Limits to insect flight performance are difficult to evaluate because the full range of aerodynamic capabilities cannot be easily elicited or controlled. Invasive experimental manipulations, such as tethering and weight addition, may adversely affect the biomechanics of the flight system as a whole. Because air density is a major determinant of aerodynamic force production, gas mixtures of variable density can be used to investigate insect flight performance non-invasively. Three species of orchid bee hovering in heliox (80% He/20% O2) exhibited dramatic increases in lift and power output relative to flight in normal air. Stroke amplitude increased significantly in heliox, while wingbeat frequency was unchanged; the Reynolds numbers of the wings decreased on average by 41%. Although lift performance of airfoils generally degrades at lower Reynolds numbers, mean lift coefficients in heliox increased significantly relative to values for hovering in normal air. Mean muscle mass-specific power output for flight in heliox mixtures ranged from 130 to 160 W kg−1, substantially exceeding values determined from isolated asynchronous muscle preparations as well as limits postulated from the results of load-lifting experiments. The use of variable-density gas mixtures to examine animal flight performance is a simple yet powerful manipulation that will permit a new evaluation of both insect and vertebrate flight mechanics.

Insect flight provides a general problem for biomechanical analysis in that the aerodynamic mechanisms used to effect flight are unresolved. Unsteady aerodynamic phenomena have been widely implicated (Ellington, 1984c; Dudley and Ellington, 1990; Brodsky, 1991; Spedding, 1992; Dickinson and Götz, 1993), but the general case of large-amplitude three-dimensional wing flapping remains analytically intractable. This deficiency in unsteady aerodynamics correspondingly renders it difficult to identify the physical limits to insect flight capacity. As an alternative approach, allometric analyses have been implemented to assess size constraints on animal flight performance (Marden, 1987; Ellington, 1991).

Such allometric analyses have relied on maximal loading experiments to infer upper limits to force production and, by implication, the mechanical power output of the flight muscle. These experiments suggested that the maximum capacity of flying animals for vertical weight-lifting ranged from 50 to 90 N kg−1 muscle mass (Marden, 1987). Using the same data set, Marden (1990) estimated the induced power expenditure under conditions of maximum load and found only slight allometric variation in the body mass-specific power requirements of flight. Through expression in muscle mass-specific form of the aforementioned load-lifting results, Ellington (1991) concluded that the allometry of power expenditure during flight was equivalent to that of power available from the muscle and proposed instead that aerodynamic force production, rather than available power, limits animal flight performance. This novel suggestion calls for further analysis of aerodynamic mechanisms at low Reynolds numbers and, in particular, requires evaluation of the maximum unsteady lift forces that flying animals can generate. It should be noted that load-lifting experiments may, for methodological reasons, estimate maximum power output inaccurately during hovering (see Ellington, 1991).

Because aerodynamic force production and power expenditure in hovering flight depend strongly upon air density (Ellington, 1984e), flight in variable-density gas mixtures necessitates alteration of wingbeat kinematics to attain the requisite force balance and associated mechanical power output. The density of heliox (80% He/20% O2) is reduced by approximately 66% relative to that of normal air, and this causes a comparable decrease in the Reynolds number, which varies in direct proportion to fluid density (Vogel, 1981). Flight in heliox thus presents a double aerodynamic challenge: lift coefficients must increase to offset the decrease in air density, while lift performance of airfoils in general degrades at lower Reynolds numbers (Ellington, 1984c). Conveniently, oxygen partial pressure is not significantly different in normal air and heliox, ensuring the physiological equivalence of the two flight media. The use of heliox as an experimental flight medium therefore permits non-invasive evaluation of the ability of insects dramatically to modulate unsteady force production and power output.

This paper describes reduced-density flight experiments on neotropical euglossine bees, which are common pollinators of orchids (Roubik, 1989) and are noted for their superb hovering abilities. The flight of individual euglossines in air and in heliox is compared to assess the nature of flight kinematics and aerodynamics within the two media. As expected, both the lift performance of the wings and the power expenditure of the flight muscle increase dramatically in the less dense medium.

Flight kinematics and morphological variables

Euglossine bees (Eulaema meriana Oliver, Euglossa imperialis Cockerell and Euglossa dissimula Dressler) were captured at cineole baits on Barro Colorado Island, Republic of Panama. Individual bees were allowed to hover freely within an airtight acrylic cube (0.018 m3). Air temperature within the flight chamber averaged 25.8°C (range 25.0–27.1°C). A video camera (Panasonic AG-160) positioned above the chamber recorded horizontal projections of wingbeat kinematics; lateral views of the hovering insect were simultaneously obtained from a mirror positioned at 45° to one face of the cube. Bees were initially filmed hovering in normal unmanipulated air. Air within the cube was replaced by filling with heliox while simultaneously pumping out the cube contents from a port at the base of the chamber. Hovering flight in heliox was then filmed; periods of filmed flight in each gas mixture lasted 1–5 min. Wingbeat frequency was monitored acoustically using a microphone (Akai ADM-15) located within the flight chamber; microphone output was recorded on the audio track of the video tape.

