Body appendages fine-tune posture and moments in freely manoeuvring fruit flies

Locomotion during migration, territory defence, routine commuting, foraging and escape behaviour is vital to the reproductive effectiveness and survival of many animals (Alexander, 2003). A critical task during locomotion is the control of body posture, which is tightly linked to the production and control of locomotor forces for propulsion and the corresponding moments for turning control (Ellington, 1984a,b). While locomotion involving contact with solid ground benefits from static stability, flying animals achieve body stability and thus flight path control with the help of aerodynamic friction of their environment. Active manoeuvring and directed aerial descent such as gliding thus depend on the animal's ability to fine-tune the benefits of three distinct, major physical mechanisms for posture control: aerodynamic lift and drag on wings and body (Pennycuick, 1968, 1971), active control of the centre of body mass and thus distance to aerodynamic force vectors (Cook and Spottiswoode, 2006; Ellington, 1984a), and modifications of the body's moments of inertia by active changes in body shape (Libby et al., 2012).

The control of moments of inertia is highly effective even in terrestrial animals, for example, during falling and jumping, in which rats maintain an upright body posture by twisting their entire body (Laouris et al., 1990) and geckos and lizards by beating their heavy tails (Jusufi et al., 2008; Libby et al., 2012). In preparation for targeted jumps, moreover, flightless mantis generate a controlled whole-body spin by adjustment of their centre of mass (Burrows et al., 2015). Since active modification in body shape leads to a change in moments of inertia, this mechanism also enables astronauts to control their body orientation without air friction (Kane and Scher, 1970; Kulwicki et al., 1962). By contrast, gliding and actively flying animals typically control moments and posture by alterations in the lift and drag characteristics of the wings (Ellington, 1984a,c, 1991). Although wing aerodynamics predominantly determine moments for posture control, an increasing number of studies suggest that aerial steering is effectively supported by the aerodynamics of body appendages such as the legs and abdomen. Arboreal ants and other wingless, gliding hexapods, for example, effectively control their aerial descent from tree to tree by steering with their hind legs (Yanoviak et al., 2010) and lateral cerci, respectively (Yanoviak et al., 2009). If the hind legs are cut, the tree trunk landing success is severely attenuated between 35 and 60%. Leg steering is also of great importance for drag control in birds. Depending on body posture, pigeons and griffon vultures, for example, may increase their total body drag coefficients during forward flight by factors of approximately 2 and 3, respectively, depending on the extension of their feet (Pennycuick, 1968, 1971). As a consequence, feet adduction in birds during smooth weather conditions leads to an increase in gliding distance whereas during manoeuvres, the feet appear (Pennycuick, 1960).

The vast majority of previous studies on the significance of body appendages for force and moment support in actively flying animals were conducted in insects such as the small fruit fly (Götz et al., 1979; Zanker, 1988b), the house fly (Zanker et al., 1991), orchid bees (Combes and Dudley, 2009) and moths (Cheng et al., 2011; Hedrick and Daniel, 2006). Early studies on various freely flying insect species suggested that leg steering and shifting the insect's centre of body mass support wing-induced moments during manoeuvring (Ellington, 1984d). This hypothesis was further investigated under visual stimulation mimicking yaw turns, during which tethered flying flies bend hind legs and abdomen in the horizontal to the inner side of the intended turn (Götz et al., 1979; Zanker, 1988a,b; Zanker et al, 1991). Visual stimulation mimicking body pitching, by contrast, leads to bending of the abdomen in the vertical, with upward bending during upward motion of the visual pattern (Dyhr et al., 2013; Frye, 2001; Hinterwirth and Daniel, 2010). Mathematical models of the latter behaviour demonstrate that abdominal steering is, at least to some extent, sufficient to maintain body posture in the hawkmoth (Cheng et al., 2011; Dyhr et al., 2013; Hedrick and Daniel, 2006). Besides vision, some insects such as desert locusts also bend their abdomen in response to changing air flow conditions (Arbas, 1986). It has been suggested that this behaviour mimics an aerodynamic rudder that helps the animal to orient into the direction of wind during flight (Camhi, 1970a,b).

