Stroke Plane Angle Research Articles

Allometry of kinematics and energetics in carpenter bees (Xylocopa varipuncta)hovering in variable-density gases

We assessed the energetic and aerodynamic limits of hovering flight in the carpenter bee Xylocopa varipuncta. Using normoxic, variable-density mixtures of O(2), N(2) and He, we were able to elicit maximal hovering performance and aerodynamic failure in the majority of bees sampled. Bees were not isometric regarding thorax mass and wing area, both of which were disproportionately lower in heavier individuals. The minimal gas density necessary for hovering (MGD) increased with body mass and decreased with relative thoracic muscle mass. Only the four bees in our sample with the highest body mass-specific thorax masses were able to hover in pure heliox. Wingbeat frequency and stroke amplitude during maximal hovering were significantly greater than in normodense hovering, increased significantly with body mass during normodense hovering but were mass independent during maximal hovering. Reserve capacity for wingbeat frequency and stroke amplitude decreased significantly with increasing body mass, although reserve capacity in stroke amplitude (10-30%) exceeded that of wingbeat frequency (0-8%). Stroke plane angle during normodense hovering was significantly greater than during maximal hovering, whereas body angle was significantly greater during maximal hovering than during normodense hovering. Power production during normodense hovering was significantly less than during maximal hovering. Metabolic rates were significantly greater during maximal hovering than during normodense hovering and were inversely related to body mass during maximal and normodense hovering. Metabolic reserve capacity averaged 34% and was independent of body mass. Muscle efficiencies were slightly higher during normodense hovering. The allometry of power production, power reserve capacity and muscle efficiency were dependent on the assumed coefficient of drag (C(D)), with significant allometries most often at lower values of C(D). Larger bees operate near the envelope of maximal performance even in normodense hovering due to smaller body mass-specific flight muscles and limited reserve capacities for kinematics and power production.

Hovering flight mechanics of neotropical flower bats (Phyllostomidae: Glossophaginae) in normodense and hypodense gas mixtures.

Existing estimates of flight energetics in glossophagine flower bats, the heaviest hovering vertebrate taxon, suggest disproportionately high expenditure of mechanical power. We determined wingbeat kinematics and mechanical power expenditure for one of the largest flower bats (Leptonycteris curasoae Martinez and Villa) during hovering flight in normodense and hypodense gas mixtures. Additional experiments examined the effects of supplemental oxygen availability on maximum flight performance. Bats failed to sustain hovering flight at normoxic air densities averaging 63% that of normodense air. Kinematic responses to hypodense aerodynamic challenge involved increases in wing positional angles and in total stroke amplitude; wingbeat frequency was unchanged. At near-failure air densities, total power expenditure assuming perfect elastic energy storage was 17-42% greater than that for hovering in normodense air, depending on the assumed value for the profile drag coefficient. Assuming a flight muscle ratio of 26%, the associated muscle-mass-specific power output at the point of near-failure varied between 90.8 W kg(-1) (profile drag coefficient of 0.02) to 175.6 W kg(-1) (profile drag coefficient of 0.2). Hyperoxia did not enhance hovering performance in hypodense air, and, with the exception of a small increase (10%) in stroke plane angle, yielded no significant change in any of the kinematic parameters studied. Revised energetic estimates suggest that mechanical power expenditure of hovering glossophagines is comparable with that in slow forward flight.

Kinematics of flap-bounding flight in the zebra finch over a wide range of speeds

