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First published online October 7, 2004
Journal of Experimental Biology 207, 3813-3838 (2004)
Published by The Company of Biologists 2004
doi: 10.1242/jeb.01229

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Neuromuscular control of aerodynamic forces and moments in the blowfly, Calliphora vicina

Claire N. Balint^1,* and Michael H. Dickinson²

¹ Department of Integrative Biology, University of California, Berkeley, CA 94720, USA
² Department of Bioengineering, California Institute of Technology, Pasadena, CA 91125, USA

View larger version (36K): [in a new window]   Fig. 1. Methods. (A) Schematic cartoon showing method of data collection (not drawn to scale). Tethered flies were positioned within view of three orthogonally arranged high-speed video cameras. A panel of infrared LEDs was placed opposite each camera to provide backlighting. (B) Sample video frame from each camera view. A wire frame image of a Calliphora wing (shown in yellow and red) was fit by eye to the outline of each wing in all three camera views simultaneously. The anterior tip of the head (blue cross) and the posterior tip of the abdomen (pink cross) were digitized once per sequence. (C) The wing's position at each time point was quantified relative to a 50°-tilted body axis (left). The progression of the three Euler angles (, and ) over time was reproduced using a mechanical model fitted with force transducers at the base of the model wing (right).

View larger version (17K): [in a new window]   Fig. 2. Resultant forces and moments relative to the body. (A) Illustration of the six degrees of body motion: the directional components (thrust, lift and sideslip) and the moments (roll, yaw and pitch). The projection of the aerodynamic force vector (FN) onto each of the three rectangular axes constitutes its contribution to thrust (Fx), lift (Fy) and sideslip (Fz). The moment depends on the position vector r and the force vector FN as described in the text. (B) Simplified sideview of A. If the sideslip component of force is negligible, lift and thrust depend primarily on the magnitude (FN) and inclination (F) of the force vector as the wing moves through the stroke (blue dots denote changes in position).

View larger version (33K): [in a new window]   Fig. 3. Kinematic variables and aerodynamic forces over a wingbeat cycle. Yellow circles indicate the dorsal reversal, and the red circle indicates the ventral reversal point. (A) Representative time course of the three Euler angles describing wing orientation: elevation (), wing angle () and deviation (). (B) Accompanying time course of aerodynamically relevant variables: wingtip velocity (Ut), rotational velocity () and angle of attack (g). (C) Resultant time course of forces: translatory (Ftrans; blue) and rotational (Frot; green) forces. The sum of translatory and rotational forces is equal to the calculated force (Calc. FN; purple). The measured force (Meas. FN; red) is the normal force measured using our dynamically scaled mechanical model. The wake capture force is the large discrepancy between measured and calculated force at the beginning of each half-stroke, indicated by the open gray boxes.

View larger version (18K): [in a new window]   Fig. 4. Kinematic modulation in relation to muscle activity. (A) Characteristic range of downstroke tip trajectories. Downstroke deviation was defined as the deviation () value at an elevation () of 0 rad (indicated by white circles). Ventral amplitude was defined as the maximum elevation () value during the ventral reversal (indicated by black circles). (B) Downstroke deviation and ventral amplitude of each cycle plotted as a function of time. Downstroke deviation points are color-coded according to the occurrence of a b2 and b1 spike (red), a b1 spike only (green) or the absence of basalare muscle spikes (open circles) within the cycle. Ventral amplitude points are color-coded according to burst activity in III2–4 (blue) or I1 (pink). The blue points were defined as Mode 2 and the pink points were defined as Mode 1. (C) Occurrence of spikes in muscles b2, b1, I1, III1 and III2–4. The blue, horizontal bar indicates maximal activity in III2–4, and the pink, horizontal bar indicates minimal activity in III2–4 paired with I1 activity. Plots in B and C share the same time scale.

View larger version (29K): [in a new window]   Fig. 5. Variation of kinematic parameters in relation to downstroke deviation. (A) Wingtip trajectories of downstrokes and accompanying upstrokes of a single individual, color-coded according to downstroke deviation value (color bar is shown on the left). Black circles indicate ventral and dorsal amplitudes. (B) Examples of wing orientations accompanying high (red) and low (blue) downstroke deviation, shown for the downstroke (above) and the upstroke (below). (C) Relationship between downstroke deviation and ventral amplitude within the experimental population (R2=0.78). A subtle distinction exists between Mode 2 (gray points; blue line is a second order regression) and Mode 1 (pink points; red line). No distinction between modes was observed for the following parameters within the experimental population: relationship between downstroke deviation and (D) dorsal amplitude (R2=0.02), (E) instantaneous wingbeat frequency (R2=0.01) and (F) downstroke/upstroke ratio (R2=0.30). Black circles in C–F indicate values for the individual shown in A.

