Wingbeat Period Research Articles

Phylogenetic and kinematic constraints on avian flight signals.

Many birds vocalize in flight. Because wingbeat and respiratory cycles are often linked in flying vertebrates, birds in these cases must satisfy the respiratory demands of vocal production within the physiological limits imposed by flight. Using acoustic triangulation and high-speed video, we found that avian vocal production in flight exhibits a largely phasic and kinematic relationship with the power stroke. However, the sample of species showed considerable flexibility, especially those from lineages known for vocal plasticity (songbirds, parrots and hummingbirds), prompting a broader phylogenetic analysis. We thus collected data from 150 species across 12 avian orders and examined the links between wingbeat period, flight call duration and body mass. Overall, shorter wingbeat periods, controlling for ancestry and body mass, were correlated with shorter flight call durations. However, species from vocal learner lineages produced flight signals that, on average, exceeded multiple phases of their wingbeat cycle, while vocal non-learners had signal periods that were, on average, closer to the duration of their power stroke. These results raise an interesting question: is partial emancipation from respiratory constraints a necessary step in the evolution of vocal learning or an epiphenomenon? Our current study cannot provide the answer, but it does suggest several avenues for future research.

Optimizing the structure and movement of a robotic bat with biological kinematic synergies

In this article, we present methods to optimize the design and flight characteristics of a biologically inspired bat-like robot. In previous, work we have designed the topological structure for the wing kinematics of this robot; here we present methods to optimize the geometry of this structure, and to compute actuator trajectories such that its wingbeat pattern closely matches biological counterparts. Our approach is motivated by recent studies on biological bat flight that have shown that the salient aspects of wing motion can be accurately represented in a low-dimensional space. Although bats have over 40 degrees of freedom (DoFs), our robot possesses several biologically meaningful morphing specializations. We use principal component analysis (PCA) to characterize the two most dominant modes of biological bat flight kinematics, and we optimize our robot’s parametric kinematics to mimic these. The method yields a robot that is reduced from five degrees of actuation (DoAs) to just three, and that actively folds its wings within a wingbeat period. As a result of mimicking synergies, the robot produces an average net lift improvesment of 89% over the same robot when its wings cannot fold.

Hovering and forward flight of the hawkmoth Manduca sexta: trim search and 6-DOF dynamic stability characterization

We show that the forward flight speed affects the stability characteristics of the longitudinal and lateral dynamics of a flying hawkmoth; dynamic modal structures of both the planes of motion are altered due to variations in the stability derivatives. The forward flight speed ue is changed from 0.00 to 1.00 m s−1 with an increment of 0.25 m s−1. (The equivalent advance ratio is 0.00 to 0.38; the advance ratio is the ratio of the forward flight speed to the average wing tip speed.) As the flight speed increases, for the longitudinal dynamics, an unstable oscillatory mode becomes more unstable. Also, we show that the up/down (wb) dynamics become more significant at a faster flight speed due to the prominent increase in the stability derivative Zu (up/down force due to the forward/backward velocity). For the lateral dynamics, the decrease in the stability derivative Lv (roll moment due to side slip velocity) at a faster flight speed affects a slightly damped stable oscillatory mode, causing it to become more stable; however, the thalf (the time taken to reach half the amplitude) of this slightly damped stable oscillatory mode remains relatively long (∼12T at ue = 1 m s−1; T is wingbeat period) compared to the other modes of motion, meaning that this mode represents the most vulnerable dynamics among the lateral dynamics at all flight speeds. To obtain the stability derivatives, trim conditions for linearization are numerically searched to find the exact trim trajectory and wing kinematics using an algorithm that uses the gradient information of a control effectiveness matrix and fully coupled six-degrees of freedom nonlinear multibody equations of motion. With this algorithm, trim conditions that consider the coupling between the dynamics and aerodynamics can be obtained. The body and wing morphology, and the wing kinematics used in this study are based on actual measurement data from the relevant literature. The aerodynamic model of the flapping wings of a hawkmoth is based on the blade element theory, and the necessary aerodynamic coefficients, including the lift, drag and wing pitching moment, are experimentally obtained from the results of previous work by the authors.