Here, we show the significance of leg and abdominal steering on moments and body posture in freely manoeuvring fruit flies, estimating instantaneous moments due to wing motion, hind leg position and abdomen posture around the yaw, pitch and roll body axes, respectively. For this investigation, we: (1) used high-speed video to three-dimensionally reconstruct the body posture and extension angles of the legs and abdomen during various flight manoeuvres, (2) measured drag coefficients of hind legs and the body trunk in a wind tunnel and (3) derived turning moments from a numerical approach. In contrast to previous hypotheses, our data suggest that body appendages mostly attenuate rather than enhance wing-flapping-induced moments. We argue, moreover, that because of their small contribution to total moments, leg- and abdomen-induced moments should be considered as control systems for fine control, rather than systems that significantly enhance the production of moments during extreme flight manoeuvres.

Our recorded flight sequences cover various flight manoeuvres of female Drosophila melanogaster fruit flies, including rectilinear horizontal flight, ascending and descending flight, shallow turns and rapid flight saccades, in which animals rotate with angular peak velocity of up to 1074 deg s⁻¹ (mean, 504±49.1 deg s⁻¹, N=6 saccades) around the vertical yaw axis (Fig. 1A,B). The mean of all data points within each flight sequence that fell within the top 1% maximum of horizontal (vertical) velocity values was 0.26±0.13 m s⁻¹ (0.15±0.11 m s⁻¹) while the mean of all data samples amounts to 0.21±0.12 m s⁻¹ (0.11±0.11 m s⁻¹, N=81 flight sequences). The free flight analysis highlights that body yaw, pitch and roll angles continuously change during manoeuvring flight, exhibiting small changes of several degrees during straight flight and pronounced changes in body posture of up to ∼30 deg roll angle during rapid turns (Fig. 1A,C). The normalized histograms of posture angles demonstrate a mean body pitch of ∼30.6±9.7 deg and a mean roll angle near zero of −0.6±9.4 deg (N=24,579 video frames) during flight.

Free flight manoeuvres in Drosophila are accompanied by extensive movements of hind legs and the abdomen. On average, the animals bend their abdomen vertically downward by ∼10.1±5.3 deg with respect to the longitudinal body axis at a mean horizontal deflection angle of the abdomen close to zero (2.0±3.5 deg). Abdomen steering angles typically vary ±15 deg around its mean value (Fig. 1D). By contrast, leg extension angles (right−left) vary between −35 and 35 deg, with mean vertical and horizontal leg extension angles of 108±15.1 deg and 112±13.7 deg, respectively (Fig. 1E,F). For a definition of angles refer to the Materials and methods.

To evaluate the contribution of moments caused by changes in aerodynamic drag on both body trunk (head, thorax, abdomen, fore and middle legs) and hind legs to wing flapping-induced moments during flight manoeuvres, we systematically analysed the magnitude and coherence of the three components for total moment control (Fig. 2B,C). Fig. 2 shows the moment components for yaw (Fig. 2E), pitch (Fig. 2F) and roll (Fig. 2G) of the flight manoeuvre in Fig. 2A. The data suggest that aerodynamic drag- and mass-shift-induced moments are only small fractions of total moments acting on the fly body (Fig. 2D–G). We derived the total moments from the changes in body posture and a numerical framework (cf. Materials and methods). The top 1% maximum, absolute total moment of all data around the yaw, pitch and roll axes was 11.2, 10.2 and 26.8 nN m, respectively (N=246 samples). On average, the individual contributions of hind-leg-induced moments were ∼41.3- (yaw), 11.2- (roll) and 78.3-times (pitch), and contributions of the body trunk ∼7.9- (yaw) and 3.8-times (pitch) smaller than total moments produced by wings, hind legs, and trunk (Table 1). Further calculations of moments using static, non-moveable legs and abdomen with average posture (M_I=0, ζ_V=105 deg, ζ_H=143 deg, ψ_V=0 deg, ψ_H=0 deg) show that ‘static’ absolute M_D* differs by ∼3.4 pN m (46%, yaw), 16.7 pN m (47%, pitch), and 3.7 pN m (21%, roll) from M_D produced by moving legs and abdomen (single animal, Fig. 3). Considering only static legs (abdomen), mean M_D* differs by ∼10.0±9.5 pN m (6.4±8.7 pN m, yaw), 19.4±18.9 pN m (29.8±21.2 pN m, pitch) and 15.0±14.9 pN m (7.1±8.0 pN m, roll) from M_D (N=81 flight sequences).

