## Thursday, August 22, 2013

### Elon Musk's Hyperloop is Bold and Ambitious

Perhaps you've heard of the recently proposed revolutionary transportation system dubbed the Hyperloop.  No?  Google it.  The vast majority of posts on the topic that I have read go beyond mere skepticism and describe the project as just short of impossible.  What is it about dreamers that brings out the haters?

The Hyperloop was described by its inventor, Elon Musk, as "a cross between a Concord, a rail gun and an air hockey table."  Picture those hollow tubes that shuttle documents through offices by way of air pressure (in movies - I've never actually seen one in real life, but I assume they exist).  Now enlarge the diameter of the tube, replace the tiny capsules with pods containing passengers, and have the ends connect two distant cities, and you begin to grasp Musk's intriguing mass-transit system.

The initial proposal calls for a train that links Los Angeles and San Francisco - the specs call for a thirty-five minute shuttle time each way.  The distance between the two cities is about 600 km.  Is this beginning to sound like a high-school mechanics problem?  Let's spice it up a bit and stipulate a 0.2 g acceleration from rest to cruise and 0.2 g deceleration from cruise to rest.  Try to calculate the cruise speed...

The cruise speed that satisfies these conditions is 309 m/s (the ramp up and down phases end up taking 2 min 38 sec each, leaving about 30 min of cruise), which is just short of the speed of sound in air, and significantly faster than the cruise speed of commercial airplanes.  The PDF proposal, which may be accessed here, actually calls for an even higher cruise speed than this (338 m/s), meaning that there will be a lower acceleration/deceleration.

Initially, let us neglect the difficulty of achieving such high speeds within this enclosed tube, and focus on one serious kinematic consequence of it.  Moving at 309 m/s is concerning if a turn is required.  If we set the lateral g-limit on a turn at 0.2 g (more than this would be uncomfortable for passengers), then the minimum allowable turning radius while cruising becomes 24.4 km!  This implies that if this were to be a circular loop (which it is not), its minimum diameter would be about 50 km.

For the purposes of the Hyperloop, this large minimum turning radius essentially means that the tube must be laid out very straight, and that any changes in direction must be extremely gradual.  Note that in Musk's proposal, he sets a lateral g-limit to 0.5 g, which allows for sharper bends than the above result, but also means one must keep one's vomit bag close at hand.

There are numerous challenges with achieving such a high speed in an enclosed tube.  The greatest challenge may be maintaining a high degree of smoothness along the surface of the inner tube.  At such high transit speeds, even a small imperfection can cause a large impulse leading to failure (which is a gentler engineering term for catastrophe).  For this reason, machining tolerances on the inner tube would need to be high, which is expensive, especially considering the incredible length of the track.  And, even if it is constructed to adequate tolerances, warping due to environmental effects would surely occur over time.

I don't think we will see a Hyperloop whisk passengers along within a decade, but I am delighted with Musk's proposal.  Keep in mind that Musk himself has not committed to building one.  He merely financed this proposal; he put it out there.  The way in which revolutionary ideas like this lead some to feel disdain is unfortunate.  In this day and age, the term "dreamer" has taken on a negative connotation.  From my point of view, to be labeled as such is a compliment.  If we do not permit ourselves to have dreams, then we deny ourselves one of the great privileges of life.

I cannot help but see the many connections between the Hyperloop and another futuristic method of transit: the Space Elevator.  Both involve a long track (much longer for the space-ward one) and pods that travel along them.  Both improve upon current transit methods and both would be expensive.  And, yes, both caused eyes to roll among experts and non-experts alike when they were first introduced.  But rather than rushing to dismiss such ideas, we should let them capture our imaginations.  Whether such projects become economically viable or not, they are products of a high degree of ingenuity.  Let us put our cynicism aside for a moment, and welcome such ideas with the sense of awe they deserve.

#### 1 comment:

Maysam said...

Informative (+some extra words for my weak English ;) )