Aircraft Route Optimization for Formation Flight

Abstract

We quantify the fuel and cost benefits of applying extended formation flight to commercial airline operations. Central to this study is the development of a bi-level, mixed integer-real formation flight optimization framework. The framework has two main components: 1) a continuous domain aircraft mission performance optimization and 2) an integer optimization component that selects the best combination of optimized missions to form a formation flight schedule. The mission performance reflects the effects of rolled-up wakes, formation heterogeneity, and formation-induced compressibility. The results show that an airline can use formation flight to reduce fuel burn by 5.8% or direct operating cost by 2.0% in a long-haul international schedule. The savings increase to 7.7% in fuel or 2.6% in cost for a large-scale, transatlantic airline alliance schedule. These results include the effects of a conservative fuel reserve for formation flight. Sensitivity studies show that a modest reduction in the cruise Mach number may be sufficient to manage the impact of formation-induced compressibility effects on system-level formation flight performance. We demonstrate that the potential savings from extended formation flight-an operational improvement using existing aircraft-can approach those claimed for advanced vehicle technologies and unconventional configurations.

Cruise Range in Formation Flight

“…For a constant lift coefficient this results in a reduction in induced drag [1]. Numerous research studies, ranging from numerical simulation studies to wind tunnel testing and in-flight demonstrations, have highlighted the potential fuel saving benefits of formation flight for commercial aircraft.…”

“…Furthermore, their approach assumes that formation flight also affects the zero lift drag coefficient which is not the case in reality. Xu et al [1] also investigate aircraft route optimization for formation flight. In their study, the induced drag coefficient of an aircraft in formation flight is calculated beforehand based on an aerodynamic model as a function of various parameters (lift coefficient, position in the formation, formation type).…”

Analytic Approach to Optimal Routing for Commercial Formation Flight

“…Section VI considers the impact on timing and introduces scheduling constraints. Studies based on individual pairings, looking only at the routing problem, have shown potential positive tradeoffs between the diversion to join formation and the reduction in drag formation flight produces [19][20][21][22][23][24]. Formation routes for five aircraft studied by Bower et al [4] focus on aerodynamic aspects such as wing tip separation.…”

“…These prior works adopt numerical trajectory optimization techniques [25][26][27] to calculate high-fidelity solutions to the routing problem. Once the routing problem is solved, evaluating the cost for each potential formation, the subsequent assignment problem is readily solved by a discrete optimization [20].…”

Dynamic Load Alleviation in Wake Vortex Encounters

“…7 In either case, advanced flight control techniques are required to ensure optimal trajectories of the vortex-generating and the follower aircraft, 8 particularly with adverse atmospheric conditions. From the point of view of airframe design, unexpected WVE can lead to large dynamic loads that create structural integrity risks.…”