The magnitude of turning moments depends on the product of moment arm and aerodynamic force, and thus on local air velocities on the legs and abdomen. These velocities result from three distinct kinematic components: the body's translational motion (for-, up- and sideward), its rotational motion around the three main body axes, and active leg motion relative to the body (Fig. 1A, Table 1). For completeness, we also considered the wing's induced flow (downwash) on legs and body, which is outlined in more detail in a section below. The moments around the fly's main axes (yaw, pitch, roll) due to translational body motion are shown in Fig. 2H, rotational motion is shown in Fig. 2I, active leg motion in Fig. 2J, and moments due to induced flow from the beating wings in Fig. 2K. The data suggest that body translation predominately determines moment control in fruit flies cruising at mean forward speed of 253±137 mm s⁻¹, while the contribution of rotational body motion is small owing to small angular speeds and a decreasing velocity gradient from leg tip to base (Table 1). Mean tarsal velocity of the hind legs due to body rotation amounts to only ∼13.4±14.7 mm s⁻¹ and the 1% maximum does not exceed 107 mm s⁻¹. The velocity component due to active leg motion (7.04±7.99 mm s⁻¹) is almost negligible and 36- and 2-times smaller than the velocities induced by body translation and rotation, respectively. We obtained similar results for active translation motion of the abdomen (3.77±1.64 mm s⁻¹) that compares to a mean body rotation-induced velocity of 6.75±4.60 mm s⁻¹.

Although our data indicate that drag-based steering by hind legs is likely to be 7.6-fold more effective than drag-based steering by the abdomen, the significance of body appendages for moment control during manoeuvring flight is limited (Fig. 4A,B). An analysis on the relative contribution of drag-, mass shift- and inertia-induced moments for yaw control shows that the sum of all three moment components exceeds wing flapping-induced moments in only 16.8% (22.9% for roll) of total flight time (Fig. 4C,D). Drag-based moments alone are higher than wing flapping moments in 1.7% (yaw) and 0.9% (roll) of the flight time (Fig. 4E,F). In other words: during half of total flight time, the total moments produced by body appendages for yaw and roll amount to only 2.0% and 3.3% of wing-induced moments, respectively.

In contrast to previous tethered flight studies on vision-induced yaw steering in Drosophila, hind leg and abdomen deflection is more variable in free flight. Our data even suggest that leg and abdomen deflection is broadly independent from total, wing flapping-dominated moment control. We found that only in 51.8% of total flight time, the sign of the instantaneous, relative (left−right), horizontal leg extension angle ζ_H (cf. Materials and methods) equals the sign of the total (sum of wing- and body-induced) yaw moment M_M. At these instants, the unsigned difference between left and right horizontal leg extension angle is 11.2 deg ±8.41 deg (mean, N=81 flight sequences). At times (48.2% flight time) at which relative leg extension angle and total yaw moment had a different sign, the unsigned difference between left and right ζ_H is 10.1 deg ±8.17 deg (mean, N=81 flight sequences). For an additional statistical test, we dichotomized the data with +1 (−1) that represents times at which leg extension and yaw moments had equal (opposite) direction. We found no significant difference between the two means for all flight sequences (0.03±0.35, Wilcoxon test, P=0.14, N=81). Statistical comparison of the relationship between yaw moments and horizontal abdomen bending yielded a similar result: times with equal sign occurred during 51.2% of the total time without a statistical difference from zero for the dichotomized data (0.02±0.34, Wilcoxon test, P=0.16, N=81).