Control of a Minimally Actuated Biomimetic Vehicle Using Quarter-Cycle Wingbeat Modulation

This paper describes a technique, called quarter-cycle constant period frequency modulation, to control the motion of wings on a flapping wing micro-air vehicle. This technique allows control over the wingbeat period and three additional points (the two zero crossings and the reversal of wing direction) within a single wingbeat cycle, allowing modulation of the wing’s velocity to provide direct control over six degrees of freedom of overall vehicle motion. Using a blade element based aerodynamic model, both instantaneous and cycle-averaged forces and moments are analytically computed for a specific type of wingbeat motion that enables nearly decoupled, multi-degrees of freedom control of an aircraft. Wing motion is controlled using oscillators whose frequencies and three additional parameters change once per wingbeat cycle. A control oriented dynamic model of the vehicle is derived, which is based on a cycle-averaged representation of the forces and moments, and control derivatives are calculated. A cycle-averaged control law is designed to provide direct control over six degrees of freedom of the vehicle.

Erratum to: Dynamic flight stability of hovering model insects: theory versus simulation using equations of motion coupled with Navier-Stokes equations

In the present paper, the longitudinal dynamic flight stability properties of two model insects are predicted by an approximate theory and computed by numerical simulation. The theory is based on the averaged model (which assumes that the frequency of wingbeat is sufficiently higher than that of the body motion, so that the flapping wings’ degrees of freedom relative to the body can be dropped and the wings can be replaced by wingbeat-cycle-average forces and moments); the simulation solves the complete equations of motion coupled with the Navier–Stokes equations. Comparison between the theory and the simulation provides a test to the validity of the assumptions in the theory. One of the insects is a model dronefly which has relatively high wingbeat frequency (164 Hz) and the other is a model hawkmoth which has relatively low wingbeat frequency (26 Hz). The results show that the averaged model is valid for the hawkmoth as well as for the dronefly. Since the wingbeat frequency of the hawkmoth is relatively low (the characteristic times of the natural modes of motion of the body divided by wingbeat period are relatively large) compared with many other insects, that the theory based on the averaged model is valid for the hawkmoth means that it could be valid for many insects.

The effect of body size on the wing movements of pteropodid bats, with insights into thrust and lift production

In this study we compared the wing kinematics of 27 bats representing six pteropodid species ranging more than 40 times in body mass (M(b)=0.0278-1.152 kg), to determine whether wing posture and overall wing kinematics scaled as predicted according to theory. The smallest species flew in a wind tunnel and the other five species in a flight corridor. Seventeen kinematic markers on the midline and left side of the body were tracked in three dimensions. We used phylogenetically informed reduced major axis regression to test for allometry. We found that maximum wingspan (b(max)) and maximum wing area (S(max)) scaled with more positive allometry, and wing loading (Q(s)) with more negative allometry (b(max)∝M(b)(0.423); S(max)∝M(b)(0.768); Q(s)∝M(b)(0.233)) than has been reported in previous studies that were based on measurements from specimens stretched out flat on a horizontal surface. Our results suggest that larger bats open their wings more fully than small bats do in flight, and that for bats, body measurements alone cannot be used to predict the conformation of the wings in flight. Several kinematic variables, including downstroke ratio, wing stroke amplitude, stroke plane angle, wing camber and Strouhal number, did not change significantly with body size, demonstrating that many aspects of wing kinematics are similar across this range of body sizes. Whereas aerodynamic theory suggests that preferred flight speed should increase with mass, we did not observe an increase in preferred flight speed with mass. Instead, larger bats had higher lift coefficients (C(L)) than did small bats (C(L)∝M(b)(0.170)). Also, the slope of the wingbeat period (T) to body mass regression was significantly more shallow than expected under isometry (T∝M(b)(0.180)), and angle of attack (α) increased significantly with body mass [α∝log(M(b))7.738]. None of the bats in our study flew at constant speed, so we used multiple regression to isolate the changes in wing kinematics that correlated with changes in flight speed, horizontal acceleration and vertical acceleration. We uncovered several significant trends that were consistent among species. Our results demonstrate that for medium- to large-sized bats, the ways that bats modulate their wing kinematics to produce thrust and lift over the course of a wingbeat cycle are independent of body size.

