[rmxt]

A 5-mile test track won't be big enough to examine the biggest concerns: thermal and seismic. The alpha brochure linked to in the OP barely touches on the two. Here [1] is a better analysis/take-down of what thermal issues such a long structure will encounter. (TL;DR: A 400-mile long continuous structure will need to accommodate 1000 feet of thermal movement over it's length and lifetime.) Seismic is another beast: it requires a much more thorough examination than the cursory glance it was given in the alpha paper.

[1] http://www.leancrew.com/all-this/2013/08/hyperloop/

Thermal effects on Maglev research: https://www.lib.utexas.edu/etd/d/2007/kimh10315/kimh10315.pd...

EDIT: Apologies for the negativity... I hope this reads as more of thoughtful criticism, rather than as being hypercritical.

[Retric]

Thermal expansion is not really an issue that gets worse with distance, as the track can simply be made from independent segments connected with expansion joints. The issue is being able to cross from segment A to segment B not the number of such segments. In other words if it works on a test track it scales just fine, but getting that first connector to work is the hard part.

Earthquakes require active dampening which defiantly increases costs, but a larger issue is how to cross fault lines as you need a very large turning radius so very long segments of track need to be able to move. AKA you can't do this: http://pubs.usgs.gov/fs/2003/fs014-03/pipeline.html Unless you’re willing to really slow down.

PS: Also of note, you are going to need safety exits on a fairly regular basis and some way to quickly add air to the pipe as people are not going to be able to walk hundreds of miles in case of an issue.

[rmxt]

Thermal is an issue that gets worse with distance. Did you look at the article that I posted above? If you are proposing expansion/slip joints at every pier, that runs directly counter to the proposal which states that expansion joints will only be needed near the stations. [1, pg. 27] If we go according to the proposal, the slip joint at the stations on the test track will only need to accommodate ~9 feet of movement (5280x5x6.5x10^-6x100)/2 compared to something an order of magnitude higher for a full-scale track.

Successfully designing for earthquakes does not necessarily mean active damping. (That is, it is not "required" as you state.) Yes, many large structures use specially designed mass or viscous dampers for dynamic loading (Citigroup Building, NYC; Taipei 101; Millennium Bridge, London), but others are designed to fail safely such that life and structure are preserved to the greatest extent possible. Specifically for bridge structures, there is the notion of plastic hinging in visible locations. [2] This way, the failures can be identified and repaired before normal use resumes. Here are some relevant state DOT guidelines. [3]

[1] http://www.spacex.com/sites/spacex/files/hyperloop_alpha-201...

[2] https://en.wikipedia.org/wiki/Plastic_hinge

[3] http://www.dot.ca.gov/hq/esc/techpubs/manual/bridgemanuals/b...

[msandford]

> Thermal is an issue that gets worse with distance.

I would respectfully disagree. The rail industry has figured out how to do Continuous Welded Rail (CWR) quite well, using the elasticity of steel.

http://blogs.agu.org/landslideblog/2011/03/08/distorted-rail...

Similarly the tube for the Hyperloop doesn't HAVE to free-float against its foundations. It might be easier or harder depending on various factors to work on expansion joints or doing the tube equivalent of CWR. You'd probably work on both to figure out which is easier in the long run.

Considering that it's a 9-11ft diameter tube with about 1" wall thickness, it's going to be pretty stiff, especially relative to traditional rails. The moment of inertia means that it should be very resistance to bending or buckling under compression and under tension steel is usually very good.

Given that there are going to be plenty of turns that the track has to make, I would look at doing a combination of two things:

1. Working towards a CWR style solution

2. Allow some movement so that the corners can take up the slack as the tube expands

The turns are very gradual and sweeping. But you could imagine that there's a virtual intersection between two straight portions that you determine by drawing lines from the straight portions until they meet. The actual turn will take place far from here, but it's instructive. So as the tube expands, the actual curve is going to move ever so slightly from the neutral position towards the virtual intersection. So long as there is enough room on the pylons to accommodate this, things will be pretty good. The tube will go from being curved 0.1 degrees per 100 feet to 0.105 degrees per 100 feet (or something like this) but this can be designed for and ensured that it doesn't cause the tube to buckle or collapse. It's engineering, not the utter unknown.