To further investigate the relationship between the various sources of body moments, we conducted moment coherence and correlation analyses on yaw and roll (Figs 5 and 6). The moment coherence analysis suggests that the sign of wing-flapping- and body-drag-induced yaw moments is opposite during ∼63% (yaw; Fig. 5A) and 65% (roll) of total flight time. This means that leg-based steering inhibits rather than supports turning moments produced by wing flapping. The result is also consistent with findings from a correlation analysis on the temporal relationship between wing-flapping- and body-drag-induced moments of each flight sequence. The latter analysis shows significant, negative correlation coefficients of −0.45±0.36 and −0.54±0.36 (Pearson tests, N=73 and 74 significant correlations with P<0.05) for yaw (Fig. 5D) and roll, respectively. Corresponding coherence and correlation values between wing-flapping- and mass-shift-induced yaw moments are shown in Fig. 5B,E and data for the relationship between wing-flapping- and inertia-induced yaw moments in Fig. 5C,F. For completeness, Fig. 6 shows the remaining dependencies between the four sources of moment production (M_W, M_D, M_S and M_I). For statistical evaluation of the data, we tested the presented mean correlation coefficients against zero. The test yielded no significant differences of coefficients calculated for M_W versus M_S (coefficient for roll, −0.01±0.48; Wilcoxon test, P>0.99, N=64) and M_W versus M_I (coefficient for roll, 0.12±0.49; Wilcoxon test, P=0.09, N=58), whereas all other correlation values for yaw and roll moments were significantly different to zero (Wilcoxon test, P<0.01, Figs 5 and 6).

We next address the potential significance of the wing's downwash on moment control by the body trunk and hind legs. Since the wings, legs and abdomen are mechanically linked, and the distance between the wings’ stroke plane and hind legs is small, we excluded downwash-induced moments from the analyses in Figs 2–6, including Table 1. This is reasonable because body lift production by wing flapping should decrease with increasing downwash-induced drag on the legs and abdomen. To maintain weight support under these conditions, the animal must moderately increase its total body lift production, which, in turn, balances the moments produced by downwash-induced drag. However, at least to some degree, the downwash from the wings dissipates after its acceleration at the stroke plane, losing kinetic energy and altering the efficacy of momentum transfer from the wings to body and hind legs. The downwash-induced moments thus depend on the distance between the wings and body appendages (legs, abdomen), which varies during manoeuvring flight. In the following section, we evaluated the potential contribution of downwash to moment balance by estimation of instantaneous downwash velocity derived from body mass, instantaneous vertical body motion and using actuator disc theory (see the Materials and methods).

We considered downwash at various strengths and compared the resulting moments for yaw, pitch and roll with our previous approach (Figs 2–4). Fig. 7A shows a time trace of downwash-induced yaw moments (grey) of the flight sequence in Fig. 2A. We subsequently added fractions of these downwash moments to total drag-induced yaw moments M_D, in steps of 10% (coloured traces in Fig. 7A, cf. M_D in Fig. 2E). To determine the maximum potential effect of downwash on M_D, we calculated means of the unsigned top 1% maximum values of all 81 flight sequences (pooled data set, N=24,596 measurements). These values are ∼4.7- (yaw), 7.6- (pitch) and 5.3-times (roll) larger than the means in Table 1. The results are shown in Fig. 7B for yaw, in Fig. 7C for pitch and in Fig. 7D for roll moments. Depending on downwash-induced moment, yaw moments change by ∼21% and have a local minimum at 40% downwash. Pitch moments linearly increase with decreasing downwash by a factor of ∼2.3, whereas roll moments appear to be widely independent of downwash-induced moments. Small effects were also obtained for the frequency of moment ratio M_D by M_W (yaw, Fig. 7E). Downwash-induced moments may also change the outcome of the correlation analysis. In two cases, the correlation coefficients decrease with increasing consideration of downwash-induced moments. This relationship is shown in Fig. 7F for coefficients of drag-induced yaw moments M_D versus M_S (blue) and M_D versus M_W (red). By contrast, the correlation coefficient of M_D versus M_I (yaw, green) is not affected by downwash and remains close to zero. We obtained similar results for roll moments (data not shown).

