A.
Aerothermodynamics
A.1
CN, CA, andCN, Derivations
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
A.7
CMCG Plots for Design Concepts
A.8
aerodat.f
A.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
CNnose


1  cos  nose   
2
K * Rcyl
sin  cos  sin  nose   tan 
  
2
tan


*

 

Sref
2  1
 tan  sin  tan  

nose


Equation 2
C Anose
 sin 2  sin   3cos 2  sin   cos 2  sin 3  



2


K * Rnose  1   
1  cos   
1

    tan 
   2 cos  tan  sin  tan   
S ref  4   2
 tan   

  sin  cos  sin  cos 



CM nose  0
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
CN cyl 
K * Lcyl * Rcyl  2   2
cos 2  cos 2  
*   sin   sin  cos  cos  

Sref
2
 3

Equation 5
CAcyl
K * Lcyl * Rcyl  4 
 sin 2 


*   cos  
 sin  cos  cos   cos 2  cos 2  
Sref
3
 2

CM cyl  CN
Lcyl *sin 
2* lref
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.- 1: 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
CN plate  2*  0.5* Lplate *W plate / S ref  sin 2 
Equation 7
CAplate  0
Equation 8
CM plate  0
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 - 2: 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.
CNlocal  2*  L flap *W flap / Sref  sin 2    
Equation 10
CN flap  CNlocal *cos 
Equation 11
CAflap  CNlocal *sin 
Equation 12
CM flap  0
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- 1: L/D contour plot for  = 80.
Figure A.6- 2: 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- 1: CMCG stability for OSP 1.
Figure A.7- 2: CMCG stability for OSP 2.
A.8
aerodat.f
A.9
Heatflux.f