Maneuvering Delta Research Articles

Generalized Image Navigation & Registration Algorithms for Ground and Space Segments

Ground segment image navigation and registration algorithms and space segment image motion compensation algorithm are presented. The fundamental ground algorithm is based on Kalman filter instead of least squares and does not require ranging or accurate orbit to be provided by flight dynamics. Kalman filter is used to estimate attitude correction angles, orbit position and velocity relative to ideal geostationary orbit, and internal misalignments of imagers with single mirror or two mirrors. Kalman filter measurements consist of landmarks extracted from the imaging instrument level 1A data blocks, maneuver delta V or coarse orbit from flight dynamics, and spacecraft attitude telemetry inserted in the imager wideband data. The ground algorithm is then shown how to be applied to systems with star and landmark measurements, systems with star only measurements with accurate orbit provided by flight dynamics or by the global positioning system, and systems with spacecraft inertial angular rate. Pixel location transformation from imager line of sight reference frame to GOES and CGMS fixed grid frames is also provided for on-ground image registration using resampling.

Support Interference for a Maneuvering Delta Wing

The results of a recent investigation of support interference in dynamic wind-tunnel testing are presented. Particular emphasis has been focused on studying the interaction of vortices generated by delta wing models at high angle of attack with a support structure. A novel approach was used whereby the effects of time-varying vortex strength could be separated from the effects of the vortex-support interaction. With this approach, it was shown that the principal effect of support interference was to cause an upstream shift in the mean breakdown location, regardless of the form of motion or forcing frequency. The magnitude of the fluctuations in the breakdown location was shown to be dictated by support interference at low forcing frequencies, but by time-varying vortex strength effects at high frequencies. A number of important observations were also made of the vortex behavior at high forcing frequencies. In particular, a curious jumping behavior of the vortex breakdown location was observed. The presence of the support reduced the magnitude of the breakdown jump, but jumping was, nevertheless, observed in all of the cases considered at high enough forcing frequencies.

Flow control over a maneuvering delta wing at high angles of attack

The possibility of delaying vortex breakdown to higher angles of attack by employing control surfaces is studied experimentally. The effect of an apex flap is tested for fixed and dynamically pitching delta wings. Flow visualization, surface pressure measurements, and laser-Doppler velocimetry are employed to map out pressure, velocity, and vorticity fields. It is found that a drooping apex flap can delay vortex breakdown by an angle of 8 deg beyond the steady flow breakdown angle of attack. The apex flap effect is equally pronounced in dynamic maneuvers.

Prediction of Unsteady Aerodynamic Forces on Maneuvering Delta Wings

A semi-empirical model was developed to study the breakdown effects on maneuvering delta wings performing very high angle of attack excursions. The basic vortical flow model used was the Brown & Michael model and an unsteady source distribution was found to simulate the breakdown of the leading edge vortices. The source distribution is based on experimental observations of the vortex breakdown chordwise propagation during pitch-down and pitch-up motion. In spite of the simplicity of the vortical model used, the new model simulates the present complicated flow field. This model succeeds in predicting the leading edge core position hysteresis, the hysteresis in the unsteady pressure distribution and the corresponding airloads at extreme angles of attack. The normal force and pitching moment results are in good agreement with experimental measurements.

Unsteady transonic airfoil computation using implicit Euler scheme on body-fixed grid

The unsteady Euler equations have been derived for the flow relative motion with respect to a frame of reference that is rigidly attached to the moving airfoil. The resulting equations preserve the conservation form. The grid is generated once by an elliptic solver without any need for dynamic grid computation. An implicit approximately factored finite-volume scheme has been developed and implemented through a fully vectorized computer program. The scheme is based on the spatial approximate factorization of Beam and Warming. Implicit second-order and explicit second- and fourth-order dissipations are added to the scheme. The boundary conditions are explicitly satisfied. The scheme is applied to steady and unsteady transonic rigid-airfoil flows. For forced harmonic airfoil motions, periodic solutions are achieved within the third cycle of oscillation. The results are in good agreement with the experimental data. sonic flows past a NACA 0015 airfoil at a constant pitch rate.18 The latter case is the same application considered in Ref. 16. The numerical solution has been obtained by using the flux-vector splitting and the flux-difference splitting meth- ods extended for dynamic meshes.19 In Ref. 18, it is noted that different turbulence models give different normal-force and pitching-moment coefficients. Numerical solutions of the unsteady Euler equations are less expensive than those of the unsteady Navier-Stokes equations. For the unsteady transonic flow, the unsteady Euler equations adequately model most of the real flow features, with the exception of viscous effects whenever they are substantial. The Euler equations model shock waves and their motion, entropy increase across shocks and entropy gradient, and vorticity production and convection behind shocks, as can be seen from Crocco's theorem and the inviscid vorticity transport equa- tion. Recently, successful time-accurate solutions of the un- steady Euler equations have been presented for pitching air- foils19 and wings in transonic flows,20 and for the rolling oscillation of delta wings—a vortex-dominated flow problem in a locally conical supersonic flows.21 To the best of bur knowledge, Ref. 21 is the first work done for unsteady vortex- dominated flows with shock waves, which is directly applica- ble to maneuvering delta wings. In this paper, we present an implicit approximately-factored finite-volume scheme for the time-accurate numerical solution of the unsteady Euler equations of the flow relative motion with respect to an airfoil-fixed frame of reference. The scheme is applied to steady and unsteady transonic flows around a NACA 0012 airfoil. For the unsteady flows, the airfoil is in pitching oscillation about a small and moderate mean angle of attack at a large amplitude. The computational results are compared with the experimental data.

