wavedrag

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 wavedrag [2017/12/07 10:57]jgravett [Plot Tab] wavedrag [2018/04/01 14:41] (current) Both sides previous revision Previous revision 2017/12/07 12:01 jgravett [References] 2017/12/07 11:43 jgravett [References] 2017/12/07 11:39 jgravett [Basic Theory] 2017/12/07 11:39 jgravett Completes Wave Draw Wiki2017/12/07 11:07 jgravett [Theory] 2017/12/07 10:58 jgravett [Plot Tab] 2017/12/07 10:57 jgravett [Plot Tab] 2017/12/07 10:54 jgravett [References] 2017/12/07 10:51 jgravett Wiki page creation WIP2017/12/07 10:27 jgravett [Plot Tab] 2017/12/07 10:23 jgravett [Sub-Surfaces and the Inflow/Outflow Tab] 2017/12/07 09:26 jgravett WIP (12/7/17)2017/12/06 17:40 jgravett Wave Drag wiki WIP2017/12/06 16:45 jgravett Creates Wave Drag Wiki (WIP) Next revision Previous revision 2017/12/07 12:01 jgravett [References] 2017/12/07 11:43 jgravett [References] 2017/12/07 11:39 jgravett [Basic Theory] 2017/12/07 11:39 jgravett Completes Wave Draw Wiki2017/12/07 11:07 jgravett [Theory] 2017/12/07 10:58 jgravett [Plot Tab] 2017/12/07 10:57 jgravett [Plot Tab] 2017/12/07 10:54 jgravett [References] 2017/12/07 10:51 jgravett Wiki page creation WIP2017/12/07 10:27 jgravett [Plot Tab] 2017/12/07 10:23 jgravett [Sub-Surfaces and the Inflow/Outflow Tab] 2017/12/07 09:26 jgravett WIP (12/7/17)2017/12/06 17:40 jgravett Wave Drag wiki WIP2017/12/06 16:45 jgravett Creates Wave Drag Wiki (WIP) Line 1: Line 1: ====== Wave Drag ====== ====== Wave Drag ====== - Wave drag is a phenomenon experienced during transonic/​supersonic flight due to the presence ​of shock waves, which leads to a sharp increase ​in the drag coefficient. In 1952, Richard Whitcomb of NACA discovered the area-ruling technique, where the cross-sectional area distribution is managed to reduce ​wave drag. + As a central goal of his MS in Aerospace Engineering thesis, Michael Waddington developed the Wave Drag tool in OpenVSP. This replaced ​the AWAVE drag tool available in earlier OpenVSP versions, which provided ​the cross-sectional area calculations necessary for an AWAVE analysis. For details of wave drag methodology,​ tool development path, implementation details, and validation studies, Michael Waddington'​s thesis is available here: [[http://​digitalcommons.calpoly.edu/​cgi/​viewcontent.cgi?​article=2604&​context=theses|Development of an Interactive Wave Drag Capability for the OpenVSP Parametric Geometry Tool]] ​ For additional information,​ Rob McDonald'​s presentation at the 2016 OpenVSP Workshop can be viewed here: For additional information,​ Rob McDonald'​s presentation at the 2016 OpenVSP Workshop can be viewed here: ​[[https://​nari.arc.nasa.gov/​vsp|OpenVSP Workshop 2016: Wave Drag Presentation]] ​[[https://​nari.arc.nasa.gov/​vsp|OpenVSP Workshop 2016: Wave Drag Presentation]] - Michael Waddington'​s MS in Aerospace Engineering Thesis, for which the Wave Drag tool was developed, is available here: [[http://​digitalcommons.calpoly.edu/​cgi/​viewcontent.cgi?​article=2604&​context=theses|Development of an Interactive Wave Drag Capability for the OpenVSP Parametric Geometry Tool]] + ===== Summary ===== - ===== Theory ===== + Wave drag is a phenomenon experienced during transonic/​supersonic flight due to the presence ​of shock waves, which leads to a sharp increase in the drag coefficient. In 1952, Richard Whitcomb ​of NACA discovered the area-ruling technique, where the cross-sectional area distribution ​is managed to reduce wave drag. This leading ​approach ​to wave drag minimization ​is known as the Whitcomb area rule, often referred to simply as ‘area-ruling’. By carefully managing the cross-sectional area distribution longitudinally as to avoid deviation from a smooth profile, a designer can prevent strong shock waves. The goal of reducing the wave drag over a body can be accomplished by minimizing the following integral: - + - A leading approach ​to the minimization ​of wave drag is proper management ​of the cross-sectional area distribution ​of an aircraft. This approach is the