Pitching moment

About: Pitching moment is a(n) research topic. Over the lifetime, 3213 publication(s) have been published within this topic receiving 38721 citation(s).

The Aerodynamics of Hovering Insect Flight. III. Kinematics

Abstract: Insects in free flight were filmed at 5000 frames per second to determine the motion of their wings and bodies. General comments are offered on flight behaviour and manoeuvrability. Changes in the tilt of the stroke plane with respect to the horizontal provides kinematic control of manoeuvres, analogous to the type of control used for helicopters. A projection analysis technique is described that solves for the orientation of the animal with respect to a cam era-based coordinate system, giving full kinematic details for the longitudinal wing and body axes from single-view films. The technique can be applied to all types of flight where the wing motions are bilaterally symmetrical: forward, backward and hovering flight, as well as properly banked turns. An analysis of the errors of the technique is presented, and shows that the reconstructed angles for wing position should be accurate to within 1-2° in general. Although measurement of the angles of attack was not possible, visual estimations are given. Only 11 film sequences show flight velocities and accelerations that are small enough for the flight to be considered as ‘hovering’. Two sequences are presented for a hover-fly using an inclined stroke plane, and nine sequences of hovering with a horizontal stroke plane by another hover-fly, two crane-flies, a drone-fly, a ladybird beetle, a honey bee, and two bumble bees. In general, oscillations in the body position from its mean motion are within measurement error, about 1-2 % of the wing length. The amplitudes of oscillation for the body angle are only a few degrees, but the phase relation of this oscillation to the wingbeat cycle could be determined for a few sequences. The phase indicates that the pitching moments governing the oscillations result from the wing lift at the ends of the wingbeat, and not from the wing drag or inertial forces. The mean pitching moment of the wings, which determines the mean body angle, is controlled by shifting the centre of lift over the cycle by changing the mean positional angle of the flapping wings. Deviations of the wing tip path from the stroke plane are never large, and no consistent pattern could be found for the wing paths of different insects; indeed, variations in the path were even observed for individual insects. The wing motion is not greatly different from simple harmonic motion, but does show a general trend towards higher accelerations and decelerations at either end of the wingbeat, with constant velocities during the middle of half-strokes. Root mean square and cube root mean cube angular velocities are on average about 4 and 9% lower than simple harmonic motion. Angles of attack are nearly constant during the middle of half-strokes, typically 35° at a position 70 % along the wing length. The wing is twisted along its length, with angles of attack at the wing base some 10-20° greater than at the tip. The wings rotate through about 110° at either end of the wingbeat during 10-20 % of the cycle period. The mean velocity of the wing edges during rotation is similar to the mean flapping velocity of the wing tip and greater than the flapping velocity for more proximal wing regions, which indicates that vortex shedding during rotation is com parable with that during flapping. The wings tend to rotate as a flat plate during the first half of rotation, which ends just before, or at, the end of the half-stroke. The hover-fly using an inclined stroke plane provides a notable exception to this general pattern : pronation is delayed and overlaps the beginning of the downstroke. The wing profile flexes along a more or less localized longitudinal axis during the second half of rotation, generating the ‘flip’ profile postulated by Weis-Fogh for the hover-flies. This profile occurs to some extent for all of the insects, and is not exceptionally pronounced for the hover-fly. By the end of rotation the wings are nearly flat again, although a slight camber can sometimes be seen. Weis-Fogh showed that beneficial aerodynamic interference can result when the left and right wings come into contact during rotation at the end of the wingbeat. His ‘fling’ mechanism creates the circulation required for wing lift on the subsequent half-stroke, and can be seen on my films of the Large Cabbage White butterfly, a plum e moth, and the Mediterranean flour moth. However, their wings ‘peel’ apart like two pieces of paper being separated, rather than fling open rigidly about the trailing edges. A ‘partial fling’ was found for some insects, with the wings touching only along posterior wing areas. A ‘ near fling ’ with the wings separated by a fraction of the chord was also observed for m any insects. There is a continuous spectrum for the separation distance between the wings, in fact, and the separation can vary for a given insect during different manoeuvres. It is suggested that these variants on Weis-Fogh’s fling mechanism also generate circulation for wing lift, although less effectively than a complete fling, and that changes in the separation distance may provide a fine control over the amount of lift produced.

