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Banked Curve Train Condominium on Mars

  1. Sep 1, 2011 #1
    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.
    Last edited: Sep 1, 2011
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  3. Sep 1, 2011 #2


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    Yachtsman, In the days before man went into space, elaborate schemes were devised to simulate Earth gravity. Rotating donut-shaped space stations were popular. The station in the movie "2001" is an example. It shows how an incoming ship would dock in the center. The crew would then experience changing gravity as they moved from the center to the rim, where they would live. They would keep in shape by doing laps around the circumference.

    But the idea of a rotating station was never put into practice. Why not? Because living on a merry-go-round would drive people crazy! For example one thing they forgot to consider was the Coriolis force. Every time you moved your hand it would be deflected sideways. Many things like antennas and solar panels need to be kept pointing in the same direction. Eventually they decided the drawbacks were too great, and it was better to just put up with the zero g.
  4. Sep 1, 2011 #3
    I appreciate any feedback, even kindly worded critique as you've done. Thanks for that. From what my research has shown, the sickness that you speak of greatly reduceds as the diameter increases; I've read many studies that show life from the "Coriolis effect" is fine with diameters of 1km or larger--and the larger the better.

    To terraform Mars we need some form of artificial gravity because studies also show that the colonists would lose their bone density at 1.5% per month there; in just a few short years Mars would "feel" like Earth gravity to them and they could never come back to Earth if they wanted. I suppose they could just go there and over time our bodies would adjust after a few centuries of breeding. But, I'd like to think that we would prefer being a people who want to stay strong, not weak, and so we would devise ways to keep the people there strong. So, with that premise in mind, I thought through options, and it seems that the only 3 ways for artificial gravity would be:

    1. A train condominium concept similar to what I'm describing
    2. frequent trips to space where you have the tethered space station concept (tethered in excess of 1km span apart)
    3. or some futuristic artificial gravity that seems impossible to imagine at this point since we're not made of metal

    If we don't have added gravity then our people there will eventually become weakened Matians who can never leave the planet; this thought is not my preference and so I'd like to imagine a solution.

    One thing that I thought of is that if i dig into the soil (I wanted to say dig into the mars, since we say dig into the earth LOL), and create a rounded trench, this allows the condo cars to travel partially subterranian, and that would greatly reduce the wind effect; so as long as my condos are not over 4 stories high and I can bury at least 1 of the stories, this has the "feeling" of being reasonbly safe assuming a wide base--as mentioned, the rail base would have to be 1.6 times with width, and so some simply math shows that 3 stories is incredibly secure with a base of 1.6 the width; the rails simply need to be strong enough to support the strain. It would be nice if I could find some formulas that help me determine if I can go with 5 stories, or 6, or 10; what is the safe height limit for a tran car that is 10 to 15 meters wide with a rail base 1.6x of that?

    I forgot to mention one important point: I was not planning for people to live on these condo's all the time--simply as a place to sleep and get some of their day spent with earth gravity; it seemed that getting some Earth G time on Mars was cheaper and better than getting it in space because at least on Mars you could get some added gravity every day, whereas the tethered space station idea requires a person to spend extended stays at the station and then rotate down back down to Mars on periodic crew schedules; at this point our colonist seem to be living more like remote oil riggers who travel to the remote site during crew changes; it's not nearly as fun of a lifestyle as getting some Earth G time while sleeping and then spending some time there during the early morning and late evening to get some walking time.

    I'm curious if any studies have thought about simply adding weight to the clothing people wear while walking around on Mars. If I am wearing clothing that has a heavy metal lined into the clothing so that my body is close to an Earth weight. This added weight would force my bones and muscles to work harder; an interesting thought.
    Last edited: Sep 2, 2011
  5. Sep 7, 2011 #4
    Apparently bones and muscles are straight up "programmed" to deteriorate in reduced gravity or with reduced action. It's an actual evolutionary survival mechanism (albeit obsolete one) that humans have, and it seems far from impossible to turn it off with some genetic engineering, or even perhaps with pills. I understand that there is active research in this field as it's obviously a potentially huge market.