Dynamic flight stability of hovering model insects: theory versus simulation using equations of motion coupled with Navier–Stokes equations

In the present paper, the longitudinal dynamic flight stability properties of two model insects are predicted by an approximate theory and computed by numerical simulation. The theory is based on the averaged model (which assumes that the frequency of wingbeat is sufficiently higher than that of the body motion, so that the flapping wings’ degrees of freedom relative to the body can be dropped and the wings can be replaced by wingbeat-cycle-average forces and moments); the simulation solves the complete equations of motion coupled with the Navier–Stokes equations. Comparison between the theory and the simulation provides a test to the validity of the assumptions in the theory. One of the insects is a model dronefly which has relatively high wingbeat frequency (164 Hz) and the other is a model hawkmoth which has relatively low wingbeat frequency (26 Hz). The results show that the averaged model is valid for the hawkmoth as well as for the dronefly. Since the wingbeat frequency of the hawkmoth is relatively low (the characteristic times of the natural modes of motion of the body divided by wingbeat period are relatively large) compared with many other insects, that the theory based on the averaged model is valid for the hawkmoth means that it could be valid for many insects.

Dynamic flight stability of a hovering model insect: lateral motion

The lateral dynamic flight stability of a hovering model insect (dronefly) was studied using the method of computational fluid dynamics to compute the stability derivatives and the techniques of eigenvalue and eigenvector analysis for solving the equations of motion. The main results are as following. (i) Three natural modes of motion were identified: one unstable slow divergence mode (mode 1), one stable slow oscillatory mode (mode 2), and one stable fast subsidence mode (mode 3). Modes 1 and 2 mainly consist of a rotation about the horizontal longitudinal axis (x-axis) and a side translation; mode 3 mainly consists of a rotation about the x-axis and a rotation about the vertical axis. (ii) Approximate analytical expressions of the eigenvalues are derived, which give physical insight into the genesis of the natural modes of motion. (iii) For the unstable divergence mode, t d, the time for initial disturbances to double, is about 9 times the wingbeat period (the longitudinal motion of the model insect was shown to be also unstable and t d of the longitudinal unstable mode is about 14 times the wingbeat period). Thus, although the flight is not dynamically stable, the instability does not grow very fast and the insect has enough time to control its wing motion to suppress the disturbances.

Automated hull reconstruction motion tracking (HRMT) applied to sideways maneuvers of free-flying insects

Flying insects perform aerial maneuvers through slight manipulations of their wing motions. Because such manipulations in wing kinematics are subtle, a reliable method is needed to properly discern consistent kinematic strategies used by the insect from inconsistent variations and measurement error. Here, we introduce a novel automated method that accurately extracts full, 3D body and wing kinematics from high-resolution films of free-flying insects. This method combines visual hull reconstruction, principal components analysis, and geometric information about the insect to recover time series data of positions and orientations. The technique has small, well-characterized errors of under 3 pixels for positions and 5 deg. for orientations. To show its utility, we apply this motion tracking to the flight of fruit flies, Drosophila melanogaster. We find that fruit flies generate sideways forces during some maneuvers and that strong lateral acceleration is associated with differences between the left and right wing angles of attack. Remarkably, this asymmetry can be induced by simply altering the relative timing of flips between the right and left wings, and we observe that fruit flies employ timing differences as high as 10% of a wing beat period while accelerating sideways at 40% g.

Dynamic flight stability of a hovering bumblebee

The longitudinal dynamic flight stability of a hovering bumblebee was studied using the method of computational fluid dynamics to compute the aerodynamic derivatives and the techniques of eigenvalue and eigenvector analysis for solving the equations of motion. For the longitudinal disturbed motion, three natural modes were identified: one unstable oscillatory mode, one stable fast subsidence mode and one stable slow subsidence mode. The unstable oscillatory mode consists of pitching and horizontal moving oscillations with negligible vertical motion. The period of the oscillations is 0.32 s (approx. 50 times the wingbeat period of the bumblebee). The oscillations double in amplitude in 0.1 s; coupling of nose-up pitching with forward horizontal motion (and nose-down pitching with backward horizontal motion) in this mode causes the instability. The stable fast subsidence mode consists of monotonic pitching and horizontal motions, which decay to half of the starting values in 0.024 s. The stable slow subsidence mode is mainly a monotonic descending (or ascending) motion, which decays to half of its starting value in 0.37 s. Due to the unstable oscillatory mode, the hovering flight of the bumblebee is dynamically unstable. However, the instability might not be a great problem to a bumblebee that tries to stay hovering: the time for the initial disturbances to double (0.1 s) is more than 15 times the wingbeat period (6.4 ms), and the bumblebee has plenty of time to adjust its wing motion before the disturbances grow large.