Moment control in insects might also benefit from changes in moments of inertia around the three main body axes due to the active control of legs and abdomen (see Introduction section). To investigate the contribution of active motion, we numerically modelled the insect body as a solid cylinder with the mass of an average fruit fly and the hind legs as cylinders using typical lengths, diameters and masses of corresponding leg segments (cf. Materials and methods, Fig. 8A, Table 2). We first calculated the dependency of yaw, pitch and roll moments of inertia from body pitch angle in a model fly in which hind leg coxae and femurs are in a fixed position relative to the thorax, and without tibiae and tarsi (truncated flies, Fig. 8B). The data suggest that moments of inertia (yaw, roll) in fruit flies may vary 9-fold from ∼0.11 to 0.99 ng m², depending on body pitch angle. By contrast, the moments of inertia due to mass motion of the hind leg tibia and tarsi are comparatively small compared with the moments derived from truncated flies, amounting to an increase in moments of ∼5% in yaw (Fig. 8C), 0.8% in pitch (Fig. 8D) and 6% in roll (Fig. 8E).

For comparison, we also evaluated the maximum instantaneous increase of moments of inertia that a fly might reach during flight by mass motion of its legs, modelling truncated flies with tibia and tarsi but empirically derived hind leg extension angles that produced maximum moments of inertia. These data are plotted as red lines in Fig. 8C–E and confirm the small benefit of leg steering for the control of moments of inertia in fruit flies. On average, the theoretical prediction differs less than 1% increase in moments of inertia from data based on the kinematic reconstructions of leg angles of tibia and tarsi (black data points, Fig. 8C–E).

Our recorded flight sequences show a broad spectrum of flight behaviour in freely flying fruit flies, ranging from straight flight, sharp turns, backward and sideward flight to pronounced changes in flight altitude (Figs 1 and 2). The 3D reconstructed body posture, leg extension angles and abdomen bending highlight active components for body stability and directional control. This is evident from the elevated correlation coefficients between horizontal abdominal bending and leg extension angles (Pearson test, R=0.69), significant correlation coefficients between wing-flapping- and drag-induced yaw moments, and the correlation between wing-flapping- and inertia-induced yaw moments (Fig. 5A,D). Our findings are also consistent with previous experiments on abdomen control in tethered flying fruit flies (Zanker, 1987). The latter study also demonstrated that abdominal movements may not be caused by flow generated from wing flapping. Moreover, Table 1 and Figs 2 and 4 show that the various contributions of hind legs and abdomen to total moments are small and typically restricted to times at which wing-flapping-induced moments are small. Our moment ratio analyses suggest that steering by the hind legs and abdomen dominates moment control in only ∼17% of total flight time (Fig. 4) and drag-induced moments are smallest compared with all other moment-generating mechanisms in fruit flies (Table 1). Thus, in analogy to ruddering of animals in water and air, the small contribution of drag due to proper motion of the legs rejects the idea that fruit flies may produce elevated moments by paddling movements of the hind legs (Ristroph et al., 2011).

