
Hyperloop: riding sound’s density peak to exploit the drag equation? - cma
http://charlesalexander2013.wordpress.com/2013/07/18/hyperloop-riding-sounds-density-peak-to-exploit-the-drag-equation/
======
jasallen
Relative to the frame of reference, it seems to me the sparse particles would
be travelling closer to the speed of the craft than the dense particles.

The "density front" travels at exactly the speed of sound, but it consists of
nearly static particles (not static from the frame of reference, from the
frame of reference they are moving backward at nearly the speed of sound),
these static particles are the relevant V.

The sparse particles just in front of the dense ones are accelerating to get
more sparse. From the perspective of the reference frame, they are therefore
moving 'backward' at slightly _less_ than the speed of sound, making there
relative velocity closer to that of the reference frame. So lower density
_and_ lower velocity. _and_ that doesn't even account for additional
compression which I don't even know enough to do armchair reasoning on.

So, I'm the farthest thing from an expert, but this is why it doesn't seem to
make sense to me.

~~~
cma
Stare at this thing for a while:

[http://www.acs.psu.edu/drussell/Demos/waves/Lwave-v8.gif](http://www.acs.psu.edu/drussell/Demos/waves/Lwave-v8.gif)

In all seriousness though I'm going through your post to see if you've found a
gaping problem =). I don't think there can be different density velocity
ratios at any point of displacement in the wave's reference frame because the
same net number of particles has to pass through each point or you start
making a permanent buildup on one side or the other of that point, which you
can't do because in the reference frame of the still air that point is moving
at the speed of sound.

A moving point passes by the same number of unique particles at the speed of
sound as it would if it were going the speed of turtle (if you ignore thermal
dispersion).

~~~
jasallen
"the same net number of particles has to pass through each point"

Agreed: the corollary to the "the sparse particles just in front of the dense
ones" is the "sparse ones just behind the next wave of dense ones", which are,
in fact, decelerating, or moving backward even closer to the speed of sound
than the dense ones relative to the reference frame. So individual particles
oscillate back and forth, but net effect is no movement (to the reference
frame of the average speed of the particles, which is a third reference frame
:-) )

------
geon
I wonder i Elon really has a plan, or if he is just kickstarting everyones
speculations to come up with an _actual_ viable design.

~~~
smoyer
The guy launches rockets and builds electric sports cars ... I tend to think
he has a plan. Allowing the speculation to persist might improve that plan but
I suspect it was viable on it's own (and perhaps the waiting period was simply
to allow some small scale testing to occur).

~~~
riledhel
I like the way he approaches problems and I think he has some plan to turn
most of his ventures in some sort of vertical market.

------
ddeck
All this speculation reminds me of the hype surrounding the Segway launch. I
recall it being being touted as a game-changer, a revolution in transportation
that would change the way cities were built...

 _[The Segway] will be to the car what the car was to the horse and buggy_
(Dean Kamen)[1]

 _John Doerr, predicted Segway would rack up $1 billion in sales faster than
any company in history_ [1]

Let's hope the Hyperloop fares better.

[1]
[http://www.wired.com/wired/archive/11.03/segway.html](http://www.wired.com/wired/archive/11.03/segway.html)

~~~
InclinedPlane
The Segway was demonstrably inferior to commonplace alternatives on simple
metrics alone: speed, capacity, cost, safety, comfort.

It was only hyped because it was "cool".

If the hyperloop, however it works, can duplicate the capabilities of a high
speed rail system in terms of passenger throughput, speed, and waiting time
and do so safely at much lower cost then even if was the uncoolest thing in
the world it would still be of immense practical benefit.

~~~
stcredzero
_> The Segway was demonstrably inferior to commonplace alternatives on simple
metrics alone: speed, capacity, cost, safety, comfort._

Metrics are like statistics, in that they can also mislead. It's really about
the experience in specific contexts.