View larger version (32K): [in a new window]   Fig. 6. Temporal variation in angle of attack, tip velocity and translatory force in a single individual, color-coded according to downstroke deviation as in Fig. 5A. All data are shown along a normalized time axis, where 0 is the beginning and 1 is the end of the half-stroke. The slope and R2 regression statistics for the correlation between each parameter and downstroke deviation are shown for normalized time intervals of 0.05. Mid-stroke was defined as a normalized time of 0.55, indicated by the vertical dotted lines. (A) Angles of attack over the downstroke. (B) Tip velocities over the downstroke. (C) Translatory forces over the downstroke. Regression statistics are shown for the individual (black circles) and the population (gray circles). (D) Angles of attack over the upstroke. (E) Tip velocities over the upstroke. (F) Translatory forces over the upstroke. Regression statistics are shown for the individual (black circles) and the population (gray circles).

View larger version (39K): [in a new window]   Fig. 7. Correlation between downstroke deviation and the mid-stroke angle of attack, tip velocity and translatory force for the experimental population. Black circles indicate values for the individual shown in Fig. 6. (A) Correlation between downstroke deviation and mid-downstroke angle of attack (R2=0.41), tip velocity (R2=0.22) and translatory force (R2=0.58). (B) Correlation between downstroke deviation and mid-upstroke angle of attack (R2=0.06), tip velocity (R2=0.05) and translatory force (R2=0.23). Five separate regressions are shown for five individuals.

View larger version (27K): [in a new window]   Fig. 8. Correlation between downstroke deviation and rotational forces. (A) Time course of rotational velocities and (B) time course of rotational forces for a single individual, color-coded according to downstroke deviation. Data are shown over a normalized time axis for the downstroke and upstroke. The filled gray box indicates the ventral rotation, and the open gray box indicates the dorsal rotation. For the ventral rotation, the pre-reversal portion occurs at the end of the downstroke, and the post-reversal portion occurs at the beginning of the upstroke. (C–G) The following data are for the experimental population. Black circles indicate values for the individual shown in A and B. Correlation between downstroke deviation and (C) pre-reversal peak rotational force (R2=0.07), (D) pre-reversal total force peak (R2=0.20), (E) post-reversal normalized time delay of rotational force peak (R2=0.15), (F) post-reversal peak rotational force (R2=0.60) and (G) post-reversal total force peak (R2=0.31).

View larger version (37K): [in a new window]   Fig. 9. Correlation between downstroke deviation and force inclination. (Ai) Time course of force inclination during the downstroke for a single individual, color-coded according to downstroke deviation. The slope and R2 regression statistics for the correlation between downstroke deviation and force inclination are shown for normalized time intervals of 0.05. Regression statistics are shown for the individual (black circles) and the population (gray circles). The vertical dotted line indicates a normalized time of 0.65. (Aii) Correlation between downstroke deviation and the mid-downstroke (normalized time 0.65) force inclination for the experimental population (R2=0.71). Black circles indicate data for the individual in Ai. (Bi) Time course of force inclination during the upstroke for a single individual, color-coded according to downstroke deviation. The slope and R2 regression statistics for the correlation between downstroke deviation and force inclination are shown at the bottom, as in Ai. The vertical dotted line indicates a normalized time of 0.55. (Bii) Correlation between downstroke deviation and mid-upstroke (normalized time 0.55) force inclination for the experimental population (R2=0.03). Black circles indicate data for the individual in Bi.

View larger version (34K): [in a new window]   Fig. 10. Mean force vector (FN) and resultant directional forces and moments. (A) Schematic illustrating the type of force vector modulation occurring during the downstroke. As downstroke deviation changes, there is a correlated modulation of force magnitude while force inclination remains relatively constant. Correlation between downstroke deviation and downstroke (B) mean force magnitude (R2=0.43), (C) mean force inclination (R2=0.02), (D) mean lift (blue; R2=0.54) and mean thrust (green; R2=0.13), and (E) mean roll (blue; R2=0.44) and mean yaw (green; R2=0.05). (F) Schematic illustrating primary type of variation in mean force vector during the upstroke. As downstroke deviation changes, force magnitude is relatively constant, but there is unexplained variation in force inclination. Correlation between downstroke deviation and upstroke (G) mean force magnitude (R2=0.16), (H) mean force inclination (R2=0.004), (I) mean thrust (green; R2=0.22) and mean lift (blue; R2=0.0001), and (J) mean yaw (green; R2=0.17) and mean roll (blue; R2=0.001). The direction of the roll and yaw moments in E and J differ depending on whether they are generated by the left or right wing. For the left wing, positive roll is a right side down roll, and positive yaw is a yaw to the right. For the right wing, positive roll is a left side down roll, and positive yaw is a yaw to the left.

