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This forum is host to visions of vessels of various kinds and sizes, intended to provide artificial gravity for space travelers.
This topic is offered for those NewMars members who might care to do some research on how to take advantage of the unique environment provided by a space vessel fitted with dual-counter-rotating-habitats.
The Unitary Habitat design of RobertDyck has a completely different set of control problems, and this topic does not seek to address those.
The dual-counter-rotating design does appear to be controllable, because the needed control can be demonstrated in a first year physics class.
We have at least two nascent designs in play in this topic...
One is the smaller 4 RPM design of GW Johnson.
The other is the much larger 500 passenger system described by kbd512 .
When links to the prior work become available I intend to add them to this topic header.
In the mean time, I think it is fair to predict that each of these systems will have exactly the same control issues to deal with.
The ideal solution is to control the orientation of the vessel without expending mass.
It should be possible to model these systems using existing software.
What is needed is modeling software with a suitable physics engine.
Blender may be such a system. Unreal Engine may be another.
Per Google:
Which is better, Blender or Unreal Engine?
It depends on your project goals. Unreal Engine excels in game development and real-time rendering, making it ideal for creating complex 3D games. Blender, on the other hand, is better for 3D modeling, animation, and asset creation. Many developers use both tools in their workflow.
Unreal Engine vs. Blender - Comparison Guide - Vagon
vagon.io › blog › unreal-engine-vs-blender-comparison-guide
This topic is available for suggestion of other software suitable for the purpose.
What I hope comes out of this initiative is a model that anyone can run on a computer with sufficient capability, to experiment with navigation using whatever steering mechanism turns out to be most practical.
The model should include two counter rotating masses that can be independently accelerated or braked, and the model should be able to operate as though it were floating freely in space, the goal is to find a solution that allows the space craft caption/pilot to point the central axis of the vessel at the star towards which navigation says a burn should be initiated. That pointing operation should be performed by accelerating or braking one or both of the wheels.
It is possible to create videos of animation, so the results of modeling can be shared without viewers having to install the modeling software.
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This post is reserved for an index to posts that may be contributed by NewMars members over time.
Post #3 starts us off in style! kbd512 provides us with the example of the Control Moment Gyroscopes used by the ISS
Post #4 follows up with a Google search for snippets about the CMG system. It found one citation about the Chinese station as well
Post #5 addresses the question of why there are normally four wheels in a CMG system instead of just three.
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Suppose we use the Control Moment Gyroscopes (CMGs) from the ISS. Each gyro exerts a force of 258Nm. Further suppose it's on a 25m long lever arm because it's located in the engineering section of the ship, aft of the counter-rotating habitation rings, near to the main engine.
Each gyro exerts a force of 6,450Nm at the connection point between the after rotating habitat ring and its bearing / connection to the non-rotating engineering module. All 4 of them, same basic configuration that the ISS uses, exert a total force of 25,800Nm of torque, or 19,029lbf. That's close enough to the output of the RL-10 rocket engine which powers the Centaur upper stage.
Now we need to compute the mass of the torus, mass distribution, and that will tell us its moment of inertia. We really need to integrate to do this properly because the habitation module is not uniformly dense. If the torus was a solid uniformly dense object with a 27.5m major radius and 3.5m minor radius, with a mass of 100,000kg (not the actual mass, merely a placeholder in the same ballpark as the anticipated hull mass), then mass moment of inertia through the center and perpendicular to the diameter is 76,543,750kg⋅m^2. That means even with a force similar to the thrust of the RL-10 pushing on it, the vehicle's attitude change rate will be rather slow, but that's probably a good thing if we care about the life of the bearings at all.
Edit:
Since the major radius is so small, there will also be a gravity gradient, which must be factored into what the true mass moment of inertia actually is. The prior sentence should actually state that "the gravity gradient must be factored into what the true force exerted is", not the mass moment of inertia.
Edit #2:
It's not entirely uniform, either, because there are "spokes" connecting the torus to the hub / center barrel portion of the structure. We really need a proper FEA program to determine what forces the vehicle is subjected to, because that will tell us how thick the hull needs to be in which areas, which will affect its moment of inertia, and thus how much or how little control we can exert over it using a given torque output from CMGs and a given lever arm. Our CMGs will help compensate for the uneven mass distribution, to the degree that they can, so at least we have that going for us.
