Over the past few years, there has been increasing
excitement about travelling to Mars, and the possibility of establishing a human colony
on the red planet. With recent breakthroughs in rocket engineering
and the onset of a modern space race, it seems almost inevitable that there will be humans
living there within the next decade. This got me thinking about what a future civilization
might look on Mars once humans become an established species there.
What will our homes look like? How will we travel from one place to another?
How will we grow crops? And how long will it take for Disney to open
the first Martian Disneyland. Even though that one’s a bit of a joke,
I started to wonder what a theme park on Mars might be like, or if it would even be fun
to visit a theme park in low gravity. Many amusement rides utilize gravity in one
way or another, but the gravitational acceleration on Mars is 62% lower than it is on Earth because
of the planet’s smaller size. A falling object on Earth will accelerate
at a rate of 9.81 m/s2, but a falling object on Mars will only accelerate at a rate of
3.71 m/s2. I decided that it might be interesting to
explore how this would impact the physics of theme park rides by taking a look at one
of the most common attractions: The roller coaster. Roller coasters are one of the best examples to use because they are driven entirely by
gravity and the law of conservation of energy. Any roller coaster always starts off by giving
the train a certain amount of energy in one of two ways.
Either with a lift hill, where the train gains gravitational energy according to the equation
Eg=m*g*h, where m is the mass of the train, g is acceleration due to gravity, and h is
the height above a reference point. Or with a launch system, where the train gains
kinetic energy according to the equation Ek=½*m*v2, where m is the mass of the train
and v is the speed of the train. The energy is then converted back and forth
between gravitational and kinetic energy as the train travels around the course, going
up and down through the various elements. Energy is gradually lost due to friction and
drag as the train travels along the track, and the train slowly loses speed throughout
the ride. The speed may also be reduced with braking
systems to dissipate energy more quickly, as is the case for mid-course brake runs,
trim brakes, and the final brake run at the end of a ride.
If we consider a generic roller coaster with a lift hill and a first drop of height h,
then we can equate the gravitational energy at the top of the ride to the kinetic energy
that it will have at the bottom in order to calculate the speed of the train.
Since the mass of the train, m, is present in both equations, it will cancel out on both
sides, indicating that the speed of the ride is not affected by the weight of the train
or the passengers. This only happenes because we are neglecting
energy losses here, otherwise there will be an additional term to deal with and we cannot
cancel out mass. Since we are only looking at one part of the
ride by itself, we are ok to neglect energy losses without introducing too much error
so that we can keep the calculation simple. If we rearrange our equation to solve for
v, then we arrive at a simple expression for the speed of the train as a function of the
drop height and gravitational acceleration. This roller coaster has a drop that is 47
m tall, and since we are currently on Earth, we will plug in g as 9.81 m/s2.
This gives a final speed at the bottom of the drop of 30.4 m/s, or about 109 km/h.
If we want to know the acceleration of the train during the drop, then we can draw a
vector for the acceleration due to gravity, and we can break it up into two components:
1 parallel to the track and 1 perpendicular to the track.
The vector component parallel to the track represents the acceleration of the train,
and it is equal to g*sin(θ), where θ is the angle of the track.
The steeper the track is, the faster the acceleration will be, and if θ is equal to 90 degrees,
then the train will essentially be in a freefall. For this coaster though, the maximum track
angle is 65 degrees, and we can calculate the acceleration as 8.9 m/s2, or about 0.9
g’s. At this rate, the train will take about 3.5
seconds to reach its top speed at the bottom of the drop, which would look something like
this from the view of the passengers. The maximum g-force that the passengers will
experience at the bottom of the drop is 4.2 g’s, which is calculated using the principle
of centripetal acceleration. Centripetal acceleration, ac, is equal to
v2/r, where v is the speed of the train and r is the radius of curvature of the track.
If we take acceleration due to gravity and add on v2/r at that same point, then we will
have the total g-force that the passengers feel as the train pulls out of the drop.
In this case, the speed of the train is 30.4 m/s and the radius of curvature is 29 m, resulting
in a total acceleration of 41.6 m/s2 or 4.2 g’s.
Similar calculations can be applied to the vertical loop, and we will find that the maximum
g-force at the bottom of the loop is 3.5 g’s, and the minimum g-force at the top of the
loop is 0 g’s. This means that the passengers will experience
a brief moment of weightlessness as the train passes around the apex.
I’m not going to dive any deeper into the physics here, but if you want to know more
about how vertical loops work and how they are designed, then I recommend checking out
my video on non-circular loops which explains the underlying physics and calculus.
But now that we have a good basic understanding of how roller coasters work, let’s see what
would happen if we built this exact same roller coaster on the surface of Mars.
Although the train would be lifted to the same height of 47 m, it will gain 62% less
gravitational energy than it did on Earth because the gravitational acceleration is
62% lower here. This means that the train will be travelling
slower at the bottom of the drop after the gravitational energy is converted to kinetic
energy, however the decrease in speed is not linearly proportional to the decrease in energy.