 _> It was only hyped because it was "cool"._

Actually, it failed because it just looked dorky. (Which Steve Jobs predicted
in his secret meeting with Dean Kamen.) Good tech badly marketed sometimes
still doesn't sell.

~~~
salemh
I believe this is what you are referring to:
[http://hbswk.hbs.edu/archive/3533.html](http://hbswk.hbs.edu/archive/3533.html)

 _" What does everyone think about the design?" asked Doerr, switching
subjects._

 _" What do you think?" said Jobs to Tim. It was a challenge, not a question._

 _" I think it's coming along," said Tim, "though we expect—" "I think it
sucks!" said Jobs._

 _His vehemence made Tim pause. "Why?" he asked, a bit stiffly._

 _" It just does."_

 _" In what sense?" said Tim, getting his feet back under him. "Give me a
clue."_

 _" Its shape is not innovative, it's not elegant, it doesn't feel
anthropomorphic," said Jobs, ticking off three of his design mantras._

 _" You have this incredibly innovative machine but it looks very
traditional." The last word delivered like a stab._

...

 _" Screw the lead times. You don't have a great product yet! I know burn
rates are important, but you'll only get one shot at this, and if you blow it,
it's over."_

~~~
stcredzero
That's exactly it.

------
shoyer
The author appears to have confused group velocity (the speed of the wave)
with particle velocity (the speed of the air molecules). This is a very basic
notion of how waves work -- the waves move, not the medium.

In this case, the wave (and the vehicle) would be moving at the speed of
sound, but the air particles they hit wouldn't. They're basically still
stationary. There is no magical force to bring them up to the speed of sound
before they hit the vehicle. Hence, the drag is not reduced.

I'm a physicist, but by no means an expert on sound. There are more details on
how sound actually works on this page:
[http://mysite.du.edu/~jcalvert/waves/soundwav.htm](http://mysite.du.edu/~jcalvert/waves/soundwav.htm).
A relevant quote: "v [the particle velocity] is much less than the phase
[wave] velocity of sound" (note: phase and group velocity are equal for sound
in air).

Edit: This criticism is not right; see below.

~~~
cma
You read it wrong; at no point were any particles in the wave assumed to be
going the speed of sound; that's why when you look from the vehicles reference
you see a standing wave but at every point on it particles are still flowing
towards the vehicle. The picture says it is in a sound-speed reference frame,
but it probably confused you if you didn't read that.

At no point is the air doing anything but apply drag to the vehicle's
movement; there is just a sweet spot to minimize drag, but it isn't minimized
to zero.

Read through this thread a bit and you'll see me talking about the exact same
difference of propagation of a disturbance vs displacement/velocity of
individual particles...

~~~
shoyer
OK, after looking at the diagram and re-reading the article you are right --
you did not in fact mix up group and particle velocity

~~~
cma
It is probably my fault cause I sort of wrote the post as I worked out the
concept and that ended up muddying a lot of the writing. And I'm not a
physicist so I'm sure I didn't quite state everything in a very traditional
way...

------
gpsarakis
Just some info: Transonic/supersonic and near-speed-of-sound aerodynamics
differ from traditional low velocity aerodynamics (I think the threshold is
approximately 0.25Vs, so up to 1/4 of the speed of sound, I am a bit rusty on
that). After that point you can't ignore _compressibility phenomena_ , meaning
that the density is no longer a constant, but also becomes a variable. You may
be able to reduce drag by going very high in the atmosphere where the air is
very thin (10^-6). Speed of sound also is an equation of the density and the
temperature.

------
shoyer
This is an intriguing proposal, but one that I think it ultimately flawed.
Once a wave is strong enough for there be to appreciable density differences
(NOT the usual case for sound waves), the usual wave equation for sound does
not apply [1]. In the case of such "Very Strong Sound Waves", you have a non-
linear wave equation and thus the shape of your wave is no longer fixed as it
moves. Eventually, you end up with shock wave, where the front of your wave is
a discontinuity.

Why is this problematic? Well, once you have a shock wave (e.g., a wave
crashing on the beach), the physics gets a lot more complicated. You are
basically riding an explosion in a tube.

At this point, it no longer safe to me to neglect factors like dissipation.
Your shock wave is going to heat up the air and eventually fizzle out. If you
want to keep it going, you'll need to be continually supplying tremendous
amounts of energy at exactly the right time along your tube. You'll also have
to be continually cooling or cycling the air to relieve the waste energy.

To me, it seems a lot simpler and more reliable (not to mention safer) to
simply evacuate your tube, which, I believe, is the original hyperloop idea.

[1]
[http://mysite.du.edu/~jcalvert/waves/soundwav.htm#H](http://mysite.du.edu/~jcalvert/waves/soundwav.htm#H)

~~~
cma
That's a great link.. should help see how far this could be practically taken.

When the wave is very strong the heat generated by compression isn't
dissipated adiabatically the wave starts losing energy to waste heat; if you
increase the wavelength you again move back to the adiabatic regime. How far
can you take it? I don't know, I'd like to see some numbers and that's
probably what I'd work on next if I keep looking into this.. probably won't
until after Elon's announcement.