Edit #3:
I was mixing concepts in my first edit, because I was thinking this entire time about the actual force exerted, but I'm leaving my mistake in there anyway. The moment of inertia does NOT change with velocity, but the force exerted by the change in rotational velocity between the center and outer edge of the torus certainly does.
Last edited by kbd512 (2024-11-23 05:33:29)
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As a follow up to Post #3 by kbd512, I asked Google for a set of snippets about the CMG system. It found plenty, but it also found a citation about the Chinese station, which uses a similar system.
ISS Double-Gimbaled CMG Subsystem Simulation using ...
NASA (.gov)
https://ntrs.nasa.gov › api › citations › downloads
by R Inampudi · 2016 — The objective is to design and implement a simplified CMG subsystem simulation that helps the flight controllers to train on it to guide the ISS to the desired ...
18 pages
Missing: Please | Show results with: Please
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FeedbackSpace Station Control Moment Gyroscope Lessons Learned
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https://ntrs.nasa.gov › api › citations › downloads
by C Gurrisi · 2010 · Cited by 69 — These CMGs with a life expectancy of approximately 10 years contain a flywheel spinning at 691 rad/s (6600 rpm) and can produce an output torque of 258 Nm (190 ...
16 pages
Missing: Please | Show results with: PleaseControl moment gyroscope
Wikipedia
https://en.wikipedia.org › wiki › Control_moment_gyro...
The objective of the CMG flight control system is to hold the space station at a fixed attitude relative to the surface of the Earth.International Space Station CMGs.
ResearchGate
https://www.researchgate.net › figure › nternational-Spa...
The ISS Control Moment Gyroscope (CMG) attitude control system consists of four large gyroscopes, each mounted in a gimbal system that can rotate the CMG about ...
Missing: installed | Show results with: installedShuttle Astronauts Repair ISS Gyroscope in Second ...
Space.com
https://www.space.com › ... › Missions › Space Shuttle
Aug 1, 2005 — Discovery's STS-114 astronautsSoichi Noguchi and Stephen Robinson swapped out one of four control moment gyroscopes(CMG) used to orientate the space station.
Missing: Please | Show results with: PleaseISS Double-Gimbaled CMG Subsystem Simulation Using ...
NASA (.gov)
https://ntrs.nasa.gov › citations
by R Inampudi · 2016 — This paper presents an evolutionary approach in simulating a cluster of 4 Control Moment Gyros (CMG) on the International Space Station (ISS) using a common ...
Missing: Please find installedSTS-118 Press releases and MCC Status Reports
NASASpaceFlight.com Forum
https://forum.nasaspaceflight.com › ...
CMG 3 failed last October. With help from the station's Canadarm2, operated by Hobaugh and Anderson, Mastracchio and Williams will remove the failed CMG and ...
Missing: find | Show results with: findCrew Dragon or Orion to Hubble for CMG Replacement?
NASASpaceFlight.com -
https://forum.nasaspaceflight.com › ...
Oct 14, 2018 — Scott Manley mentioned an interesting idea, send up a rocket and change the orbit. After that the astronauts on ISS could service the telescope.
Missing: find | Show results with: findDesign and Application Prospect of China's Tiangong ...
Science Partner Journals
https://spj.science.org › doi › space
by X Wang · 2023 · Cited by 6 — The attitudes of the Tiangong space station are controlled by control moment gyros (CMGs) and a reaction control system. For continuously high-precision ...Skylab Space Station
eoPortal
https://www.eoportal.org › Satellite Missions
Jun 15, 2012 — Each CMG was a double-gimbal-mounted unit, electrically driven with a nominal spin of 9100 rpm, and capable of providing an angular momentum of ...
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I asked Google for information about why four wheels are used instead of just three. Redundancy appears to be the main reason, since bearings can and do fail. However, the citations also explain why magnetic bearings are not used:
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Use of 4 reaction wheels in place of 3
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8I am researching for a student nano-cubesat program, and came across the use of flywheels for attitude control. I looked up some successful projects and found that one university had used 4 reaction wheels in place of 3. Why would that be? Wouldn't using 3 be simpler? Is it just because of the redundancy? If so, isn't this a heavy price to pay in terms of operating complexity for the safety gained?
