Speculating about the Hyperloop

Elon Musk has been dropping hints about his Hyperloop idea.  (We cannot call it a proposal because he has not actually proposed it yet.)  There is a lot of curiosity about what it might be.  Given Elon's history, the idea will sound audacious and yet will actually be workable.

Jacques Mattheij recently speculated on the topic.  His proposal has the serious problem in that the friction of the air on the sides of the tunnel would lose way too much energy.  But it got me thinking, and I have what may be a more realistic proposal.

First, imagine a tube that goes in a loop from Los Angeles to San Francisco.  Let's put flaps on the walls.  When they are open, air pressure can equalize.  When they are closed, they don't leak much.  Now let's put large, heavy objects going around and around the loop.  For lack of a better name, let's call them plungers.  The plungers can be floated and moved very efficiently with maglev technology.  As each plunger approaches, the flaps open so that air can get pushed out, then closes so that it doesn't come back in.  This is not an evacuated tube (Elon explicitly says that his technology isn't an evacuated tube), but results in a decent vacuum away from the shockwaves in front of each of plunger.  That eliminates most of your friction losses.  I don't know how low, but Elon claims low enough that solar panels on top of the device provide more than enough energy to keep it permanently going.  I see no reason to disbelieve that solar panels could do that.

Now where do the people fit in?  People go into vehicles that I'll call cars, even though they aren't really cars.  These cars can be fired by a railgun to match speeds with the tube, and injected in front of a plunger.  We can build the plunger with a space in its front that the car fits in.  This space has air trapped in it by the shock wave and so the people can breathe.  On its own that space would heat up due to the friction on the gas, but you can put a heat sink (eg a block of ice) in the car and keep it comfortable inside.  Near the end of your journey the plunger ejects the car from this space on a course that launches it out of the tube while the plunger continues on its way.  The car is then stopped with regenerative braking that recovers most of the launch energy, resulting in surprisingly little energy loss for taking the trip.

Now what would some of the specs be?  Well, Elon claims 30 minutes from downtown Los Angeles to downtown San Francisco.  According to google maps that's 382 miles, which is about 600 km.  So the loop should be going around 1200 km/hour.  If we put 12 plungers on the loop, and have plenty of vehicles, then you get in your vehicle and have a launch opportunity every 5 minutes.  Increase the number of plungers, and the time to launch can be decreased while the capacity of the system can be increased.  If we space the plungers a third of a km apart, we would have 3600 of them and could be launching every second into the system.  It probably is more efficient if you instead make plungers larger so that cars carry more people.  So instead of car think "bus".  But after the initial system is built, you can later add new entrance/exit ramps and ramp up capacity.  As Elon has promised, you would not need to reserve tickets - you'd pretty much arrive and then go.

Elon also claims that his system could store a lot of energy, enough to collect energy during the day and run off of it at night.  The obvious place to store energy is in the kinetic energy of the plungers.  How much energy are we talking?  Well 1200 km/hour is a third of a km per second.  That's 55.5 kJ of energy per kg of plunger.  So 64,800 kg (about 143,000 pounds) of plunger is a megawatt-hour of power.  Suppose that is one plunger.  If you've got a thousand plungers, and each is storing a full megawatt-hour, you could permanently consume 50 megawatts of energy.  You'd use up over half of it at night, then regain it during the day.  Trips taken in the early morning commute might take 50% longer than during the evening, but it is doable.  This gets better if we make plungers bigger, have a more efficient system, or have more plungers.  I'm sure that Elon has thought about the ideal parameters.  But if heavy plungers are good, well, put in enough metal for maglev to work and then add rock.  You'd store a lot of energy.

