Upstroke wing clapping in bats and bat-inspired robots improves both lift generation and power economy

We present results for two cases at the extreme of the robot’s kinematic space: near-zero wing folding, $\theta=0^{\circ}$, and extreme wing folding with a wing clap $\theta=100^{\circ}$ (Fig. 3). For both cases the freestream $U=4$m/s, which corresponds to $St=0.21$.

We observed smooth flapping motion that followed the prescribed motion with reasonable fidelity (Fig. 4A1 and A2, green lines). For the near-zero prescribed folding angle case (Fig. 4A1), the folding angle of the handwing varies passively over the wingbeat cycle, with values ranging from $-20^{\circ}$ to $5^{\circ}$. The observed folding angle is closer to the prescribed value for the larger folding angle case, with values similar to those prescribed in magnitude but with a phase lag of about $t/T=0.1$ (Fig. 4A2). See also the hand wing total angles with respect to mid-stroke plane in supplementary Fig. S7.

The mechanics and energetics of the two folding cases differ substantially. The magnitude and trend of the aerodynamic lift coefficient, $C_{L}$ ($C_{L}=F_{z}/0.5\rho U^{2}S$, where $F_{z}$ is the dimensional force, $\rho$ is the fluid density, and $S$ is the total area of the two handwings), for the case of near-zero folding is similar when measured by the force transducer (FT) and predicted by our quasi-steady model, [4, 5] (Fig. 4A3). Positive lift is generated during downstroke, and negative lift during upstroke. The quasi-steady model diverges from the FT data primarily by an overprediction (more positive lift) of $C_{L}$ in late downstroke/early upstroke ($t/T=0.3-0.6$), and an underprediction (less positive lift) around the upstroke to downstroke reversal ($t/T=0.8-1$). For the extreme wing folding case (Fig. 4A4), downstroke is responsible for most of the positive lift ($t/T=0-0.5$), but there is more variation across the wingbeat cycle and a more pronounced difference between the lift estimates of the measurement and the quasi-steady model . Specifically, the model produces a more pronounced underprediction of $C_{L}$ in comparison to the FT measurement at the beginning of downstroke (snapshot i), and slightly overpredicts lift around the mid-downstroke (between snapshots i and ii). The quasi-steady and FT measurement agree well late in downstroke (snapshot ii). At time $t=0.8$, when the wing claps (Fig. 4A4, snapshot iii), the quasi-steady model fails to predict the peak in lift generation $C_{L,clap}$ in Fig. 4A4. Towards the end of upstroke ($t/T\sim 0.9$, Fig. 4A4, snapshot iv) when the wing has completed the upstroke movement from the ventral to the dorsal side of the body and prepares for the next downstroke, the quasi-steady model captures the negative lift measured by the force transducer, albeit with a slight overprediction and phase delay.

Computations of the quasi-steady model predict moderate peaks in power consumption during the middle of the downstroke and the upstroke (Fig. 4A5). These predictions are supported by the power measurements from the robot, although there is a delay (with the quasi-steady model leading by $t/T=0.1$) in the power maximum. When wing folding is at its maximum ($\theta_{o}=100$, Fig. 4A6), the model predicts a more complex time course for power consumption, but the overall pattern of power use measured from Flapperoo is a close match to the simulation, with the exception of an underprediction of power at snapshot iii ($t/T\sim 0.8$), and a sharp rise in predicted power late in the upstroke at $t/T\sim 0.9$, (snapshot iv) which is not observed by the measurement.

PIV measurements of the flow field along the midline plane of Flapperoo show a prominent jet that is directed downward and to the rear of the “animal”, which appears as a result of wing clapping at $t/T\sim 0.8$, (snapshot iii, and Fig. 4B). Because the velocity measurement is restricted to the centerline plane between the two wings, the control volume (CV) analysis of the aerodynamic forces associated with this jet (Fig. 4A4 - blue line), are only expected to yield accurate force estimates during the portion of the wingbeat cycle in which wing clapping occurs (refer to sec. 2 for a more detailed description). During this time period, $C_{L}$ agrees well with FT measurement. During other portions of the wingbeat cycle, flow in this plane closely follows the freestream and $C_{L}$ = 0 (see video in supplementary S1). The $C_{L}$ calculated from the CV approach is independent of the CV boundary (once a large enough volume is chosen).

