Severi varieties and branch curves of abelian surfaces of type (1,3)

Let (A,L) be a principally polarized abelian surface of type (1,3). The linear system |L| defines a 6:1 covering of A onto P2, branched along a curve B of degree 18 in P2. The main result of the paper is that for general (A,L) the curve B irreducible, admits 72 cusps, 36 nodes or tacnodes, each tacnode counting as two nodes, 72 flexes and 36 bitangents. The main idea of the proof is to use the fact that for a general (A,L) of type (1,3) the closure of the Severi variety V in |L| is dual to the curve B in the sense of projective geometry. We investigate V and B via degeneration to a special abelian surface.Comment: 17 page

Application of Hybrid Laminar Flow Control to Global Range Military Transport Aircraft

A study was conducted to evaluate the application of hybrid laminar flow control (HLFC) to global range military transport aircraft. The global mission included the capability to transport 132,500 pounds of payload 6500 nautical miles, land and deliver the payload and without refueling return 6500 nautical miles to a friendly airbase. The preliminary design studies show significant performance benefits obtained for the HLFC aircraft as compared to counterpart turbulent flow aircraft. The study results at M=0.77 show that the largest benefits of HLFC are obtained with a high wing with engines on the wing configuration. As compared with the turbulent flow baseline aircraft, the high wing HLFC aircraft shows 17 percent reduction in fuel burned, 19.2 percent increase in lift-to-drag ratio, an insignificant increase in operating weight, and a 7.4 percent reduction in gross weight

Lockheed laminar-flow control systems development and applications

Progress is summarized from 1974 to the present in the practical application of laminar-flow control (LFC) to subsonic transport aircraft. Those efforts included preliminary design system studies of commercial and military transports and experimental investigations leading to the development of the leading-edge flight test article installed on the NASA JetStar flight test aircraft. The benefits of LFC on drag, fuel efficiency, lift-to-drag ratio, and operating costs are compared with those for turbulent flow aircraft. The current activities in the NASA Industry Laminar-Flow Enabling Technologies Development contract include summaries of activities in the Task 1 development of a slotted-surface structural concept using advanced aluminum materials and the Task 2 preliminary conceptual design study of global-range military hybrid laminar flow control (HLFC) to obtain data at high Reynolds numbers and at Mach numbers representative of long-range subsonic transport aircraft operation