- Email: [email protected]
List of Figures
LIST OF FIGURES Figure 1.1 Figure 1.2 Figure 1.3 Figure 1.4 Figure 1.5 Figure 1.6 Figure 1.7 Figure 1.8
Figure 1.9
Figure 1.10
Figure 1.11 Figure 2.1 Figure 2.2 Figure 2.3 Figure 2.4 Figure 2.5 Figure 2.6
Figure 2.7 Figure 2.8
Figure 2.9 Figure 2.10 Figure 2.11
Flight capability of flapping wing flyers. Mission applications for unmanned air vehicles. (A) Civilian and (B) Military. (A) Natural flyers demonstrate glide, hover, dive, and perch. (B) Example of maneuverability performance of natural flyers. Concept vehicle exhibit adjustable stiffness across the wing. Fuselage body accelerations in state-of-the-art flapping wing robotic. Position state of fuselage of ornithopter test platform. Lift and thrust generating mechanisms of flapping wing flight (A) downstroke and (B) upstroke. Wing tip path as indicator or dominant wing motion shown on natural flyers (A) albatross in fast-forward flight mode, (B) pigeon in slow flight mode, (C) horseshoe bat in fast-forward flight mode, and (D) horseshoe bat in slow flight mode. Passive wing morphing. (A) Bioinspired test platform wing morphing though thrust flap region and (B) radical shape morphing wing. Active wing morphing bioinspired test platform. (A) Ornithopter platform. (B) Extended half wingspan versus retracted half wingspan. First ornithopter vehicle designs. (A) DaVincis 1490 and (B) Lilienthal 1894. Ornithopter schematic: rigid multi-body system. Ornithopter schematic: linear elastic multi-body systems. Ornithopter schematic: nonlinear elastic multi-body systems. SimXpert: flexible multi-body dynamics model implementation. SimXpert: Image of fully integrated flexible multi-body dynamics model of ornithopter. Ornithopter vehicle dynamics models. (A) Single rigid body, (B) rigid multi-body dynamics, and (C) flexible multi-body dynamics model. Quasi-steady blade element model. CFD analysis showing (A) vorticity contours on the flexible deformed wing and (B) deformed grid at 50% span location during upstroke of the wing at start of upstroke. Rigid-body ornithopter fit in flight test data for aerodynamic model structure determination. Modeling methodology: workflow stage 1. Modeling methodology: workflow step 2.
2 3 4 5 6 7 9
11
16
16 17 24 24 25 31 32
33 38
42 43 44 45
xi
j
xii Figure 2.12 Figure 2.13 Figure 2.14 Figure 2.15 Figure 2.16 Figure 3.1 Figure 3.2 Figure 3.3 Figure 3.4 Figure 3.5 Figure 3.6 Figure 3.7 Figure 3.8 Figure 3.9 Figure 3.10 Figure 3.11 Figure 3.12 Figure 3.13 Figure 3.14
Figure 3.15
Figure 3.16
Figure 3.17
Figure 3.18
List of Figures
Modeling methodology: workflow step 3. Modeling methodology: workflow stage 4. Modeling methodology: workflow stage 5. Modeling methodology: workflow stage 6. Modeling methodology: workflow stage 7. Primary test platform Morpheus Lab custom-build test ornithopter (ML101). Secondary test platform modified ornithopter Shawn Kinkade (MSK004). Wing structure bioinspired ornithopter test platform (ML101). Design feature wing spars (ML101); (A) leading edge spar, (B) diagonal spar, (C) finger spar (ML101). Schematic and nomenclature stiffening carbon fiber spar configuration. A bat (Cynopterus brachyotis) in flight. Lower wing surface of a natural avian flyer photo. Design feature tail (ML101). Design feature fuselage (ML101). Definition flapping angle and upstroke and downstroke on shoulder joint/bar linkage (ML101). Upstroke and downstroke sequence ornithopter (ML101) scale. MSK004 wings with tracking markers. MSK004 and Vicon camera system for the measurement of ornithopter wing and configuration motions. Harmon aerodynamic model results and bench test results measured integrated forces ML101 at 5 Hz flapping frequency, over a flapping cycle t/T, (A) vertical propulsive force (VPF), (B) horizontal propulsive force (HPF), (C) normalized FA. Harmon bench test results measured integrated forces ML101 at 5 Hz flapping frequency, over a flapping cycle t/T, (A) vertical propulsive force (VPF), (B) horizontal propulsive force (HPF) versus normalized flapping angle (FA). Harmon aerodynamic model results and bench test results measured integrated forces ML101 at 6.17 Hz flapping frequency, over a flapping cycle t/T, (A) vertical propulsive force (VPF), (B) horizontal propulsive force (HPF), (C) normalized flapping angle (FA). Harmon bench test results measured integrated forces ML101 at 6.17 Hz flapping frequency, over a flapping cycle t/T, (A) vertical propulsive force (VPF), (B) horizontal propulsive force versus normalized flapping angle (FA). Results and bench test results measured integrated forces ML101 versus flapping frequency, over a flapping cycle t/T, (A) mean absolute value vertical propulsive force (MAVPF), (B) mean horizontal propulsive force (MHPF) versus flapping angle.
