User’s Guide for call_aerodynamics.m
Written by Jayme Zott
Revision 2.0 – 3/18/08
Description:
The purpose of the code ‘call_aerodynamics.m’ is to output all aerodynamic loads pertinent to
the launch vehicle design. These outputs include Mach number, coefficient of drag (both
historically based and dimensionally based), normal coefficient, pitching moment coefficient,
the center of pressure location, shear forces acting on the launch vehicle, and moments acting
on the launch vehicle. All of these aerodynamic loads are output with respect to Mach number,
and angle of attack (in essence, time).
Files necessary to run call_aerodynamics.m:
Filename
Author
Solve_cd_int.m
(Jayme Zott)
CP_Structure.m
(Alex Woods)
CP_Volume_two.m
(Alex Woods)
CP_overall_int.m
(Jayme Zott)
Atmosphere4.m
(historical code)
CP_Dimensions.m
(Jayme Zott)
CP_Linear_two.m
(Alex Woods, Jayme Zott)
Assumptions:
There are quite a few assumptions made within the call_aerodynamics.m code. Assumptions
can be broken down for each output.
Mach number – comes directly from trajectory’s output. Any assumptions trajectory
makes in their code can also be regarded as assumptions for the aero code.
Cd (historical) - The coefficient of drag with respect to Mach number and angle of attack
for a multitude of historically successful launch vehicles was analyzed and compressed
into a single equation for each region of flight, subsonic, transonic, and supersonic.
These equations became the basis for the historical coefficient of drag code.
Normal – the normal force acting on the launch vehicle was found by assuming linear
supersonic flow. The launch vehicle was broken up into sections so the coefficient of
normal force could be calculated for each section. Once each section had been found,
their values were added together to output the final coefficient of normal force, which
is then multiplied by the dynamic pressure.
Pitching moment – the pitching moment acting on the launch vehicle was found in the
same manner as the normal force stated above. Linear supersonic flow was also
assumed.
Xcp – the location of center of pressure is measured in meters from the tip of the nose.
The same assumptions used in solving CN and CM are also assumed in the case of solving
Xcp as the location of the center of pressure is simply the ratio of the pitching moment
coefficient to the normal coefficient.
Shear – The shear force acting on the launch vehicle is found by integrating the normal
force over a specified length of the launch vehicle.
Bending Moment – the moment is computed by measuring the center of pressure for a
specified length of the launch vehicle and then multiplying the distance between that
center and the stage by the integrated normal force.
Axial – The axial force acting on the launch vehicle is found by integrating the pressure
distribution around the launch vehicle and multiplying it by the radius of the launch
vehicle at each measured location. These values are then added up in much the same
manner as the CM and CN were.
CD (dimensional) – Calculated using the axial force coefficient, normal force coefficient,
and angle of attack. Assumptions used in finding those values hold here as well.
Important Notes:
In the final design, trajectory’s code uses Cd (historical), and the angle of attack is considered to
be 0 degrees at all times.
Input Section:
The call line of the function is:
[M, Cd, Normal, Pitching_Moment, Xcp, Shear_Force, Bending_Moment, Axial, CD] = call_aerodynamics(V,r,a,D)
All of the variables that are passed into the function are described below:
Variable Name
Description
V
Velocity – can be input in the form of an array, or as a
single variable [UNITLESS]
a
Angle of Attack – measure of the angle between the free
stream velocity and the centerline of the launch vehicle.
Can be input in the form of an array, or as a single
variable. It must, however, have the same length as M.
It would be wise to check: length(a) = length(M)?
[DEGREES]
r
Radius – measure of distance from surface of the Earth
to the rocket. This value cannot exceed 290,000 ft, as
this is considered the end of the atmosphere. It also
happens to be the location at which atmosphere4.m falls
apart.
Rocket Dimensions – Must be input as a matrix
comprised in the following manner:
D = [N,L,D,T]
N - the location of the geometry in order starting from
the nose of the launch vehicle
- example: nose = 1, shoulder = 2, stage 2 = 3,…
D
L - length of specified portion of launch vehicle [METERS]
-example: nose = 3, shoulder = 4, stage 2 = 6,…
D - diameter of specified portion of launch vehicle
[METERS]
-example: nose = 1, shoulder = 2, stage 2 = 2,…
T - Type of geometry used in the vehicle
1 specifies conical nose
(example: nose cone)
2 specifies cylinder
(example: all stages)
3 specifies Shoulder or Boattail (example: skirt)
This is an example of what the Vanguard launch vehicle's
"D" matrix would look like:
D = [N, L D T]
D = [ 1,86.4,.84, 1
2,159-86.43,.84,2;
3,358-159,.84,2;
4,57.638,1.14,3;
5,448.19,1.14,2; ]
Output Section:
Variable Name
Description
M
Mach number [UNITLESS]
Cd
Coefficient of drag (historical)[UNITLESS]
Normal
Normal Force [N]
Pitching Moment
Pitching moment [N-METERS]
Xcp
Location of Center of Pressure – measured from tip of
nose cone [METERS]
Shear
Shear force – shear force acting on each stage [N]
Bending Moment
Moment – moment force acting on each stage [NMETERS]
Axial
Axial Force – axial force acting on the launch vehicle [N]
CD
Coefficient of Drag (dimensional) [UNITLESS]
Sample Output:
The variables named in the output section will print to the screen. Outputs occur at intervals of
1 second. Nothing other information will be output. Suggestion: write all output variables to an
excel file using the xlswrite(‘filename’, variable) command in MATLAB.