Computation of steady and unsteady vortex-dominated flows with shockwaves

The unsteady Euler equations have been derived in the conservation form for the flow relative motion with respect to a rotating frame of reference. The resulting equations are solved by using a central-difference finite-volume scheme with four-state Runge-Kutta time stepping. For steady flow applications local time stepping is used, and for unsteady applications the minimum global time stepping is used. A three-dimensional fully vectorized computer program has been developed and applied to steady and unsteady maneuvering delta wings. The capability of the three-dimensional program has been demonstrated for a rigid sharp-edged delta wing undergoing uniform rolling in a conical flow and rolling oscillations in a locally conical flow.

Linear guidance laws for space missions

A general analysis of guidance laws is presented along with a review of the propagation of state perturbations. Linearized guidance laws are derived for fixed and variable time of arrival, and for the Shuttle phasing and height guidance maneuvers. In general, six interrelated partials are involved in each guidance law. These partials relate the maneuver delta velocity and time of flight to perturbations in initial position, velocity, and time. The partials can be expressed as a function of a single fundamental guidance partial, which relates the maneuver to the final position perturbation, and the partials from the upper row of the augmented time transition matrix (augmented with the dynamical state vector). Guidance can be interpreted as a form of offset targeting. PACE trajectories involve a series of coast phases separated by maneuvers. The maneuvers can be derived by imposing sufficient guidance constraints to uniquely define the maneuver. The guidance constraints can be imposed on the maneuver, postmaneuyer trajectory, or some combination thereof. Impulsive maneuvers may be assumed for many space missions. The impulsive maneuvers can be computed exactly or with a linearized model. The linearized model could be used for real-time software because trajectory perturbations are generally small, but a more likely use is in preflight covariance analysis. The linear model contains guidance matrices for up- dating through the maneuvers, and transition matrices for up- dating through the coasting phases. This paper presents two general techniques for solving the linear guidance problem. Most applications of linearized guidance laws have been based on fixed- and variable-time-of-arrival guidance.1'4 Many other linearized laws can be introduced by imposing dif- ferent constraints on the maneuver and postmaneuver trajec- tory.5'6 Some general properties of linearized guidance laws were established by Cicolani.7 A general solution to the linear guidance problem was proposed by Tempelman5 by introduc- ing a generalized linear constraint equation. This paper at- tempts to define some general techniques for establishing the relationship between the maneuver and the perturbations in position, velocity, and time using a more intuitive approach than presented in Ref. 5. Fixed- and variable-time-of-arrival guidance laws are reviewed to demonstrate the techniques and to serve as an introduction to more complicated maneuvers, such as the Shuttle phasing and height maneuvers.

Modeling aerodynamic responses to aircraft maneuvers - A numerical validation

The regime of validity of an aerodynamic mathematical model, applicable to describe the nonlinear aerodynamic reactions to a delta wing maneuvering at high angles of attack, is investigated. An unsteady vortexlattice method is used to compute the unsteady flowfields, and thus to evaluate the aerodynamic data required by the model, in terms of specified characteristic motions. Time-histories of the aerodynamic responses to complex motions are generated by means of the model and the evaluated aerodynamic data and are compared with baseline aerodynamic responses obtained from direct vortex-lattice computations. The validity of the mathematical modeling approach for the maneuvering delta wing is demonstrated by agreement of the force and moment responses obtained from the two approaches.