45 45 46 46 46 51 52 52 52 52 53 54 54 54 56 56 57 58
59
59
60
60
61
List of Figures
Figure 3.19
Figure 3.20 Figure 3.21
Figure 3.22 Figure 3.23
Figure 3.24 Figure 3.25 Figure 3.26 Figure 3.27 Figure 3.28 Figure 3.29 Figure 3.30 Figure 3.31 Figure 3.32
Figure 3.33
Figure 3.34
Figure 4.1 Figure 4.2 Figure 4.3 Figure 4.4
xiii
Vicon Vision wing kinematic sequencedthree position state tracking markers i¼1e110, (A) isometric view, (B) side view in a fuselage fixed reference frame CB0. Vicon camera system for the measurement of ornithopter wing and configuration motions. Aerodynamic forces on the wingsdresults system ID model by Grauer. FA, flapping angle; HPF, horizontal propulsive force; VPF, vertical propulsive force. Asymmetric retroreflective markers on the wing (seen as white dots) and wing tip location (marked in red). Retroreflective marker position on the wing measured with Vicon Vision system markers i¼1e53. Markers i¼1e5 were mounted on the fuselage. Image small Unmanned Aerial System flight test facilitydVicon Vision system cameras. Test setup schematicdtest chamber dimensions: 700 (W)350 (D) 350 (H). Schematic ornithopter and reference frames used for the processing of free-flight test data. Data set marker position during free flight in the inertia reference frame CI0. Data set marker position i¼1e53 during free flight in the inertia reference frame CI0dview ZI0/ZI0. Data set marker position i¼1e53 during free flight in the inertia reference frame CI0dview YI0/XI0. Position states all tracking markers on the wing/volume shows test data used for model developmentd3.5 flapping cycles. Single position state on ornithopter shows all tracking markers i ¼ 1 to 53 in the fuselage fixed reference frame CB0. Vertical propulsive forces acting on the fuselage center of massdobtained from experiment. VF, vertical force; HF, horizontal force; FA, flapping angle. Vacuum chamber at NASA Langley Research Center. (Left) Test platform mounted on six degrees of freedom load cell, (Right) vacuum chamber. Results of vacuum chamber test ML101 test platform versus flapping frequency, (A) inertial horizontal propulsive force IHPF (B) inertial horizontal propulsive force (C) inertial pitching moment (IPM) versus magnitude. Schematic five-body dynamics system. Schematic inertial and fuselage body fixed reference frames. Schematic wing fixed reference frames. Articulated multi-body system representation of the ornithopter.