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asked Dec 21, 2015 at 10:14
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Related: Optimal placement of 4 reaction wheels? (and especially the document linked in the single answer there). –
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CommentedDec 21, 2015 at 11:50
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5Three is indeed simpler. However, reaction wheels, being moving parts, are more prone to failure than purely electrical systems, especially for missions lasting many years where bearings may eventually wear out, especially if lubrication retention is not adequately addressed. Adding a 4th wheel makes some of the math more complex for the ADCS software, but it's typically a trivial issue compared to the rest of the problem and it's a nice way to add just one part that backs up three potential failure points, so it can be a good trade for missions needing a little more reliability. For most cubesats, the short lifetimes and limited volume mean that 3 wheels is the best choice, especially if the wheels come from a commercial provider who has a good heritage of success on orbit. If the wheels are student built or experimental, you might still want a 4th just in case, even for a cubesat.
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edited Feb 4, 2016 at 0:13
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answered Jan 30, 2016 at 19:33
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If the wheels could be held in place by magnets instead of bearings, and could be spun in a vacuum, you'd think they'd last just about forever. See en.wikipedia.org/wiki/Magnetic_bearing –
Howard Miller
CommentedJan 31, 2016 at 0:28
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Yes, magnetic bearings are great in space at 0 g for avoiding long term wear, however, the challenge typically is having them survive the launch vibration where the gap actually would allow the part to move, potentially rattling against a hard stop somewhere and damaging itself. Also, magnetic items on spacecraft have to be carefully managed to avoid either inducing a torque on the spacecraft as it interacts with the earth's magnetic field, or contaminating the on board measurement of the earth's magnetic field which is often used for course attitude determination. –
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CommentedFeb 1, 2016 at 6:03
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I asked Google for images of a four wheel CMG system, and it found a very nice set of drawings by:
Figure 4 - uploaded by Jingrui Zhang
HomeBeijing Institute of TechnologySchool of Aerospace EngineeringJingrui Zhang
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https://www.researchgate.net/figure/Ske … _274950131
The drawings show the wheels arranged in a tetrahedron with angles that do not match X, Y or Z. Mathematics is used to determine how to change the momentum of the wheels to achieve a desired effect.
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The two wheels of the proposed counter rotating habitat vessel are themselves gyroscopes.
While the ISS uses a four wheel system (see post #3 by kbd512) the question I am asking for our members to consider is how the great mass of the habitat wheels might be enlisted to perform steering.
The two wheels are necessarily aligned on the same axis. They are coupled to each other through bearings at the axis, and through magnetic "bearings" at the outermost rims. The magnetic bearings at the rims will carry the greater part of the load as the two wheels work against each other.
The two wheels can be accelerated or braked with respect to each other.
My hypothesis is that the interaction of the wheels (as they are braked or accelerated) will result in torque that can be used to steer the vessel.
I am hoping our members might find exploring this hypothesis interesting.
There are two possibilities.
We might have a member with mathematics skills sufficient to find a solution.
We might have a member who can create a model of such a system using a 3D modelling system with a physics engine.
Blender and Unreal Engine are both equipped with physics engines.
The model would consist of two counter rotating wheels on a central axis.
For modeling purposes I would suggest a mass for each wheel of 1 kilogram.
For modeling purposes I would propose a diameter of 100 millimeters and thickness of 10 mm.
For modeling purposes I would propose a central axis length of 100 millimeters and diameter of 10 mm.
If everyone participating in this study will use the same measurements, the results can be compared directly.
I am hoping that each participant in the study will report frequently via this topic.
Efforts by one member in a particular direction may inspire others (member or reader) to attempt the same thing.
There is nothing particularly difficult about installing Blender or Unreal Engine. The difficulty arises in learning how to ** use ** these programs! There is plenty of opportunity to share in the experience, because this forum provides a convenient venue for communication.
I expect we will learn that in a CMG system with only two wheels, the behavior of the system will be surprising to the experimenter.
It might be possible to build a physical model that would float in water.
Such a model could be designed so that mass is distributed so that the flotation device can rotate in any axis without imbalance in any direction. That would be an impressive feat of engineering.
