A. AerothermodynamicsA.1 CN, CA, andCN, DerivationsA.2 CMcg DerivationA.3 Skin Friction CalculationsA.4 Heatflux Nose Tip and Flat Plate Heating DerivationsA.5 Heatflux Leading Edge Heating AnalysisA.6 Trade StudiesA.7 CMCG Plots for Design ConceptsA.8 aerodat.fA.9 Heatflux.f

A. Aerothermodynamics

A.1 CN, CA, andCN, Derivations

Vehicle Nose

The nose of the vehicle was represented as a hemispherical wedge (Ref 9.4 –1,

p5-8). The radius of the nose (Rnose) is a free parameter that was used to optimize

the performance of the vehicle throughout the analysis. The equations for the

normal, axial, and moment coefficients are given in Equation -3.

Equation 1

Equation 2

Equation 3

The pitching moment about the reference point is zero because all forces are

directed towards the center of the hemisphere (Ref 4.1, Section 2.1.1.3).

Vehicle Leading Edge

The leading edge is defined by a flat topped swept ¼ cylinder (Ref 4.1, Section

2.1.4). The free variables cyl , Rcyl were used to optimize the performance of the

vehicle in the analysis test runs. The length of the cylinder is dependent upon the

length of the plate and is set to Lcyl = Lplate / cos (90-). The equations used to

calculate the normal, axial, and moment coefficients for the swept cylinder

leading edge are found in Equations 4-6

Equation 4

Equation 5

Equation 6

Windward Surface

Figure 4.2-1 defines the parameters for the triangular flat plate. The length of the

plate (Lplate) is a free variable and the width is dependent upon the length and

sweep angle () by Wplate = 2 * Lplate * tan (90-).

Figure A.- : Windward surface triangular flat plate.

The equations used to calculate the normal, axial, and moment coefficients for the

triangular flat plate are given in Equations 7-9

Equation 7

Equation 8

Equation 9

The axial coefficient is zero because there is no force along the x-axis of the

triangular flat plate. The moment is zero due to the moment being referenced to

the center of pressure of the plate; this point is the block circle in Figure A-1. The

center of pressure for a triangle is located at 2/3 the length of the triangle. (Ref

9.5)

Vehicle Flap

Figure A.10.4-4 defines the parameters for the rectangular flat plate. The length

of the flap (Lflap ) is a free variable and the width is equal to the width of the

windward surface, triangular flat plate.

Figure A - : Flap rectangular plate.

The equations used to calculate the normal, axial, and moment coefficients for

the flat plate flap and can be found in Equation 10-13.

Equation 10

Equation 11

Equation 12

Equation 13

In the case of the flap, the flap angle () creates an axial component coefficient.

The flap angle is defined in the Figure 3.0-1 and is positive downward. The

moment is zero for the flap because it is referenced about the center of pressure

for the plate as shown in Figure 4.2-2 by the black circle.

A.2 CMcg Derivation

A.3 Skin Friction Calculations

A.4 Heatflux Nose Tip and Flat Plate Heating Derivations

A.5 Heatflux Leading Edge Heating Analysis

A.6 Trade Studies

Figure A.6- : L/D contour plot for = 80.

Figure A.6- : L/D contour plot for = 65.

Leading Edge Radius Trim Stability Study

Cone Half Angle Trade Study

A.7 CMCG Plots for Design Concepts

Figure A.7- : CMCG stability for OSP 1.

Figure A.7- : CMCG stability for OSP 2.

A.8 aerodat.f

A.9 Heatflux.f