62 62
63 64
65 65 66 67 68 68 69 69 70
70
71
72 80 81 81 82
xiv Figure 4.5 Figure 4.6 Figure 4.7 Figure 4.8
Figure 4.9 Figure 4.10 Figure 4.11 Figure 4.12 Figure 5.1 Figure 5.2 Figure 5.3 Figure 5.4 Figure 5.5 Figure 5.6 Figure 5.7 Figure 6.1 Figure 6.2 Figure 6.3 Figure 6.4 Figure 6.5 Figure 6.6 Figure 6.7
Figure 6.8 Figure 6.9
List of Figures
Position vector of rigid multi-body model of ornithopter. Position vector of flexible multi-body model of ornithopter. Schematic notation definition for generalized coordinates of the flexible multi-body system. Position vector of flexible multi-body model of ornithopter, luff region [blue (darker gray in print versions) and red (light gray in print versions)], thrust flap region [orange (dark gray in print versions) and red (lighter gray in print versions)]. Schematic finite element model wing structure carbon fiber spars and wing. Thrust flap region mesh nodes ¼ 352, elements ¼ 860. Thrust flap region mode shapes contour plot. Model image flexible wing component connections. Blade element grid schematic aero-model A. (A) Blade element grid schematic aero-model B. (B) Blade element (BE) grid schematic aero-model C. Variables for calculation of aerodynamic forces. ML101 ornithopter configuration blade element (BE) selection. Blade element (BE) selection thrust flap region ML101 ornithopter configuration. Aerodynamic loads modeldworkflow. FMBD, flexible multi-body dynamics. Aerodynamic loads modeldworkflow Aero Load Initialized Experimental Coupled. FMBD, flexible multi-body dynamics. Isometric view of the position states path of all Vicon markers over one flapping cycle at 6.06 Hz. Side view of the position states path of all Vicon markers over one flapping cycle at 6.06 Hz. Top view of the position states path of all Vicon markers over one flapping cycle at 6.06 Hz. Top view of the ornithopter markers position state 0 deflection plane. Top view of the Y coordinate flexibility in the wing fixed reference plane CW. Top view of the X coordinate flexibility in the wing fixed reference plane CW. Bioinspired ornithopter test platform in free flight: three experimental orientations during a wing beat: viewed in the fuselage body fixed reference frame CB0. Wing fixed reference frame CW. Bioinspired ornithopter test platform wing in free flight: maximal elastic deflections of the wing in the wing fixed reference frame during a wing beat; viewed in the fuselage fixed reference frame CB0.
89 90 92
94 103 105 105 106 111 111 115 119 119 120 122 129 130 130 131 132 132
133 134
135
List of Figures
Figure 6.10
Figure 6.11
Figure 6.12
Figure 6.13 Figure 6.14
Figure 6.15
Figure 6.16
Figure 6.17 Figure 6.18 Figure 6.19
Figure 6.20 Figure 6.21 Figure 6.22 Figure 6.23
Figure 6.24 Figure 6.25 Figure 6.26
Figure 6.27
xv Bioinspired ornithopter test platform wing in free flight: maximal occurring elastic deformation in the thrust flap region of the wing in the wing fixed reference frame CW. Bioinspired ornithopter test platform ML101 wing in free flight: maximal occurring elastic deflections luff region in the wing fixed reference frame CW. Bioinspired ornithopter test platform wing in free flight: maximal occurring elastic deflections of the wing fixed reference frame during a wing beat; viewed in the fuselage reference frame CB0. Schematic location thrust flap region reference frame CBT. Bioinspired ornithopter test platform wing in free flight: X-axis of modeled thrust flap region reference frame in 34 position states viewed in the fuselage fixed reference frame CB0. Bioinspired ornithopter test platform wing in free-flight marker location: XBT-axis location on experimental test platform resulting in minimal deformation of a reference YBT/ZBT reference plane using a 1 degree of freedom flapping motion. Flapping angle zeta and beta location on shown in experimental wing test data (maximal deformation of CW,0 reference plane, and XBT position states). Modeled flapping angle (FA) time history based on flight test data versus FA in flight test data E-2. Experimental thrust flap reference motion in 34 position states in the fuselage fixed reference plane CB0. Modeled thrust flap reference motion in 34 position states in the fuselage fixed reference plane CB0 versus wing at zero deformation (PS0). Experimental elastic deflections in the fuselage fixed reference frame CB0 during a wing beat. Experimental elastic deformation in the wing fixed reference frame CW during a wing beat. Model image SimXpertdML101 five-body flexible multi-body dynamics model (fuselage reference frame CB is highlighted). Verification bench testdmodel 3 Adscale ML101 (6.17 Hz). FMBD, flexible multi-body dynamics; HFI, horizontal force inertia; HPF, horizontal propulsive force; VPF, vertical propulsive force. Wing tip locationdviewed at one experimental position state (mid-downstroke). Results wing kinematics model 5 experiment: flight test: (left) back view and (right) side view. Propulsive forces acting on the fuselage center of massdobtained from experiment (E-2) and five-body vehicle dynamics model using aerodynamic model C. Simulated inertia forces on fuselage center of mass CB in free flight (inertial vertical propulsive force)dupstrokeedownstroke transition.
135
136
136 137
137
138
139 139 140
141 142 142 143
145 146 147
148
149
xvi Figure 6.28
Figure 6.29
List of Figures
Results inertia forces (E3) with error bars versus simulation results with STD, (A) inertial horizontal propulsive force (IHPF), (B) inertial vertical propulsive force (IVPF), (C) inertial pitching moment (IPM) versus magnitude. Results: body force magnitude system ID model (MSK004 E1-I)d body force magnitudedaero-model C.
