The first stage of the Saturn V (also called the S-IC) provided thrust to lift the second stage, third stage, and payload to an altitude of about 100km within the first 150 seconds of flight, at which point it experienced a maximum acceleration of 38/² . The first stage structure (the shell around the propellant tanks) transmitted the force produced by the engines to the upper stages through its outer skin. This skin was composed of 2219-T87 aluminum, which has a Young's modulus of 73.1GPa, a yield strength of 390MPa, a density of 2840 /³ , and a thermal expansion coefficient of 22 10^-6-1 . We will perform an analysis of the S-IC structure and the loads it carried through a series of scenarios. The exception is for Part 5, which must be done by hand as it requires significant drawing and only uses symbolic variables, no numerical calculations. I also recommend setting up the equations for Part 4 by hand and then using the .m file to perform the actual computations.

The S-IC stage shell was required to support the load of the second stage, third stage, instrument unit, and Apollo spacecraft modules, both on the pad and during launch. The maximum mass it had to support was when the fully-fueled vehicle was sitting on the pad, and the maximum acceleration it experienced was immediately before stage burnout (when the S-IC was empty but all the other stages were full). Assume the S-IC tank structure is a smooth cylinder with an outer diameter of 10 meters, a thickness of 5.5 mm, and a height of 41 meters when nothing is mounted on top of it. The empty mass of everything above the stage is 9.7 10⁴ , and the mass of everything above the stage is 2.9 10⁶ when fully fueled.

Find:

How much the stage shrinks when the empty stages are placed atop the S-IC

How much the stage shrinks when the vehicle is fully fueled

How much the stage shrinks under full acceleration

The average axial stress experienced in each of these three cases

The factor of safety in each of these three cases Ignore the mass of the S-IC structure itself and propellant; all we care about is how the tank has to deal with supporting the masses above it.