Robust nonlinear control of a hypersonic aircraft

Abstract: For the longitudinal motion of a hypersonic aircraft containing twenty-eight inertial and aerodynamic uncertain parameters, robust flight control systems with nonlinear dynamic inversion structure are synthesized. The system robustness is characterized by the probability of instability and probabilities of violations of thirty-eight performance criteria, subjected to the variations of the uncertain system parameters. The design cost function is defined as a weighted quadratic sum of these probabilities. The control system is designed using a genetic algorithm to search a design parameter space of the nonlinear dynamic inversion structure. During the search iteration, Monte Carlo evaluation is used to estimate the system robustness and cost function. This approach explicitly takes into account the design requirements and makes full use of engineering knowledge in the design process to produce practical and efficient control systems. A4 MY, m 4 Nomenclatm-e speed of sound, ftls drag coefficient lift coefficient moment coefficient due to pitch rate moment coefficient due to angle of attack moment coefficient due to elevator deflection thrust coefficient reference length, 80 ft drag, lbf altitude, ft moment of inertia, 7 X lo6 slug-ft2 lift, lbf Mach number pitching moment, lbf-ft mass, 9375 slugs pitch rate, radis radius of the Earth, 20,903,500 ft radial distance from Earth’s center, ft reference area, 3603 ft2 thrust, lbf velocity, ft/S angle of attack, rad throttle setting flight-path angle, rad elevator deflection, rad gravitational constant, 1.39 X 1Or6 ft3/s2~ density of air, slugsIft

Investigation of flow over an oscillating airfoil

Abstract: The characteristics of the unsteady boundary layer and stall events occurring on an oscillating NACA 0012 airfoil were investigated by using closely spaced multiple hot-film sensor arrays at . Aerodynamic forces and pitching moments, integrated from surface pressure measurements, and smoke-flow visualizations were also obtained to supplement the hot-film measurements. Special attention was focused on the behaviour of the spatial-temporal progression of the locations of the boundary-layer transition and separation, and reattachment and relaminarization points, compared to the static values, for a range of oscillation frequency and amplitude both prior to, during and after the stall. The initiation, growth and rearward convection of a leading-edge vortex, and the role of the laminar separation bubble leading to the dynamic stall, as well as the mechanisms responsible for the stall events observed at different test conditions were also characterized. The hot-film measurements were also correlated with the aerodynamic load and pitching moment results to quantify the values of lift increment and stall angle delay as a result of the observed boundary layer and stall events. The results reported here provide an insight into the detailed nature of the unsteady boundary-layer events as well as the stalling mechanisms at work at different stages in the dynamic-stall process.

Low Reynolds Number Aerodynamics of Low-Aspect-Ratio, Thin/Flat/Cambered-Plate Wings

Abstract: The design of micro aerial vehicles requires a better understanding of the aerodynamics of small low-aspect-ratio wings An experimental investigation has focused on measuring the lift, drag, and pitching moment about the quarter chord on a series of thin flat plates and cambered plates at chord Reynolds numbers varying between 60,000 and 200,000 Results show that the cambered plates offer better aerodynamic characteristics and performance It also appears that the trailing-edge geometry of the wings and the turbulence intensity in the wind tunnel do not have a strong effect on the lift and drag for thin wings at low Reynolds numbers Moreover, the results did not show the presence of any hysteresis, which is usually observed with thick airfoils/wings