MODULATION OF NEGATIVE WORK OUTPUT FROM A STEERING MUSCLE OF THE BLOWFLY CALLIPHORA VICINA

Of the 17 muscles responsible for flight control in flies, only the first basalar muscle (b1) is known to fire an action potential each and every wing beat at a precise phase of the wing-beat period. The phase of action potentials in the b1 is shifted during turns, implicating the b1 in the control of aerodynamic yaw torque. We used the work loop technique to quantify the effects of phase modulation on the mechanical output of the b1 of the blowfly Calliphora vicina. During cyclic length oscillations at 10 and 50 Hz, the magnitude of positive work output by the b1 was similar to that measured previously from other insect muscles. However, when tested at wing-beat frequency (150 Hz), the net work performed in each cycle was negative. The twitch kinetics of the b1 suggest that negative work output reflects intrinsic specializations of the b1 muscle. Our results suggest that, in addition to a possible role as a passive elastic element, the phase-sensitivity of its mechanical properties may endow the b1 with the capacity to modulate wing-beat kinematics during turning maneuvers.

Temperature dependence and response characteristics of the isolated wing hinge stretch receptor in the locust

1. A preparation is described by which the wing hinge stretch receptor (SR) ofLocusta migratoria is mechanically isolated so that it can be subjected to stretch stimuli while avoiding interference with wing hinge mechanics. 2. Using this approach and sinusoidal stretches of different amplitudes the SR can be stimulated up to a definite saturation frequency. The discharge frequency at a given stretch and the saturation frequency both depend dramatically on ambient temperature. High instantaneous frequencies (up to 650 Hz, as found in flying locusts) were only obtained at a high temperature of 32 °C. 3. The instantaneous spike frequency of the SR in response to short stretches (within the time range of wing beat period) reflects exactly the amount of the stretch and not its rate of change. Thus, the SR is a receptor signalling the momentary position of the sclerites to which it is attached.

Proprioceptive feedback dominates the central oscillator in the patterning of the flight motoneuron output inTipula (Diptera)

1. Action potentials were recorded from units of the indirect power flight muscles dvm1 and dlm of tethered flying crane flies (Tipula paludosa). The normal wingbeat frequencies of the animals were in the range of about 50 to 60 Hz. By mutilating or loading the wings the wingbeat frequencies could be adjusted to any values between 25 Hz and 160 Hz. 2. There is a strong tendency for the action potentials to be phase-locked with respect to the wingbeat period at all wingbeat frequencies up to about 120 Hz (Figs. 4, 5). This holds true in spite of the fact that the action potentials do not occur in every wingbeat period (Fig. 6). Thus, wingbeat synchronous afferences influence phasically (trigger) the production of spikes in the output systems. -The dvm1-units and the dlm-units fire at different phase bands within the wingbeat period. 3. If both wing nerve afferences are disrupted then in most cases only very short flights can be initiated. It can be concluded that these afferences are involved in the maintenance of flight. Prolonged flights can be elicited only exceptionally. In all cases, however, the tendency of the spikes to accumulate at small phase bands within the wingbeat cycle is drastically reduced (Fig. 8). Thus, wingbeat synchronous afferences travelling along the wing nerves contain important timing cues for the production of the neuromotor output. 4. In the absence of wing nerve afferences the motor output systems supplying the flight muscle units of the dvml and the dlm, respectively, fire with their own inherent rhythm; the occurrences of spikes in the dlm are strongly correlated with the occurrences of spikes in the dvm1 and vice versa (Figs. 11B, 12). This demonstrates the existence of a central nervous mechanism which is able to produce a rhythmic motor output autonomously. -Under physiological conditions, however, the endogenous rhythm is overridden by timing cues from wingbeat synchronous afferences. 5. The neural output driving the indirect flight muscles inTipula is compared with the neural output supplying the flight muscles in “higher” Diptera on the one hand and in locusts on the other. It is suggested that the tipulid flight motor system represents an early stage in the evolution of the highly specialized systems of the “higher” Diptera. -Some features of the flight motor in Diptera are summarized in a block diagram (Fig. 13).

