Like a lot of Fast Company readers, I was intrigued by the mention of a “space elevator” concept under development at Google’s skunkworks lab, known simple as Google X.
"You know what a space elevator is, right?" DeVaul asks. He ticks off the essential facts--a cable attached to a satellite fixed in space, tens of thousands of miles above Earth. To DeVaul, it would no doubt satisfy the X criteria of something straight out of sci-fi.
Space elevators would be a game-changer on the level of electricity or powered flight. As an engineer who has designed space elevator concepts for Boeing's space systems division, and occasional FastCoLabs contributor, I thought I’d add some details to this promising, mirage-like concept.
Space is already a $304 billion business, but it has the potential to be much larger if it weren’t so extremely expensive to get there. Any future business like space tourism (which involves shipping people) or asteroid mining (which requires shipping raw materials) runs up against the current cost to deliver anything to space.
SpaceX offers the least expensive launch prices at $2,550/kg, or about four times the price of silver. When your costs are measured in multiples of a precious metal, you need to cut costs. So engineers like myself look for cheaper ways to get things into space.
One appealing way to reduce the cost of shipping cargo and people into space is a “space elevator.”
And it would presumably be transformative by reducing space travel to a fraction of its present cost: Transport ships would clip on to the cable and cruise up to a space station. One could go up while another was heading down. "It would be a massive capital investment," DeVaul says, but after that "it could take you from ground to orbit with a net of basically zero energy. It drives down the space-access costs, operationally, to being incredibly low."
Exactly--this idea of a space elevator is simple, appealing, but most likely wrong. In order to see why it’s wrong--and how we can salvage parts of the concept--we need to look deeper into their design and economics to see what approach makes the most sense, and when we might build such a thing later in this century. As the piece says:
Not surprisingly, the team encountered a stumbling block. If scaling problems are what brought hoverboards down to earth, material-science issues crashed the space elevator. The team knew the cable would have to be exceptionally strong-- "at least a hundred times stronger than the strongest steel that we have," by Piponi's calculations. He found one material that could do this: carbon nanotubes.
Carbon nanotube cables are theoretically 12 times stronger than the best steel, but 5 times lighter, thus 60 times better in strength-to-weight, which is what matters for space elevators. Pound for pound that’s 60 times stronger.
The design of any structure, whether skyscraper, bridge, or space elevator is governed by the need to support all the loads present at each point. In a tall building that not only includes the contents, but also the support columns above the point you are looking at. So the lower floors must be stronger to carry the weight of everything above them.
If the steel or concrete holding up the building is the same strength throughout, the only way to make the columns stronger is by making them larger. Tapering from bottom to top is most visible in the Burj Khalifa and Eiffel Tower, but it also goes on under the skin of boxy office buildings.
Read the feature story that inspired this response: The Truth About Google X: An Exclusive Look Behind The Secretive Lab's Closed Doors
The structure for a space elevator also has to handle the loads all along its length, but instead of being supported from the ground, it is mostly hanging from synchronous orbit. At that altitude, gravity and the centrifugal acceleration of the orbit are balanced; this is true of every stable orbit, which is why things remain in orbit and don’t fall down.
However, as you move down the elevator, gravity gets stronger and the centrifugal acceleration gets less; you are moving slower as you get closer to the Earth. The elevator structure also sees this difference as weight it needs to support with more structure.
Net forces can be demonstrated in a moving car: you always feel the Earth's gravity, but when you accelerate forward, you also feel that force. Something dangling from the rearview mirror will hang at a backward angle from the combined force. On a space elevator, gravity pulls you down, and centrifugal acceleration pulls you up, and your apparent weight is the difference.
In other words, that hanging elevator structure has to support more and more weight from everything below as you go up from near the ground to synchronous orbit. That includes the structure itself, and any contents like cargo capsules, rails, power cables, or aircraft warning lights.
If we use the strongest available material, currently carbon fiber, then the elevator must get thicker as we go up, to support all the weight below that height. How much thicker it needs to get can be found from two properties of any material: the strength and the density. Strength tells you how much you need to support a given load, and density tells you how much more load is added by the material itself. The ratio is called “specific strength.” For the best carbon fiber, with reasonable design margins for safety and overhead, this is 150 km.
When you do the math, it works out you need to increase the area and weight of the cable by a factor of “e” (2.718…) for each 150 km of load, to keep the cable stress from going above your design limit. Unfortunately, the Earth’s gravity well from the ground to synchronous orbit is equivalent to 6,230 km. Therefore the cable mass will be the factor e 41.5 times (e41.5 ) or 1.1 million trillion times the cargo mass. You can never ship enough cargo to justify such a massive cable.
We either need a stronger material, or to make the elevator shorter, so it doesn’t have such an extreme mass. As the original article says, carbon fiber isn’t the only option. There are also carbon nanotubes.
But no one has manufactured a carbon nanotube strand longer than a meter. And so elevators "were put in a deep freeze," as Heinrich says, and the team decided to keep tabs on any advances in the carbon nanotube field.