View larger version (24K): [in a new window]   Fig. 11. Mean pitch. (A) Correlation between downstroke deviation and mean pitch from each wingbeat cycle. Regression lines for five individuals super-imposed. A relatively strong correlation exists within each individual (R2=0.65 turquoise, 0.87 green, 0.97 orange, 0.83 pink, 0.76 purple), but the correlation differs across individuals (total R2=0.49). (B) Upstroke lift from Fig. 10I, with regression lines for the same five individuals from A super-imposed.

View larger version (12K): [in a new window]   Fig. 12. Variation of kinematic parameters in relation to dorsal amplitude. (A) Wingtip trajectories during the upstroke, shown for three individuals differing in dorsal amplitude. Colored circles indicate dorsal amplitudes. (B) Examples of wing orientations accompanying large (purple), intermediate (green) and small (turquoise) dorsal amplitude during the upstroke. (C) Relationship between dorsal amplitude and downstroke/upstroke ratio within the experimental population (R2=0.45). Colored circles indicate data for the three individuals shown in A.

View larger version (23K): [in a new window]   Fig. 13. Correlation between dorsal amplitude and upstroke translatory forces. Colors indicate data from three individuals with large (purple), intermediate (green) and small (turquoise) dorsal amplitudes. All time-course data are shown along a normalized time axis. The slope and R2 regression statistics for the correlation between each parameter and dorsal amplitude are shown for normalized time intervals of 0.05. Mid-upstroke was defined as a normalized time of 0.55, indicated by the vertical dotted line. (Ai) Time course of the angle of attack over the upstroke, shown for three individuals. (Aii) Correlation between dorsal amplitude and mid-upstroke angle of attack, for the experimental population (R2=0.71). (Bi) Time course of the tip velocity over the upstroke, shown for three individuals. (Bii) Correlation between dorsal amplitude and mid-upstroke tip velocity, for the experimental population (R2=0.73). (Ci) Time course of the translatory force over the upstroke, shown for three individuals. (Cii) Correlation between dorsal amplitude and mid-upstroke translatory force, for the experimental population (R2=0.04).

View larger version (18K): [in a new window]   Fig. 14. Correlation between dorsal amplitude and upstroke force inclination. (A) Time course of force inclination during the upstroke, shown for the three individuals in Fig. 13. The slope and R2 regression statistics for the correlation between dorsal amplitude and force inclination in normalized time intervals of 0.05 for the experimental population are shown at the bottom. Mid-upstroke, defined as a normalized time of 0.55, is indicated by the vertical dotted line. (B) Correlation between dorsal amplitude and mid-upstroke force inclination for the experimental population (R2=0.76).

View larger version (16K): [in a new window]   Fig. 15. Mean force vector and resultant directional forces and moments. (A) Schematic illustrating primary type of variation in mean force vector during the upstroke as in Fig. 10F. Differences in force inclination were well correlated with dorsal amplitude. Correlation between dorsal amplitude and upstroke (B) mean force magnitude (R2=0.009), (C) mean force inclination (R2=0.75), (D) mean lift (blue; R2=0.79) and mean thrust (green; R2=0.09), and (E) mean roll (blue; R2=0.58) and mean yaw (green; R2=0.18).

View larger version (10K): [in a new window]   Fig. 16. Variation of kinematic parameters in relation to mode. (A) Comparison of wingtip trajectories during Mode 2 (black) and Mode 1 (pink). Blue circles indicate ventral amplitudes during Mode 2, and red circles indicate ventral amplitudes during Mode 1. (B) Examples of wing orientations during the upstroke for Mode 2 (black) and Mode 1 (pink).

View larger version (53K): [in a new window]   Fig. 17. Comparison of temporal variation in angle of attack, tip velocity and translatory force between modes. Time course of each parameter over the downstroke and upstroke shown along a normalized time axis. Mode 2 strokes are shown in black, and Mode 1 strokes are shown in pink. Mid-stroke was defined as a normalized time of 0.55, indicated by the vertical dotted lines. (A) Angles of attack over the downstroke. (B) Tip velocities over the downstroke. (C) Translatory forces over the downstroke. (D) Angles of attack over the upstroke. (E) Tip velocities over the upstroke. (F) Translatory forces over the upstroke.