150 152
Figure 1.9
Figure 1.10
Figure 1.11 Figure 2.1 Figure 2.2 Figure 2.3 Figure 2.4 Figure 2.5 Figure 2.6
Figure 2.7 Figure 2.8
Figure 2.9 Figure 2.10 Figure 2.11
Flight capability of flapping wing flyers. Mission applications for unmanned air vehicles. (A) Civilian and (B) Military. (A) Natural flyers demonstrate glide, hover, dive, and perch. (B) Example of maneuverability performance of natural flyers. Concept vehicle exhibit adjustable stiffness across the wing. Fuselage body accelerations in state-of-the-art flapping wing robotic. Position state of fuselage of ornithopter test platform. Lift and thrust generating mechanisms of flapping wing flight (A) downstroke and (B) upstroke. Wing tip path as indicator or dominant wing motion shown on natural flyers (A) albatross in fast-forward flight mode, (B) pigeon in slow flight mode, (C) horseshoe bat in fast-forward flight mode, and (D) horseshoe bat in slow flight mode. Passive wing morphing. (A) Bioinspired test platform wing morphing though thrust flap region and (B) radical shape morphing wing. Active wing morphing bioinspired test platform. (A) Ornithopter platform. (B) Extended half wingspan versus retracted half wingspan. First ornithopter vehicle designs. (A) DaVincis 1490 and (B) Lilienthal 1894. Ornithopter schematic: rigid multi-body system. Ornithopter schematic: linear elastic multi-body systems. Ornithopter schematic: nonlinear elastic multi-body systems. SimXpert: flexible multi-body dynamics model implementation. SimXpert: Image of fully integrated flexible multi-body dynamics model of ornithopter. Ornithopter vehicle dynamics models. (A) Single rigid body, (B) rigid multi-body dynamics, and (C) flexible multi-body dynamics model. Quasi-steady blade element model. CFD analysis showing (A) vorticity contours on the flexible deformed wing and (B) deformed grid at 50% span location during upstroke of the wing at start of upstroke. Rigid-body ornithopter fit in flight test data for aerodynamic model structure determination. Modeling methodology: workflow stage 1. Modeling methodology: workflow step 2.
2 3 4 5 6 7 9
11
16
16 17 24 24 25 31 32
33 38
42 43 44 45
xi
j
xii Figure 2.12 Figure 2.13 Figure 2.14 Figure 2.15 Figure 2.16 Figure 3.1 Figure 3.2 Figure 3.3 Figure 3.4 Figure 3.5 Figure 3.6 Figure 3.7 Figure 3.8 Figure 3.9 Figure 3.10 Figure 3.11 Figure 3.12 Figure 3.13 Figure 3.14
Figure 3.15
Figure 3.16
Figure 3.17
Figure 3.18
List of Figures
Modeling methodology: workflow step 3. Modeling methodology: workflow stage 4. Modeling methodology: workflow stage 5. Modeling methodology: workflow stage 6. Modeling methodology: workflow stage 7. Primary test platform Morpheus Lab custom-build test ornithopter (ML101). Secondary test platform modified ornithopter Shawn Kinkade (MSK004). Wing structure bioinspired ornithopter test platform (ML101). Design feature wing spars (ML101); (A) leading edge spar, (B) diagonal spar, (C) finger spar (ML101). Schematic and nomenclature stiffening carbon fiber spar configuration. A bat (Cynopterus brachyotis) in flight. Lower wing surface of a natural avian flyer photo. Design feature tail (ML101). Design feature fuselage (ML101). Definition flapping angle and upstroke and downstroke on shoulder joint/bar linkage (ML101). Upstroke and downstroke sequence ornithopter (ML101) scale. MSK004 wings with tracking markers. MSK004 and Vicon camera system for the measurement of ornithopter wing and configuration motions. Harmon aerodynamic model results and bench test results measured integrated forces ML101 at 5 Hz flapping frequency, over a flapping cycle t/T, (A) vertical propulsive force (VPF), (B) horizontal propulsive force (HPF), (C) normalized FA. Harmon bench test results measured integrated forces ML101 at 5 Hz flapping frequency, over a flapping cycle t/T, (A) vertical propulsive force (VPF), (B) horizontal propulsive force (HPF) versus normalized flapping angle (FA). Harmon aerodynamic model results and bench test results measured integrated forces ML101 at 6.17 Hz flapping frequency, over a flapping cycle t/T, (A) vertical propulsive force (VPF), (B) horizontal propulsive force (HPF), (C) normalized flapping angle (FA). Harmon bench test results measured integrated forces ML101 at 6.17 Hz flapping frequency, over a flapping cycle t/T, (A) vertical propulsive force (VPF), (B) horizontal propulsive force versus normalized flapping angle (FA). Results and bench test results measured integrated forces ML101 versus flapping frequency, over a flapping cycle t/T, (A) mean absolute value vertical propulsive force (MAVPF), (B) mean horizontal propulsive force (MHPF) versus flapping angle.
