Supersonic and Hypersonic Minimum Drag for Bodies of Revolution

51st AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition

2013

This study investigates the creation of analytic hypersonic pitch moment coefficients by converting the traditional Newtonian surface integration into a mathematically equivalent curl calculation. This manipulation enables analytic pitch moment coefficients to be derived for shapes of increasing complexity. The analytic solutions are obtained by converting the physical moment calculation across the unshadowed surface to an equivalent volumetric curl calculation of a mathematical vector field that is directed away from the center of gravity location. This capability is made possible by the analytic expression of the Newtonian moment calculation and is not available in present-day studies that rely on approximate panel methods. The results of this investigation enable the construction of analytic relations for new hypersonic configurations of interest, and this approach serves as the foundation to construct efficient hybrid exact-approximate solutions for more complex configurations. A state-of-the-art hypersonic design tool validates all of the analytic relations developed in this investigation. The rapid longitudinal analysis made possible by the analytic pitch moment relations enable packaging considerations and trim control surface deflections to be incorporated into conceptual design studies.

Section: Ib Absence Of Analytic Aerodynamics In Present-day Analysesmentioning

confidence: 84%

The Construction of Analytic Hypersonic Pitch Moment Coefficients Using a Curl Transformation

51st AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition

2013

“…Rather, the advent of the digital computer resulted in the widespread adoption of panel and CFD methods over historical relations. 7,8,9,19,20,21,22,23 This can be observed by the many recent shape design studies that employ panel methods. 24,25 Recent advances in symbolic manipulations tools, such as Mathematica 26 and Maple, 27 enable the modern construction of analytic relations for various shapes.…”

Section: Ib Absence Of Analytic Aerodynamics In Present-day Analysesmentioning

confidence: 84%

“…For example, the general spherical potential shown in Eq. (22) has a gradient magnitude shown in Eq. (23), where the potential recovery technique is only capable of eliminating a single variable (chosen to be x).…”

Section: Ivc Parabola Of Revolutionmentioning

confidence: 98%

The Extension of Analytic Hypersonic Force Coefficients for Conceptual Design Using the Divergence Theorem

AIAA Atmospheric Flight Mechanics Conference

Braun

2012

This study investigates the type and performance of analytic Newtonian aerodynamic solutions made possible using the Divergence Theorem. A reformulation of the Newtonian surface pressure calculation enables a mathematically equivalent divergence calculation to be performed as a substitute. This manipulation enables analytic force coefficients to be derived for shapes of increasing complexity while also reducing computational cost when compared to existing analytic solutions. The divergence solutions are obtained by converting the physical flow field into a mathematical flow field that is constant in direction but with magnitude that is equivalent to the Newtonian pressure coefficient. This unique property allows various mathematical techniques that are not available with the traditional Newtonian calculation to be performed that further reduce computational cost. The results of this investigation enable the construction of analytic relations for new hypersonic configurations of interest, and this approach serves as the foundation to construct efficient hybrid exact-approximate solutions for more complex configurations. Comparisons of the current analytic database to a state-of-the-art hypersonic design tool illustrate the computational advantages of the analytic relations to support hypersonic conceptual design.

“…Variational methods 15 have been used at zero angle of attack to determine optimal profiles to minimize the pressure drag of Newtonian flow theory for various geometric constraints. 16,17 The resulting minimum drag bodies of revolution from this work are shown in Figure 4. In order to accommodate nonzero angles of attack, generic bodies of revolution were approximated as a series of open rings at various stations along the axis of revolution.…”

Section: Iva2 Historical Bodies Of Revolutionmentioning

confidence: 99%

“…In order to reduce the integration complexity associated with a spherical segment, analytic relations were derived using a total angle of attack, , that is a function of both angle of attack and sideslip as shown in Eq. (17). The resulting normal and axial force coefficients in the total angle of attack frame, C N and C A , are converted back to the body frame using Eq.…”

Section: Vb Spherical Segment Familymentioning

confidence: 99%

Analytic Hypersonic Aerodynamics for Conceptual Design of Entry Vehicles

48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition

Braun

2010

Capitalizing on the advances in symbolic manipulation technology, analytic hypersonic aerodynamic relations are developed based on Newtonian flow theory. Analytic relations for force coefficient, moment coefficient, and stability derivatives have been developed for basic shapes, including sharp cones, spherical segments, cylindrical segments, and flat plates at varying angles of attack and sideslip. Each basic shape has been generically parametrized, requiring the development of only a single set of analytic relations for each basic shape. These basic shapes can be superimposed to form common entry vehicles, such as spherecones and blunted biconics. Using Bezier curves of revolution, more general bodies of revolution are studied in which the location of the control nodes that define the shape of the curve is also generically parametrized. Analytic relations at unshadowed total angles of attack have been developed for these configurations. Analytic aerodynamic equations are orders of magnitude faster than commonly used panel methods and were validated using the NASA-developed Configuration Based Aerodynamics tool. Consequently, rapid aerodynamic trades and shape optimization can be performed. Additionally, the relations may impact guidance design using onboard trajectory propagation, real-time ablation modeling in simulations, and simultaneous vehicle-trajectory optimization.