ABSTRACTIt has been proposed elsewhere that flap-bounding, an intermittent flight style consisting of flapping phases interspersed with flexed-wing bounds, should offer no savings in average mechanical power relative to continuous flapping unless a bird flies 1.2 times faster than its maximum range speed (Vmr). Why do some species use intermittent bounds at speeds slower than 1.2Vmr The ‘fixed-gear hypothesis’ suggests that flap-bounding is used to vary mean power output in small birds that are otherwise constrained by muscle physiology and wing anatomy to use a fixed muscle shortening velocity and pattern of wing motion at all flight speeds; the ‘body-lift hypothesis’ suggests that some weight support during bounds could make flap-bounding flight aerodynamically advantageous in comparison with continuous flapping over most forward flight speeds. To test these predictions, we studied high-speed film recordings (300 Hz) of wing and body motion in zebra finches (Taenopygia guttata, mean mass 13.2 g, N=4) taken as the birds flew in a variable-speed wind tunnel (0–14 m s−1). The zebra finches used flap-bounding flight at all speeds, so their flight style was unique compared with that of birds that facultatively shift from continuous flapping or flap-gliding at slow speeds to flap-bounding at fast speeds. There was a significant effect of flight speed on all measured aspects of wing motion except percentage of the wingbeat spent in downstroke. Changes in angular velocity of the wing indicated that contractile velocity in the pectoralis muscle changed with flight speed, which is not consistent with the fixed-gear hypothesis. Although variation in stroke-plane angle relative to the body, pronation angle of the wing and wing span at mid-upstroke showed that the zebra finch changed within-wingbeat geometries according to speed, a vortex-ring gait with a feathered upstroke appeared to be the only gait used during flapping. In contrast, two small species that use continuous flapping during slow flight (0–4 m s−1) either change wingbeat gait according to flight speed or exhibit more variation in stroke-plane and pronation angles relative to the body. Differences in kinematics among species appear to be related to wing design (aspect ratio, skeletal proportions) rather than to pectoralis muscle fiber composition, indicating that the fixed-gear hypothesis should perhaps be modified to exclude muscle physiology and to emphasize constraints due to wing anatomy. Body lift was produced during bounds at speeds from 4 to 14m s−1. Maximum body lift was 0.0206 N (15.9 % of body weight) at 10 m s−1; body lift:drag ratio declined with increasing air speed. The aerodynamic function of bounds differed with increasing speed from an emphasis on lift production (4–10 m s−1) to an emphasis on drag reduction with a slight loss in lift (12 and 14 m s−1). From a mathematical model of aerodynamic costs, it appeared that flap-bounding offered the zebra finch an aerodynamic advantage relative to continuous flapping at moderate and fast flight speeds (6–14 m s−1), with body lift augmenting any savings offered solely by flap-bounding at speeds faster than 7.1 m s−1. The percentage of time spent flapping during an intermittent flight cycle decreased with increasing speed, so the mechanical cost of transport was likely to be lowest at faster flight speeds (10–14 m s−1).

A computational fluid dynamic study of hawkmoth hovering

A computational fluid dynamic (CFD) modelling approach is used to study the unsteady aerodynamics of the flapping wing of a hovering hawkmoth. We use the geometry of a Manduca sexta-based robotic wing to define the shape of a three-dimensional 'virtual' wing model and 'hover' this wing, mimicking accurately the three-dimensional movements of the wing of a hovering hawkmoth. Our CFD analysis has established an overall understanding of the viscous and unsteady flow around the flapping wing and of the time course of instantaneous force production, which reveals that hovering flight is dominated by the unsteady aerodynamics of both the instantaneous dynamics and also the past history of the wing. <P> A coherent leading-edge vortex with axial flow was detected during translational motions of both the up- and downstrokes. The attached leading-edge vortex causes a negative pressure region and, hence, is responsible for enhancing lift production. The axial flow, which is derived from the spanwise pressure gradient, stabilises the vortex and gives it a characteristic spiral conical shape. <P> The leading-edge vortex created during previous translational motion remains attached during the rotational motions of pronation and supination. This vortex, however, is substantially deformed due to coupling between the translational and rotational motions, develops into a complex structure, and is eventually shed before the subsequent translational motion. <P> Estimation of the forces during one complete flapping cycle shows that lift is produced mainly during the downstroke and the latter half of the upstroke, with little force generated during pronation and supination. The stroke plane angle that satisfies the horizontal force balance of hovering is 23.6 degrees , which shows excellent agreement with observed angles of approximately 20-25 degrees . The time-averaged vertical force is 40 % greater than that needed to support the weight of the hawkmoth.

