, photography should produce more accurate data.

Despite some inconsistency in data when fw and fR were measured separately, a 1:1 coupling of fw and fR has now been recorded in bats of five species across a size range of approximately 0 ·10 to 0 ·87 kg. In bats measured at the extremes of this size range, P. hastatus and P. alecto (asP. gouldii, synonomy according to Tate, 1942), the coupling occurs across all airspeeds at which the animals would fly (Suthers et al. 1972; Thomas, 1981). Thus, it seems justifiable to assume that fw data are indirect measures of their fR values.

Fig. 11 plots the minimum fw data for a variety of bats, indicating those individuals in which fw and fR are known to be coupled for at least one airspeed. The slope of the regression line for these data differs significantly from zero (P < 0 ·01), as well as from a regression line fitted to fR data for flying birds (Fig. 11; equations 10, 11, Table 7). There is less agreement between these two data sets than for the fH data, which might be expected in view of the greater differences in mammalian and avian respiratory systems. But understanding the significance of such similarities or differences depends on further work like that of Thomas (1981), and quantitative data on all aspects of the O₂ delivery system across the range of sizes of fliers.

In view of the nice endurance data for Ra 3 and the wide power curve for Hm 11, it is regrettable that the complementary data are missing for each bat. However, some assumptions about their patterns may be made. It would be contrary to the pattern for other bats if the endurance of Hm 11 at V = 6 or 7ms⁻¹ had been significantly greater than that at V = 5 m s⁻¹. Further, the power curve of Ra 3 probably increased only gradually with increasing speeds above its speed of maximum endurance, which was probably its V_mp. If so, then its cost of transport would have been minimal at V= 8ms⁻¹.

The effect of velocity on the endurance of all three bats has the same energetic implications that it did for two P. poliocephalus (Carpenter, 1985). The relative distances that might be possible at each V_t were calculated by assuming that bats could fly for 3600 s at V_mp, and multiplying the other relative endurances (in s) by the respective V_t values (Table 6). The endurances at V_mp so greatly exceeded those at the velocities of ‘maximum range’ that the maximum ranges in still air would actually have been achieved at slower but less economical speeds. It is interesting that the V_mp of Eh 3 was close to the middle of the range of flight speeds (4 ·5 –8 ·3 m s⁻¹) reported for this species in the wild (Kulzer, 1968). In such cases, the actual costs of transport (Table 3) in still air would probably be greater than the minimum values at maximum speeds; this cost would be especially high for Hm 11, which had a high power input at its relatively slow V_mp. If Ra3 maximized its range by flying at V= 6 m s⁻¹ (Table 6), and its P_{i, min} were accurately predicted by equation 3 of Table 7, then its actual cost of transport would be about 1·3. As with P. poliocephalus (Carpenter, 1985), the products of P_i and endurance at each speed (the ‘metabolic capacity’) were unequal across the range of speeds. This indicates that endurance was not limited at every velocity merely by fuel reserves as one would expect of an aeroplane.

If endurance is dependent on P_i, it should be fairly constant at those velocities causing small changes in P_i, as was the case with Eh 3 at V = 7 and 8ms⁻¹. But the magnitude of the negative exponent in equation 13 is so great that only a 10% increase in relative P_i would reduce endurance to about 50 % of that at V_mp. Even if the exponent were the more conservative 95 % confidence limit of –4 ·46, endurance would be only 65 % of that at V_mp with a 10 % increase in P_i.

In athletes, endurance is inversely proportional to power input (E ∝ P⁻¹; Wilkie, 1980). This seems intuitively correct, since it could be the result of an animal expending energy at some rate until the accessible fuel was exhausted. But the exponent in equation 4 results in a much greater decline in endurance with increased P, than the expected inverse relationship. In effect, this expresses again the calculations of very unequal metabolic capacities (Table 6), for which roughly similar values would be expected at all airspeeds, if fuel were always the factor limiting endurance.

The actual limitations are unknown. A previous suggestion (Carpenter, 1985) that O₂ delivery was insufficient at extreme velocities seems justified at the lowest airspeeds, which caused animals to be clearly out of breath after very brief flights. At velocities closer to the centre of the power curve, endurance may be limited by fatigue of specific muscle groups required for control at atypical velocities. There seems no a priori reason that all muscles should become incapable of normal function after the same interval, especially at flight speeds requiring unusual contributions to the wingbeat.

The fact that the V_mr is apparently the same as the V_mp in representatives of four bat species raises more strongly the question of whether such patterns exist in migratory birds. Even without metabolic data, wind tunnel measurements of endurance could identify the V_mr, presumably with more definitive results than have been obtained by measurement of birds’ freely chosen airspeeds in nature (Tucker & Schmidt-Koenig, 1971; Schnell & Hellack, 1979).

I am grateful for contributions from the following sources. Equipment and shipping expenses were provided by a grant from San Diego State University Foundation. Travel and field collections in Gabon were supported by a grant from the National Geographic Society and funds from N.S.F. grant no. BNS-76-04400 to J. Bradbury, who, with K. Fristrup, collected most of the bats returned from Gabon. S. Ellis assisted in training bats and L. Nichols assisted with photography and temperature measurements. J. Conly measured drag of the mask. I also thank L. R. McClenaghan for computer programming and J. Bradbury and an anonymous reviewer for comments on earlier drafts of this paper.