The jet is produced as a result of left and right wings clapping, “squeezing” air out. We predict that the strength of the jet created by two wings clapping will depend on the distance between the wingtips, which, in turn, depends on the clapping amplitude, $\theta_{o}$) and the speed of the approaching wings, $f\theta_{o}b$, where $f$ is the flapping frequency and $b$ is the length of the handwing, measured from the wrist to the wingtip. We define a local lift coefficient, $C_{L,clap}$, from the peak lift force during the clap (Fig 4A4), and observe a clear dependence of $C_{L,clap}$ on clapping amplitude, $\theta_{o}$, and the wingtip velocity (normalized by the flight speed to form a clapping Strouhal number: $St_{clap}=f\theta_{o}b/U$)(Fig 4C).

Wing folding confers aerodynamic benefits but requires actuation, and so incurs energetic costs. Examination of the cycle-averaged lift coefficient, $C_{L}$, and power economy (the ratio of $C_{L}$ to $C_{P}$) as a function of Strouhal number, $St$ (Fig. 5A) shows that for the non-folding case, $\theta_{o}=0$, the cycle-averaged $C_{L}$ is close to zero for all values of $St$ (the upstroke-downstroke wing motion is symmetric when wing folding amplitude, $\theta_{o}$, is non-zero, and hence no net lift is expected). With wing folding, the cycle-averaged lift coefficient increases with $St$, up to a maximum value of $C_{L}\sim 0.8$ for $(St,\theta_{o})=(0.41,100^{\circ})$. For a given Strouhal number the lift coefficient increases with wing folding amplitude, $\theta_{o}$, and increases more steeply close to the clapping condition (see supplementary Fig. S4, for $\theta_{o}=90$ to $100$).

Power economy, $C_{L}/C_{P}$, does not monotonically increase with fold angle nor fold angle (Fig. 5B and Fig. 6). For low to moderate $St$ ($St=0.16-0.27$ - moderate to fast flight), power economy increases monotonically with folding amplitude $\theta_{o}$ and peaks at the highest fold angle $\theta_{o}=100$. For higher $St$ ($St=0.33-0.41$ - lower flight speed), the most economical solution to gain lift occurs around $\theta_{o}=30$, although Power economy does start to increase again due to wing clapping at high folding amplitude $\theta_{o}$ (Fig. 6). Thus at high $St$, power economy features twin peaks, one at moderate folding, and the other at extreme folding amplitude. Note that right around $St=0.27$, both folding angle of $\theta_{o}=30$ and $100$ are indistinguishably optimal.

To calculate the lift generated by wing clapping by hovering birds, Chang et al. [19, 20] conducted frontal and parasagittal plane PIV measurements during hovering flight of these birds, and a coherent vortex ring is visible as a result of ventral wing clapping. Lift is estimated from the circulation of this vortex ring during downstroke, under the assumption of an aerodynamically passive upstroke, and explains approximately $80\%$ of weight support. Here, we do not assume a vortex ring structure, but apply a control volume (CV) approach, which lends itself well to the spatially and temporally complex flow in terms of pressure, momentum flux, and acceleration of fluid by the wing motion.

By phase-averaging the flow field over $40$ wingbeat cycles, we found that the contribution from turbulent velocity fluctuations (see Supp. Mat.) is negligible in estimating $C_{L,clap}$ compared to the mean (phase-averaged) values, suggesting that a coherent vortex ring dominates lift production. This agrees with the observation by Chang et al.[19, 20].