As outlined in the Materials and methods, estimation of wing-flapping-induced moments is crucial in our analysis on the relative contribution of abdomen- and leg-induced moments to total moments. Thus, we here compare our estimated wing-flapping-dominated total moments with the moments measured in tethered studies of Drosophila flying under various flight and visual feedback conditions. Table 1 shows that moments around the fly's yaw, pitch and roll axes peak at ∼11.2, 10.2 and 26.8 nN m. In tethered fruit flies flying under open-loop visual feedback conditions, for comparison, yaw varies between 3 and 8 nN m (Götz et al., 1979; Heisenberg and Wolf, 1979, 1988; Mayer et al., 1988) with peak values of 17 nN m (Tammero et al., 2004), pitch may reach 6 nN m (Blondeau and Heisenberg, 1982), and roll varies between 3 and 20 nN m (Blondeau and Heisenberg, 1982; Sugiura and Dickinson, 2009). Computational fluid dynamic modelling using free flight kinematics of fruit flies performing a saccadic turn reported a peak yaw moment of 2.0 nN m (mean ∼1.1 nN m, Ramamurti and Sandberg, 2007) and peak yaw moment derived from a robotic wing mimicking a saccadic turn amounted to ∼1.9 nN m in the same species (Fry et al., 2003). These values are broadly similar to the values shown in Table 1, which gives credence to the method used in the present study for estimation of total moment.

Previous studies on flight control in tethered flies suggest that hind leg steering during optomotor yaw response reinforces wing-flapping-induced moments by strongly increasing (decreasing) the leg extension angle on the inner (outer) side of an intended yaw turn (Zanker, 1988a, 1991). The author proposed that this synergy increases the fly's agility and manoeuvrability, which may, in turn, increase survival rate during aerial predation by dragonflies (Combes et al., 2012). Our data reject the above hypothesis for unrestrained flying fruit flies. We found no preference for the idea that leg extension and abdomen bending angles coherently support turning direction of the animal. In contrast to leg kinematics, we even found that sequence-averaged yaw moments due to drag on legs and abdomen significantly inhibit rather than support wing-flapping-induced moments (negative correlation coefficient in Fig. 5D), which might enhance posture stability. The same holds for mass-shift-induced moments, suggesting a synergistic function of motor pathways to hind legs and abdomen (Fig. 5E). However, counter moments during yaw turning might also result from an increase in local velocities at the hind leg on the outer side of a flight curve, despite its smaller leg extension angle. Data indeed show that an increase in rotational velocity of the body is positively correlated with an increase in hind leg velocity on the outer side of a turn (Pearson correlation, R=0.77). Therefore, while the above mechanism might passively restrict angular velocity in turning flight caused by aerodynamic damping, flies actively shift their centre of mass (abdomen bending) to the body side that counteracts moments generated by wing flapping. The latter mechanism is independent of angular turning rate because it solely relies on changes in the length of the moment arm between the fly's centre of mass and the centre of flight force at mid up- or downstroke (Fig. 2C).

The apparent synergy between drag- and mass-shift-induced moments and their attenuation on wing-flapping-induced moments is also supported by its positive correlation coefficients during yaw and roll control (Fig. 6A,D, yaw). This result is consistent with previous findings on the coherence of leg and abdominal movements in the tethered housefly (Zanker, 1991). The latter study demonstrated that hind legs and abdomen move in-phase and in the same direction during vision-controlled flight. However, our finding that positive (yaw, 51%; roll, 47%) and negative moment coherence (yaw, 49%; roll, 53% flight time) occur with approximately the same frequency suggests a highly flexible system with quite independently acting system components for moment control.

This study considered induced flow (wing downwash) in detail because of its unsettled contribution to drag-induced moments. Wings and legs are mechanically connected and thus any increase in downwash-induced force pushing legs and body downward in the vertical attenuates body lift production by wing flapping via the mechanical link. After its initial acceleration, downwash velocity and vorticity are thought to decrease with increasing distance from the wings’ stroke plane owing to the viscous forces of the surrounding air. However, owing to the small distance of less than a millimetre between stroke plane and legs, this effect is assumed to be small. The different lengths of moment arm for wing-flapping- and drag-induced moments do not allow simple predictions of moment control by changes in downwash velocity. We tackled this problem by calculation of moments, in which we considered downwash as an intervortex stream with uniform velocity but various strengths. Our results in Fig. 7 suggest that induced flow alters total moments depending on the rotational axis: roll moment is rather independent of induced flow and changes only up to 5%, while yaw moments may potentially change up to 22% and pitch moments up to 56% of total moment. Despite the pronounced percentage changes, consideration of moments caused by induced flow does not alter the main result of this study; however, these changes might matter when wing-induced moments are relatively small. Collectively, the exact contribution of downwash to body posture and turning control remains somewhat unclear and requires further investigation.

