William Blake

Modeling of Aerodynamic Coupling Between Aircraft in Close Proximity

A method is developed for modeling the aerodynamic coupling between aircraft Hying in close proximity. Velocities induced on a trailing aircraft by vortices from an aircraft upstream are written as a function of the relative separation and relative orientation between the two aircraft. The nonuniform vortex-induced wind and wind gradients acting on the trail aircraft are approximated as effective uniform wind and wind gradients. In a dynamic simulation, the effective wind can be used directly in the equations of motion, whereas the wind gradient can be used in the standard buildup equations for the aerodynamic moments. This removes necessity to explicitly compute the induced forces and moments. Various vortex models for estimating induced velocities and averaging schemes for computing effective wind components and gradients are assessed

Comparison of Predicted and Measured Formation Flight Interference Effects

Results from a wind-tunnel test of two delta-wing aircraft in close proximity are presented and compared with predictions from a vortex lattice method. Large changes in lift, pitching moment, and rolling moment are found on the trail aircraft as it moves laterally relative to the lead aircraft. The magnitude of these changes is reduced as the trail aircraft moves vertically with respect to the lead aircraft. Lift-to-drag ratio of the trail aircraft is increased when the wing tips are slightly overlapped. Wake-induced lift is overpredicted slightly when the aircraft overlap in the spanwise direction. Wake-induced pitching and rolling moments are well predicted. A maximum induced drag reduction of 25% is measured on the trail aircraft, compared with a 40% predicted reduction. Three positional stability derivatives, change in lift and pitching moment with vertical position and change in rolling moment with lateral position, are studied. Predicted boundaries between stable and unstable regions were generally in good agreement with experimentally derived boundaries.

Derivation of the dynamics equations of receiver aircraft in aerial refueling

This paper describes the derivation of a new set of nonlinear, 6{DOF equations of motion of a receiver aircraft undergoing an aerial refueling, including the efiect of timevarying mass and inertia properties associated with the fuel transfer and the tanker’s vortex induced wind efiect. Since the Center of Mass (CM) of the receiver is time{varying during the fuel transfer, the equations are written in a reference frame whose origin is at the CM of the receiver before fuel transfer begins and stays flxed at that position even though the CM is moving during the refueling. Due to the fact that aerial refueling simulation and control deal with the position and orientation of the receiver relative to the tanker, the equations of motion are derived in terms of the translational and rotational position and velocity with respect to the tanker. Further, the derivation of the equations takes into account the momentum transfer into the receiver due to the fuel transfer. The receiver aircraft before fuel transfer is treated as a rigid body made up of ‘n’ particles. The dynamic efiects due to fuel transfer are modeled by considering the mass change to be conflned to a flnite number of lumped masses, which would normally represent the fuel tanks on the receiver aircraft. Once the refueling begins, by using the design parameters such as the shape, size and location of the individual fuel tanks and the rate of fuel ∞owing into each of them, the mass and location of the individual lumped masses are calculated and fed into the equations of motion as exogenous inputs. The new receiver equations of motion are implemented in an integrated simulation environment with a feedback controller for receiver station-keeping as well as the full set of nonlinear, 6{DOF equations of motion of the tanker aircraft and a feedback controller to ∞y the tanker on a U-turn maneuver.

Control and Simulation of Relative Motion for Aerial Refueling in Racetrack Maneuvers

T HIS paper focuses on the development of an integrated simulation environment and control algorithms for a receiver aircraft in boom–receptacle refueling (BRR) operation while the tanker flies in a racetrack maneuver. A racetrack maneuver is the standard pattern flown by tanker aircraft, with straight legs and bank turns [1]. This paper applies the earlier work by the authors on mathematical modeling of relative motion [2,3] and aerodynamic coupling [4] to the simulation of aerial refueling, and it develops control laws for the motion of the receiver relative to the tanker that flies in racetrack maneuvers. An integrated simulation environment is developed to take into account tanker maneuvers, motion of the receiver relative to the tanker, and the aerodynamic coupling due to the trailingwake vortex of the tanker. The separate dynamicmodel of the tanker, including its own controller, allows the simulation of the standard racetrack maneuvers of the tanker in aerial refueling operations. The mathematical model of the receiver expressed in terms of the relative position and orientation with respect to the tanker’s body frame facilitates the formulation, in a single framework, of maneuver and stationkeeping of the receiver behind the tanker. For the racetrack maneuvers of the tanker, a linear quadratic regulator (LQR)-based multi-input/multi-output (MIMO) state feedback and integral control technique is developed to track commanded speed, altitude, and yaw rate. Similarly, for the relative motion of the receiver, an LQR-based MIMO state feedback and integral control technique is designed to track the commanded trajectory expressed in the body frame of the tanker. Both controllers schedule their corresponding feedback and integral gains based on the commanded speed and yaw rate of the tanker. The tanker aircraft model represents KC-135R, and the receiver aircraft model is a tailless fighter aircraft with innovative control effectors (ICE) and thrust-vectoring capability. Because the receiver has redundant control variables, various control allocation schemes are investigated for trajectory tracking and stationkeeping while the tanker flies in various racetrack maneuvers with different commanded turn rates.

