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

Fellow Countrymen:

At this second appearing to take the oath of the presidential office, there is less occasion for an extended address than there was at the first. Then a statement, somewhat in detail, of a course to be pursued, seemed fitting and proper. Now, at the expiration of four years, during which public declarations have been constantly called forth on every point and phase of the great contest which still absorbs the attention, and engrosses the energies of the nation, little that is new could be presented. The progress of our arms, upon which all else chiefly depends, is as well known to the public as to myself; and it is, I trust, reasonably satisfactory and encouraging to all. With high hope for the future, no prediction in regard to it is ventured.

On the occasion corresponding to this four years ago, all thoughts were anxiously directed to an impending civil war. All dreaded it – all sought to avert it. While the inaugural address was being delivered from this place, devoted altogether to saving the Union without war, insurgent agents were in the city seeking to destroy it without war – seeking to dissolve the Union and divide effects, by negotiation. Both parties deprecated war, but one of them would make war rather than let the nation survive, and the other would accept war rather than let it perish. And the war came.

One-eighth of the whole population were colored slaves, not distributed generally over the Union, but localized in the Southern part of it. These slaves constituted a peculiar and powerful interest. All knew that this interest was, somehow, the cause of the war. To strengthen, perpetuate, and extend this interest was the object for which the insurgents would rend6 the Union, even by war; while the government claimed no right to do more than to restrict the territorial enlargement of it. Neither party expected the war, the magnitude, or the duration, which it has already attained. Neither anticipated that the cause of the conflict might cease with or even before, the conflict itself should cease. Each looked for an easier triumph, and a result less fundamental and astounding. Both read the same Bible and pray to the same God, and each invokes His aid against the other.

It may seem strange that any man should dare to ask just God’s assistance in wringing their bread from the sweat of other men’s faces, but let us judge not that we are not judged. The prayers of both could not be answered; that of neither has been answered fully. The Almighty has His own purposes. “Woe unto the world because of offenses! for it must needs be that offenses come; but woe to that man by whom the offense cometh!”

If we shall suppose that American Slavery is one of those offences which, in the providence of God, must needs come, but which, having continued through His appointed time, He now wills to remove, and that He gives to both North and South, this terrible war, as the woe due to those by whom the offence came, shall we discern therein any departure from those divine attributes which the believers in a Living God always ascribe to Him? Fondly do we hope – fervently do we pray – that this mighty scourge of war may speedily pass away. Yet, if God wills that it continue until all the wealth piled by the bondman's two hundred and fifty years of unrequited toil shall be sunk, and until every drop of blood drawn with the lash, shall be paid by another drawn with the sword, as was said three thousand years ago, so still it must be said: “the judgments of the Lord, are true and righteous altogether.”

With malice toward none; with charity for all; with firmness in the right, as God gives us to see the right, let us strive on to finish the work we are in; to bind up the nation’s wounds; to care for him who shall have borne the battle, and for his widow, and his orphan to do all which may achieve and cherish a just, and lasting peace, among ourselves, and with all nations.

How does paragraph 6 contribute to the development of ideas in the text?

hersheysmom111

Fellow Countrymen:

At this second appearing to take the oath of the presidential office, there is less occasion for an extended address than there was at the first. Then a statement, somewhat in detail, of a course to be pursued, seemed fitting and proper. Now, at the expiration of four years, during which public declarations have been constantly called forth on every point and phase of the great contest which still absorbs the attention, and engrosses the energies of the nation, little that is new could be presented. The progress of our arms, upon which all else chiefly depends, is as well known to the public as to myself; and it is, I trust, reasonably satisfactory and encouraging to all. With high hope for the future, no prediction in regard to it is ventured.

On the occasion corresponding to this four years ago, all thoughts were anxiously directed to an impending civil war. All dreaded it – all sought to avert it. While the inaugural address was being delivered from this place, devoted altogether to saving the Union without war, insurgent agents were in the city seeking to destroy it without war – seeking to dissolve the Union and divide effects, by negotiation. Both parties deprecated war, but one of them would make war rather than let the nation survive, and the other would accept war rather than let it perish. And the war came.

One-eighth of the whole population were colored slaves, not distributed generally over the Union, but localized in the Southern part of it. These slaves constituted a peculiar and powerful interest. All knew that this interest was, somehow, the cause of the war. To strengthen, perpetuate, and extend this interest was the object for which the insurgents would rend6 the Union, even by war; while the government claimed no right to do more than to restrict the territorial enlargement of it. Neither party expected the war, the magnitude, or the duration, which it has already attained. Neither anticipated that the cause of the conflict might cease with or even before, the conflict itself should cease. Each looked for an easier triumph, and a result less fundamental and astounding. Both read the same Bible and pray to the same God, and each invokes His aid against the other.

It may seem strange that any man should dare to ask just God’s assistance in wringing their bread from the sweat of other men’s faces, but let us judge not that we are not judged. The prayers of both could not be answered; that of neither has been answered fully. The Almighty has His own purposes. “Woe unto the world because of offenses! for it must needs be that offenses come; but woe to that man by whom the offense cometh!”

If we shall suppose that American Slavery is one of those offences which, in the providence of God, must needs come, but which, having continued through His appointed time, He now wills to remove, and that He gives to both North and South, this terrible war, as the woe due to those by whom the offence came, shall we discern therein any departure from those divine attributes which the believers in a Living God always ascribe to Him? Fondly do we hope – fervently do we pray – that this mighty scourge of war may speedily pass away. Yet, if God wills that it continue until all the wealth piled by the bondman's two hundred and fifty years of unrequited toil shall be sunk, and until every drop of blood drawn with the lash, shall be paid by another drawn with the sword, as was said three thousand years ago, so still it must be said: “the judgments of the Lord, are true and righteous altogether.”

With malice toward none; with charity for all; with firmness in the right, as God gives us to see the right, let us strive on to finish the work we are in; to bind up the nation’s wounds; to care for him who shall have borne the battle, and for his widow, and his orphan to do all which may achieve and cherish a just, and lasting peace, among ourselves, and with all nations.

How does paragraph 5 contribute to the development of ideas in the text?

hersheysmom111

69 CS651 Lecture Notes - Lecture 50: Dynamic Array

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