When activated, the interaction of the wheels could be controlled and observed by electromagnetic radiation of some kind.
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tahanson43206,
We don't need to use subscale models for testing. The entire point behind having a powerful FEA and simulation program is to simulate the part(s) you wish to test at full scale without having to actually build and measure the forces exerted empirically.
For a torus, I believe the formula is as follows (looks very familiar):
KE = 0.5 * I * ω^2
KE = Kinetic Energy
I = moment of inertia
ω^2 = angular velocity, in radians per second, squared
Torus Description
major radius: 27.5m
tube radius: 3.5m
surface area: 4,283m^2
radius of revolution is 31m
mass: 100,000kg (a made-up number in the same ballpark as its actual anticipated mass)
moment of inertia (center): 76,543,750kg⋅m^2
moment of inertia (diameter): 38,578,125kg⋅m^2
I = 76,543,750kg⋅m^2 (moment of inertia for a 27.5m radius torus, tube radius of 3.5m)
ω = 0.59716451212832 (angular velocity for a 27.5m radius providing 1g, in radians per second; rotating at 5.7025rpm)
ω^2 = 0.356605454545454 (angular velocity squared)
KE = 0.5 * 76,543,750 * 0.356605454545454 (formula with the appropriate values plugged in)
KE = 13,647,959kgf (assuming I did that correctly)
13,647,959kgf / 4,283m^2 = 3,186.5kg/m^2 (about 4.532psi)
Let's say the actual mass of each ring is closer to 200,000kg. That seems like the upper limit of plausible mass per torus. That means the upper limit is 9.064psi. That is also why I asserted that the dominate force is internal pressurization loads, at 14.7psi.
Force exerted per square foot is 1,305.216psf from rotation at 5.7rpm and internal pressurization is 2,116.8psf, for a combined total of 3,422.016psf. The yield strength of Mangalloy steel is 50,000psi to 75,000psi. If the wall thickness is 0.120" (3mm = 0.118"), then the hoop stress (about the entire interior wall of said pressure vessel) from an internal pressurization load acting upon a 275.590"D (7m diameter tube) , is about 25,341.9psi with 22.05psi worth of internal pressurization (14.7psi + 50% maximum overload or over-pressurization).
Since that is the maximum internal pressurization overload that commercial airliner pressure hulls are designed to withstand, I think that little bit of amateur engineering holds water, or "air" in this case. We're sitting around 50% of the yield strength of Mangalloys, which they can tolerate for quite a bit of time if there are no surface imperfections and they're corrosion-protected.
However, Houston, I still have a problem. I don't want to use a perfectly circular tube, even though that is the ideal shape for resisting pressurization loads. I want my "tube" to more closely resemble the ITER Tokamak "tube", with its "flatter" (less circular) floor. The Tokamak tube has a rounded "D" shape to it. That is what I want. I also want the inner radius of the Tokamak torus structure to become the outer radius of my habitation module structure, specifically because it's more reasonably "flat" (still rounded) and can therefore act more like a normal "floor" for the colonists to walk on, thus providing more floor area to use. I want them to be able to "go for a jog" around the torus, with the cabins lining either side of the torus, making the ship appear far less confined / much larger than it truly is. This is where engineering efficiency is taking a little bit of a back seat to human factors efficiency, to provide what I would call "more usable" habitation volume. Humans need reasonably flat floors to walk on. The inner radius of ITER's Tokamak is an example of a "reasonably flat floor to walk on".
How much of a mass penalty will I take by using a torus structure more optimal for human habitation (more akin to ITER's Tokamak than a pure cylindrical tube)?
I need a FEA program to tell me that. I need stress calculations to tell me where to stiffen and strengthen this structure, to optimize mass allocation. I cannot use simple pencil-and-paper calculations.
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For kbd512 re #8
The observation made in the post, of the potential value of a Finite Element Analysis program, inspired me to ask Google about these programs.
Learn more
Computer Aided Design Pt 4: FEA | MISUMI Mech Lab Blog
Finite element analysis (FEA) software is a computerized tool that simulates how a product will react to real-world forces, such as heat, fluid flow, and vibration. FEA software is used to predict how a product will perform in the real world, and to make adjustments before building a prototype.