    Point is, by the time we'll be vacationing/ living on Mars, reduced gravity could very well be a rather minor problem. If this reduced gravity problem is just a nuisance in your story then that might be one way to make it go away. If it's the fundamental part of your story though, then, well...please ignore my post :)
  6. Sep 7, 2011 #5
    I know we've all watched sci-fi and laughed about how fake it was; I would never want to do such a thing, so while the focus is not on the gravity, I do need to have some explanation about how we're dealing with the gravity--this is typically done in side passing conversations where it's not so obvious that a gravity lesson is being given; e.g. a Martian school teacher or parent is teaching a child about something, two scientists joking about how it was in the old days before it was solved, a TV program talks about a landmark anniversary and the news anchor explains how it was in the old days, ect.

    If a pill is the solution then I need to watch someone take a pill and then have some explanation as to what the pill does and give credibility to the movie.

    Movies are very visual, in fact the rule is to show it rather than say it if you can; and having a huge train of condo's is certainly visual and can be incorporated into a story-line in a captivating manner. My movie does not rely upon a train.

    Thanks for idea about the pill, I had not seen or thought of that. The math used for doing the train idea has been fun. Maybe I'll have the trains and show them being phased out because the pill is now perfected. That gives me my visual plus shows how technology improves. I would imagine people would still like the trains as a training gravity in preparation of traveling back to earth--even if our muscles are artificially stronger than normal based upon Mars gravity, a person would need to come off of the drugs when traveling to Earth if they behave more like a steroid rather than simply halting decay--my premise for this is that the drug are steroid like, and under greater gravity stress it seems plausible that the muscles grow even more under the greater stress.

    However this brings another interesting idea with such a pill, which is what happens when "some" people on Earth want superhuman strength (we always have bodybuilders and those who seek the ideal body to be impressive, plus athletes, etc)? And the same for our Martian brothers and sisters?

    With all "advances" we seem to give up something--there seems to be a dark side with the benefits no matter what the human race seems to invent.

    Thanks for your thoughts.
    Last edited: Sep 7, 2011
  7. Sep 8, 2011 #6
    This is a large driving force behind such a solution. People spend long hours at the gym fighting an ultimately uphill battle against the muscle degradation which their own body is commanding. If you could reduce the rate of muscle degradation (which is regulated internally) the time spent at the gyum would be more effective and long lasting.

    It's not so much about "superhuman" strength as it is about efficiency. After all, if you want superhuman strength you can already get it simply by spending many hours a day at the gym with a personal trianer. Yet, there's no ethical issues about this...in fact, these people are generally praised and admired. If there's a way to streamline the whole process without any side effects, it might be very beneficial to everybody...especially now when there are more fat people in the world then there are hungry people.
  8. Sep 8, 2011 #7
    I agree with so much of what you are saying here; although I tend to be more of a person of "balance" and feel that anything can be taken to excess that is eventually bad, it seems there is a lot of gray between where that "excess" line falls--we are all unique and should be applauded for pursuing our love and ambitions.

    My pondering of the super-human idea (both physical and mental IQ) is very close to the concept presented in the movie Gattaca where designer babies become a reality. Here is my favorite quote from the movie from the Geneticist who is trying to talk the parents into going with a designer baby rather than a natural birth, "We want to give your child the best possible start. Believe me, we have enough imperfection built in already. Your child doesn't need any more additional burdens. Keep in mind, this child is still you. Simply, the best, of you. You could conceive naturally a thousand times and never get such a result."