Heck, the solar panel angle is fun but not really necessary.  From the point of view of the electric power grid, it would be very, very good to have a large energy sink that can even out power fluctuations.    Renewable energy sources often arrive at different times than we'd like to get power out.  Sometimes, like with wind, we get very sharp spikes that we need to even out.  If designed properly, the Hyperloop can absorb pretty much any power spike, and can bleed enough power out to be interesting.  Therefore if the power utilities are smart then they should be willing to pay to add more plungers.  Not because they care about the fact that they are improving peak capacity and reducing waiting time, but because they want to be able to store more power in it.

I'm sure that there are many improvements on this design that I have not thought of but which Elon has.  I'm also sure that Elon has detailed blueprints that take this from a half-baked concept to something you can start to put cost estimates on.  But this idea looks doable to me, and looks like it could - at least in principle - justify all of the claims that Elon has been making for the Hyperloop.

Finally I'd love to see this built.  I'd love to see it built in California.  But, unless someone like Elon pushes it, I'd be willing to bet that the Chinese get it first.

BTW for further discussion, see Hacker News

How did pterosaurs get so big?

The pterosaurs got going something like 230 million years ago. They died out with the dinosaurs 65 million years ago. Over their history they came in all sizes, from Rhamphorhynchus who was the size of a sparrow to Quetzalcoatlus with a wingspan of variously estimated as being 30-40 feet. Spread out it was a similar size to a t-rex, and on the ground its estimated height was close to a giraffe's. The largest bird ever, Argentavis was much, much smaller than that.

However the birds arose about 150 million years ago. Feathers were a big advantage in flight, and over time the birds took over a lot of what the pterosaurs were doing. But the pterosaurs did not go away. Instead they wound up being in niches for very big flying animals. This is competition through specialization, which I talked about some time ago when I discussed the Neanderthals.

This coexistence provides evidence that birds were generally better fliers, but there was a niche for very big fliers that the pterosaurs were better at. The question I'm curious about is why the pterosaurs were better at being big fliers than birds were.

I have a theory. But before I can explain it I need to provide some background.

Wings have evolved in vertebrates three times in pterosaurs, birds, and bats. All three started with the basic vertebrate limb structure and found different ways of constructing a wing out of it. In both bats and birds the arm bones form part of the wing. Now an important fact about vertebrate bones is that different bones grow at different rates as you grow. In particular arm bones start off shorter and catch up later. The result is that in birds and bats, babies have the wrong proportions for their wings to be useful. Therefore baby birds and bats can't learn to fly until they have achieved a significant fraction of their full size.

Pterosaurs were different. Their wings were entirely constructed from wrist and hand bones. (Fully half the wing was supported by an elongated 4th finger.) Hand bones stay in proportion your whole life. Comparisons of fossils of pterosaurs at different ages in the same species verifies that their wings always had good proportions for flight. Furthermore we have fossils from baby pterosaurs that died miles out at sea, which is direct evidence that they flew young.

What does this have to do with the eventual size of the animals? Well birds cannot learn to fly until they are near full growth. Which means that they need intensive care from their parents until they reach that growth. This care is a significant fact of life for bird species, and is why most types of birds have both parents providing care. Unlike most mammals where the mother is generally capable of taking care of young on her own. The larger the bird is, the harder this care is to provide.

By contrast pterosaurs were probably able to take care of themselves at a much younger age, and smaller size. Which means that they were free to grow for a lot longer, to a lot larger size, without unduly taxing their parents. (In truth we don't have any data indicating how much or little parental care baby pterosaurs got. But I suspect it was less than birds get.) And, I believe, that is why they were able to get so much larger than birds.

Random trivia I came across in preparing this post. The reason bats can't fly during the day is that their wings are vulnerable to sunburn. There is evidence that pterosaurs had a protective layer so they didn't have this issue. Also birds have stiffer wings than bats do, which provides better lift and less maneuverability. Pterosaurs had more joints in their wings than birds do, but didn't have finger bones inside of the structure of their wings like bats, which suggests to me that their wings would have been somewhere between.

And my whole train of thought was started by watching National Geographic - Sky Monsters. If you're interested in pterosaurs, it is a worthwhile video.