Net pressure and fluid acceleration start to build well before the wings clap (Fig. S1), suggesting that the wing-wing interaction occurs much earlier than the actual instant of clapping (see also [37]), and lasts a substantial fraction of a wingbeat ($t/T=0.65-0.8$ in Fig. S1). Indeed, the wings do not need to be physically touching to effect the jet, but instead can be separated by a small distance (Fig. 4C).

For the case without wing folding (near-zero case), the agreement between the force measurements and the quasi-steady predictions is generally very good, both in terms of the overall trend and the magnitude of the lift force (Fig. 4A3). Because the the wing motion – up- and downstroke – is symmetric (Fig. 4A1), the model predicts the upstroke and downstroke forces to be equal and opposite, and the measurements largely support this – with the deviation due to slight asymmetry in the realized kinematics. Measured and predicted forces differ just ahead of the down- and upstroke reversals, at $t=0.4$ and $t=0.9$ respectively. At mid downstroke and upstroke ($t/T\sim 0.25$ and $\sim 0.75$), the velocity and effective angle of attack (eAoA) peak (supplementary Fig. S3A). As a result, the lift force peaks at these points in the cycle. The wing slows as it reaches stroke reversal, and the lift force predicted by the quasi-steady analysis approach zero. However, the measured lift drops to zero somewhat earlier in the wingbeat cycle.

This discrepancy between measured and predicted lift exposes one of the key weaknesses of the quasi-steady approach: it fails to account for the wake capture around the up- to downstroke reversal. At the end of downstroke, a leading edge vortex (LEV) forms on the dorsal side of the wing, [38, 39, 40]. This vortex contributes additional lift and, as long as it stays attached, can be modelled accurately by the quasi-steady approach using a generalized lift coefficient [41]. However, for large effective angles of attack, the vortex separates and when it moves away from the wing, the lift force drops precipitously. Simulations of vortex formation and shedding of a 2D airfoil have shown that for eAoA = 72^∘, the vortex is much stronger and sheds more quickly than for the case of eAoA = 4.5^∘, in which the core is weaker and remains attached [42]. Here, the eAoA at the 3/4-span section for the zero folding case ($\theta_{o}=0$) varies between -40 to 40 degrees (SFig. S3A). We suggest that at these points in the wingbeat cycle the LEV is likely shed into the wake, leading to the early drop in the lift coefficient, which is not captured by the low-order model.

For the case of 100^∘ wing folding, the amplitudes of the forces are accurately captured and the overall trends match well, but we do see significant differences between measurements and the model predictions (Fig. 4A4). In particular, at the start of the downstroke ($t/T\sim 0.1$), at the beginning of the upstroke ($t/T\sim 0.6$), and lastly mid-upstroke ($t/T\sim 0.8$). The first two of these points in the cycle can be explained using the same reasoning as with the straight wing. In this case, the cycle of the effective angle of attack of the wing, and its return to zero is delayed due to the kinematics of wing folding (supplementary Fig. S3B), and the eAoA is high ($\sim\pm 50^{\circ}$) at the stroke reversals ($t/T=0,0.5$) and does not drop to zero until $t=0.1$ and 0.7 respectively. As before, the quasi-steady analysis predicts zero lift when the eAoA is zero (as it should), while the measurements show that the lift has already dropped to zero ahead of the zero eAoA point due to the LEV separation.

At $t/T\sim 0.65$, during the upstroke of the high folding case, $\theta_{o}=100$, the wings are almost perpendicular to the ground (Fig. 3),leading to a near zero prediction of $C_{L}$ from the quasi-steady model. The direct force measurement demonstrates a negative trough at this time, which may be due to the LEV on the dorsal side of the wing that generates unfavorable (negative) lift as it separates into the wake. However, shortly after this, at $t/T\sim 0.8$ (stage iii in Fig. 3), while the model still predicts negligible lift due to the vertical orientation of the wing surfaces (Fig 3), the force measurements record a positive lift peak, also captured by the PIV measurements. This lift augmentation arises from wing clapping(Fig. 4B), as a brief jet of air is squeezed downwards, similar to jetting in swimming jellyfish or squid [32]. This momentary rise of $C_{L}$ due to wing clapping is not captured by the quasi-steady analysis, which cannot incorporate wing-wing interactions. The wing motors must provide extra energy to produce the jet and this additional power requirement is also absent from the quasi-steady model (Fig. 4A6, $t/T\sim 0.8$, see also snapshot iii in Fig. 3).

