Saturn V First-Stage Structural Analysis 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 38𝑚/𝑠2 . 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 𝑘𝑔/𝑚3 , and a thermal expansion coefficient of 22 ∗ 10-6𝐾-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.

Part 1:

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 𝑘𝑔, and the mass of everything above the stage is 2.9 ∗ 106 𝑘𝑔 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.

Part 2:

In reality, the stage did not have a uniform cross section; it was composed of steps of decreasing thickness toward the top of the S-IC, to save structural mass. Suppose the tank wall thickness decreased from 6.5 mm at the bottom to 4.3 mm at the top in eight steps of equal height. Each of the eight "rings" would have a constant wall thickness, the same height as the other rings, and the total height of the stage would still be 41 meters. Repeat the first three bullet points from Part 1, to find how much the stage will contract with the stepped cross sections instead of the uniform. Additionally, find the mass savings by constructing the tank in this manner.

Part 3:

If the 41m height measurement given in Part 1 was taken at an ambient temperature of 25C, how much would the entire S-IC shrink due to thermal contraction (with no load atop the stage) at an operating temperature of -100C? You may choose either the uniform or stepped cross-section configuration from Part 1 or Part 2 to solve this problem, but there is one optimal solution within the scope of this project. Explain which option you chose and why.

Part 4: Consider the planar truss section shown. Suppose four of these held the S-IC stage upright on the mobile launch platform. If the weight each had to support was 6.9MN (labeled F in the diagram), find the reaction forces at joints B and C (a total of three quantities) and the internal forces in the rods AB, AC, and BC. You may assume that the load is balanced and there is no moment about point A. ABC is an equilateral triangle. Be sure to include your sanity check of the static equilibrium of the whole structure. Briefly describe why the analysis would be complicated by making point C a fixed reaction joint like point B instead of a roller joint.

Part 5: Draw a SMD for the transverse axis of the S-IC using symbolic values (no numbers). The diagram should reflect: 1. A constant, even transverse pressure the vehicle experiences due to wind at the pad (note that this must include the wind pressure experienced by the upper stages, collectively referred to as 𝑃𝑊). 2. The fixed base of the vehicle on the pad. 3. A fueling arm located at 𝑙/2 from the base of the rocket that exerts a load 𝑃𝑓 in a direction counter to the wind. 𝑃𝑓 is not large enough to counteract all the shear experienced by the stage at station 𝑙/2. 07 Apr 2022 Hint: for this problem, continue drawing the SMD along the X axis, with the fixed base at the bottom of the rocket.

Part 6:

The LOX tank bottom is hemispherical, with a total tank height of 19.5 meters tip-to-tip. Suppose the tank were pressurized to 151 kPa and contained LOX with a density of 1141 𝑘𝑔/𝑚3 . Use the Bernoulli equation to find the pressure at the bottom of the tank (at surface gravity) and the thin wall pressure vessel stress experienced by the bottom of the hemispherical tank bottom. At burnout, the tank was empty of liquid oxygen but still under gaseous pressure of 151 kPa. Find the longitudinal and circumferential stresses about the central cylindrical section of the tank. For this part, ignore acceleration, axial forces, thermal deformation, ambient pressure, etc.

Part 7: Even if composite materials (like carbon fiber) had been widely available in the 1960s, give three reasons why they would be less desirable for an application like the S-IC stage than aluminum or titanium

m2gollc

Saturn V First-Stage Structural Analysis 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 38𝑚/𝑠2 . 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 𝑘𝑔/𝑚3 , and a thermal expansion coefficient of 22 ∗ 10-6𝐾-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.

Part 1:

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 𝑘𝑔, and the mass of everything above the stage is 2.9 ∗ 106 𝑘𝑔 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.

Part 2:

In reality, the stage did not have a uniform cross section; it was composed of steps of decreasing thickness toward the top of the S-IC, to save structural mass. Suppose the tank wall thickness decreased from 6.5 mm at the bottom to 4.3 mm at the top in eight steps of equal height. Each of the eight "rings" would have a constant wall thickness, the same height as the other rings, and the total height of the stage would still be 41 meters. Repeat the first three bullet points from Part 1, to find how much the stage will contract with the stepped cross sections instead of the uniform. Additionally, find the mass savings by constructing the tank in this manner.

Part 3:

If the 41m height measurement given in Part 1 was taken at an ambient temperature of 25C, how much would the entire S-IC shrink due to thermal contraction (with no load atop the stage) at an operating temperature of -100C? You may choose either the uniform or stepped cross-section configuration from Part 1 or Part 2 to solve this problem, but there is one optimal solution within the scope of this project. Explain which option you chose and why.

m2gollc

Overview:

In this assignment you will be using the scientific method to develop your own experiment. You will not be conducting the experiment but you will develop one based on a hypothesis. You will submit a project containing the needed information outlined under the "Project" section.

Background Information:

The scientific method is a process used by scientists to develop experiments and test hypotheses. This process begins by making observations. The next step is to develop a question based on these observations, such as how something works.

Based on the question under investigation, a hypothesis is created. A hypothesis should be a prediction of what happens. It is written in an "if, then" format. An is designed to test a specific hypothesis. A scientific experiment should have an independent variable, dependent variable, and a control group. The independent experiment variable is what is changed in the experiment. The dependent variable is what is measured in the experiment.

A control group is a group in which the independent variable undergoes no change. The control group in an experiment serves as a baseline to measure the results of the experiment and can be very useful in isolating unknown factors which may influence the dependent variable.

Remember that a good experiment includes multiple repetitions for each experimental group.

Once an experiment has been conducted, all of the data collected is analyzed. Scientists look for trends in the data and use statistical analysis to compare all of the experimental groups. This is then compared to the hypothesis to see if the data does or does not support the hypothesis. Through this method scientists draw conclusions about their hypothesis based on whether or not their experiment was successful.

Project:

Below are the instructions for each section of the project. For this assignment you will follow the steps of the scientific method and develop your own experiment.

You will need to include all of the following information: