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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.
In the final design, trajectory’s code uses Cd (historical), and the angle of attack is considered to be 0 degrees at all times.
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:
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.
User’s Guide for wing_fin.m
Written by Brian Budzinski
Revision 2.0 – 3/29/08
The purpose of the code ‘wing_fin.m’ is to output all aerodynamic coefficients and loads needed for the addition of a wing and/or fins for an aircraft launch. These outputs include lift coefficient, drag coefficient, normal coefficient, axial coefficient, pitching moment coefficient, and shear coefficient. All of these aerodynamic coefficients and loads are output with respect to Mach number, and angle of attack.
Several assumptions are made within the ‘wing_fin.m’ function. The assumptions can be further explained as follows:
Mach number – The Mach number is assumed to range from Mach 1.0 to Mach 15.0. This is assumed because for an aircraft launch the initial Mach would be near 1.0 and the wing would remain attached up until near Mach 15.0.
Angle of Attack – The angle of attack is assumed to range from an initial horizontal configuration (AoA = 0°) to a final vertical configuration (AoA = 90°).
Normal – The normal force was found assuming the Newtonian Method. Though the Newtonian Method is geared towards hypersonic flow, the launch vehicle will quickly enter the hypersonic regime with an aircraft launch. Therefore, this remains a reasonable assumption.
Axial – Similarly, the axial force was found assuming the Newtonian Method.
Shear – The shear force acting on the launch vehicle from the wing and/or fin is assumed to be equivalent to the normal force acting on the wing and/or fin itself.
Pitching Moment – The pitching moment is found by calculating the normal and axial forces and multiplying them by their corresponding distances from the center of mass.
All of the variables that are passed into the code are described below:
All of the variables that are passed out of the code are described below:
The variables listed in the output section will be plotted as functions of angle of attack.
Author: Brian Budzinski
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