Birds and bats adjust wing folding amplitude with flight speed [3, 43, 6]. But among diverse robotic flyers, few studies have implemented wing folding [9, 10, 44, 21, 44]. Of these, Wissa et al. [10] employed passive mechanisms, while Send et al. [9] implemented active wing folding with fixed amplitude and timing. Chen et al. [21] used a string-based approach to actuate variable-amplitude wing folding and found that wing folding helps reduce negative lift during upstroke in hovering condition. Through PIV measurements along the streamwise center plane of their robots, they demonstrated that the folded wings in upstroke are free of the impact of low pressure region under the wings, which otherwise would contribute to more negative lift.

Without wing folding ($\theta_{o}=0$), the positive lift generated during the downstroke is balanced by the negative lift produced during the upstroke (Fig. 5A). For a given Strouhal number, $St$, as wing folding,$\theta_{o}$, increases, we observe two benefits. First, handwing effective velocity increases because of the additional rotation with respect to the armwing, and this enhanced velocity increases the local effective angle of attack. As a result, both factors can contribute to greater lift (snapshot ii, Fig. 4A4 and Fig. 3). Second, the effective wing surface area is reduced during upstroke, which alleviates negative lift, as has also been demonstrated in CFD simulations [45]. The additive effect of these factors results in net positive cycle-averaged lift, $C_{L}$, that increases with the folding amplitude, $\theta_{o}$, (Fig. 5A).

We observe a qualitatively distinct phenomenon when wing folding amplitude $\theta_{o}$ exceeds a certain threshold (see schematics in Fig. 4C). The handwing lags the armwing, and when the armwing transitions from down- to upstroke, the handwing continues through its ‘downstroke’ trajectory. The two wingtips move toward one another as they approach the midline, in a manner that can be described heuristically as “scooping” the air, producing a trough of negative lift (Fig. 4A4, between snapshots ii and iii). This phenomenon is also observed in small hovering birds [19, 20].

As the handwings approach and ultimately clap (Fig. 4B), air is propelled dorsally and ventrally from the small gap between the wings (Fig. 4C). The net effect is a downward, ventral, momentum jet that produces positive lift, comparable in magnitude to that generated during downstroke (Fig. 4A4). In contrast, when Gouldian Finches clap, they position their wings to prevent dorsally-directed air movement [20]).

The wingtips separate after the clap and are re-positioned prior to the next downstroke (snapshot iv, Fig. 4A4). With no modification of the movement, this preparatory movement could incur a substantial negative lift penalty, however, birds and bats adopt similar mitigation strategies. In both groups, the handwing supinates (rotates about the spanwise, long axis in the palm-upward direction) at the wrist and the wing retracts along the span by flexion at the elbow. The posture of the handwing may come close to a vertical plane before moving dorsally – as it “slices” through air – during the upstroke [46, 4, 2, 7]. Upstroke kinematics of bats and birds reduce negative lift [19, 39, 2] and generate a small amount of thrust [36, 47]. The wings of Flapperoo presented in this manuscript can neither twist nor retract, and the resulting unfavorable orientation of wing surfaces during rapid upstrokes leads to substantial negative lift. However, we did then designed, built and tested a Flapperoo with twisting capability, and found that twisting significantly decreased both power consumption, and negative lift during upstroke (accepted to present in IROS 2024, arXiv link [48]).

