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Yachtsman
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I am researching for a sci-fi screenplay that I am writing for fun. To keep bone density from losing the estimated 1.5% per month on Mars I want to simulate Earth gravity by having the colonists live aboard condominiums that are fitted with a rail car suspension and travel in a perfect circle in a banked curve. I envision two pairs (4 total) of rails for each track system to provide safety with the redundancy of a second set of rails and wheels as backup for any failure.
This is sci-fi and so I am able to make certain reasonable assumptions in this pretend world for our future Martian colonists; I envision that we are able to easily power the needs of this future city on rails.
I've worked on the math and can easily determine the speed necessary for a frictionless banked curve (I chose frictionless because I want gravity to feel like it's falling straight down through the floor) at the various radius' that I choose for each track, and I calculate the necessary bank angle to be approximately 67.21 =DEGREES(ACOS(3.8/9.81)). Wow, a really steep bank--the reason is because the Martian gravity is so weak compared to the target gravity of 9.81m/s2. There is great debate regarding the Martian gravity, I'm most impressed with the latest estimates of 3.8/s2, so I chose that for my math.
OK, all that to finally ask my question:
What are reasonable width and height dimensions for these railed condos? I want to know what formula's and rules of thumb I can use to determine what is safe and reasonable design.
Does length of the "rail car-condo" have any effect, or is it simply width and height based upon the angle, speed and gravity?
Obviously a very tall and narrow car will be more dangerous, especially during a wind storm, so what is the math to show how wind will effect the cars--remember, they have some strength of a bicycle wheel because all cars are connected together in a circle; and the connection points can be stronger than a typical rail car because the angle is typically fixed--except for the rare occurrence where we'll have cars change tracks so that repairs or maintenance can be done to a particular track. Because of this I think that part of the math will depend upon how much I want to rely upon this strength in the linkage points; because of they were truly very solid and strong, then it would be impossible for wind to blow over a 1km diameter ring regardless of the height being a few stories tall; but failure does happen and so it's safer to not rely heavily upon this strength.
A rail with a radius of 500m traveling along the banked rail will require a velocity of approximately 67.246m/s; I derive this using =SQRT(500 * SQRT(9.812 - 3.82))
I'm interested to know what would make for safe and reasonable height and width for the condos--I am especially interested in the formulas used.
Other design consideration are, what to do if power fails. Let's say that we have a 3-story tall condo banked at over 67°, it would be best to have a way to automatically adjust the angle of the train car and/or the track so that they don't fall over, and especially so that people don't fall out of bed in the middle of the night during such a disaster.
Good movies think through things like this, I want to create a quality design for my script.
Thank you in advance for any ideas or thoughts that you may have on the subject.
Edit: I had a thought, rather than having the wheels under the cars like a normal train, I could place them in front and back of the cars, make the rails wider than the car for safety, attach each car to the wheels via a central pivot point that is located above the center of gravity for the car; in this way the cars would automatically tilt to the perfect angle based upon the acceleration of the car. With this design the pivot point must be located high above the rail or the rails are wide enough for the bottom of the car to swing in between the rails; this actually becomes possible when the rails are about 1.6 times the width of the car; in this design a rounded trench would be dug between the banked rails or outer rail would be raised above ground. It would be cheaper and safer to dig the trench.
This is sci-fi and so I am able to make certain reasonable assumptions in this pretend world for our future Martian colonists; I envision that we are able to easily power the needs of this future city on rails.
I've worked on the math and can easily determine the speed necessary for a frictionless banked curve (I chose frictionless because I want gravity to feel like it's falling straight down through the floor) at the various radius' that I choose for each track, and I calculate the necessary bank angle to be approximately 67.21 =DEGREES(ACOS(3.8/9.81)). Wow, a really steep bank--the reason is because the Martian gravity is so weak compared to the target gravity of 9.81m/s2. There is great debate regarding the Martian gravity, I'm most impressed with the latest estimates of 3.8/s2, so I chose that for my math.
OK, all that to finally ask my question:
What are reasonable width and height dimensions for these railed condos? I want to know what formula's and rules of thumb I can use to determine what is safe and reasonable design.
Does length of the "rail car-condo" have any effect, or is it simply width and height based upon the angle, speed and gravity?
Obviously a very tall and narrow car will be more dangerous, especially during a wind storm, so what is the math to show how wind will effect the cars--remember, they have some strength of a bicycle wheel because all cars are connected together in a circle; and the connection points can be stronger than a typical rail car because the angle is typically fixed--except for the rare occurrence where we'll have cars change tracks so that repairs or maintenance can be done to a particular track. Because of this I think that part of the math will depend upon how much I want to rely upon this strength in the linkage points; because of they were truly very solid and strong, then it would be impossible for wind to blow over a 1km diameter ring regardless of the height being a few stories tall; but failure does happen and so it's safer to not rely heavily upon this strength.
A rail with a radius of 500m traveling along the banked rail will require a velocity of approximately 67.246m/s; I derive this using =SQRT(500 * SQRT(9.812 - 3.82))
I'm interested to know what would make for safe and reasonable height and width for the condos--I am especially interested in the formulas used.
Other design consideration are, what to do if power fails. Let's say that we have a 3-story tall condo banked at over 67°, it would be best to have a way to automatically adjust the angle of the train car and/or the track so that they don't fall over, and especially so that people don't fall out of bed in the middle of the night during such a disaster.
Good movies think through things like this, I want to create a quality design for my script.
Thank you in advance for any ideas or thoughts that you may have on the subject.
Edit: I had a thought, rather than having the wheels under the cars like a normal train, I could place them in front and back of the cars, make the rails wider than the car for safety, attach each car to the wheels via a central pivot point that is located above the center of gravity for the car; in this way the cars would automatically tilt to the perfect angle based upon the acceleration of the car. With this design the pivot point must be located high above the rail or the rails are wide enough for the bottom of the car to swing in between the rails; this actually becomes possible when the rails are about 1.6 times the width of the car; in this design a rounded trench would be dug between the banked rails or outer rail would be raised above ground. It would be cheaper and safer to dig the trench.
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