Mechanics of Flight

Abstract: Preface. Acknowledgments. 1. Overview of Aerodynamics. 1.1. Introduction and Notation. 1.2. Fluid Statics and the Atmosphere. 1.3. The Boundary Layer Concept. 1.4. Inviscid Aerodynamics. 1.5. Review of Elementary Potential Flows. 1.6. Incompressible Flow over Airfoils. 1.7. Trailing-Edge Flaps and Section Flap Effectiveness. 1.8. Incompressible Flow over Finite Wings. 1.9. Flow over Multiple Lifting Surfaces. 1.10. Wing Stall and Maximum Lift Coefficient. 1.11. Wing Aerodynamic Center and Pitching Moment. 1.12. Inviscid Compressible Aerodynamics. 1.13. Compressible Subsonic Flow. 1.14. Supersonic Flow. 1.15. Problems. 2. Overview of Propulsion. 2.1. Introduction. 2.2. The Propeller. 2.3. Propeller Blade Theory. 2.4. Propeller Momentum Theory. 2.5. Off-Axis Forces and Moments Developed by a Propeller. 2.6. Turbojet Engines: The Thrust Equation. 2.7. Turbojet Engines: Cycle Analysis. 2.8. The Turbojet Engine with Afterburner. 2.9. Turbofan Engines. 2.10. Concluding Remarks. 2.11. Problems. 3. Aircraft Performance. 3.1. Introduction. 3.2. Thrust Required. 3.3. Power Required. 3.4. Rate of Climb and Power Available. 3.5. Fuel Consumption and Endurance. 3.6. Fuel Consumption and Range. 3.7. Power Failure and Gliding Flight. 3.8. Airspeed, Wing Loading, and Stall. 3.9. The Steady Coordinated Turn. 3.10. Takeoff and Landing Performance. 3.11. Accelerating Climb and Balanced Field Length. 3.12. Problems. 4. Longitudinal Static Stability and Trim. 4.1. Fundamentals of Static Equilibrium and Stability. 4.2. Pitch Stability of a Cambered Wing. 4.3. Simplified Pitch Stability Analysis for a Wing-Tail Combination. 4.4. Stick-Fixed Neutral Point and Static Margin. 4.5. Estimating the Downwash Angle on an Aft Tail. 4.6. Simplified Pitch Stability Analysis for a Wing-Canard Combination. 4.7. Effects of Drag and Vertical Offset. 4.8. Effects of Nonlinearities on the Aerodynamic Center. 4.9. Effect of the Fuselage, Nacelles, and External Stores. 4.10. Contribution of Running Propellers. 4.11. Contribution of Jet Engines. 4.12. Problems. 5. Lateral Static Stability and Trim. 5.1. Introduction. 5.2. Yaw Stability and Trim. 5.3. Estimating the Sidewash Gradient on a Vertical Tail. 5.4. Estimating the Lift Slope for a Vertical Tail. 5.5. Effects of Tail Dihedral on Yaw Stability. 5.6. Roll Stability and Dihedral Effect. 5.7. Roll Control and Trim Requirements. 5.8. The Generalized Small-Angle Lateral Trim Requirements. 5.9. Steady-Heading Sideslip. 5.10. Engine Failure and Minimum-Control Airspeed. 5.11. Longitudinal-Lateral Coupling. 5.12. Control Surface Sign Conventions. 5.13. Problems. 6. Aircraft Controls and Maneuverability. 6.1. Longitudinal Control and Maneuverability. 6.2. Effects of Structural Flexibility. 6.3. Control Force and Trim Tabs. 6.4. Stick-Free Neutral and Maneuver Points. 6.5. Ground Effect, Elevator Sizing, and CG Limits. 6.6. Stall Recovery. 6.7. Lateral Control and Maneuverability. 6.8. Aileron Reversal. 6.9. Other Control Surface Configurations. 6.10. Airplane Spin. 6.11. Problems. 7. Aircraft Equations of Motion. 7.1. Introduction. 7.2. Newton's Second Law for Rigid-Body Dynamics. 7.3. Position and Orientation: The Euler Angle Formulation. 7.4. Rigid-Body 6-DOF Equations of Motion. 7.5. Linearized Equations of Motion. 7.6. Force and Moment Derivatives. 7.7. Nondimensional Linearized Equations of Motion. 7.8. Transformation of Stability Axes. 7.9. Inertial and Gyroscopic Coupling. 7.10. Problems. 8. Linearized Longitudinal Dynamics. 8.1. Fundamentals of Dynamics: Eigenproblems. 8.2. Longitudinal Motion: The Linearized Coupled Equations. 8.3. Short-Period Approximation. 8.4. Long-Period Approximation. 8.5. Pure Pitching Motion. 8.6. Summary. 8.7. Problems. 9. Linearized Lateral Dynamics. 9.1. Introduction. 9.2. Lateral Motion: The Linearized Coupled Equations. 9.3. Roll Approximation. 9.4. Spiral Approximation. 9.5. Dutch Roll Approximation. 9.6. Pure Rolling Motion. 9.7. Pure Yawing Motion. 9.8. Longitudinal-Lateral Coupling. 9.9. Nonlinear Effects. 9.10. Summary. 9.11. Problems. 10. Aircraft Handling Qualities and Control Response. 10.1. Introduction. 10.2. Pilot Opinion. 10.3. Dynamic Handling Quality Prediction. 10.4. Response to Control Inputs. 10.5. Nonlinear Effects and Longitudinal-Lateral Coupling. 10.6. Problems. 11. Aircraft Flight Simulation. 11.1. Introduction. 11.2. Euler Angle Formulations. 11.3. Direction-Cosine Formulation. 11.4. Euler Axis Formulation. 11.5. The Euler-Rodrigues Quaternion Formulation. 11.6. Quaternion Algebra. 11.7. Relations between the Quaternion and Other Attitude Descriptors. 11.8. Applying Rotational Constraints to the Quaternion Formulation. 11.9. Closed-Form Quaternion Solution for Constant Rotation. 11.10. Numerical Integration of the Quaternion Formulation. 11.11. Summary of the Flat-Earth Quaternion Formulation. 11.12. Aircraft Position in Geographic Coordinates. 11.13. Problems. Bibliography. Appendixes. A Standard Atmosphere, SI Units. B Standard Atmosphere, English Units. C Aircraft Moments of Inertia. Nomenclature. Index.