A tube whistle on the chamber floor was remotely activated to generate an acoustic tone immediately prior to and following filmed flight sequences. Because the resonant frequency of a simple tube increases in pure heliox by 74%, the change in dominant whistle frequency following heliox substitution was used to determine the air density within the flight chamber (Beranek, 1949). A density of 1.21 kg m−3 was assumed for control air. The dynamic viscosities of heliox and of mixtures intermediate between heliox and normal air were calculated using the formulae of Reid et al. (1977).

Wingbeat kinematics were determined from frame-by-frame video playbacks (using a Panasonic AG-7150 video player) and the acoustic recordings of wingbeat frequency. Wingbeat kinematics measured for each flight sequence, include wingbeat frequency n, stroke amplitude Φ, stroke plane angle β and body angle χ (definitions follow Ellington, 1984b).

Stroke amplitude represents the angular extent of wingtip motion in a stroke plane to which wing motions are nominally confined. Body angle is the angle from horizontal of the longitudinal body axis when the insect is viewed laterally. For each flight sequence, mean values of kinematic variables were determined from 3–5 separate measurements. Only those sequences in which the insect exhibited controlled, unaccelerated flight in the center of the flight chamber were used for analysis; vertically ascending or maneuvering flight was ignored.

A QuickImage frame grabber was used with a Quadra 700 microcomputer to obtain still video frames for digitization of wing and body coordinates. The projection of the stroke amplitude onto the horizontal plane was obtained from wing positions at the extremes of the wingbeat. Stroke plane angle and body angle were measured from lateral projections of the flying insect when the longitudinal body axis in dorsal perspective was parallel to the plane of the mirror.

The fundamental frequency of acoustic waveforms was determined using a 12-bit analog-to-digital converter (MacAdios, GW Instruments) and sound analysis software (Soundscope, GW Instruments). Mean wingbeat frequency over approximately 1 s of hovering flight was determined using a peak-picking algorithm; peaks with greater than 30% variation from adjacent wingbeat periods were rejected.

Morphological variables used in aerodynamic calculations were determined on all filmed insects (Ellington, 1984a; see Table 1). These included body mass m (which includes the mass of both wing pairs), relative wing mass for both wing pairs (expressed as a fraction of body mass), wing length R, body length and total wing area S (the area of both wing pairs). Body mass was measured before and after filming; the mean value was used in subsequent calculations. Wing loading pw (mg/S, where g is gravitational acceleration) and aspect ratio were calculated for each bee. Non-dimensional radii for moments of wing mass, virtual mass and wing area were determined following standard methods (Ellington, 1984c).

Table 1.

Mean morphological variables for three species of euglossine bee

Mean morphological variables for three species of euglossine bee
Mean morphological variables for three species of euglossine bee

Thoracic muscle mass was determined indirectly by weighing the thorax (shorn of legs), cutting it in half, removing non-muscular features such as fat and elements of the digestive system, soaking the two thoracic halves in 0.5 mol l−1 NaOH for 24 h, and then weighing the cuticular residue. Relative thoracic muscle mass was expressed as a fraction of total body mass.

Aerodynamic analysis

To evaluate lift and power production in variable-density mixtures, the hovering aerodynamic model of Ellington (1984d,e) was implemented using the kinematic and morphological data obtained on individual euglossines. Reynolds numbers (Re) for wings were calculated using the mean wing chord and mean wingtip velocity, assuming simple harmonic motion. Because of approximately horizontal wing motions (mean β 8°, range 1–19°), the downstroke and upstroke were assumed to contribute equally to vertical force production (see Ellington, 1984e). Mean lift coefficients were calculated such that vertical force production averaged over the wingbeat period equalled body weight.

Mechanical power requirements of flight were estimated by evaluating individual components of profile (Ppro), induced (Pind) and inertial power. Profile power represents energetic expenditure to overcome profile drag forces on the wings, while induced power corresponds to the power necessary to generate sufficient downward momentum to the surrounding air so as to offset the body weight (Ellington, 1984e). In calculations of induced power, the cosine correction for horizontally projected area of the actuator disc was negligible at the observed low values of β (see Results), but was nonetheless incorporated in energetic estimates.

