A.126.96.36.199.1 Evolution of Final Code1
The structures code tanks incorporates the inter-stage skirt code into the launch vehicle. The inter-stage skirt code consists of two parts: the inter-stage skirt analysis code skirt_analysis_str_v3 which accomplishes the structural analysis of a given skirt geometry and the overall inter-stage skirt code skirt_v3 which compiles the inert mass, length, and cost values for the total inter-stage skirt package for each launch vehicle. The inputs to the inter-stage code are the inert masses of all stages, the propellant masses of all stages, the diameters of each stage, and the maximum forces applied to the launch vehicle. The outputs of the inter-stage skirt code are the inert mass, vertical length, and cost of each skirt required for a particular launch vehicle.
The overall code takes the necessary inputs from the tanks code, and sums all masses for each stage. Then, we multiply the resultant masses by the gravitation velocity and the maximum vertical G-forces to get the axial loading force. Also, the input shear force is multiplied by the maximum normal G-forces to get the applied shear force. Next, the overall inter-stage skirt code calls the inter-stage skirt analysis code for each skirt required for the launch vehicle configuration. For example, if the launch vehicle has two stages only one inter-stage skirt is required, whereas, if the launch vehicle has three stages two inter-stage skirts are required. The inter-stage skirt analysis code determines the final outputs by minimizing individual skirt cost. The overall code then takes the results from the analysis code, compiles the final inter-stage skirt data, and outputs the information to the tanks code.
The first iteration of the inter-stage skirt analysis code does not include any internal supports. Therefore, we only use the buckling analysis of a thin-walled tapered cone to determine the required thickness of the inter-stage skirt skin. The use of only the buckling analysis was determined to be appropriate because the only force currently considered is axial loading.
This iteration of the inter-stage skirt analysis code varies the taper angle of the truncated cone, the skin thickness and the skin material, with given values for the upper and lower stage diameters to minimize skirt cost. Figure 1 shows the inter-stage skirt configuration used for this iteration.
Fig. A.188.8.131.52.1.1: General skirt geometry without internal structural support
We quickly conclude that this configuration is not feasible due to the launch vehicle stages inert mass values. This skirt code results in an unreasonably large inter-stage skirt thickness due to the large axial loading and lack of internal support structure. Also, we must take applied shear force into consideration during the structural analysis of the skirt, and a thin-walled structure with no stringers will not support shear force.
Since the first iteration of the inter-stage skirt analysis code is infeasible, we revise the code to include stringers as internal supports. The stringers have a rectangular cross-section and run length-wise along the skirt skin. We assume that the stringers take the entire axial loading force. Therefore the inter-stage skirt skin acts as a non-load-bearing fairing, and its thickness is set at 4.0mm to correspond to the common tank thickness. This iteration of the inter-stage skirt analysis code varies the taper angle of the truncated cone, the number of stringers, the stringer thickness and the stringer material to minimize skirt cost. Since the thickness of the skirt skin remains constant, the material that will result in minimum cost is aluminum. Therefore, the skirt skin material is set as aluminum.
The second iteration of the inter-stage skirt analysis code results in a very large number of stringers required to support the axial forces. A large number of stringers results in a greater skirt inert mass and a greater manufacturing and attachment cost.
To resolve this undesirable result, we iterate the inter-stage skirt analysis code to add ring supports to the inter-stage skirt structure. These ring supports also have a rectangular cross-section. The addition of the ring supports results in creating shorter stringers, which can withstand greater axial loading. This iteration of the inter-stage skirt analysis code varies the taper angle of the truncated cone, the number of stringers, the stringer thickness, the stringer/ring support material, and the number of ring supports to minimize skirt cost. Figure 2 displays the inter-stage skirt configuration with added stringers ring supports.
Fig. A.184.108.40.206.1.2: Inter-stage skirt stringer and ring support configuration
In this third iteration of the inter-stage skirt analysis code, we incorporate the applied shear force. Up until this iteration, the applied shear force was ignored. We ensure that the number of stringers required to overcome the axial loading are also able to withstand the maximum shear force applied to the shear center of the inter-stage skirt. This maximum calculated shear stress multiplied by the reserve factor must be less than the ultimate shear strength of the stringer material. If the previously determined number of stringers does not meet this requirement, the inter-stage skirt analysis code outputs a “no” value and more stringers must be added.
Since this iteration of the inter-stage skirt analysis code varies so many parameters, when the skirt_v3 code is run in the tanks code, it produces a very long run time. To overcome the long run time, we decide to set many parameters constant. The stringer/ring support material is set to aluminum to reduce manufacturing and assembly costs. The taper angle of the truncated cone is set to 10° because that is the most common taper angle that resulted from the structural analysis. Also, the number of stringers is set to a fraction of the total number of stringers that will fit in the minimum radius of the skirt. Therefore, even though this number will vary according to the launch vehicle geometry, it will not result in a for-loop in the code. We discover through multiple runs of the inter-stage skirt analysis code that the approximate minimal number of stringers required to overcome all necessary loading for all skirts is 1/6th of the total number of possible stringers.
The final iteration of the inter-stage skirt analysis code varies only two parameters. The stringer thickness and the number of ring supports are iterated within the inter-stage skirt analysis code to minimize skirt cost. The upper and lower stage diameters, skirt skin and internal support material, taper angle of the truncated cone, and the number of stringers are held constant for each inter-stage skirt configuration. This final iteration of the inter-stage skirt analysis code is called skirt_analysis_str_v3 and is incorporated in the skirt_v3 overall code called by tanks.
Author: Jesii Doyle