Wake Sensing for Aircraft Formation Flight

Abstract

It is well established that flying aircraft in formation can lead to improved aerodynamic efficiency. However, successfully doing so is predicated on having knowledge of the lead aircraft's wake position. Here, a wake-sensing strategy for estimating the wake position and strength in a two-aircraft formation is explored in a simplified proof-ofconcept setting. The wake estimator synthesizes wing-distributed pressure measurements, taken on the trailing aircraft, by making use of an augmented lifting-line model in conjunction with both Kalman-type and particle filters. Simple aerodynamic models are introduced in constructing the filter to enable fundamental wake-sensing challenges to be identified and reconciled. The various estimation algorithms are tested in a vortex lattice simulation environment, thus allowing the effects of modeling error to be analyzed. It is found that biases in the position estimates no longer arise if a particle filter is used in place of the Kalman-type filters. Filter divergence is observed when the relative aircraft separations are held fixed. This divergent behavior can be alleviated with the introduction of relative aircraft motions, for example in the form of a cross-track dither signal.

Observability-Based Optimal Sensor Placement for Flapping Airfoil Wake Estimation

“…The results showed that vortex location and strength are observable using two velocity sensors, and that active motion of the airfoil (i.e., flapping) improves vortex observability, similar to the way that the dither signal in [13] improved estimator performance. An unscented Kalman filter (UKF) was used in simulation to estimate the location and strength of vortices in the wake of the flapping airfoil [14].…”

“…The activation of each sensor is given by α α∕ν, and the resulting condition number of the observability Gramian is γ. If the solution of problem (14) yields sensor activations such that α i ∈ f0; 1g ∀ i (within numerical precision), then the solution to the relaxed problem (14) is also the solution to problem (13). Otherwise, the original problem (13) must be solved using mixed-integer programming techniques.…”

“…The input data to problems (13)(14)(15)(16) are an array of observability Gramians: one for each of the r feasible sensor locations. Because the observability Gramian may not be easy to calculate for highdimensional or complex systems, the empirical observability Gramian is a good method for computing the problem input data.…”

“…The wake of a flapping foil is modeled using unsteady potential flow theory (see [37] Chapter 6, [13], and [38, Chapter 6]), where discrete point vortices are shed from the trailing edge at each time step to simultaneously satisfy the Kutta condition and Kelvin's circulation theorem. The potential flow around the foil is computed through the Joukowski conformal mapping to a circular cylinder, as shown in Fig.…”

“…In [12], an observability-based sensor placement problem was solved by exhaustive search for sensor locations on a hydrofoil that improves angle-of-attack estimates, which were used in a feedback control of a Joukowski-foil model of an underwater vehicle. Wake estimation in aircraft formation flight was studied in [13], where pressure sensors on the leading edge of the trailing aircraft's wing were used in a vortex lattice simulation to track the lead aircraft's wake. The wake estimators were found to diverge without the use of a cross-track dither signal to excite the measurement dynamics, indicating that actuation may be required for wake observability.…”