The inertial power during the first half of a half-stroke (Pacc) was estimated from the moment of inertia of the wing and the maximum angular velocity, assuming simple harmonic motion of the wings in the stroke plane. Total inertial power requirements through the wingbeat will be zero if the kinetic energy of the oscillating wing mass and virtual mass can be stored in elastic elements of the thorax and subsequently released to reaccelerate the wings. In this ideal case of perfect elastic energy storage, mechanical power requirements will equal the sum of profile and induced power. By contrast, in the absence of elastic storage of wing inertial energy, additional power will be required to accelerate the wing during the first half of a half-stroke. During the second half of the half-stroke, aerodynamic power requirements can be met by the kinetic energy of the decelerating wings and the remaining negative power requirement for deceleration is metabolically negligible (Ellington, 1984e). Mechanical power output averaged over the half-stroke will then equal (Ppro+Pind+Pacc)/2. For each hovering flight sequence, the total power expenditure was calculated for the two cases of perfect (Pper) and zero (Pzero) elastic storage of wing inertial energy.

For purposes of comparison with published values, Pper and Pzero were expressed in body mass-specific form. Muscle mass-specific mechanical power output (Pmuscle) was also calculated assuming perfect elastic energy storage, as this condition represents the likely minimum rate of energetic expenditure during hovering.

Mean morphological variables for the three euglossine species are given in Table 1. The two Euglossa species are fairly similar in body size and derived variables, whereas Eulaema meriana is a much heavier bee with a substantially higher wing loading. Thoracic muscle mass for all three species averages about 30% of body mass.

Using species and gas mixture as treatment variables, two-factor analysis of variance (ANOVA) was used to assess responses in kinematic and aerodynamic variables to the experimental and control gas mixtures. Whereas wingbeat frequency and stroke plane angle did not differ significantly in the two gas mixtures, stroke amplitude increased substantially in heliox (Tables 2, 3). Wingbeat frequency and stroke plane angle were also significantly different among species. Significant increases in mean lift coefficients were evident for hovering flight in heliox (Tables 2, 3). Concomitant with the increases in the mean lift coefficient, the mean Reynolds numbers of the wings decreased in heliox to about 41% of values in normal air (Table 2).

Table 2.

Mean kinematic and aerodynamic results for three euglossine bee species hovering in air and in heliox

Mean kinematic and aerodynamic results for three euglossine bee species hovering in air and in heliox
Mean kinematic and aerodynamic results for three euglossine bee species hovering in air and in heliox
Table 3.

Results of a two-way ANOVA for kinematic and aerodynamic variables in two variable-density gas mixtures (normal air/heliox) and for three euglossine species

Results of a two-way ANOVA for kinematic and aerodynamic variables in two variable-density gas mixtures (normal air/heliox) and for three euglossine species
Results of a two-way ANOVA for kinematic and aerodynamic variables in two variable-density gas mixtures (normal air/heliox) and for three euglossine species

Body and muscle mass-specific power expenditure increased in heliox assuming both zero and perfect elastic energy storage (Table 2). Given the assumption that wing inertial energy was stored using perfectly elastic mechanisms, muscle mass-specific power expenditure of euglossines was significantly elevated in heliox (Tables 2, 3) to values averaging about 130 W kg−1 in the two Euglossa spp. and 160 W kg−1 in Eulaema meriana. The primary effect of air density reduction was to increase induced and inertial power requirements; profile power, by contrast, remained relatively constant between the two gas mixtures (Table 2).

Kinematics and lift performance

Mean lift coefficients in heliox increased by about 50% relative to values in normal air (Table 2). The lift coefficients in heliox substantially exceed both values previously estimated for insects hovering with a horizontal stroke plane (Ellington, 1984e) and the maximum lift coefficients measured on insect wings in quasi-steady flow (see Dudley and Ellington, 1990). The aerodynamic means by which lift production is enhanced in heliox are unclear, particularly as hovering in normal air is already inconsistent with quasi-steady mechanisms of lift production (Ellington, 1984e; Spedding, 1992). However, a typical increase of 30–45% in stroke amplitude (Table 2) will increase wing angular velocities and accelerations by an equivalent amount, given simple harmonic motion. Increased wing accelerations can augment lift production in linear translation by overcoming the limitations of the Wagner effect (Dickinson and Götz, 1993). Because maximum wing positional angles increased in heliox by an average of 8°, the decreased distance between opposite wings at the dorsal end of the wingbeat could augment the effectiveness of a near clap-and-fling mechanism (Ellington, 1984b). Lift coefficients might also increase through faster wing rotation at the ends of half-strokes, as wing rotational velocities and mean lift coefficients are positively correlated for bumblebees flying over a range of forward airspeeds (Dudley and Ellington, 1990). Further analysis of the kinematic mechanisms used to effect high lift must await greater temporal resolution of wing motions. It is clear, however, that hovering in normal air does not necessarily represent the maximum aerodynamic performance of insects; considerable reserves of force production can be elicited from the flight apparatus under appropriate conditions.

