L-1011 testing with relaxed static stability

Wind tunnel and flight tests indicate that fuel savings of 2 percent can be achieved by center of gravity (C.G.) management for an L-1011 with the current wing configuration. The normal c.b. location is at 25 percent mean aerodynamic center (MAC). The maximum fuel saving occurs for a C.G. location of 35 percent MAC. However, flight at 35 percent requires that the C.G. range be extended aft of the 35-percent point. Flight at C.G. locations aft or 35 percent requires a pitch active control system (PACS) so that handling qualities are not significantly degraded. The development of this PACS is discussed

Topological invariants of rotationally symmetric crystals

Recent formal classifications of crystalline topological insulators predict that the combination of time-reversal and rotational symmetry gives rise to topological invariants beyond the ones known for other lattice symmetries. Although the classification proves their existence, it does not indicate a way of calculating the values of those invariants. Here we show that a specific set of concentric Wilson loops and line invariants yields the values of all topological invariants in two-dimensional systems with pure rotation symmetry in class AII. Examples of this analysis are given for specific models with twofold and threefold rotational symmetry. We find new invariants that relate to the presence of higher-order topology and corner charges