For extreme cases of high-amplitude waves where the particle velocity itself
is getting close to the speed of sound, I definitely don't know what all
happens, but somewhere in the write-up or comments here I at least had going
that far as a bound on how far you could push things before you didn't really
even have sound waves anymore.

------
whiddershins
that's a really clever theory. I can't wait to find out if it is true.

~~~
cma
Tweet it at Elon =) but yeah.. I'm just waiting on the flaw haha

------
w_t_payne
Presumably the pressure wave is maintained by a continuous array of big-ass
subwoofers along the whole length of the tube - If this is the case, then
keeping the noise pollution down will be a bit of a challenge - unless some
sort of active-noise cancellation technology is used for the outside.

Hmmm... This should not be too tricky, since you are generating the original
signal yourself, but if one of the exterior noise-cancellation speakers breaks
down - it's gonna be LOUD.

~~~
redwood
The whole idea of a wave guide is to trap the energy of the wave inside, so
presumably a lot of it would not escape.

------
Taek
What I remember from physics class makes me think this isn't viable.

If you have sound moving through the tube, you have energy pushing the sound.
Either you have to keep the whole tube 'humming' or you have to send people
off in a blast wave. With the humming idea, you might be able to create
vacuums that travel around the tube at the speed of sound (sound works by
changing the density of air, oscillating from high pressure to low pressure),
and then you can move vehicles around the tube at the speed of sound with very
little drag.

So then you need some way to keep the vehicles floating, and you need to get
them to the speed of sound in the first place (rail gun?). I'm going to
pretend that we have a cheap way to do both of those things.

So, how expensive would it be to keep 100s of miles of hyperloop humming with
a sound powerful enough to create vacuums large enough to fit transportation
units in? Even if you are only using cars large enough to hold 1 person and a
suitcase, you are going to need a lot of energy powering the sound waves
throughout the tube.

You might be able to do some acoustics-like engineering to keep the sound loud
at little energy cost, but I don't think that solar power above the tunnel is
going to be enough. Using this model, Musk would need a handful of
technological advances up his sleeve.

So I think the big 'secret' that makes a hyperloop viable is not this one.
Then again, with the Tesla and his space adventures, he has had to deal with
at least a handful of difficult obstacles. So maybe he is expecting to develop
multiple technologies to make this viable.

~~~
cma
The point of this approach was not to keep the whole tube humming (that would
have almost as much friction loss as just circulating all the air in the whole
loop), but rather just send waves in small bundles.

If you read my post it has nothing to do with vacuums and instead somewhat
counter-intuitively keeps the vehicle within the densest part of the sound
wave the entire time.

------
beambot
I still believe the top contender is Jacques Mattheij's proposal of a
pressurized tunnel: [http://jacquesmattheij.com/elon-musk-and-the-
hyperloop](http://jacquesmattheij.com/elon-musk-and-the-hyperloop)

~~~
bencollier49
Didn't EM say it wasn't pressurised? Could be misdirection, mind.

~~~
wcoenen
No, he said that it is "not an evacuated tunnel".

------
antninja
Someone should build a prototype of such a tube and see if it's efficient. The
mystery around Hyperloop generates a lot of ideas that should be tested.
Railroad infrastructures are ageing, maybe some tuberoads can replace them.

------
throwmeaway33
I remember doing the math in my undergraduate physics studies. Air molecules
actually do not move very far when a vibration (ie. sounds) goes through them.
Amazingly, high frequency sounds move air back and forth only a few angstroms.

I can't find a link describing the calculation. This link talks about how the
change in pressure is equivalent to "140 molecules for every million
molecules"
[http://www.silcom.com/~aludwig/musicand.htm](http://www.silcom.com/~aludwig/musicand.htm)

So there is no way you are going to create a bubble of vacuum!

~~~
geon
The article talks about low frequency and high amplitude. The sound waves near
a subwoofer definitely moves the air more than a few ångström...

And you don't want low pressure, but _high_ , so the air _speed_ is low. Drag
is proportional to the density, but proportional to the square of the speed.

------
marshray
I think the best you could do would be to stay near the trailing end of the
pressure wave. This would be where the air was moving (slightly) in the same
direction as your travel. You would also travel through the lowest density.

But I suspect you'd always be better off by simply evacuating the tube as much
as possible.

Or possibly there is a medium other than air being considered, one in which
the speed of sound was much lower at a given density. Perhaps interesting
things could happen if the working fluid was a refrigerant and the sound wave
was intense enough to induce a phase change cycle.