Mechanical power output

Whereas lift coefficients in heliox are striking, estimates of the mechanical power requirements of flight suggest that insect muscle can produce substantially more power than has previously been recognized. Mechanical power output of euglossines in heliox increased by 38–50% to values well in excess of those typical for hovering hymenopterans (Ellington, 1984e; see Casey and Ellington, 1989, specifically for euglossine bees). Because of the increase in stroke amplitude but constant wingbeat frequency in heliox (Table 2), the energy expended per wing stroke must also increase at reduced air density. Muscle power output is proportional to the product of contraction frequency, muscle strain and myofibrillar stress (Weis-Fogh and Alexander, 1977; Pennycuick and Rezende, 1984). For euglossines, the simplest means of enhancing power output would be to rely solely on increased muscle strain; the relative increase in stroke amplitude (40–50%) is comparable to that demanded by the increase in mechanical power output. The relative contribution of increased myofibrillar stress to enhanced power output cannot be assessed.

The estimated muscle power output for euglossines in heliox is substantially greater than the maximum values determined on isolated asynchronous muscle preparations. Upper values of 29 and 88 W kg−1 were obtained on beetle and bumblebee flight muscles, respectively (Machin and Pringle, 1959). A maximum value of 113 W kg−1 was estimated for the muscle of the the giant waterbug Lethocerus cordofanus and L. annulipes operating at normal frequency and strain, while theoretical considerations suggest that the maximum power output of asynchronous flight muscle is about 250 W kg−1 (Ellington, 1985). Interestingly, the highest power estimate for an individual euglossine bee in heliox (Eulaema meriana) was 175 W kg−1 muscle mass, assuming perfect elastic energy storage. Both body mass-specific and muscle mass-specific induced power expended by euglossines in heliox exceed limits postulated from load-lifting experiments. For example, mean induced power of Euglossa imperialis in heliox exceeds by 43% a predicted maximum value at the corresponding body mass (Marden, 1990). Similarly, mean muscle mass-specific induced power output for the three euglossine species in heliox is 57–69% greater than the maximum values derived for Hymenoptera (see Ellington, 1991). In the light of the high power outputs exhibited by euglossine bees flying in heliox, the suggested upper limit of 100 W kg−1 for fast aerobic muscle (Josephson, 1993), as well as the mechanical power limits postulated from load-lifting data (Marden, 1990, 1994), should now be regarded as incorrect.

Furthermore, there is no indication that hovering flight in heliox represents maximum possible performance. All euglossine bees flown in heliox were capable of vertical ascent, during which mechanical power expenditure will exceed that of stationary hovering (Pennycuick, 1975; Norberg, 1990). Although not utilized in normal hovering, such excess capacity may be required for maneuvers, nectar loading and mate or prey transport (see, for example, Heinrich, 1975; May, 1991). Field observations of euglossines at cineole baits confirm their highly developed aerial agility, but the specific forces of natural and perhaps sexual selection that require such performance are at present unknown.

The experimental manipulation of gas density to investigate free flight aerodynamics has not previously been performed at normal oxygen partial pressures, although Chadwick and Williams (1949) investigated the effects of different helium–oxygen mixtures on wingbeat frequencies of tethered Drosophila (see also Chadwick, 1951; Sotavalta, 1952). More recently, insect and avian flight metabolism has been investigated at reduced total pressure. Oxygen consumption of flying honeybees declined as air pressure and density were increased (Withers, 1981). Berger (1974) found that hummingbirds increased their stroke amplitude but maintained a constant wingbeat frequency while hovering at 40% of normal pressure and density; oxygen consumption increased by 6–8%. These latter simulations of elevational change altered total air pressure, and thus air density, but necessarily lowered the partial pressure of oxygen. A salient advantage of density manipulation is that oxygen partial pressure is maintained at normal values, ensuring that diffusive limitations on metabolic power production cannot adversely influence muscle performance. The physical effects of gas substitution on air density and viscosity are straightforward and easily quantified, allowing direct experimental manipulation of the aerodynamic flow around wings. In addition, the short-term and, in most cases, chronic toxic effects of the noble gases are minimal (Schreiner, 1966, 1968; Hamilton et al. 1970). Because of the indirect manipulation of aerodynamic mechanisms that variation in gas density provides, the use of physically variable mixtures can elucidate novel features of animal flight performance.

Financial support from the Smithsonian Tropical Research Institute, the University Research Institute of the University of Texas at Austin and a Reeder Fellowship are gratefully acknowledged. Larry Gilbert, Mark Kirkpatrick and Mike Ryan provided useful comments on the manuscript.

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