FEA software works by breaking a product down into many small elements, and then using mathematical equations to predict the behavior of each element. The computer then adds up the individual behaviors to predict the behavior of the entire product.
FEA software is used in many industries, including aerospace, automotive, consumer products, and electronics. Some advantages of FEA software include:
Analyzing complex geometries: FEA can analyze structures that would be difficult or impossible to evaluate otherwise.
Simulating multiple physics: FEA allows engineers to model multiple physics problems at once.
Saving time and money: FEA reduces the need for physical prototypes, allowing engineers to evaluate a design's safety and performance before building it.
Some key players in the FEA software market include ANSYS, Inc., Synopsys, Inc., Autodesk, Inc., Dassault Systèmes, and IBM Corporation.
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Then I asked ChatGPT4o if it aware of any FEA programs that might run on Linux.... it came back with suggestions:
FEA Finite Element Analysis - Hello Again! I'm hoping you might be able to suggest an FEA program that is available to run under Linux?
ChatGPT said:
ChatGPT
Hello again! Absolutely, there are several FEA (Finite Element Analysis) programs that run under Linux, ranging from open-source to commercial software. Here are some options to consider:Open-Source FEA Software
CalculiXDescription: Open-source FEA software that uses Abaqus-style input files. It's capable of solving structural, thermal, and coupled problems.
Features:
Well-suited for linear and nonlinear problems.
Pre- and post-processing can be done with CGX (CalculiX GraphiX).
Linux Compatibility: Fully supported.
Website: CalculiX
Code_AsterDescription: Developed by EDF (French utility company), Code_Aster is a powerful FEA tool for structural analysis, thermal analysis, and more.
Features:
Robust for nonlinear problems.
Strong community and documentation.
Linux Compatibility: Fully supported and maintained for Linux.
Website: Code_Aster
Elmer FEMDescription: Open-source multiphysical FEA software developed by CSC (Finland).
Features:
Strong in thermal, fluid, and electromagnetic simulations.
GUI available for easier use.
Linux Compatibility: Fully supported.
Website: Elmer FEM
OpenFOAMDescription: Primarily a computational fluid dynamics (CFD) tool, but with FEA modules for solid mechanics and thermodynamics.
Features:
Highly customizable.
Uses finite volume methods, so slightly different focus.
Linux Compatibility: Open-source and Linux-native.
Website: OpenFOAM
Commercial FEA Software
ANSYSDescription: One of the leading FEA tools, offering comprehensive capabilities in structural, thermal, electromagnetic, and fluid dynamics.
Linux Compatibility: Available for Linux, with enterprise support.
Website: ANSYS
ABAQUS (SIMULIA)Description: Advanced FEA tool used widely for structural analysis, including composites, nonlinear, and dynamic problems.
Linux Compatibility: Supported under Linux for professional users.
Website: ABAQUS
COMSOL MultiphysicsDescription: Multiphysics simulation software with a user-friendly GUI and support for a wide range of physics-based simulations.
Linux Compatibility: Fully supported on Linux.
Website: COMSOL
FEAP (Finite Element Analysis Program)Description: Academic and research-focused FEA program developed by UC Berkeley.
Linux Compatibility: Works well on Linux, typically compiled from source.
Website: FEAP
User-Friendly FEA GUIs
If you'd prefer a graphical user interface (GUI) for easier interaction, consider:FreeCAD (with FEA modules, like CalculiX integration)
Salome-Meca (bundled with Code_Aster for pre- and post-processing)
Would you like more details or installation guidance for any of these? ?
That is quite a list. I hope to find time to learn more.
I have reported on OpenFOAM elsewhere in the forum archive.
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I decided to ask ChatGPT4o to compare modeling software such as Blender or Unreal Engine, to what might be available in the list of FEA offerings given above.
I had the impression that FEA program were (are) limited to static situations, and i am interested in solving the dynamic problem of spacecraft navigation when the vessel contains two gigantic counter-rotating wheels. ChatGPT4o confirmed my expectation, but then surprised me by saying that modern implementations can also handle dynamic models.
I had considered using Blender or Unreal Engine software, because both have physics engines, and the ability to create models that can be tested with the physics engines. A member of the small international group suggested using FEA software. I was (and still am) under the impression that FEA programs might be limited to static situations. Was I mistaken? Can an FEA program model the gigantic rotating wheels structure I've described? We are talking about wheels that are 50 or more meters in diameter, and 20 or more meters in width.