An alternative benefit of active control of legs and abdomen during manoeuvring flight resides in the associated changes in moments of inertia around the three body axes. Since moments of inertia depend on mass distribution, any changes in vertical and horizontal position of legs and abdomen may potentially modulate this measure. It has previously been shown that orchid bees flying in turbulent air laterally extend their hind legs. This increases drag by ∼30% but also moments of inertia around the animal's roll axis by up to 53%, which, in turn, should enhance flight stability (Combes and Dudley, 2009). Owing to the smaller hind leg mass in fruit flies of ∼9.42 μg or 1.2±0.3% body mass compared with orchid bees (5.9% body mass), the changes in moments of inertia are comparatively small: hind leg motion in Drosophila alters moments of inertia of not more than 6% (Fig. 8). Moreover, compared with a model fruit fly without hind leg tibia and tarsi, moments of inertia during yaw, pitch and roll steering may not increase more than 8% of the moments of inertia of the body trunk. The largest benefit of hind leg control in fruit flies is on roll stability, which is consistent with data obtained from the orchid bee. Consequently, leg extension in small insects such as the fruit fly appears to be of little significance for posture stability but, nevertheless, might slightly enhance stability of animals flying under turbulent environmental conditions that require elevated steering performance.

This study shows how freely flying fruit flies control their flight path by synergistic action of three independently working motor control systems, enhancing the degrees of freedom for heading and posture control. In general, turning moments produced by wing motion dominate both: moments produced by aerodynamic drag on body and hind legs and positional changes of the fly's centre of mass by movements of hind legs and abdomen. Their small contribution suggests that fruit flies use their hind legs and abdomen to fine-tune moments for flight rather than to produce large moments required during flight saccades or optomotor responses. The latter highlights the potential importance of leg and abdominal steering for aerial manoeuvring during straight flight. Nevertheless, while maximum body-drag-induced yaw moments (0.19 nN m) correspond to a unilateral wing stroke equivalent of only ∼0.7 deg amplitude, maximum alteration in positional change of centre of body mass (2.6 nN m) converts into a pronounced unilateral change in stroke amplitude of 8.8 deg (Hesselberg and Lehmann, 2007). Alternatively, motion control of body appendages might be part of the insect's trimming reflexes to trim out bilateral imbalances in forces and moments during flight. These imbalances may result from unilateral aerodynamic effective changes such as wing damage, abnormal asymmetries of the flight apparatus, and an imbalance in muscle mechanical power output and control for wing motion (Bender and Dickinson, 2006; Hesselberg and Lehmann, 2009). In this regard, legs in insects are aerodynamic rudders, similar to those that correct for the counter torque from the propeller in airplanes.

Seen in a larger context, drag-based leg control in flying Drosophila appears similar to the function of middle and hind legs in apterygote hexapods, such as wingless gliding ants, for aerial manoeuvrability and gliding performance (Yanoviak et al., 2009, 2010). From an evolutionary point of view, fruit flies might thus have inherited leg and abdominal motor control systems from their wingless ancestors. The small benefit of leg control in Drosophila on moments of inertia, however, runs counter to the idea that leg steering has primarily evolved as a mechanism to enhance posture stability. In this respect, the male orchid bee might be an exception because its hind leg tibia is greatly enlarged compared with that of other insect species in order to collect scents (Combes and Dudley, 2009).

