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The Hyperloop: BUSTED

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T3sl4co1l:

--- Quote from: StillTrying on July 28, 2016, 02:39:36 am ---
--- Quote from: T3sl4co1l on July 28, 2016, 02:24:12 am ---The inner surface of a "pneumatic tube" is the entire length of the tube!

--- End quote ---
I was surprised in the simulation above, that the air wavefront didn't quickly become very bullet shaped, it didn't look right to me.

--- End quote ---

Wave physics!  You'll see that at the entry opening, but it's a plane wave (more or less) that pushes ahead.

The ripples are from dispersion, because the pipe is an acoustic waveguide (which, unlike EM waveguide, does support low frequencies -- acoustic waves are longitudinal, so a pipe goes all the way down to DC, which requires a coax cable (supports TEM mode) for EM waves).  Wave velocity varies with frequency, so the frequency components in the wavefront spread out as they propagate.

Dispersion also has another effect:

Because the frequency components separate, the wave front is no longer a sharp rising edge, but a series of ripples (something like a sinc(t) function, although it's more of a chirp wavelet).  This manifests as a weaker overpressure, less peak acceleration when the wave hits something.

This is geometric in origin, and independent of loss.  But losses will also contribute to dispersion, and considerably reduce the amount of pressure being supplied towards the wavefront.  (Essentially, very low frequencies are significantly attenuated and delayed: hence, still more dispersion.)  Which is akin to a tsunami, where the amplitude may not be much (a few feet / 10s of kPa), but even if the wavefront doesn't cause immediate damage, the constant and maintained flow will soon overwhelm anything in the way, pushing it around like matchsticks.

A shockwave is a phenomenon where so much energy has been pushed into the wavefront, that it heats up (adiabatically), thus raising the speed of sound and allowing the wavefront to propagate faster than the cool air it moves into.  This is impossible* from atmospheric pressure alone, so we don't have to worry about shockwaves here.

*Well, maybe if the air rushes into a vacuum tube (as we're talking about here, but not so long that the wavefront disperses), then hits a rigid end wall and bounces back.  That causes the wavefront to double back on itself, raising the pressure inside the tube (from the capped end towards the mouth) to about double, which will therefore heat it, and accelerate the return wave.  The result will be a ringdown waveform (nominally a square wave, since it's a constant cross-section transmission line) with an odd duty cycle.

Tim

StillTrying:
I'm still convinced that the front should be bullet shaped.
https://www.google.com/search?hl=en-GB&gbv=2&tbm=isch&q=laminar+flow+in+pipe

rs20:

--- Quote from: StillTrying on July 28, 2016, 03:30:11 am ---I'm still convinced that the front should be bullet shaped.
https://www.google.com/search?hl=en-GB&gbv=2&tbm=isch&q=laminar+flow+in+pipe

--- End quote ---

Only if friction/loss is factored in. (Not taking a position on whether it should be or not, it's just silly to have a debate on "whether the front should be bullet shaped" because the answer to that question is totally contingent on whether you want to factor in wall friction.)

StillTrying:

--- Quote from: rs20 on July 28, 2016, 03:51:17 am ---Only if friction/loss is factored in. (Not taking a position on whether it should be or not, it's just silly to have a debate on "whether the front should be bullet shaped" because the answer to that question is totally contingent on whether you want to factor in wall friction.)

--- End quote ---

As T3sl4co1l said "Tremendous resistance from the pipe itself". So no need to take that into account then.  :)

T3sl4co1l:

--- Quote from: rs20 on July 28, 2016, 03:51:17 am ---Only if friction/loss is factored in. (Not taking a position on whether it should be or not, it's just silly to have a debate on "whether the front should be bullet shaped" because the answer to that question is totally contingent on whether you want to factor in wall friction.)

--- End quote ---

But it's not dependent. :)

Tim

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