The mechanics of flight in the hawkmoth Manduca sexta. I. Kinematics of hovering and forward flight.

High-speed videography was used to record sequences of individual hawkmoths in free flight over a range of speeds from hovering to 5 ms-1. At each speed, three successive wingbeats were subjected to a detailed analysis of the body and wingtip kinematics and of the associated time course of wing rotation. Results are presented for one male and two female moths. The clearest kinematic trends accompanying increases in forward speed were an increase in stroke plane angle and a decrease in body angle. The latter may have resulted from a slight dorsal shift in the area swept by the wings as the supination position became less ventral with increasing speed. These trends were most pronounced between hovering and 3 ms-1, and the changes were gradual; there was no distinct gait change of the kind observed in some vertebrate fliers. The wing rotated as two functional sections: the hindwing and the portion of the forewing with which it is in contact, and the distal half of the forewing. The latter displayed greater fluctuation in the angle of rotation, especially at the lower speeds. As forward speed increased, the discrepancy between the rotation angles of the two halfstrokes, and of the two wing sections, became smaller. The downstroke wing torsion was set early in the halfstroke and then held constant during the translational phase.

Flight kinematics of black-billed magpies and pigeons over a wide range of speeds

To investigate how birds that differ in morphology change their wing and body movements while flying at a range of speeds, we analyzed high-speed (60 Hz) video tapes of black-billed magpies (Pica pica) flying at speeds of 4-14 m s-1 and pigeons (Columba livia) flying at 6-20 m s-1 in a wind-tunnel. Pigeons had higher wing loading and higher-aspect-ratio wings compared with magpies. Both species alternated phases of steady-speed flight with phases of acceleration and deceleration, particularly at intermediate flight speeds. The birds modulated their wingbeat kinematics among these phases and frequently exhibited non-flapping phases while decelerating. Such modulation in kinematics during forward flight is typical of magpies but not of pigeons in the wild. The behavior of the pigeons may have been a response to the reduced power costs for flight in the closed wind-tunnel relative to those for free flight at similar speeds. During steady-speed flight, wingbeat frequency did not change appreciably with increasing flight speed. Body angle relative to the horizontal, the stroke-plane angles of the wingtip and wrist relative to the horizontal and the angle describing tail spread at mid-downstroke all decreased with increasing flight speed, thereby illustrating a shift in the dominant function of wing flapping from weight support at slow speeds to positive thrust at fast speeds. Using wingbeat kinematics to infer lift production, it appeared that magpies used a vortex-ring gait during steady-speed flight at all speeds whereas pigeons used a vortex-ring gait at 6 and 8 m s-1, a transitional vortex-ring gait at 10 m s-1, and a continuous-vortex gait at faster speeds. Both species used a vortex-ring gait for acceleration and a continuous-vortex gait or a non-flapping phase for deceleration during flight at intermediate wind-tunnel speeds. Pigeons progressively flexed their wings during glides as flight speed increased but never performed bounds. Wingspan during glides in magpies did not vary with flight speed, but the percentage of bounds among non-flapping intervals increased with speed from 10 to 14 m s-1. The use of non-flapping wing postures seemed to be related to the gaits used during flapping and to the aspect ratio of the wings. We develop an 'adverse-scaling' hypothesis in which it is proposed that the ability to reduce metabolic and mechanical power output using flap-bounding flight at fast flight speeds is scaled negatively with body mass. This represents an alternative to the 'fixed-gear' hypothesis previously suggested by other authors to explain the use of intermittent flight in birds. Future comparative studies in the field would be worthwhile, especially if instantaneous flight speeds and within-wingbeat kinematics were documented; new studies in the laboratory should involve simultaneous recording of wing kinematics and aerodynamic forces on the wing.

