A.5.2.14
The structures codes incorporate analysis of several stresses including, internal pressure, axial buckling, buckling due to bending, and shear. All the analyses compare a critical stress value, based on the geometry and materials of the launch vehicle, to an applied stress value, based on the performance of the vehicle. The analysis models come from research on the large stresses that occur on launch vehicles. The vehicle overall also incorporates a reserve safety factor of 1.25, and many other components of the vehicle, such as the tank size, are given an extra factor of safety to incorporate unforeseen factors that could make applied stresses larger and critical stresses smaller. Thus, the tanks are designed slightly stronger than necessary, for example.
Once the initial design of the vehicle was complete, with the analysis of internal pressure, axial buckling, buckling due to bending, and shear, we researched other potential stresses that can occur on launch vehicles. We researched other potential stress to ensure that are codes were still correct, that any other stresses were small in comparison and that with the safety factors in place, the vehicle would not fail with the addition of these stresses.
The structures codes were always designed not to just fail, but to add support to vehicle until the vehicle was safe. But these final stress considerations were performed once was the vehicle was completely designed, so the goal of these final stress analyses were to ensure that a resize of the rocket was not necessary. The method was to run all the structures codes multiple times over and adding applied stresses consistent with those found in research, and determining if that added stress was within the safety factor of 1.25, or if a resize of the vehicle was necessary.
Thrust vector control was the first source of extra stress. The structures codes were designed with the assumption that the thrust was applied exactly vertically. When the thrust is angled for control purposes, the thrust has a horizontal component and leads to bending stress9. The structures codes were ran for each payload, and adding an additional bending stress resulting from the horizontal component of the thrust at all angles, ranging from 0 to 90 degrees. Even at 90 degrees, the thrust pointing exactly horizontal, the adding bending stress did not require extra support. The number and size of the support structures remained the same.
Another stress source is thrust misalignment. The thrust can misaligned in any direction, and can lead to extra bending and torsion8. The thrust at various angles was inputted into the structures codes again, this time as a source of shear stress. Again, for all angles, even for 90 degrees, the thrust misalignment did require extra support structure.
Spin stabilization is another source. While the spin rate does not cause any stress, the rate at which the launch vehicle spins up becomes a source of stress. From Newton’s laws, a change in angular momentum causes a moment8, which causes torsion on the vehicle. The structures code had to be run to find the limit on how fast spin-up could take place. The shear stress was gradually increased to the point where it got large enough that a resize was necessary, and from that value, the spin-up rate was calculated. The result was that the spin-up rate must exceed 170 rpm/sec.
The properties of the materials used on the launch vehicle change slightly with increasing or decreasing temperature9. The material properties in the structures codes were all assumed constant at the room temperature values. Charts were found on the effect of temperature on Young’s Modulus and Poisson’s Ratio. One such chart is shown in Figure A.5.2.14.1 below.
Fig. A.5.2.14.1: Effect of Temperature of Young’s Modulus
(Engineering Toolbox14)
If Young’s Modulus decreases, the critical stress decreases. The codes were run again for all known values of the changing properties, and once again, even for the extreme values the launch vehicle did not require extra support.
Thermal expansion is another source of stress commonly seen in launch vehicles. If there are different materials adjacent to each other, they expand at different rates, and this can lead to strain and stress9. However, most of the launch vehicle was made of aluminum, and nearly all components that need to be attached to each other were designed to be the same material. Therefore, the effects of thermal expansion could be ignored.
Acoustics can lead to unseen stress as well. The vibrating air and expanding gasses leaving the engines lead to increased vibrations8. Basic vibration analysis was performed as part of the finite element method. Although a complete analytical method was not performed at this time, the acoustic vibrations did not require extra support. In general, acoustics are more of a concern for liquid propelled launch vehicles as opposed to solid and hybrid, and for ground launches as opposed to balloon launches.
All research has pointed out that a common source of failure in launch vehicles is on the local level. Stress concentrations in places like joints, corners, and fastenings often lead to the failure of launch vehicles in the past9. This project was not designed on the local level, so a local stress analysis was beyond the scope of this project, but it should noted that for an actual vehicle of the project to be built, a local analysis must be done first.
Author: Steven Izzo