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The Vortex lattice method, (VLM), is a numerical method used in computational fluid dynamics, mainly in the early stages of aircraft design and in aerodynamic education at university level. The VLM models the lifting surfaces, such as a wing, of an aircraft as an infinitely thin sheet of discrete vortices to compute lift and induced drag. The influence of the thickness, viscosity is neglected. VLMs can compute the flow around a wing with rudimentary geometrical definition. For a rectangular wing it is enough to know the span and chord. On the other side of the spectrum, they can describe the flow around a fairly complex aircraft geometry (with multiple lifting surfaces with taper, kinks, twist, camber, trailing edge control surfaces and many other geometric features). By simulating the flow field, one can extract the pressure distribution or as in the case of the VLM, the force distribution, around the simulated body. This knowledge is then used to compute the aerodynamic coefficients and their derivatives that are important for assessing the aircraft's handling qualities in the conceptual design phase. With an initial estimate of the pressure distribution on the wing, the structural designers can start designing the load-bearing parts of the wings, fin and tailplane and other lifting surfaces. Additionally, while the VLM cannot compute the viscous drag, the induced drag stemming from the production of lift can be estimated. Hence as the drag must be balanced with the thrust in the cruise configuration, the propulsion group can also get important data from the VLM simulation. ==Historical background== John DeYoung provides a background history of the VLM in the NASA Langley workshop documentation SP-405.〔NASA, ''Vortex-lattice utilization''. NASA SP-405, NASA-Langley, Washington, 1976.〕 The VLM is the extension of Prandtl lifting line theory,〔Prandtl. L, ''Applications of modern hydrodynamics to aeronautics'', NACA-TR-116, NASA, 1923.〕 where the wing of an aircraft is modeled as an infinite number of Horseshoe vortices. The name was coined by V.M. Falkner in his Aeronautical Research Council paper of 1946.〔Falkner. V.M., ''The Accuracy of Calculations Based on Vortex Lattice Theory'', Rep. No. 9621, British A.R.C., 1946.〕 The method has since then been developed and refined further by W.P. Jones, H. Schlichting, G.N. Ward and others. Although the computations needed can be carried out by hand, the VLM benefited from the advent of computers for the large amounts of computations that are required. Instead of only one horseshoe vortex per wing, as in the lifting line theory, the VLM utilizes a lattice of horseshoe vortices, as described by Falkner in his first paper on this subject in 1943.〔Falkner. V.M., ''The Calculations of Aerodynamic Loading on Surfaces of any Shape'', (R&M 1910 ), British A.R.C., 1943.〕 The number of vortices used vary with the required pressure distribution resolution, and with required accuracy in the computed aerodynamic coefficients. A typical number of vortices would be around 100 for an entire aircraft wing; an Aeronautical Research Council report by Falkner published in 1949 mentions the use of an "84-vortex lattice before the standardisation of the 126-lattice" (p. 4).〔Falkner. V.M., ''A Comparison of Two Methods of Calculating Wing Loading with Allowance for Compressibility'', (R&M 2685 ), British A.R.C., 1949.〕 The method is comprehensibly described in all major aerodynamic textbooks, such as Katz & Plotkin,〔J. Katz, A. Plotkin, ''Low-Speed Aerodynamics, 2nd ed., Cambridge University Press'', Cambridge, 2001.〕 Anderson,〔J.D. Anderson Jr, ''Fundamentals of aerodynamics'', 2nd ed., McGraw-Hill Inc, 1991.〕 Bertin & Smith〔J.J. Bertin, M.L. Smith, ''Aerodynamics for Engineers'', 3rd ed., Prentice Hall, New Jersey, 1998.〕 Houghton & Carpenter〔E.L. Houghton, P.W. Carpenter, ''Aerodynamics for Engineering Students'', 4th ed., Edward Arnold, London, 1993.〕 or Drela,〔M. Drela, ''Flight Vehicle Aerodynamics, MIT Press'', Cambridge, MA, 2014.〕 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Vortex lattice method」の詳細全文を読む スポンサード リンク
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