Biomechanics of Flight in Neotropical Butterflies: Morphometries and Kinematics

ABSTRACT Wing and body kinematics of free cruising flight are described for 37 species of Panamanian butterflies ranging over two orders of magnitude in body mass. Butterflies exhibit considerable diversity in body and wing shape, but morphological design is, in general, isometric. Wing loading and mean body diameter show positive allometry. The cruising flight of butterflies is characterized by low wingbeat frequencies (here averaging 11 Hz), stroke amplitudes averaging 103°, and forward speeds in excess of 1ms−1. Body angles during flight are close to horizontal, and stroke plane angles are correspondingly high. Advance ratios are typically greater than 0.9, indicating that the forward and flapping velocity vectors are of comparable magnitude. Flight speed scales with morphological parameters in general accordance with predictions based on isometric design. Interspecifically, no consistent correlation exists between wing kinematics and absolute flight speed. However, maximum positional angle and stroke amplitude tend to increase while body angle decreases with increased relative flight speed.

Mechanics of Forward Flight in Bumblebees: I. Kinematics and Morphology

ABSTRACT Using high-speed cinematography, bumblebees in free flight were filmed over a range of forward airspeeds. A detailed description of the wing tip and body kinematics was obtained from a three-dimensional reconstruction of the twodimensional film image. A technique for determining quantitatively the angle of attack of the wing was developed. Kinematic parameters found to vary consistently with airspeed were body angle, stroke plane angle, geometrical angle of attack, and rotational angles of the wings at the ends of half-strokes. Results of a morphological analysis of the wings and bodies of those insects filmed in free flight are presented for use in later calculations of the lift and power requirements of forward flight.

Kinematic Analysis of Symmetrical Flight Manoeuvres of Odonata

ABSTRACT By analysis of slow-motion films of dragonflies and damselflies in free flight, released in front of a backdrop or startled during flight, the following flight parameters have been quantified for symmetrical manoeuvres: wingbeat frequency, relative durations of up-and downstroke, phase relationships of the beats of fore-and hindwings, stroke amplitude, mean stroke velocity, flight velocity, nondimensional flight velocity, advance ratio, acceleration, angle of attack and stroke plane. The wingbeat frequencies are higher in the smaller species and in those with relatively large wing loading. As a rule, Zygoptera have a wingbeat frequency only half that of Anisoptera. The stroke amplitude is almost always much larger in Zygoptera than in Anisoptera, which have a greater range of variation in this respect. Stroke velocity is higher in Anisoptera than in Zygoptera; it is also higher in the more elaborate flight manoeuvres than in others. The calculated stroke velocities resemble those actually measured. Anisoptera fly more rapidly than Zygoptera. With respect to the nondimensional flight velocities, it is notable that although the values for Anisoptera are higher than those for Zygoptera, they are exceeded by the Calopterygidae; the latter can fold their wings back during rapid forward flight and shoot away, as in the ‘ballistic’ flight of small songbirds. However, the advance ratio is higher in Anisoptera than in Calopterygidae. Anisoptera also perform better than Zygoptera with respect to acceleration. Three categories of phase relationships between the beats of the fore-and hindwings are established: counterstroking, phase-shifted stroking and parallel stroking. Counterstroking produces uniform flight, whereas the flight produced by phase-shifted and, in particular, parallel stroking is irregular. The angles of attack of the wings are shown to be associated with particular flight manoeuvres, as are the stroke planes. Flight manoeuvres are discussed without drawing detailed aerodynamic conclusions. The flight of Anisoptera is compared with that of Zygoptera.

Kinematics and aerodynamics of the greater horseshoe bat, Rhinolophus ferrumequinum, in horizontal flight at various flight speeds.

The kinematics and aerodynamics of the greater horseshoe bat, Rhinolophus ferrumequinum, in horizontal flight at a range of velocities are described. As flight speed increases there is a gradual change in the bat's wingbeat kinematics, wingbeat frequency decreasing and wingbeat strokeplane angles increasing. Associated with these changes are changes in the wings' incidence angles, particularly during the upstroke. At low speeds these are large and negative, suggesting thrust generation, while at high speeds these are positive and large, indicating that weight support and negative thrust are being generated. The change from one kinematic pattern to the other occurred gradually. The possible energetic and aerodynamic reasons for these changes are discussed.