The flies were scored in a free-flight arena, allowing automated recordings of body posture, abdominal bending and hind leg motion using three-dimensional high-speed video (Shishkin et al., 2012, Fig. 9). To stimulate 0.1 μg fluorescence dye markers on the fly (Fig. 9B,C), we flashed UV-emitting diodes with 60 µs short voltage pulses. Position accuracy of the video-tracked markers was within ±30 µm and images were recorded inside a volume of 20 mm width×20 mm length×25 mm height at 3500 Hz frame rate (Hedrick, 2008). We scored 81 flight sequences of 14 female, 3- to 5-day-old wild-type Drosophila melanogaster (Canton S) with an average body mass of 1.26±0.04 mg. Total flight time of all analysed sequences was 7.03 s, with individual sequences ranging from 15.7 ms to 355 ms, and mean ambient temperature was 23.6°C.

We simplified the reconstruction of leg extension angles, performing pre-tests on leg movements in tethered flying flies (N=7, Fig. 10). A conventional infra-red video camera recorded the animal from lateral (V, vertical angle) and the bottom (H, horizontal angle), while the fly changed wing and leg motion in response to a visual stimulus. We scored the angles between (1) femur and tibia (δ), (2) tibia and tarsi (ε), (3) femur and a connection line through the femur-tibia joint and the fifth tarsal segment (ζ) and (4) femur and longitudinal body axis (κ). From these angles, we calculated mean angles and variances (N=10 images of each fly and camera view) that yielded: 74.2±36.7 deg (δ_V), 125±18.3 deg (δ_H), 128±25.9 deg (ε_V), 161±10.5 deg (ε_H), 105±27.5 deg (ζ_V), 143±11.9 deg (ζ_H), 58.4±2.4 deg (κ_V) and 45.9±4.8 deg (κ_H).

where m_b is the body mass, g is the gravitational constant and t is time.

in which D is drag, u_leg is the velocity at the centre of area of the body segment and S is the frontal surface area of the segment facing the flow. At 90 deg angle of attack at which the flow is normal to hind legs and body trunk, drag coefficients were 2.96 and 1.41, respectively. For comparison, drag coefficients for hind leg and body trunk, modelled as a simple cylinder in Eqn 4 at comparable Re, are 3.14 and 1.44, respectively, which is only 2–6% higher than the measured coefficients (Fig. 11).

where M_D is body-drag-induced, M_S is body-mass-shift-induced, M_I is inertia-induced and M_DW is downwash-induced moment. Downwash-induced moments were only considered in the analysis shown in Fig. 7.

We calculated drag-induced moments M_D from the x-, y- and z-components of the cross product between drag on body, abdomen and hind legs using Eqn 7 and the corresponding moment arm. The local flow vector was derived from the vector sum of body motion, active leg motion, and, in cases in which we considered downwash, from induced velocity and instantaneous body lift in Eqns 5 and 6, respectively. To derive abdomen-induced mass shift moments M_S, we used a simplified approach: we defined the moment arm as the distance between the aerodynamic centre of force of each wing at 56% wing length and the fly's centre of body mass (Ramamurti and Sandberg, 2007). Since this distance varies throughout the wing flapping cycle, we used a mean moment arm at mid half stroke, when the wing's longitudinal axis was in the horizontal and normal to the fly's longitudinal body axis (Fig. 2C). At mid half stroke and zero vertical body velocity, instantaneous vertical lift of each wing equals to ∼6.18 µN (m_b=1.26 mg, cf. Eqn 6), and instantaneous horizontal drag of each wing is ∼2.25 µN. We calculated the latter value according to: (1) the drag characteristics of a robotic fruit fly wing (Re=134, Dickinson et al., 1999); (2) mean wing velocity at the wing's centre of force; (3) mean wing area of one wing of 1.74 mm² of Drosophila; and (4) using Eqn 7.

with χ the pitch angle. Eventually, to achieve total moments of inertia, we calculated the moments of inertia for hind leg tibia and tarsi using Eqn 10 and added these values to the moments of inertia of the body trunk.

If not mentioned otherwise, all data are given as means±s.d. throughout the manuscript.

We thank Peter Schützner for providing flight data and Ursula Seifert for her comments on the manuscript.