View larger version (31K): [in a new window]   Fig. 18. Comparison of mid-stroke translatory forces between modes. (A) Relationship between downstroke deviation and mid-downstroke angle of attack, tip velocity and translatory force within Mode 2 (gray points) and Mode 1 (pink points). The regression of downstroke deviation vs mid-downstroke translatory force is shown for Mode 2 (black line; R2=0.58) and Mode 1 (red line; R2=0.63). (B) Relationship between dorsal amplitude and mid-upstroke angle of attack, tip velocity and translatory force within Mode 2 (gray points) and Mode 1 (pink points). The regression of dorsal amplitude vs mid-upstroke translatory force is shown for Mode 2 (black line; R2=0.04) and Mode 1 (red line; R2=0.05). (C) Relationship between downstroke deviation and mid-upstroke translatory force within Mode 2 (gray points) and Mode 1 (pink points). The regression of downstroke deviation vs mid-upstroke translatory force is shown for Mode 2 (black line; R2=0.23) and Mode 1 (red line; R2=0.43).

View larger version (30K): [in a new window]   Fig. 19. Comparison of rotational forces between modes. (A) Time course of rotational velocities and (B) time course of rotational forces within Mode 2 (black) and Mode 1 (pink). The filled gray box indicates the dorsal rotation, and the open gray box indicates the ventral rotation. For the dorsal rotation, the pre-reversal portion occurs at the end of the upstroke, and the post-reversal portion occurs at the beginning of the downstroke. (C–G) The following data are for the experimental population. Correlation between downstroke deviation and (C) post-reversal normalized time delay of rotational force peak, (D) post-reversal peak rotational force, (E) post-reversal total force peak, (F) pre-reversal peak rotational force and (G) pre-reversal total force peak for Mode 2 (gray points; black line regression) and Mode 1 (pink points; red line regression).

View larger version (32K): [in a new window]   Fig. 20. Mean force vector and resultant directional forces and moments. (A) Schematic illustrating the difference in mean force vector during the downstroke between modes. While force magnitude is similarly modulated within each mode, the mean forces can be slightly lower during Mode 1. Correlation between downstroke deviation and downstroke (B) mean force magnitude and (C) mean force inclination for Mode 2 (gray points; black line regression) and Mode 1 (pink points; red line). Correlation between downstroke deviation and downstroke (D) mean lift and (E) mean roll for Mode 2 (blue points; black line) and Mode 1 (pink points; red line). (F) Schematic illustrating the difference in mean force vector during the upstroke between modes. While force inclination is similarly modulated within each mode (not shown), the mean force magnitudes are much lower during Mode 1. (G) Correlation between downstroke deviation and upstroke mean force magnitude. (H) Correlation between dorsal amplitude and upstroke mean force inclination. Correlation between downstroke deviation and upstroke (I) mean thrust and (J) mean yaw for Mode 2 (green points; black line) and Mode 1 (pink points; red line).

View larger version (25K): [in a new window]   Fig. 21. Mean calculated vs measured forces for Mode 2 wingstrokes. (A) Two frequency preferences displayed by the experimental population, mean 155 Hz (black points; blue line) and mean 129 Hz (gray points; red line). (B) Mean calculated force magnitudes for the two frequency groups when wingtip velocity is normalized for a wingbeat period of 0.0065 ms. (C) Mean calculated forces for the two frequency groups when wingtip velocity is not normalized. (D) Mean measured forces for the two frequency groups. (E) Regressions from C and D shown together. The relationship between the calculated forces and downstroke deviation and between the measured forces and downstroke deviation is roughly the same. The difference in forces due to wingbeat frequency is roughly the same for calculated and measured forces. The measured forces are larger than the calculated forces by a roughly constant amount.

View larger version (23K): [in a new window]   Fig. 22. Summary diagram of the relationship between steering muscle activity and control of the aerodynamic force vector. (A) Firing phase preference of the basalare muscles (left). Basalare muscle activity is correlated with strong modulation of the downstroke force and weak modulation of the upstroke force magnitude. Firing phase preference of pterale III muscles (right). Upstroke force magnitudes are relatively large during Mode 2. (B) Firing phase preference of muscle I1. Upstroke force magnitudes are much smaller during Mode 1 than during Mode 2. (C) Presumed firing phase of unknown muscle and modulation of the upstroke force inclination correlated with dorsal amplitude.

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