45 45 46 46 46 51 52 52 52 52 53 54 54 54 56 56 57 58
59
59
60
60
61
List of Figures
Figure 3.19
Figure 3.20 Figure 3.21
Figure 3.22 Figure 3.23
Figure 3.24 Figure 3.25 Figure 3.26 Figure 3.27 Figure 3.28 Figure 3.29 Figure 3.30 Figure 3.31 Figure 3.32
Figure 3.33
Figure 3.34
Figure 4.1 Figure 4.2 Figure 4.3 Figure 4.4
xiii
Vicon Vision wing kinematic sequencedthree position state tracking markers i¼1e110, (A) isometric view, (B) side view in a fuselage fixed reference frame CB0. Vicon camera system for the measurement of ornithopter wing and configuration motions. Aerodynamic forces on the wingsdresults system ID model by Grauer. FA, flapping angle; HPF, horizontal propulsive force; VPF, vertical propulsive force. Asymmetric retroreflective markers on the wing (seen as white dots) and wing tip location (marked in red). Retroreflective marker position on the wing measured with Vicon Vision system markers i¼1e53. Markers i¼1e5 were mounted on the fuselage. Image small Unmanned Aerial System flight test facilitydVicon Vision system cameras. Test setup schematicdtest chamber dimensions: 700 (W)350 (D) 350 (H). Schematic ornithopter and reference frames used for the processing of free-flight test data. Data set marker position during free flight in the inertia reference frame CI0. Data set marker position i¼1e53 during free flight in the inertia reference frame CI0dview ZI0/ZI0. Data set marker position i¼1e53 during free flight in the inertia reference frame CI0dview YI0/XI0. Position states all tracking markers on the wing/volume shows test data used for model developmentd3.5 flapping cycles. Single position state on ornithopter shows all tracking markers i ¼ 1 to 53 in the fuselage fixed reference frame CB0. Vertical propulsive forces acting on the fuselage center of massdobtained from experiment. VF, vertical force; HF, horizontal force; FA, flapping angle. Vacuum chamber at NASA Langley Research Center. (Left) Test platform mounted on six degrees of freedom load cell, (Right) vacuum chamber. Results of vacuum chamber test ML101 test platform versus flapping frequency, (A) inertial horizontal propulsive force IHPF (B) inertial horizontal propulsive force (C) inertial pitching moment (IPM) versus magnitude. Schematic five-body dynamics system. Schematic inertial and fuselage body fixed reference frames. Schematic wing fixed reference frames. Articulated multi-body system representation of the ornithopter.
62 62
63 64
65 65 66 67 68 68 69 69 70
70
71
72 80 81 81 82
xiv Figure 4.5 Figure 4.6 Figure 4.7 Figure 4.8
Figure 4.9 Figure 4.10 Figure 4.11 Figure 4.12 Figure 5.1 Figure 5.2 Figure 5.3 Figure 5.4 Figure 5.5 Figure 5.6 Figure 5.7 Figure 6.1 Figure 6.2 Figure 6.3 Figure 6.4 Figure 6.5 Figure 6.6 Figure 6.7
Figure 6.8 Figure 6.9
List of Figures
Position vector of rigid multi-body model of ornithopter. Position vector of flexible multi-body model of ornithopter. Schematic notation definition for generalized coordinates of the flexible multi-body system. Position vector of flexible multi-body model of ornithopter, luff region [blue (darker gray in print versions) and red (light gray in print versions)], thrust flap region [orange (dark gray in print versions) and red (lighter gray in print versions)]. Schematic finite element model wing structure carbon fiber spars and wing. Thrust flap region mesh nodes ¼ 352, elements ¼ 860. Thrust flap region mode shapes contour plot. Model image flexible wing component connections. Blade element grid schematic aero-model A. (A) Blade element grid schematic aero-model B. (B) Blade element (BE) grid schematic aero-model C. Variables for calculation of aerodynamic forces. ML101 ornithopter configuration blade element (BE) selection. Blade element (BE) selection thrust flap region ML101 ornithopter configuration. Aerodynamic loads modeldworkflow. FMBD, flexible multi-body dynamics. Aerodynamic loads modeldworkflow Aero Load Initialized Experimental Coupled. FMBD, flexible multi-body dynamics. Isometric view of the position states path of all Vicon markers over one flapping cycle at 6.06 Hz. Side view of the position states path of all Vicon markers over one flapping cycle at 6.06 Hz. Top view of the position states path of all Vicon markers over one flapping cycle at 6.06 Hz. Top view of the ornithopter markers position state 0 deflection plane. Top view of the Y coordinate flexibility in the wing fixed reference plane CW. Top view of the X coordinate flexibility in the wing fixed reference plane CW. Bioinspired ornithopter test platform in free flight: three experimental orientations during a wing beat: viewed in the fuselage body fixed reference frame CB0. Wing fixed reference frame CW. Bioinspired ornithopter test platform wing in free flight: maximal elastic deflections of the wing in the wing fixed reference frame during a wing beat; viewed in the fuselage fixed reference frame CB0.