So, will those work?
Carbon nanotubes have extraordinary theoretical strength, but in reality it cannot reach those levels of strength because of defects. A study predicts an actual cable strength, allowing for design margins, of 623 km, or about 4 times better than current carbon fiber. This is now 1/10th of the Earth’s gravity well, and the cable mass falls dramatically to e10 = 22,000 times the cargo mass.
So does that mean a space elevator is feasible is this idea in the future?
A cable mass of 22,000 times the cargo is a vast improvement over a million trillion, but is still not low enough to make a viable elevator. For the moment, we will ignore that today we can only make carbon nanotubes in microscopic fibers. We assume that researchers will eventually be able to make it in enough quantity and cable thickness for the elevator structure.
But there’s another problem: payback time for the elevator.
The mass ratio of the cable to the cargo capsule it carries is fixed for a given material and design. If you have multiple cargo capsules in transit, you also need multiple amounts of cable to support them. For simplicity, we can then consider one capsule and one unit of cable.
There has to be some kind of mechanism to raise the capsules from the ground to synchronous altitude (35,000 km). Conventional elevators are raised by cables, but that is too slow to consider. The fastest existing elevator, in the Taipei 101 tower, would take 24 days. Instead, let’s assume you use magnetic levitation as fast as the fastest existing maglev train (581 km/h). That would get you to the top in 60 hours.
To deliver 22,000 cargoes--or about as much mass as the elevator cable itself--would then take 150 years. That’s right. If we started today, it would take until 2164 to deliver its own weight.
Since you have to launch the space elevator itself into space, you want it to deliver more cargo than its own mass. Otherwise why not skip the elevator and just launch the cargo directly?
So if it takes 150 years to do this, your rate of return is a 0.6% percent per year, which just isn’t viable from an economics standpoint. But what about making them smaller?
The original idea for a space elevator, from the ground to synchronous orbit as one giant structure, was first described by rocketry pioneer Konstantin Tsiolkovsky in 1895. It was intended to be theoretical, like Isaac Newton’s illustration of a cannon on a mountain firing into orbit. It was not intended to be a practical design.
And indeed, it isn’t: 60 hours, or 2.5 days, to deliver 1/22,000 of the elevator's mass as cargo means it takes a long time--150 years--to deliver enough to make the elevator worth building. As an analogy, imagine a tractor trailer (big truck) that can deliver 3 pounds every 2.5 days. Not very useful, is it?
So let’s dispense with two assumptions in the [original] idea: that it needs to be one giant structure, and that it needs to do the whole job of reaching orbit.
The larger lesson here is that any Google X idea that hinges on some kind of new development in material science cannot proceed. This is not the case with electronics--X could go forward with a device that depends upon near-term improvements in computing capability because Moore's law predicts an exponential increase in computing power. That is why DeVaul's team is confident that Google Glass will get less awkward with each passing year. But there is no way to accurately predict when a new material or manufacturing process will be invented. It could happen next year, or it could be 100 years.
This is one place where the community of space elevator researchers diverges from the Google X folks. We all want stronger materials, because that makes the cable much lighter--but for Earth, even with ideal materials, it's too hard to do a one-piece full elevator.
The Moon and Mars have smaller gravity wells, so we can consider one-piece solutions, but for Earth we need to break it up into smaller pieces and offload some of the work to a rocket.
We have more control over the viability of a space elevator than we think, by questioning the two assumptions above.
You see, conventional rockets also have a mass ratio problem. To reach synchronous orbit, they are about 100 times as heavy as the payload they deliver. Most of this is fuel, and the rest, until now, has been expensive aerospace hardware which was thrown away after one use. So it makes sense to divide the work between a rocket and an elevator. This lowers the mass ratios of both, and the sum of the combined mass ratios will be lower.
We can also divide the space elevator into two parts, one in low orbit and one near synchronous orbit. The lower one passes the cargo capsule to the upper one using orbital mechanics, rather than a maglev rail. Crossing the gap between them using nothing but physics will be cheaper than a maglev rail--they are not cheap. The smaller elevators will also have exponentially lower mass ratios than a single one doing the same job.
To put some numbers to it, the rocket supplies 4,600 m/s (plus various losses like drag), the lower elevator supplies 4,800 m/s to the cargo, and the upper one adds another 1,500 m/s. Since the rocket is doing far less of the work, it’s mass ratio is now 10-15 instead of 100. The exact number will depend on how much of the savings is used to make it last much more like an airplane (20,000 flights) than a disposable rocket.
The lower elevator, using existing off-the-shelf carbon fiber--not some future nanotube stuff--will have a mass ratio of 14, and the upper one 1.4. These are much more sensible numbers. These numbers may not be the optimum, they will depend on a number of design trade-offs which nobody has done yet, but they are much more encouraging than the “one big elevator” approach.
In sum, a space elevator may be impossible--but smaller rockets assisted by space elevators may indeed happen within our lifetimes.
[Image: Flickr user Ryan Somma]