In summary, two different mechanism to obtain optimal efficiency, characterized by power economy, are displayed here, and we may classify them as symmetry-breaking lift augmentation (small folding amplitude $\theta_{o}$) and appendage-based jet propulsion (extreme folding amplitude $\theta_{o}$). At low speed or high $St$ (Fig. 5B), it takes extra effort to actuate large wing folding to effect air jet for extra lift, thus the symmetry-breaking strategy (moderate folding amplitude $\theta_{o}\sim 30^{\circ}$ ) is more cost effective, in terms of $C_{L}/C_{P}$; on the other hand, for fast flight speed or low $St$, while symmetry-breaking strategy is still rewarding, jet propulsion with large folding angle becomes much more efficient (Fig. 6). It is remarkable to note that flapping wing flight has both strategies at its disposal.

The characteristic “clap-and-fling” mechanism of insects and slowly flying birds [49, 37, 50] relies on the two wings coming together during the wingbeat cycle, but it differs fundamentally from the ventral clapping motion considered here. In clap-and-fling, the ‘fling’ part of the motion generates thrust and enhances lift by augmenting circulation around the wing during early downstroke on the dorsal side [37]. The ventral clapping mechanism that we describe here generates lift during upstroke by producing a directed jet of air.

In both clap-and-fling and ventral wing clapping, however, negative lift is produced as a result of an upward jet, which can persist before and during the clapping ($C_{L}$ of case $\theta_{o}=100$, Fig. 4A4) [20, 37], Fig. 4B). The magnitude of net lift increase for insects, due to clap-and-fling, is small (Fig. 4 in [37]), whereas we observe a more substantial boost, with a peak in the clapping-derived lift force comparable to that generated during the downstroke. This distinction might be due to differences in the swept area. In clap-and-fling, the wings simultaneously rotate and translate (panel M-P in Fig. 7 in [37]) so that the leading edge of the wings meet first, subsequently ”squeezing” air out at the trailing edge. However, the volume of air trapped during this motion is much less than that the corresponding volume of air trapped by Flapperoo, where the armwings never come close and the handwings are on opposite sides of the relatively large body.

The potential benefits of ventral wing clapping, as demonstrated here, may inform future design of flapping wing robots with high payload or endurance requirements. Wing folding in birds and bats is implemented primarily by flexion and extension at the wrist joint [51, 52].

Even though a passively wrist joint with well-tuned stiffness to a specific speed may achieve beneficial folding angles, the flight efficiency may not adapt to the speed changes.For example, the cycle-averaged power consumption of one passively deforming, bird-inspired ornithopter, Park Hawk [53], was approximately $60W$, which is considerably higher than the $20W$ power requirement reported for SmartBird, a seagull-inspired robot that performs active wing folding and twist [9, 10], even though SmartBird has a greater wingspan and weighs more than Park Hawk. Here, we find that the cycle-averaged lift increases monotonically with wing folding angle across $St=0.2-0.4$ (Fig. 5A). This translates directly to the capacity to carry larger payloads, and suggests that the energetic penalty for actuating the wing folding motion provides an effective compromise between generating lift and energetic cost (Fig. 5B).

The controlled, selective variation in wing folding angles with flight speed by birds and bats [3, 5, 43], suggests that a flexible capability to modulate lift generation relative to energetic cost confers performance benefits. Adjustable folding angle could be incorporated in future designs for flapping wing robots to enhance their performance. For example, when agility is important, such as when navigating through a tight turn, an instantaneous boost of lift conferred by wing clapping might provide additional benefits with little impact on overall energetics due to the brief and temporary increase in power consumption. Moreover, ventral clapping is observed during fast flight ($U=7.4$ m/s or $St$ ~ $0.2$ [5]) in Cynopterus brachyotis, where larger thrust is likely required to overcome high drag.

Indeed, the next generation of Flapperoo is also able to perform wing twists [48], and demonstrates the air jet due to ventral wing clapping, as discussed in this paper, can be directed wing angling at the moment of clap, where the leading edge almost touch but the trailing edge positioned slightly apart. This angled clapping produce streamwise propulsion (thrust) in addition to lift. This novel appendage-based propulsion offers many great opportunities to further probe into the optimal wing kinematics involving highly unsteady vortex dynamics, and also offers new control authority in both lift and thrust directions.