Static and dynamic wind tunnel testing of air vehicles in close proximity

Bihrle Applied Research Inc. has developed unique capabilities for investigating the aerodynamic effects on aircraft in close formation. Wind-tunnel experiments were conducted at the Langley Full-Scale Tunnel using special hardware and computer equipment developed specifically for formation testing. It was demonstrated that static and dynamic force and moment data, as well as surface pressure data and wake survey data, can be acquired and utilized to analyze and model vehicle in close formation flight. The data acquired is well suited for use in flight vehicle simulation for development of control laws for automated formation flight and automated refueling. Unique to this wind tunnel testing was the simultaneously collection of force and moment data from two separate models positioned differently during each run. Also unique was the dynamic testing conducted to determine the control surface deflections required to trim the trail vehicle in various formation positions.

Modeling of bow wave effect in aerial refueling

This paper develops a simple method of modeling the bow wave e ect in aerial refueling. Inviscid ow modeling around solid bodies based on the stream function de ned with various types of singularities are used. The ow eld induced by the presence of aircraft bodies is superimposed on the ow eld generated by horseshoe vortices. The induced total nonuniform ow eld is approximated by e ective uniform translational and rotational ow velocity components. The approximations are used in build-up equations for lift, drag and pitching moment coe cients of both tanker and receiver aircraft. The variations of the aerodynamic coe cients are calculated as the receiver aircraft position is varied (i) longitudinally from two and a half wing spans behind the contact position to half a wing span ahead of the contact position, and (ii) laterally from about one wing span left of the contact position to one wing span right. Comparisons with CFD results show that the vortex-based approaches alone are inadequate for modeling the bow wave e ects. The combination of the vortex-induced and the volume induced ow eld as implemented in this research results in much better agreement with the CFD results.

UAV Aerial Refueling - Wind Tunnel Results and Comparison with Analytical Predictions

Abstract : Results from a wind tunnel. test of a delta wing UAV behind a KC-135R are presented and compared with predictions from a planar vortex lattice code. Both the predictions and data show wake interference effects on the UAV that vary significantly with relative lateral and vertical position, and weakly with relative longitudinal position. Predicted trends are excellent for all force and moments except for drag, and magnitudes are reasonably well predicted. The distribution of lift between the tanker wing and tail is shown to have a strong effect on the receiver aerodynamics.

Application of Sweet Spot Determination to a Conventional Pair of Aircraft

of the trail aircraft at all points in the grid. The location of highest lift-to-drag ratio is then designated as the sweet spot based on the static simulation. A dynamic simulation is then used to determine if the sweet spot remains the same after considering the eects of trimming the aircraft. The trail KC-135R thrust required, along with the magnitudes of its control eectors, were investigated in the dynamic study, using the same grid as in the static case. The metric for sweet spot location in the dynamic case is the location of the least thrust required for the trail KC-135R. The results showed that the location of the sweet spot remains the same as that obtained using the static simulation. The eect on the static sweet spot, of varying the mass of the leader was also studied. It was observed that increasing the mass of the leading KC-135R aircraft aected only the aerodynamics of the trail aircraft and not the location of the sweet spot.

Wake-Vortex Induced Wind with Turbulence in Aerial Refueling - Part B: Model and Simulation Validation

This paper is the second of a series of two papers. The first paper (Part A) presents the analysis of the data obtained in an automated aerial refueling test flight conducted with a KC-135 as the tanker and a Learjet 25 as the receiver. The purpose of the analysis is to identify the turbulence and wind induced by the tanker wake and their effect on the receiver aircraft. This paper presents the methods used to model (i) prevailing wind, (ii) wake vortex induced wind and (iii) turbulence as the three sources of wind that the aircraft are exposed to and the approach used for incorporating the wind effect into the dynamic simulation of the aircraft. The test flight is simulated in various cases with different turbulence models and flight controllers. The simulation results are analyzed and compared with the flight data in terms of the power spectral densities and mean variations in order to validate the wind and turbulence modeling techniques.

Effect of Trail Aircraft Trim on Optimum Location in Formation Flight

Aircraft flight generates vortices that induce nonuniform wind distribution in their wake. A trailing/follower aircraft will experience induced wind components and gradients with various magnitudes and directions, depending on its location relative to the leader. This paper explores two methods of determining the relative location for optimum formation flight, termed the sweet spot. The relative location with the highest lift-to-drag ratio on the follower is denoted as the static sweet spot. In the second method, the trail aircraft is trimmed by adjusting the thrust and control surfaces to maintain its commanded position relative to the lead. The relative location requiring the least thrust is then assigned as the dynamic sweet spot. The results showed that, depending on the trail aircraft size, the static sweet spot might differ from the dynamic sweet spot. The effect of the leader weight and follower size on both static and dynamic sweet spot was also studied. It was discovered that the static and dynam...