[HCIdivision17]

That is one of the coolest articles on field engineering I've seen in a while. Thanks a lot for sharing it - it really brings out how something like the hyperloop can be tackled. So far, thermal effects have been my main point of curiosity, but the idea of calibrating the steel to take care of it will likely be the ... easiest? way around the problem.

At their desired vacuum pressures, the steel doesn't need to be anything special, so I would love to see the mechanical engineering that goes into designing the 5 mile track's materials.

[msandford]

The engineering to do a 5 mile section is pretty straightforward. It's only 5 miles long (25000 feet) and around 250 joints.

1. Giant foundations and just handle the thermal stress by not letting anything move

2. Figure out the slip joints really well to soak up the ~125 feet of travel and still hold a good vacuum

3. Figure them out OK and just install extra vacuum pumps since there are only ~250 joints

4. Try out some/all of these options on 500 feet of tube in parallel to see how it all performs and don't make a final decision on the whole 5 miles until you have real cost numbers

The other thing I'll mention is that you don't need the steel to be continuous in order to hold a vacuum. You need the inside face of the tube to be smooth in order to not jerk around the vehicles, but all the sealing could be done on the outside with clamp-on seals. If the average continuous tube piece is 100 feet long and the max thermal expansion is 0.5% then you only need a half-inch gap between the tube pieces.

If your air bearings are say 3 feet long each and divided into 10 sections internally which are fed through orifices so that no one section can rob all the pressurized air flow then you're never going to lose more than 10% of your bearing force and you should be able to glide right over these 1/2" gaps with no problems. And if there are some problems a few accumulators (plain air tanks or pressurized bladders) inline with the supply lines would probably increase the momentary recharge capabilities enough to negate the problem.

700mph is 1000 feet per second or 12 inches per millisecond. That means a 1/2" gap is crossed in just 40 microseconds or so.

[rmxt]

Thank you for the additional info. I am skeptical merely because they were quite hand-wavy about temperature accommodations, and it certainly is/was simplistic to think that ALL thermal movements can be accommodated for only at stations. (Especially if it's a direct and exclusive SF-LA route) Yes, the cross-sectional properties of the tube are going to be phenomenal, but I've always operated under the assumption that you don't try to resist thermal movements, regardless of the strength of the cross-section. You let them dissipate and design for the deflection (e.g., at the bearings and abutments), rather than the stress (buckling/tensile) in the beam. If we start allowing stress to develop in the superstructure tube, I can't imagine what the cyclic fatigue impacts of that temperature stress will be. (Maybe it's not significant...)

I am no rail expert (though I am a civil/structural guy), but even continuous welded rail isn't always continuous for hundreds of miles. [1] I think that there are two factors at play: continuity in the maglev/rail structures, and continuity in the superstructure/tube. I do not know what maglev devices look like, but if they do look like traditional rail, then agreed that a CWR solution seems to be the way to go. That being said, no matter how stiff the tube is, it too will have to accommodate thermal movement. My gut reaction is to call everything tube related simply supported, allow for (6.5x10^-6x100ft.x100deg = 0.065 feet) ~= 0.75" of expansion or contraction at each pier, and surround this expansion zone with a metal sleeve of 2"+ greater diameter than the main tube. Simply supported, multi-span structures are a well-studied problem. Adding in the continuity of the rail/maglev structures are what make it hairy, IMO, and the interplay between seismic considerations and thermal considerations becomes important. As far as I can see, it's very important for the maglev structures to be continuous to ensure for smoothness and speed of the ride.