The kinematics of Heteroptera in free flight

The kinematics of six species of Heteroptera in free flight are analysed and compared. Using nested analysis of variance techniques, statistically significant variation was detected between species for several of the flight parameters measured: mean angular velocity; pronation/supination ratio; upstroke/downstroke ratio; and wing beat frequency. In each case this is discussed in terms of variation in flight behaviour. Beneficial aerodynamic forces are generated during the upstroke and the downstroke, in both fast forward and rising flight. When the insects change from level, forward flight to near vertical, rising flight, the following parameters are altered in most of the sequences analysed: the stroke plane angle becomes steeply, negatively inclined, associated with an increase in body angle; the stroke amplitude is reduced; wing beat frequency is lowered, associated with a drop in mean angular velocity; the speed of stroke reversal (rotational velocity) is increased. This may be associated with increased wing torsion and tip flexion which in turn could improve any beneficial unsteady aerodynamic effects generated at stroke reversal. The reasons for this change in flight performance and the deviations from that seen in other insects are discussed.It is shown that Heteroptera may make use of wing drag in flight, particularly during rising flight.

Correlations between stationary measurable parameters of wing movement and aerodynamic force production in the blowfly (Calliphora vicina R.-D.)

With the aid of a mechanical aerodynamic two component balance, stroboscopes and photographic projections, the following dynamic and kinematic parameters were determined from short periods of stationary flight recorded in tethered blowflies which flew for several hours in a wind tunnel: weight, lift, flight speed, wing-beat frequency, nine angles characteristic for right and left wing-beat positions and a value characterizing the angle of the stroke plane. The data were subjected to a correlation analysis; the total correlation coefficients and the first order partial correlation coefficients were calculated with a significance of 5% and 1% respectively. The correlation between wing-beat frequency and lift was found to be strongly positive. Frequency, lift and flight speed are positively correlated with the sum of the wing-beat angles. Although under the given experimental conditions a significant tendency towards compatible adjustment has been demonstrated lift and thrust can be controlled independently in individual cases. Negative correlations of wing-beat angles of the right and left wing are generally caused by shifting the lower turning points and indicate a neuromotoric counter action of the two wings during turning reactions. A decreasing wing-beat amplitude is often coupled with an increase of the mean stroke plane angle. Numerous other correlations and detailed descriptions are given and compared to functional morphological and neuromotoric data.

The tethered flight performance of a laboratory population of Triatoma infestans (Klug) (Hemiptera: Reduviidae)

AbstractThe flight performance of a laboratory population of Triatoma infestans (Klug) was tested on a flight balance. Bugs adopted a typical flight posture which is described. They were capable of steady flight and produced reasonable amounts of lift. Flight durations were generally short, but capacity for flight rose to a peak in the third week after adult eclosion with the longest recorded flight being one of 2 h 40 min by a male. Sexual differences were slight; males had a slightly higher mean wing-beat frequency (57·8 Hz against 55·6 Hz), and a few more females than males made longer flights. Differences were noted between short and long fliers; the latter producing significantly more lift and showing signs of a flight pattern divisible into rising, steady and falling phases. The short fliers showed only rising and falling phases. Lift and wing-beat frequency were correlated, but it is evident that lift also depends on other variables such as stroke-plane angle, body angle and wing-beat amplitude, which are discussed.

Development of flight behaviour in maturing adults of Locusta migratoria: I. Flight performance and wing-stroke parameters

In tethered Locusta migratoria suspended from a flight balance, flight performance, wing-stroke frequency, stroke angle, and stroke plane angle were studied throughout adult life. No correlation between flight performance and age was found in adults older than 2 days. During continuous flight in locusts of all ages the wing-stroke frequency and the wing-stroke angle of both wings decreases, and the wing-stroke plane angle (forewing) increases slightly. Within 2 weeks of adult life the wing-stroke frequency increases by a factor of ca. 2, whereas the wing-stroke angles and the stroke plane angles remain constant.