------
benjamincburns
I'm confused by this... If the air molecules are staying roughly still, but
the density of the air surrounding the vehicle rises by a factor of n, isn't
the vehicle colliding with n times as many particles as it would have
otherwise? How is this more efficient?

Is the velocity in the drag equation relative to the vehicle, or to a
stationary frame of reference?

Edit: Or is the point that the velocity of the air particles within the
density peak is at its maximal forward-traveling rate before they start to
loop back around and form their ellipse?

~~~
icegreentea
The velocity in the drag equation is relative to the vehicle.

------
Aaronneyer
I'm starting to think Elon has absolutely nothing planned, and just wanted to
see what everyone thought he was doing, to help bring about all these awesome
ideas for high speed travel :)

------
opminion
I can only hope that the Mythbusters are on this already.

~~~
stcredzero
Not that I don't like the Mythbusters (I do like them) but the math and
physics are already beyond them.

------
acd
Can the hyperloop be combined with quantum levitation? To provide very low
friction high speed travel?
[http://www.ted.com/talks/boaz_almog_levitates_a_superconduct...](http://www.ted.com/talks/boaz_almog_levitates_a_superconductor.html)

~~~
Taek
I think the problem with that idea is you have to keep the superconductor very
cold, which might be too expensive for large objects that need to levitate for
30 minutes.

------
jjindev
I once sailed upwind from LA to SF over 5 days. I flew home in an hour. The
flight gave me a long(!?) time to ponder the nature of time and transport.

In that context, I don't really see a transformational improvement going from
one 1 hour to 0.5 hours.

~~~
nakedrobot2
Sorry, let me clarify your statement: You spent 4 hours in the airport (or
getting there, parking, getting sodomized by security) and 1 hour flying. Then
another 30-60 minutes disembarking. So you spent around 6 hours in transit
from SF to LA.

6 hours compared to 30 minutes (or more likely, 1.5 hours including the
necessary boarding / unboarding) is a VAST difference.

~~~
jjindev
Why do you presume less "lobby time"? I'd think a train twice as fast as a
plane would inspire at least as much security theater.

~~~
georgemcbay
Even if it did, the amount of "lobby time" would still be drastically lessened
just based on frequency of departures and decoupling of passengers and
elimination (presumably) of the checked baggage situation.

TSA security checkpoints suck, but IME they "only" represent about 15 or so
minutes of the extra time required for airport lobby time (on average;
sometimes more sometimes less. Which is at least 14 minutes too many, but
hardly the whole 1-4 hour overhead often cited).

Most of the overhead of plane travel in terms of airport and tarmac waiting
time is due to deadlocking problems that occur in coordinating all the
passengers into a single vehicle that is as full as possible (to maximize the
airline's profit per trip), so you get a very uneven/lumpy demand curve based
on when flights are scheduled, all sorts of complexity due to the system of
having to check bags into a separate physical compartment, etc. A continually
operating system where you could just show up whenever, your bags stay with
you for the ride, etc could easily smooth that out. Solve the deadlocking
issue (and most of the hyperloop guesses I've seen do) and even if the
security checkpoint stuff stays mostly the same you'll still have a far more
efficient embark/disembark system.

~~~
TeMPOraL
True. In Europe we don't have TSA and yet one still would be wise to arrive at
least an hour before departure (if one has checked baggage; half an hour
otherwise) to an airport which is usually located 30+ minutes from the center
of the city.

Times always add up like this - 0.5h to get to the airport, 1.5h on the
airport, X h of flight and then up to 0.5h to leave the airport and another
0.5h to get to the city.

------
Qantourisc
Sound: a vacuum and a high pressure alternating ... Using wind would be far
cheaper and better I think :-) I mean really really low sound frequencies are
the same anyway. (As far as my physics go)

------
nmeofthestate
This seems like nonsense to me - any sound waves will be massively disrupted
by the bloody great vehicle ploughing through the air, no?

------
worldsayshi
Will not constantly travel at the speed of sound maintain a continuous sound
bang that would break every window passed by the train?

~~~
jlgreco
In case this is unclear to anyone; all transonic, supersonic, or hypersonic
flight/movement causes a 'continuous' sonic boom. A Bell X-1 at Mach 1.06
causes a continuous sonic boom along it's path, as does a Mach 2 Concorde and
a Mach 2.6 Browning 50 cal machine gun bullet. "Sonic booms" are not discrete
events that occur when you cross the 'sound barrier' or continuous when you
stay at it. They are continuous at it and past it, not stopping until your
velocity drops down below it again.

