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, td, 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 td 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.

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 sim- ulation. 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 bumblebee in forward flight

The longitudinal dynamic flight stability of a bumblebee in forward flight is studied. The method of computational fluid dynamics is used to compute the aerodynamic derivatives and the techniques of eigenvalue and eigenvector analysis are employed for solving the equations of motion. The primary findings are as the following. The forward flight of the bumblebee is not dynamically stable due to the existence of one （or two） unstable or approximately neutrally stable natural modes of motion. At hovering to medium flight speed [flight speed Ue = （0-3.5）m s^-1; advance ratio J = 0-0.44], the flight is weakly unstable or approximately neutrally stable; at high speed （Ue = 4.5 m s^-1; J = 0.57）, the flight becomes strongly unstable （initial disturbance double its value in only 3.5 wingbeats）.

Dynamic Flight Stability of a Model Hoverfly in Inclined-Stroke-Plane Hovering

Most hovering insects flap their wings in a horizontal plane, called ＇normal hovering＇. But some of the best hoverers, e.g. true hoverflies, hover with an inclined stroke plane. In the present paper, the longitudinal dynamic flight stability of a model hoverfly in inclined-stroke-plane hovering was studied. Computational fluid dynamics was used to compute the aerodynamic derivatives and the eigenvalue and eigenvector analysis was used to solve the equations of motion. The primary findings are as follows. （1） For inclined-stroke-plane hovering, the same three natural modes of motion as those for normal hovering were identified： one unstable oscillatory mode, one stable fast subsidence mode, and one stable slow subsidence mode. The unstable oscillatory mode and the fast subsidence mode mainly have horizontal translation and pitch rotation, and the slow subsidence mode mainly has vertical translation. （2） Because of the existence of the unstable oscillatory mode, inclined-stroke-plane hov- ering flight is not stable. （3） Although there are large differences in stroke plane and body orientations between the in- clined-stroke-plane hovering and normal hovering, the relative position between the mean center of pressure and center of mass for these two cases is not very different, resulting in similar stability derivatives, hence similar dynamic stability properties for these two types of hovering.

Lateral Flight Stability of Two Hovering Model Insects

The longitudinal disturbance motion of different insects at hovering flight has the same modal structure. Here, we consider the case of lateral motion. The lateral dynamic flight stability of two model insects, hoverfly and honeybee, at hovering flight is studied. The method of computational fluid dynamics is applied to compute the stability derivatives. The techniques of eigenvalue and eigenvector analysis are used to solve the equations of motion. Results show that the lateral disturbance motion of the hoverfly has three natural modes of motion： an unstable divergence mode, a stable oscillatory mode and a stable subsidence mode, and the flight is unstable; while the honeybee has a different modal structure （a stable slow subsidence mode, a stable fast subsidence mode, and a nearly neutrally stable oscillatory mode） and the flight is nearly neutrally stable. The change in modal structure between the two insects is due to their roll-moment/side-velocity derivative having different sign, and the sign difference is because that the hoverfly has a relatively small, but the honeybee has a relatively large, distance between the wing roots and the center of mass. Thus, unlike the case of longitudinal motion, for lateral motion, some insects have different modal structures and stability properties from others.

Study of vertically ascending flight of a hawkmoth model

This paper provides insight into the wing kinematics,the power requirement and the dynamic stability characteristics of a hawkmoth model in vertically ascending flight.The wing kinematics of the hawkmoth model is obtained based on the minimum required power assumption.The optimization process is conducted using genetic and simplex algorithms that are coupled with an artificial neural network to rapidly predict the aerodynamic force and required power.The training data for the neural network are generated from an unsteady vortex-lattice method.Compared to hover,the results in this study show the larger flapping frequency and the smaller rotation amplitude of the hawkmoth wing kinematics in ascending flight.Additionally,more power is required when the ascending speed increases.While conducting a dynamic modal analysis based on a cycle-average approach,the certain effect of the ascending speed on the modal structures of the hawkmoth model was observed.

Aeroservoelastic modeling and analysis of a canard-configured air-breathing hypersonic vehicles

Air-breathing hypersonic vehicles （HSVs） are typically characterized by interactions of elasticity, propulsion and rigid-body flight dynamics, which may result in intractable aeroservoelastic problem. When canard is added, this problem would be even intensified by the introduction of low-frequency canard pivot mode. This paper concerns how the aeroservoelastic stability of a canard-configured HSV is affected by the pivot stiffnesses of all-moveable horizontal tail （HT） and canard. A wing/pivot system model is developed by considering the pivot torsional flexibility, fuselage vibration, and control input. The governing equations of the aeroservoelastic system are established by combining the equations of rigid-body motion, elastic fuselage model, wing/pivot system models and actuator dynamics. An unsteady aerodynamic model is developed by steady Shock-Expansion theory with an unsteady correction using local piston theory. A baseline controller is given to provide approximate inflight characteristics of rigid-body modes. The vehicle is trimmed for equilibrium state, around which the linearized equations are derived for stability analysis. A comparative study of damping ratios, closed-loop poles and responses are conducted with varying controller gains and pivot stiffnesses. Available bandwidth for control design is discussed and feasible region for pivot stiffnesses of HT and canard is given.