    What is the world like when it's impossible to "rise above your station in life" without being augmented with technology? Who received the "gift" of augmentation? it's an interesting thought.
  9. Sep 8, 2011 #8


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    Lemme ask this. Is your reason that the Martian people want to stay strong plausible? If they are living most of their lives there, then I don't see any big issue with weakening, especially if you have to go out of your way to exercise or spend money on drugs to keep you strong. If you have to go to Earth, I could easily see bulking back up or taking the drugs for a period of time before heading back, or even on the trip itself.
  10. Sep 9, 2011 #9
    Yeah, I know what you mean... you're right and I'd speculated on that too from time to time; each time I think about it the two thoughts that run through my mind are:

    1. people tend to always want to be strong not weak, and if a simple pill (assuming that it's not grossly expensive or has side effects) solves the problem that I can't imagine many choosing to become weak if they had the option not to.
    2. people from Earth will visit and they will be so much stronger; Martian dwellers would be weak and vulnerable to such people if they were truly 1.5, 2 or even up to 3-times stronger.

    An interesting questions is whether Earthlings will always be stronger because whatever drugs help the Martians will also be used by Earthlings and "assuming" gravity allows a person to grow stronger than their current state, it's possible that Earthlings would always be stronger; perhaps there is a limit to how much advantage the extra gravity provides, and so it seems there is a law of diminishing return where the gap decreases; so it has the highest potential of an Earthling being 3-times stronger and then through diminishing returns could decrease to 2x and finally down to potentially 1x (no advantage).

    Part of my movie is going to deal with the issues of augmentation and so this is an interesting thought; it's certainly going to be our future at some point.
  11. Sep 9, 2011 #10


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    I'd say there are many things to consider, not just whether someone chooses to be weak or strong. Personal views on medication being necessary or not, how rich/poor someone is, how physical a persons job is, their hobbies, etc. Many people probably wouldn't even care if the loss of bone and muscle didn't have a negative impact on their day to day lives. Hell, I could easily see the existence of activists that promote adapting to Mars and to not take pills.

    Maybe. Remember the trip to Mars probably isn't going to be a short one, so unless they are taking medications themselves then they will lose muscle and bone mass over time as well. I can imagine some interesting plot options when you have an influx of people that are physically stronger than the natives. And that probably also influences peoples view on augmentations.
  12. Sep 11, 2011 #11
    I agree with you; I think the activist idea is pretty funny, it made me laugh, and has some truth to it--also the fact that people choose so many different paths for their life's journey.

    Regarding the trip over there, it would either be done with bone density drugs and/or a rocket design that provides for artificial gravity with centripetal force; studies have shown that it does not matter what direction the rotation is in relationship to the rocket's travel toward Mars.

    My favorite designs are where you use the massive weight of the rocket booster as a counterweight and then extend the smaller habitation station at the end of a long tether that is about 500 to 1000m long; the longer the better for comfort and yet the longer the more risk for having the tether break; you would want to use multiple tethers and have enough fuel aboard the station to get back to the counterweight should massive tether failure occur where all of the lines are cut. Getting back to the counterweight assumes that you can repair and start rotating again, and if repairs are not possible you still need to have fuel to reach this general location so that you are still back on course; the counterweight would also be "off course" but not as much since it's larger and I assume it would have some fuel left over to get it back on course as well.

    I think that it's safer to have the rotation as perpendicular to the line of travel rather than in parallel because if such a failure did occur close to Mars or Earth with a parallel rotation they have a 10 to 20% chance of being catapulted straight into the gravitational field of these planets with little time to react. During such an event it seems that it would be best to use the fuel to obtain the best possible planetary orbit safely rather than trying to get back to the counterweight. You'd try to stabilize your spin so that you can point your rockets toward the planet and then start slowing down your speed in a direction and manner to achieve orbit.

    The science of terraforming Mars is quite interesting as well; what an incredible feat of engineering that would be. It seems that it would take at least 150 Earth years or more to achieve. I've read things that show 3 stages of warming the planet, planting trees, and then finally breathable atmosphere. I read speculation that the oxygen left the planet because of the weaker gravity; if this is true then we may need to plant extra trees to provide for the gradual oxygen loss. It's certainly an interesting problem.

    Thanks for the ideas.
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