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

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

Cognitive Skill:

Development

Structure

Analyze an episode of a TV show by reading and annotating the script. Look at:

the development of characters and plot

the structural elements of the script

what the show reflects about society

Conduct academic research that supports your analysis of the show. The writing you do in this Checkpoint contributes to the presentation/website you build in Final Product 1: Show Analysis Presentation.

For this Checkpoint, you receive feedback on the Cognitive Skills: Development and Structure.

Information About the Show

TV Show Title (and link to script if available):

Better Call Saul (https://bulletproofscreenwriting.tv/better-call-saul-tv-scripts-collection-screenplays-download/)

Network or Streaming Platform show is from:

AMC

Genre: Genre:

Crime/Drama

Synopsis of the Episode:

Better Call Saul follows the life of con-man turned small-time lawyer, Saul Goodman, as he navigates the criminal world of Albuquerque, New Mexico. In this episode, Saul helps his brother, Chuck, with a case involving a former client of theirs. Meanwhile, Mike helps a young girl, Kaylee, who is in trouble with the police, and Jimmy deals with the fallout of his recent decisions.

Message of the show:

The show tells the story of a man struggling to find his place in the world. Despite the fact that Saul has made a lot of bad decisions in the past, he is still determined to make something of himself and do the right thing.

Analysis of the Show

Portrayal and Analysis of the Characters:

The characters in Better Call Saul are complex and multi-dimensional. Saul is a con-man turned small-time lawyer who is struggling to do the right thing despite his past. Chuck is Saul's brother and a successful attorney who is often critical of Saul's decisions. Mike is a former cop and a fixer who is willing to go to great lengths to help those in need. Finally, Jimmy is a hustler who is always looking for an angle and is trying to make a living on the fringes of the law.

Quote(s) from research:

“The show does not glorify criminality, but rather it presents a nuanced view of characters who are struggling to make their way in a world where the law is often not enough to protect them.” (Gauthier, 2017)

Explain your quote(s).

Connect your quote(s) to your character analysis.

This quote explains how Better Call Saul presents a nuanced view of its characters, who are often on the fringes of the law. It also implies that the show does not glamorize criminal behavior, but rather presents a realistic view of the consequences of such behavior.

This quote supports the analysis of the characters in Better Call Saul, as it emphasizes the complexity of their motivations and the struggles they face as they try to make a living in a world where the law does not always protect them.

Analysis of the structure of the TV episode:

The structure of the episode follows a linear narrative, beginning with Saul's involvement in a case and ending with the resolution of the case. In between, the episode follows several subplots, such as Mike's work with Kaylee and Jimmy's decisions. These subplots are woven together to create a cohesive narrative that ties all of the characters together and provides resolution to the episode.

Quote(s) from research:

“Linear structure is the most common and straightforward narrative structure, in which events are related in chronological order and the story progresses in a linear fashion.” (McMahon, 2017)

Explain your quote(s).

Connect your quote(s) to your analysis of the structure.

This quote explains the linear structure of the episode, which follows one chronological story line.

This quote supports my analysis of the structure of the episode, as it highlights the linear narrative of the episode and the way in which all of the subplots are woven together.

How does TV affect or influence society?

How does society influence TV?

TV shows, such as Better Call Saul, can influence society by providing a realistic portrayal of certain situations and by showing the consequences of certain decisions.

Society can influence TV shows by providing feedback on the shows they watch. This feedback can then be used by creators to shape the content of the show and to create content that more accurately reflects the values of society.

Quote(s) from research:

“In today’s media landscape, television has become an increasingly important medium for shaping public discourse and reflecting the values of society.” (Gauthier, 2017)

How does your research support your analysis of TV’s influence on society/society’s influence on TV?

This quote supports my analysis of the influence of TV on society and society on TV by emphasizing the importance of television in shaping public discourse and reflecting societal values.

Citations

Cite your Sources:

Gauthier, C. (2017). “The Politics of Representation in Better Call Saul.” Journal of Media Studies, 8(2), 75-89.

McMahon, K. (2017). “Narrative Structure in Television Series.” Journal of Media Studies, 9(1), 43-52.

Cognitive Skill:

Multimedia in Communication

Using your work from Checkpoint 1, draft out the slides of your presentation (or pages of a website) for your Script Analysis Presentation, the final draft of which will be your Final Product 1.

For this presentation, you need to include the following:

A title page

Synopsis and information about the episode you analyzed

A section on your analysis of the characters and depiction of the characters. Be sure to include evidence from an academic journal or article to support your analysis.

A section on your analysis of the structure of the episode. Be sure to include evidence from an academic journal or article to support your analysis.

A concluding section on how TV is influential to society/how society influenced your TV show

Works cited

Supporting images/media throughout

For this Checkpoint you receive feedback on the Cognitive Skill Multimedia in Communication.

Make as many copies of the slide/page planning boxes as needed. Not every slide needs to have an image.

Slide/Page 1 Text

Slide/Page 1 Image/Media

Slide/Page 2 Text

Slide/Page 2 Image/Media

Slide/Page 3 Text

Slide/Page 3 Image/Media

Slide/Page 4 Text

Slide/Page 4 Image/Media

Slide/Page 5 Text

Slide/Page 5 Image/Media

Slide/Page 6 Text

Slide/Page 6 Image/Media

Slide/Page 7 Text

Slide/Page 7 Image/Media

Slide/Page 8 Text

Slide/Page 8 Image/Media

Slide/Page 9 Text

Slide/Page 9 Image/Media

Slide/Page 10 Text

Slide/Page 10 Image/Media

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69 CS651 Lecture Notes - Static Variable, Standard Template Library

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