GIF that does a good job of explaining this:
[http://upload.wikimedia.org/wikipedia/commons/e/e4/Doppleref...](http://upload.wikimedia.org/wikipedia/commons/e/e4/Dopplereffectsourcemovingrightatmach1.4.gif)
That leading edge where all the circles are kind of meeting up? That is where
the sonic boom is. It continuously sweeps across the landscape behind the
source, as long as the source is moving faster than the speed of sound.

~~~
worldsayshi
But I take it that the magnitude of the boom will get less severe the faster
you go beyond the speed of sound?

~~~
jlgreco
Yes, though not as much as you may think.

Going faster tightens that pressure wave cone, but there are a lot of other
factors too. Vehicle geometry seems to be a pretty dominating factor for
example, longer aircraft have less severe sonic booms. Depending on the shape
of your aircraft you may or may not get several shockwaves originating from
different points that after a distance combine to form a larger shockwave.
Altitude is a biggie too, the higher you are the less intense it will be.

Take note of how the F-104 and Concorde compare
([http://en.wikipedia.org/wiki/Sonic_boom#Measurement_and_exam...](http://en.wikipedia.org/wiki/Sonic_boom#Measurement_and_examples)).
The F-104 moves slightly slower, slightly lower, but has a much weaker sonic
boom.

------
rfugger
So the vehicle basically surfs a sound wave?

------
gaze
Cool. So how do I accelerate into this "bubble"

------
PaulHoule
wouldn't it be awfully loud? traffic noise is bad enough in California as it
is. Would it be loud inside?

------
jlebrech
what if it's not in a vacuum, and it's magnetic rings with a cylinder going
through the rings.

------
SideburnsOfDoom
pictures of Machu Pichu are mostly irrelevant to the article. And cliched.

------
berntb
If this works, I wonder about the logic of making it a SF-LA thing? At least,
there should be another use case.

Why not go from Silicon Valley to a mountain area where you've bought a large
area of land, ready to build on?

You could get investments from all over the tech industry, since it would
lower living costs (and increase the maximum number) of the people that
Silicon Valley can have (less infrastructure and living area "load").

Use the sales slogan "let's supersize the Silicon Valley!" for this new
commuting solution.

~~~
JPKab
Here's a crazy thought: Let's get outside the West Coast bubble here and think
about this in a vastly more practical manner when it comes to population
density and distance between urban cores.

Every time I hear this project spoken of, I have to hear people who live in
the Bay Area talking about "SF to LA in half an hour"

I think what would be much more sensible would be "NY to Boston in 15 minutes"
and then extending it to Philadelphia and DC. Where would the line go after it
hit SF? Portland and Seattle? Denver? The populations of these places don't
support the cost of the infrastructure. The east coast makes much more sense
for this project.

~~~
akamaka
Why LA-SF? It's the second busiest air route in the country, and also one of
the shortest, so it's ripe to be disrupted.

[https://en.wikipedia.org/wiki/World%27s_busiest_air_routes#U...](https://en.wikipedia.org/wiki/World%27s_busiest_air_routes#United_States_.282009.29)

~~~
JPKab
You are assuming that there are not millions upon millions of people who can't
justify flying from Boston to New York due to the fact that the car trip (when
you factor in arrival at airport 90 mins ahead of time) isn't drastically
slower than flying.

I say this as a seasoned east coast corporate whore. Many, many business
travellers are forced to just drive from New York to Boston due to the fact
that the trip is 3 and a half hours long in a car. NYC to DC is about 3 hours
44 minutes by car. These are distances which are just short enough to make a
company tell an employee to drive instead of fly, but long enough that nobody
in their right mind would want to commute this way on a semi-regular basis.

[http://www.wolframalpha.com/input/?i=population+of+metro+was...](http://www.wolframalpha.com/input/?i=population+of+metro+washington+dc+%2B+population+of+metro+philadelphia+%2B+population+of+metro+new+york+city+%2B+population+of+metro+boston)

Not counting Baltimore, the East Coast corridor has over 35 million people in
the big city's metro area. If the price of this service is expected to be
similar to air travel, then I get it (SF-LA), if this is simply about selling
speed for a premium price...... but I think this is really about doing it
faster AND cheaper. If its efficient enough, this could lead to a decoupling
of workplace from home location, the way telecommuting was supposed to.

