Geometrical Relationships for Osculating Cones and Osculating Flowfield Waveriders

Rodi, Patrick E.; Exploration, Lockheed Martin

doi:10.2514/6.2011-1188

Cited by 21 publications

(8 citation statements)

References 7 publications

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“…The top of the leading edge (at point X=10, Y=1) is tangential with a horizontal line representing the waverider upper surface on this osculating plane. The first control point is at American Institute of Aeronautics and Astronautics (10,0), the beginning of the leading edge. The second control point at (9.738, 0.035) is located along on a line angled at eight degrees to the X-axis to generate the tangency of the Bezier Curve with the waverider lower surface.…”

Section: Employing Bezier Curves As Leading Edge Geometriesmentioning

confidence: 99%

Integration of Optimized Leading Edge Geometries Onto Waverider Configurations

Rodi

2015

53rd AIAA Aerospace Sciences Meeting

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Most popular waverider design approaches produce vehicles that have sharp leading edges. Manufacturing and/or thermal limits require that some degree of finite radius be employed at the leading edge. Earlier research has produced an optimized leading edge generation process suitable for high speed vehicles such as waveriders. In that effort, Bezier Curves were employed to represent the candidate leading edge cross sectional geometries which were then optimized using a number of cost functions including: minimum peak heating, minimum total heating, minimum drag, and minimum pressure gradient.In the current work, Bezier Curve leading edges have been optimized to reduce the peak leading edge laminar heating for use on waverider-based vehicles designed for three typical hypersonic applications: a Mach 5 Air-Breathing Missile, a Mach 10 Hypersonic Cruise Vehicle, and a Mach 20 Boost-Glide Vehicle. These leading edge geometries have been incorporated onto the vehicles and the resulting integrated aerodynamic performance has been quantified and compared to similar vehicles with conventional hemi-cylindrical leading edge configurations. The largest drag reduction was for the Mach 5 missile, where a 6.2% reduction was predicted when using optimized leading edges on both the inlet and fins. Nomenclature h = altitude n = power law body exponent q = local convective heating rate qbar = freestream dynamic pressure r = power law body local radius r b = power law body base radius r CL = leading edge centerline radius r swept = radius for a swept leading edge t = independent parameter in the Bezier Curve equation C p = pressure coefficient D = drag L = lift, streamwise length of waverider on a given osculating plane M = freestream Mach number X = streamwise distance from the waverider's nose, also streamwise distance on a leading edge Y = spanwise distance from the centerline of the waverider, also vertical distance on a leading edge Z = vertical distance on the waverider measured from a waterline datum θ = leading edge wedge angle θ c = cone angle of power law body on the osculating plane λ loc = local leading edge sweep angle φ = leading edge position angle, measured from the most forward point on a leading edge

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Section: Employing Bezier Curves As Leading Edge Geometriesmentioning

confidence: 99%

Integration of Optimized Leading Edge Geometries Onto Waverider Configurations

Rodi

2015

53rd AIAA Aerospace Sciences Meeting

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“…The forward end of the curve is usually at the symmetry plane and the aft end defines where the base plane of the design method lies, as shown from different perspectives in Figure 1. In order to construct the appropriate shockwave shape we utilize the geometrical relationships for osculating cones and osculating flowfield waveriders as used by Rodi [5] . These relate the effective leading edge sweep, the effective angle of the shockwave, and the angle between the leading edge curve and shockwave profile from a base plane perspective, shown in Figure 2.…”

Section: Methods Descriptionmentioning

confidence: 99%

Waverider Design Based on Three-Dimensional Leading Edge Shapes

Kontogiannis

Sóbester

Taylor

2017

Journal of Aircraft

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“…In general, waveriders created with the Osculating Flowfield Method have modestly superior L/D performance over those created using the Osculating Cones Method 9 . Geometrical relationships have been defined which permit waveriders to be constructed with specific vehicle characterizes 10 .…”

Section: Introductionmentioning

confidence: 99%

High Lift-to-Drag Ratio Waveriders for Missions in the Martian Atmosphere

Rodi

Martin²,

Bennett³

2012

30th AIAA Applied Aerodynamics Conference

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An exploratory study has been performed on applying modern, high lift-to-drag ratio waveriders to a number of missions in and through the atmosphere of Mars. Earlier studies have most commonly employed lower lift-to-drag ratio conical-based waverider designs. The recent Osculating Flowfield Waverider Method can generate vehicles with greater aerodynamic performance than those from earlier methods. This improved waverider performance has favorable impacts for most of the examined missions.Waverider vehicles have been applied to a variety of missions including, aero-gravity assist during fly-bys, aerobraking for orbit capture, lifting entry from entry interface to landing, lifting ascents of return vehicles such as for sample-return missions, and boost-glide missions for travel from one surface location to another. The greater lift-to-drag ratio available from modern waveriders is a significant enhancer for most of the missions examined where this ratio has a positive influence. Nomenclature Cp= pressure coefficient D = aerodynamic drag L = aerodynamic lift L/D = lift-to-drag ratio M = freestream Mach number R = gas constant γ = ratio of specific heats

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Geometrical Relationships for Osculating Cones and Osculating Flowfield Waveriders

Cited by 21 publications

References 7 publications

Integration of Optimized Leading Edge Geometries Onto Waverider Configurations

Integration of Optimized Leading Edge Geometries Onto Waverider Configurations

Waverider Design Based on Three-Dimensional Leading Edge Shapes

High Lift-to-Drag Ratio Waveriders for Missions in the Martian Atmosphere

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