ChatGPT said:
ChatGPT
Memory updated
You’re correct that traditional FEA software often focuses on static or quasi-static problems, such as stress, strain, and thermal analysis under given loads. However, many modern FEA tools also include capabilities for dynamic analysis, including rotational dynamics, vibration analysis, and even fluid-structure interactions. For a system like the one you describe—gigantic rotating wheels on a spacecraft—FEA could play a role in analyzing certain aspects, though it may have limitations compared to physics engines in game engines like Blender or Unreal Engine.What FEA Can Do for Your Scenario
FEA programs can model:Structural Integrity:
Analyze the stresses, strains, and deformations in the rotating wheels under centrifugal forces.
Evaluate how the structure responds to dynamic loads, such as those introduced by braking or accelerating the wheels.
Study the effects of thermal expansion or contraction due to frictional heating in the braking system.
Modal Analysis:Determine the natural frequencies and mode shapes of the wheels and spacecraft structure to avoid resonant conditions during rotation.
Dynamic Response:Simulate transient forces (e.g., braking torque) and evaluate how they propagate through the structure.
Investigate gyroscopic effects, though this might require coupling with specialized dynamic solvers.
Coupled Analysis:Some advanced FEA tools allow coupling with other physics domains, such as fluid dynamics (e.g., for air resistance in an atmosphere) or thermal dynamics, which could be relevant if internal systems generate heat.
Limitations of FEA in Your Use Case
Rigid-Body Dynamics:FEA excels at modeling flexible bodies but is not as well-suited for analyzing rigid-body dynamics, such as the rotational motion and gyroscopic effects of the entire spacecraft. For these, multibody dynamics (MBD) tools are more appropriate.
Computational Cost:FEA can be computationally expensive, especially for large-scale dynamic problems like rotating structures spanning tens of meters with high precision.
Interaction with the Environment:While FEA can model contact and friction, game engines or specialized dynamics tools are often better suited for handling real-time simulation of complex interactions, such as collisions or adaptive braking forces.
What Blender/Unreal Can Do
Physics engines in Blender and Unreal Engine provide:Real-Time Simulation:
Rapid prototyping of dynamic systems like rotating wheels, including torque application, gyroscopic effects, and interactions with the spacecraft body.
Visual Feedback:
Immediate visualization of forces, motion, and interactions, which is valuable for conceptual exploration and presentations.
Interactivity:
Easy manipulation of parameters like wheel speed, torque, and mass distribution to observe the effects on steering and stability.
Recommendations for Your Case
Combine Approaches:Use Blender or Unreal Engine for early-stage conceptual exploration and testing of gyroscopic effects and control strategies.
Use FEA for in-depth structural and modal analysis of the wheels and spacecraft under extreme conditions.
Consider Specialized Dynamics Software:For large rotating structures and gyroscopic effects, consider using tools like MSC Adams, Simpack, or MATLAB/Simulink with rigid-body dynamics capabilities.
FEA with Dynamics Modules:Some advanced FEA tools (e.g., ABAQUS, ANSYS) have dynamic analysis modules that could be used for transient and rotational analyses, though they might require significant computational resources.
Let me know if you’d like help setting up a test in Blender or Unreal, or if you’d like guidance on an FEA tool for structural analysis!
(th)
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The primary issue I see with using the habitation rings for attitude control, even though they'd be fantastic for that, is that without at least 3 and preferably 4 habitation rings, it's simply not possible to effect full attitude control. I really do like the idea, but I think you'd need to use ceramic composite habitation rings to reduce the mass, which has the desirable side benefit of reducing the tremendous moment of inertia of each ring, as well as the stress imparted to each habitation ring. You also have some measure of redundancy built into the design if pressurization is lost in one of the habitation rings from a hull penetration. We should explore this idea further because it has the potential to make the vehicle fairly maneuverable, meaning rapid attitude changes are possible, if required, without expending any propellant.