Proprioceptive input on the locust flight motor revealed by muscle stimulation

1. The locust is suspended in the laminar air stream of an open jet wind tunnel. During flight the 1st basalar muscle of the hindwing (M127) or of the forewing (M97) is stimulated every 6th or 8th wing beat with a single electric pulse triggered by simultaneously recorded action potentials of another downstroke muscle. The exact time relationship of the stimulus relative to the wing beat cycle is varied systematically (Fig. 1). 2. In response to the electric stimulus the time of occurrence of other downstroke muscles changes slightly depending on the phase of the stimulus respective to the wing beat period. Stimulation of M127 (hindwing) leads to the following results: all recorded muscles react qualitatively in the same manner. If the stimulus occurs during the downstroke phase (first half of wing beat period) up to 3 subsequent wing beat intervals in the direct downstroke muscles are slightly elongated (Fig. 2). If the stimulus occurs during the upstroke phase the next following interval is decreased and the subsequent interval slightly increased (Fig. 3). 3. If the stimulated muscle is cut near its apodeme at the wing hinge region the influence of the stimulus on the other muscles vanishes (Fig. 6). Thus, the effect depends on the mechanical action of the stimulated muscle on the wing hinge. Therefore, the possibility is excluded that the antidromic spike evoked in the motor axon of the stimulated muscle is responsible for the described reactions. 4. The latency between the stimulus and the next influenced muscle action potential may be as short as 20 ms (Fig. 7). 5. Stimulation of the forewing 1st basalar muscle shows reactions which are different from animal to animal. In contrast to the “hindwing stimulation” different muscles may react differently to a particular stimulus (Fig. 8). 6. The general conclusion which can be drawn is that the sensory equipment of the wing and wing hinge region monitors wing movement quite specifically and exerts subtle influences on motor elements of the flight system.

Co-ordinating interneurones of the locust which convey two patterns of motor commands: their connexions with flight motoneurones.

1. Some flight motoneurones receive two superimposed rhythms of depolarizing synaptic potentials when the locust is not flying; a slow rhythm which is invariably linked to the expiratory phase of ventilation, and a fast rhythm with a period of about 50 ms which is similar to the wingbeat period in flight. 2. By recording simultaneously from groups of motoneurones, the synaptic potentials which underly these rhythms have been revealed in 30 flight motoneurones in the three thoracic ganglia. The inputs occur in elevator motoneurones and some depressors but are of lower amplitude in the latter. The inputs have not been found in leg motoneurones. 3. The rhythmic depolarizations are usually subthreshold but sum with sensory inputs to evoke spikes in flight motoneurones at intervals equal to or multiples of the wingbeat period in flight. 4. Both rhythms originate in the metathoracic ganglion and are mediated by the same interneurones. They can be adequately explained by supposing that there are two symmetrical interneurones which each make widespread connexions with left and right flight motoneurones in the three ganglia. 5. The slow rhythm is coded in the overall burst of interneurone spikes during expiration and the fast rhythm in the interval between the spikes of a burst.

The role of delayed excitation in the co-ordination of some metathoracic flight motoneurons of a locust

Intracellular recordings have been made from the somata of two metathoracic flight motoneurons, one innervating an elevator muscle of the hindwing, the tergosternal muscle 113 and the other a depressor, the first basalar muscle 127. The locust,Ghortoicetes terminifera was mounted ventral side uppermost with the thorax restrained and opened for access to the thoracic ganglia. Patterns of electrical activity recorded from the thoracic muscles were similar to those shown by a locust during flight when tethered in a more normal posture. In flight the left and right 113 motoneurons each receive a single impulse together at every stroke of the wing, with the 127 muscles active in approximate antiphase. A spike in a 113 motoneuron causes a delayed wave of excitation simultaneously upon itself and its contralateral partner (Fig. 2). The epsp's which form these waves summate and may cause a spike which follows the original one with a delay equal to the wingbeat period. The delayed excitation of the contralateral motoneuron is of larger amplitude than the ipsilateral one so that spikes in either motoneuron must activate separate but symmetrical pathways. A single spike may cause multiple waves in either motoneuron, each separated by intervals equal to the wingbeat period (Fig. 3). In the pathway must be neurons capable of reverberation.

Muscle activity during flight in some large Lepidoptera.

ABSTRACT The names and functions of the main mesothoracic flight muscles in Lepidoptera are reviewed. The wingbeat period in satumiid moths and monarch butterflies is long and variable. The three parameters, wingbeat period, burst length (number of times a motor unit is activated per wingstroke) and stroke amplitude are interdependent and positively correlated. Partial amputation of the wings in satumiids decreases wingbeat period. Cutting the sensory nerves from the wings increases the period. These results indicate that the influence of wing movement on wingbeat period is mediated by receptors near the base of the wing. The central nervous mechanisms which generate motor patterns during flight in Lepidoptera are discussed and compared with those in locusts. It is proposed that both mechanisms can be described by a single model, with minor differences in the mechanism of burst production.