Closed wing
A closed wing is a wing that effectively has two main planes which merge at their ends so that there are no conventional wing tips. Closed wing designs include the annular wing (commonly known as the cylindrical or ring wing), the joined wing, the box wing and spiroid tip devices. Like many wingtip devices, the closed wing aims to reduce the wasteful effects associated with wingtip vortices which occur at the tips of conventional wings. Although the closed wing has no unique claim on such benefits, many closed wing designs do offer structural advantages over a conventional cantilever  monoplane. Characteristics. Wingtip vortices form a major component of wake turbulence and are associated with induced drag, which is a significant contributor to total drag in most regimes. A closed wing avoids the need for wingtips and thus might be expected to reduce wingtip drag effects. In addition to potential structural advantages over open cantilevered wings, closed wing surfaces have some unique aerodynamic properties: The upshot is that although closed systems can produce large induced-drag reductions relative to a conventional planar wing, there is no significant aerodynamic advantage that uniquely accrues to their being closed rather than open. Configurations . Various types of closed wing have been described: History. Pioneer years. An early example of the closed wing was on the Blériot III aircraft, built in 1906 by Louis Blériot and Gabriel Voisin. The lifting surfaces comprised two annular wings mounted in tandem. The later Blériot IV replaced the forward annular wing with a biplane and added a canard foreplane to make it a three-surface aircraft. It was able to leave the ground in small hops before being damaged beyond repair. Based on the work of G.J.A. Kitchen, Cedric Lee and G. Tilghman Richards built and flew several annular -wing aeroplanes in which the fore and aft segments were on the same level. The first was a biplane. It was followed by a series of monoplanes, the last of the line remaining in use until 1914. World War II. In 1944, the German designer Ernst Heinkel began working on an annular-wing VTOL multirole single-seater called the "Lerche", but the project was soon abandoned. Postwar. During the 1950s, the French company SNECMA developed the Coléoptère, a single-person VTOL annular wing aircraft. The aircraft proved dangerously unstable despite the development and testing of several prototypes, and the design  was abandoned. Later proposals for closed-wing designs included the Convair Model 49 Advanced Aerial Fire Support System (AAFSS) and the 1980s Lockheed "Flying Bog Seat" concept. Dr. Julian Wolkovitch continued to develop the idea in the 1980s, claiming it was an efficient structural arrangement in which the horizontal tail provided structural support for the wing as well as acting as a stabilizing surface. The Spiroid winglet, a design currently under development by Aviation Partners, is a closed wing surface mounted at the end of a conventional wing. The company announced that the winglets fitted to a Gulfstream II reduced  fuel consumption in the cruise phase by over 10%. The Finnish company FlyNano flew a prototype of a closed wing ultralight aircraft, the FlyNano Nano on . An aircraft was also designed and constructed with a closed wing in Belarus. Miscellaneous modern examples include: Closed wings remain mostly confined to the realms of studies and conceptual designs, as the engineering challenges of developing a strong, self-supporting closed wing for use in the large airliners which would benefit most from increases in efficiency have yet to be overcome. The closed wing is also used in water, for surfboard fins of the  type also known as the tunnel fin. Lockheed Martin Environmentally Responsible Aviation Project. During 2011, the Environmentally Responsible Aviation Project at NASA's Aeronautics Research Mission Directorate invited study proposals towards meeting NASA's goal of reducing future aircraft fuel consumption by 50% compared to 1998. Lockheed Martin proposed a box wing design along with other advanced technologies. Prandtl Box Wing. In 1924, the German aerodynamicist Ludwig Prandtl suggested that a box wing, under certain conditions, might provide the minimum induced drag for a given lift and wingspan. In his design, two offset horizontal wings have vertical wings connecting their  tips and shaped to provide a linear distribution of side forces. The configuration is said to offer improved efficiency for a range of aircraft. In the 1980s, the Ligeti Stratos used this approach. The name "PrandtlPlane" was coined in the 1990s in research by Aldo Frediani "et al." of the University of Pisa. It is currently also used in some ultralight aircraft, IDINTOS (IDrovolante INnovativo TOScano) is a research project, co-funded by the regional government of Tuscany (Italy) in 2011 in order to design and manufacture an amphibious ultralight PrandtlPlane. The research project has been carried out by a  consortium of Tuscan public and private partners, led by the Aerospace Section of the Civil and Industrial Engineering Department of Pisa University, and has resulted in the manufacturing of a 2-seater VLA prototype. The configuration is also claimed to be theoretically efficient for wide-body jet airliners. The largest commercial airliner, the Airbus A380, must make efficiency trade-offs to keep the wingspan below the 80-meter limit at most airports, but a closed wing with optimal wingspan could be shorter than that of conventional designs, potentially allowing even larger aircraft to use the current infrastructure. C-wing. The  C-wing is a theoretical configuration in which much of the upper centre section of a box wing is removed, creating a wing that folds up and over at the tips but does not rejoin in the centre. A C-wing can achieve very nearly the same induced-drag performance as a corresponding box wing, as shown by the calculations illustrated below. Each of the first three rows in the illustration shows a different C-wing configuration as it is taken through a sequence of theoretical induced-drag calculations in which the wingtips are brought closer together, culminating in the  limiting case on the right, where the gap has been taken to zero and the configuration has become a closed box wing (referred to as the "Quasi-closed C-wing" because the calculations were carried out in the limit as the gap went to zero). The parameter ε is the optimal aerodynamic efficiency ratio and represents the ratio between the aerodynamic efficiency of a given non-planar wing and the corresponding efficiency of a reference classical cantilevered wing with the same wing span and total lift. Both efficiencies are evaluated for their respective optimal lift distributions. Values of ε greater  than 1 indicate lower induced drag than that of a classical cantilevered wing for which ε = 1. Note that all of the C-wing configurations have ε greater than 1 and that there is little difference (no difference to the two decimal places shown in two of the cases) between a configuration with a substantial gap (the second entry in each row) and the corresponding closed configuration (the third entry in each row). This is because the optimum lift loading calculated for the quasi-closed cases is very small over the upper centre section, and that part of the  wing can be removed with little change in lift or drag. The lift distributions shown here for the quasi-closed cases look different from those typically shown for box wings in the classical literature (see Durand, figure 81, for example). The classical solution in Durand was obtained by a conformal-mapping analysis that happened to be formulated in a way that led to equal upward loadings on the horizontal panels of the box. But the optimum lift distribution is not unique. A constant inward loading (corresponding to a particular constant circulation) can be added to a classical loading like that  shown by Durand to obtain a loading like those in the quasi-closed cases below. The two methods of analysis give different-looking versions of the optimum loading that are not fundamentally different. Except for small differences due to the numerical method used for the quasi-closed cases, the two kinds of loading are in principle just shifted versions of each other.