As we saw before, the speed at the bottom of the drop can be calculated using v=sqrt(2*g*h),
where speed is proportional to the square root of g.
Plugging in our height of 47 m and gravitational acceleration of 3.71 m/s2, we find that the
maximum speed is 18.7 m/s, or 67 km/h. That’s about 39% slower than the maximum
speed on Earth, which comes from the fact that 1 minus the square root of g on Mars
divided by g on Earth is equal to 0.39. This also tells us that the train will take
about 61% longer to reach the bottom of the drop, at just under 6 seconds, which would
look something like this. The simulation of the roller coaster on Mars
probably looks unnatural to you, and it might even make you feel a little uncomfortable
since we are accustomed to the gravity on Earth.
But not only does the coaster look unnatural, it would also feel unnatural to ride because
of the lower forces. The g-force values themselves would actually
be the same as on Earth, with 4.2 g’s at the bottom of the drop, 3.5 g’s at the bottom
of the loop, and 0 g’s at the top of the loop, however g-force is relative to gravitational
acceleration. The base measurement of 1 g on Earth corresponds
to an acceleration of 9.81 m/s2, but 1 g on Mars corresponds to an acceleration of 3.71
m/s2. And because force is equal to mass times acceleration,
the passengers will experience 62% less force throughout the entire ride compared to the
identical roller coaster back on Earth. It’s interesting to note, though, that if
you feel weightless on a certain part of the ride on Earth, then you will also feel weightless
at the same point on Mars because 0 g’s still means zero acceleration and zero force.
But since roller coasters on Mars would produce lower forces overall and they would also travel
quite a bit slower than their Earth counterparts, they probably would not be very exciting for
humans raised on Earth, aside from being located on another planet.
This would not be the case for humans raised on Mars though, since they would be accustomed
to living in lower gravity. If a person born and raised on Mars were to
ride a roller coaster on their home planet, they would perceive the exact same g-forces
as a person born and raised on Earth riding the same roller coaster on their home planet.
The difference in gravity only becomes apparent when we have humans travelling from one planet
to another, since the actual force magnitudes would be quite different.
And while a human from Earth might find a Martian roller coaster to be somewhat boring,
it would be extremely dangerous for a human from Mars to visit a theme park on Earth because
the forces would be more than 2.5 times what they are used to, and they would probably
black out on just about any roller coaster. This is something to keep in mind for the
future coaster enthusiasts on Mars who want those interplanetary credits.
Now, at this point, you may be wondering about those launched roller coasters that I briefly
mentioned earlier, and what would happen if we built one of those on Mars.
Most of the launch systems that are used for roller coasters rely on the principles of
pneumatics, hydraulics, and electromagnetism instead of gravity, and these systems would
be able to launch a train to the same speed on Mars as they do on Earth.
Since the amount of kinetic energy that they deliver is not dependent on gravitational
acceleration, using a launch system on Mars is one way that we could create a faster ride
and a more intense experience. However, we will probably never see a powerful
strata-launched coaster like Red Force or Top Thrill Dragster on Mars, since the ride
would need to be more than 2.5 times taller in order to convert all the kinetic energy
into gravitational energy. If we were to build an exact replica of Top
Thrill Dragster, the launch would accelerate the train nearly 4 times faster than Mars
gravity, and it would have enough speed to reach a height of 340 m.
It simply would not be practical to build a roller coaster this tall on any planet,
and I think it’s far more likely that we would see a more traditional roller coaster
with an added launch like the Incredible Hulk at Universal Orlando.
In this case, the launch speed could even be adjusted to provide varying levels on intensity
depending on whether the passengers are accustomed to Earth gravity or Mars gravity.
So now that we’ve taken a look at how gravity would affect the physics of roller coaster
on Mars, there’s only one more thing that we need to consider before wrapping up the
video, and that’s the atmosphere. At the surface of Mars, the atmosphere is
about 98% less dense than it is on Earth, and it is not suitable for humans to breathe.
The environment is also very dry with frequent dust storms, which would make it difficult
to operate and maintain a roller coaster outdoors. The wind forces are actually quite negligible
on Mars because the air is so thin, even though the average wind speed is higher than it is
on Earth, but the extremely fine dust would cover the entire ride and possibly cause moving
parts to seize. For these reasons, it would likely be necessary
for any Martian roller coaster to be built inside a pressurized building or tunnel with
similar atmospheric conditions to Earth. Unfortunately, this would detract from the
novelty of riding a roller coaster on another planet, but it would be necessary to protect
the passengers and the ride itself from the harsh environment.
And of course, this would have zero impact on the low gravity physics of the ride, so
I’m confident that the experience would still be something out of this world. Hey everyone, I hope you enjoyed today’s more
abstract topic about roller coasters on Mars. Please consider subscribing if you want to
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