If you’re into science, technology, and/or space, chances are you’ve heard of the space
elevator.
And if you’re paying any attention at all, you’ve seen just about every famous advocate
of space or science parrot out pretty much the same facts for the last 10 years.
Just last week as I was writing this, the illustrious whooshing-animation YouTube channel
Kurzgesagt released a video on this very topic.
But yet again, it was same bland analogies and overall glossing over of the details.
Well I may not have an expert animation team or a sexy British accent, but what I lack
in charm, I’m going to try and make up for by diving into the quote-unquote meat and
potatoes of engineering this literal stairway to the heavens.
Hey I’m Grady.
Today on Practical Engineering we’re designing a space elevator.
I’ll go through the background quickly because chances are you’ve already heard it from
at least a few people who are more handsome and charismatic than I am.
The space elevator consists of a long tether between a geostationary satellite and an anchor
point somewhere on the earth’s equator.
A climber would ride along the cable to take cargo and even humans into space.
The goal of the elevator is to reduce the complexity and risk associated with rockets
and make access to space more routine.
Some have estimated that it could reduce the costs of getting a payload to orbit by 95%.
Unfortunately, there are some major engineering challenges that we need to overcome before
the idea of an elevator to space can ever become a reality.
Let’s take a look at what they are.
To analyze the space elevator, it helps if we use a rotating reference frame.
This simplifies the math by making the elevator static or unmoving.
Having a massive static structure just like a bridge or dam puts us squarely within the
realm of civil engineering, which most of us agree is the best kind of engineering.
But how do you analyze a static structure?
It’s simple: make sure all the forces cancel each other out.
Since the structure is at rest, its acceleration is zero.
Force is mass times acceleration, so the net force must be zero as well.
Let’s add up the forces on a satellite first.
We have gravity which pulls straight down, but the force of gravity varies with distance
from the earth.
This is based on the inverse square law which basically says that gravity gets weaker and
weaker the further you get from its source.
Gravity is the centripetal force pulling the satellite toward the earth.
Since we’re within a rotating reference frame, the satellite also has a centrifugal
force pulling in the opposite direction.
This force is also dependent on the distance from the earth.
For a given angular velocity, there’s a particular distance from the earth where these
two forces are equal and cancel each other out, making the satellite static within its
reference frame.
If you’re trying to keep a satellite above a single spot on earth, or geostationary,
the angular velocity has to be the same as earth’s rate of rotation, approximately
one revolution per day.
The centripetal and centrifugal forces for a geostationary satellite are equal at a distance
of approximately 26000 miles or 42000 kilometers from the center of the earth.
This is known as the Clark belt.
Below the Clark Belt, gravity is stronger, and above it, the centrifugal force is stronger.
But what happens if we add a new force to the satellite, say for example, the tension
from a gigantic elevator cable?
Now we’ve increased the centripetal force, so we need more centrifugal force to balance
it out.
Looking at the equation, we basically have two options (both of which come with costs):
increase the distance of our satellite from earth or increase its mass.
This is the reason why some have proposed using a captured asteroid for the counterweight.
Next, let’s take a look at the climber.
Unlike the rest of the space elevator, the structure of a climber is fairly easy to conceive.
But it does have it’s own engineering challenges, the main one of which is power.
A trip of over 22,000 miles or 35,000 kilometers is no short journey.
Unfortunately, running an extension cord is just not feasible at these scales.
What about solar power?
We can do a thought experiment just to test out the idea: Just for fun let’s assume
we could take all of the power from a high-performance thin-film solar panel and magically convert
it into work just to lift the solar panel itself.
Using the wonders of calculus, we can estimate that it would take on the order of a week
to get from sea level to the Clark Belt.
That sounds pretty reasonable until you consider the fact that it doesn’t include any of
the weight of lifter’s structure or motors or payload or friction or drag et cetera.
It’s a very generous theoretical minimum trip duration using solar power.
The reality is much bleaker, so bleak in fact, that solar power itself has been pretty much
ruled out for powering the lifter.
Actually the only feasible way we’ve come up with so far is beaming power either through
microwaves or gigantic lasers.
And I’m using the word “feasible” loosely here, because even though practically every
engineer ever has waited their entire lives for a problem where the solution was a gigantic
laser, it’s actually not much better than solar power.
The most power-intensive part of the journey for the climber is at the bottom, where gravity
is strongest and centrifugal force is weakest.
This is also the part of the journey where there’s lots of atmosphere that would distort
and abberate the beam of the laser, reducing its efficiency even down to about a quarter
of a percent.
That’s like using an entire nuclear power plant for a single mid-rise office building.
Luckily, scientists and engineers have developed adaptive optics, a system of measuring and
compensating for atmospheric distortion in real time.
This is like noise-cancelling headphones but for mirrors.
It’s normally used for large earth-based telescopes to produce sharper images through
the atmosphere, but it could also be applied to sharpen the beam of a laser passing up
to power our lifter, possibly increasing the efficiency by tenfold over a non-adaptive
system.
Finally, let’s take a look at the tether.
If a 26,000 mile rope is unimaginable to you, you’re not alone.
The tether is generally considered the most significant impediment to the overall space
elevator concept.
The amount of stress a cable can withstand before breaking is called its ultimate tensile
strength, and it’s measured in force divided by the cross sectional area.
A thicker cable can withstand more force because it’s cross sectional area is larger.
And that jives with our common sense.
Ignoring the weight of the lifter for now, the only force on the cable is the force of
gravity due to the weight cable itself.
The tension in each part of the cable is the weight of everything below it.
As you keep moving up, the cable is having to hold up more and more of itself, so its
diameter must keep getting bigger and bigger to stay below the tensile strength.
Again using the wonders of calculus we can estimate the taper ratio or the ratio between
the tether’s diameter at the bottom of the elevator, and its diameter at the point of
maximum tension at the Clark Belt.
Obviously this ratio is extremely sensitive to the density and strength of the tether
material.
For steel, the taper ratio is 10^33.
That means if we have a 1 centimeter cable at the bottom, it would have to be 11000 times
the diameter of the observable universe at geostationary height just to be able to hold
itself up.
In other words, absolutely, positively, categorically untenable.
For kevlar, things look a bit better with a ratio of 10^8.
But that’s still 1000 kilometers in diameter, still completely unfeasible.
I’m sure you see where this is going: nanomaterials.
Here I, and indeed most people who have looked into this question, take small scale laboratory
test results and wantonly scale them up larger than anything humanity has ever constructed
in real life, completely skipping any intermediate steps because, well, the technology hasn’t
even made it that far yet.
Current estimates put the taper ratio for a carbon nanotube tether at somewhere between
2 and 20, which is a massive improvement over currently available materials.
But only time will tell whether these superlight weight ultrastrong materials ever become a
reality outside the lab.
Is what I’ve done here a simplification?
Yes.
Is it a gross simplification?
Absolutely not.
They say the devil’s in the details, but that’s not really true for the space elevator.
The biggest hang ups in this concept are the most fundamental aspects of its design: the
mass of the counterweight, getting power to the climber, the strength of the tether.
I didn’t even have time for details and trust me there are a lot.
It’s almost to impossible speak in hyperbole about the space elevator.
We’ve never built anything remotely similar in terms of size or technical complexity.
And there’s no doubt that if we could build it, it would completely change the world by
making access to space routine.
If it ever does happen, it will be creative and passionate engineers leading the way.
Thank you for watching and let me know what you think.
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