89 90 92
94 103 105 105 106 111 111 115 119 119 120 122 129 130 130 131 132 132
133 134
135
List of Figures
Figure 6.10
Figure 6.11
Figure 6.12
Figure 6.13 Figure 6.14
Figure 6.15
Figure 6.16
Figure 6.17 Figure 6.18 Figure 6.19
Figure 6.20 Figure 6.21 Figure 6.22 Figure 6.23
Figure 6.24 Figure 6.25 Figure 6.26
Figure 6.27
xv Bioinspired ornithopter test platform wing in free flight: maximal occurring elastic deformation in the thrust flap region of the wing in the wing fixed reference frame CW. Bioinspired ornithopter test platform ML101 wing in free flight: maximal occurring elastic deflections luff region in the wing fixed reference frame CW. Bioinspired ornithopter test platform wing in free flight: maximal occurring elastic deflections of the wing fixed reference frame during a wing beat; viewed in the fuselage reference frame CB0. Schematic location thrust flap region reference frame CBT. Bioinspired ornithopter test platform wing in free flight: X-axis of modeled thrust flap region reference frame in 34 position states viewed in the fuselage fixed reference frame CB0. Bioinspired ornithopter test platform wing in free-flight marker location: XBT-axis location on experimental test platform resulting in minimal deformation of a reference YBT/ZBT reference plane using a 1 degree of freedom flapping motion. Flapping angle zeta and beta location on shown in experimental wing test data (maximal deformation of CW,0 reference plane, and XBT position states). Modeled flapping angle (FA) time history based on flight test data versus FA in flight test data E-2. Experimental thrust flap reference motion in 34 position states in the fuselage fixed reference plane CB0. Modeled thrust flap reference motion in 34 position states in the fuselage fixed reference plane CB0 versus wing at zero deformation (PS0). Experimental elastic deflections in the fuselage fixed reference frame CB0 during a wing beat. Experimental elastic deformation in the wing fixed reference frame CW during a wing beat. Model image SimXpertdML101 five-body flexible multi-body dynamics model (fuselage reference frame CB is highlighted). Verification bench testdmodel 3 Adscale ML101 (6.17 Hz). FMBD, flexible multi-body dynamics; HFI, horizontal force inertia; HPF, horizontal propulsive force; VPF, vertical propulsive force. Wing tip locationdviewed at one experimental position state (mid-downstroke). Results wing kinematics model 5 experiment: flight test: (left) back view and (right) side view. Propulsive forces acting on the fuselage center of massdobtained from experiment (E-2) and five-body vehicle dynamics model using aerodynamic model C. Simulated inertia forces on fuselage center of mass CB in free flight (inertial vertical propulsive force)dupstrokeedownstroke transition.
135
136
136 137
137
138
139 139 140
141 142 142 143
145 146 147
148
149
xvi Figure 6.28
Figure 6.29
List of Figures
Results inertia forces (E3) with error bars versus simulation results with STD, (A) inertial horizontal propulsive force (IHPF), (B) inertial vertical propulsive force (IVPF), (C) inertial pitching moment (IPM) versus magnitude. Results: body force magnitude system ID model (MSK004 E1-I)d body force magnitudedaero-model C.
150 152