Whitcomb area rule, often referred to simply as ‘area-ruling’. By carefully managing the cross-sectional area distribution longitudinally as to avoid deviation from a smooth profile, a designer can prevent strong shock waves. The goal of reducing the wave drag over a body can be accomplished by minimizing the following integral: + $$I=- \frac{1}{2\pi} ​ \int_0^1 \int_0^1 ​ S''​(x)S''​(y) log|x-y|dxdy$$ $$I=- \frac{1}{2\pi} ​ \int_0^1 \int_0^1 ​ S''​(x)S''​(y) log|x-y|dxdy$$ - where x and y are Cartesian coordinates,​ S represents area distribution,​ and the body length has been normalized to unity. A Fourier analysis of the equation, as proposed by Eminton, allows the minimum value of the integral to be found. + where x and y are Cartesian coordinates,​ S represents area distribution,​ and the body length has been normalized to unity. A Fourier analysis of the equation, as proposed by Eminton ​and Lord<​sup>​1​, allows the minimum value of the integral to be found. ===== Wave Drag GUI ===== ===== Wave Drag GUI ===== Line 50: Line 48: Controls for managing the visual interaction tools were segregated into the “Plot” tab of the Wave Drag GUI. A rotation index selector under the “Displayed Rotation” header allows the user to select which of the available θ rotation cross-sectional area plots to visualize. An additional text field to the right of the header is provided to display the value, in degrees, of the currently selected θ. Controls for managing the visual interaction tools were segregated into the “Plot” tab of the Wave Drag GUI. A rotation index selector under the “Displayed Rotation” header allows the user to select which of the available θ rotation cross-sectional area plots to visualize. An additional text field to the right of the header is provided to display the value, in degrees, of the currently selected θ. - {{:​wavedragplane.png?​nolink&​350 |}} + {{:​wavedragplane.png?​nolink&​275 |}} A visual indicator of the current x-location of interest is shown on the cross-sectional area plot, as well as in the form of a translucent cutting plane on the geometry window. The slider under “Slice Reference” header controls the x-location of these indicators. The cutting plane visualizer is discussed in additional detail later in this section, and can be toggled on and off using the “Plane” button to the right of the “Slice Reference” header. A visual indicator of the current x-location of interest is shown on the cross-sectional area plot, as well as in the form of a translucent cutting plane on the geometry window. The slider under “Slice Reference” header controls the x-location of these indicators. The cutting plane visualizer is discussed in additional detail later in this section, and can be toggled on and off using the “Plane” button to the right of the “Slice Reference” header. Line 80: Line 78: ===== References ===== ===== References ===== - - E. Eminton ​and W. T. Lord. “Note on the Numerical Evaluation of the Wave Drag of Smooth Slender Bodies Using Optimum Area Distributions for Minimum Wave Drag”. In: Journal of the Royal Aeronautical Society 60 (1956), pp. 61–63. + - Eminton, ​E. and Lord, W. T. “Note on the Numerical Evaluation of the Wave Drag of Smooth Slender Bodies Using Optimum Area Distributions for Minimum Wave Drag”. In: Journal of the Royal Aeronautical Society 60 (1956), pp. 61–63. - - Holt Ashley and Marten Landahl. Aerodynamics of Wings and Bodies. New York, NY: Dover Publications,​ 1985. + - Holt Ashley and Marten Landahl. ​"Aerodynamics of Wings and Bodies". New York, NY: Dover Publications,​ 1985. + - Waddington Michael. "​Development of an Interactive Wave Drag Capability for the OpenVSP Parametric Geometry Tool". California Polytechnic State University, San Luis Obispo (2015).  ​ [[start|Back to Landing Page]] [[start|Back to Landing Page]] - This page was created and edited by:  --- //​[[justin.gravett@esaero.com|Justin Gravett]] 2017/09/21 16:00// + This page was created and edited by:  --- //​[[justin.gravett@esaero.com|Justin Gravett]] 2017/12/07 10:00//