If you have 4 habitation rings, then you have a center "node module" that looks remarkably like the semi-spherical Russian node modules aboard the ISS, rather than a pair of center barrel sections. A node module is good for reducing weight and increasing strength. Apart from the forward habitation ring, the other 3 rings would have their own docking ports, so 3 Starships (crew, food, water) could dock with the large ship at the same time to transfer the crew and consumables cargo in one operation. That simplifies logistics, because the entire crew can be present for the first working party to stow their consumables. In an "abandon ship" scenario, the observation / meeting room module attached to the front of the ship can serve as a temporary lifeboat.
When it comes time to maneuver the ship, you're torquing on the absolute strongest parts. This suggestion by tahanson43206 is actually a better design than what I had originally envisioned, for a variety of practical reasons. Thanks to tahanson43206 for making a fantastic design contribution. I don't know what his original intent was, if it was all about steering the ship or something else, but after doing some quick math, this will actually be a lighter / stronger / more user-friendly design, but probably requires the use of some more expensive materials than steel.
I was recently looking at the prices for Ti-6Al-4V, and cost per metric ton is only about $2,500, so perhaps Titanium could be an acceptable substitute for steel. Titanium, or at least the most common Ti-6Al-4V Titanium alloy, apparently has a fatigue limit like steel does, meaning it can theoretically survive an infinite number of stress cycles below that limit, which happens to be around 600MPa (87ksi). For whatever reason, I previously thought Titanium behaved more akin to the way Aluminum does. Aluminum weakens by just a little bit with every stress cycle, so it will eventually fail irrespective of how low that stress cycle happens to be.
350,000kg equates to 79m^3 (4,430kg/m^3) of Titanium alloy to work with, vs only 44.4m^3 (7,880kg/m^3) for Mangalloys. That might be enough material for a node module and 4 habitation rings. This is important because it takes a certain volume of material, of whatever variety, to enclose a given volume of space. It takes a certain thickness to resist the inertial and pressurization forces, although internal pressurization at 14.7psi will still dominate the stress which must be resisted by the structure. Using 4 habitation rings instead of 2, we can reduce the interior volume of each habitation ring, thereby reducing the hoop stress from pressurization.
Ti-6Al-4V Grade 5 Titanium yields around 160ksi, but fully annealed it will yield at 128ksi. Mangalloys yield at 50ksi to 75ksi. CMCs of the variety I was investigating yield around the same point as Mangalloys, but they're very similar in density to Aluminum alloys. Rather than going for absolute maximum tensile strength, perhaps we should instead pursue a rather "springy" fully annealed Titanium, since it won't be as hard and brittle, won't behave as badly after a hot fire, and won't require an expensive heat treatment. In practical terms, it's still about twice as strong as the other two hull materials, per unit weight. I'm most interested in "happy mediums" here, rather than "maxed out material properties", which tends to have severe downsides.
A maraging steel would be far stronger than any of the materials listed here, but they're not as corrosion resistant. RobertDyck brought up atomic Oxygen corrosion damage if welding is required on-orbit, which may be meaningless over short periods of time or could be very nasty, but would be a very expensive mistake if he's right. Maraging steels cannot be left exposed to cryogenic temperatures for long periods of time or it changes the crystalline grain structure of the steel, which is something I missed when first contemplating what steel to make the ship's hull from. I have no idea how expensive it will be to heat treat a maraging steel with the precision required, but I know it's not cheap because it's mentioned as a cost driver which precludes using it for crankshafts or other high-stress components in engines. Heat treatment process control is critical to achieving "full hard" / "full strength" for C250/C300/C350 maraging steels. The cost for C350 is also sitting at $2,100/t. That probably means there's no functional cost differential between annealed Ti-6Al-4V and C350 after a proper heat treatment has been applied to C350.
Due to the F-22 and F-35 programs, our specialty metal workers now have extensive experience with forging, extruding, machining, and welding Titanium alloys.
So... 4 habitation design using a nice middle-of-the-road Titanium alloy?
350t Ti-6Al-4V: $875,000
350t Mangalloy: $280,000
350t C350: $735,000
350t 304L: $840,000
350t Sylramic and SiC (60/40 fiber-to-ceramic) Ceramic Composite: $924,280,000
SiC is ~$2,000/t, but Sylramic fiber ~$4,400,000/t
Material costs must be a consideration at some level, unless we're building stealth bombers.
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