For example, given that you make the superstructure spans simply supported, you have these nearly perfect "mass-on-a-stick" seismic models with well defined, and relatively short periods. Then, you have much longer continuous sections of rail/maglev equipment that contain releases on a far fewer number of span segments. These will have much longer periods of vibration. Maybe I'm stretching here, but the connections between the maglev/rail and superstructure seem like a place that is rife with potential for failure and stress during a seismic event. (I would not want a life-safety issue being my most prominent failure point.)

[1] http://boards.straightdope.com/sdmb/showthread.php?t=471152

[msandford]

If you're dealing with bridges or buildings then you're right of course, you don't stress anything and you just let the stress dissipate through various movements.

But thermal stresses are very small, for "normal" steel it's 13e-6 per degree C. If you figure that the temperature variations in CA aren't going to be more than say 40C (and that's probably too much) then you're looking at 520e-6 or basically 5e-4.

As far as strain goes, that's not a terribly big number at less than 0.1% especially considering that most of the stress/strain graphs will go up to 10% or more and the first 1% are usually WELL within the linear elastic region. That means that you're talking about doing perhaps only using a few ksi of the steel's strength for the thermal effects.

[rmxt]

Excuse my arcane units, but it is what I am familiar with:

ΔL=αΔtL; ΔL/L=αΔt; ϵ=ΔL/L; ϵ=αΔt; E=f/ϵ; f=ϵ/E; so f=αΔtE

ΔL = change in length due to temperature

L = restrained length

f = stress that arises due to full restraint

E = Young’s modulus

ϵ= strain

α= coefficient of linear thermal expansion

Using AASHTO numbers for structural steel:

f= 6.5x10^-6 (1/F)* 100 F * 29000 ksi = 18.85 ksi

That's a big chunk of the elastic 50 ksi range, and it's greater than a good portion of the allowable ranges from the table on page 41 of this PDF [1]. As you might already seem to know, AASHTO doesn't consider temperature loading for fatigue limit states, and in the Strength limit states it considers the force effects to be halved. (Though the displacement effects are multiplied by 1.2) Regardless, fully restraining these things at their ends doesn't seem like a good idea. Am I missing something in what you're talking about? Yes, the strain is low but fatigue generally works in terms of stresses.

[1] http://downloads.transportation.org/LRFDUS-6-Errata.pdf

[tcpekin]

Correct me if I'm wrong, but the linear elastic region usually ends somewhere around 0.2-5%, meaning 1% strain is not well within the linear elastic region. If you just do σ_y/E, you'll get the yield strain. Using rmxt's numbers you get 0.17% yield strain. Using [1] for 1018 steel you get 0.155% yield strain. The strains you calculated are not insignificant.

[1]http://www.matweb.com/search/datasheet.aspx?matguid=3f2ce033...

[Retric]

If their test has a station every X feet, then the track needs to follow that same rule. Granted, if they suggest you can build a test track station every X feet and the full scale model over 10x feet then that's an issue with their model. But, again it does not get worse due to the total number of stations just the ratio of stations to track.

Anyway, you don't need active dampening to keep the structure intact, but a 750mph vehicle suddenly needing to lift 10 feet in the air you’re going to need a lot of head room not to hit the top of the tube. Not to mention rapid left right displacement. Granted, cost/benifit let em die yada yada.

[seanflyon]

The design only calls for one station at each end. Many people have said that the best way to deal with thermal expansion is to let the ends (at the 2 stations) move ~500 feet at each end. The alternative is expansion joint every so often along the tube.

[msandford]

If you do that, though, then all of your support structures the whole way through need to allow the tube to move inside of them. The tube is supposed to be supported every 100 feet or so (if I remember correctly) so that means that the last pylon has to be at least 500 feet from the station and that the tube has to be able to slide inside the support.

I suspect that you'd see a lot of wear on the tube that's sliding over the pylon supports as it might go through at least one if not several heating and cooling cycles daily. I could see two cycles if you've got side heating after dawn, midday shade under the solar panels, and then late afternoon heating after the solar panels stop casting a shadow over the tube. You might get another cycle if you have two parallel tubes with two parallel lines of solar panels above them.

[seanflyon]

I think that there are a lot of options for reducing friction wear. My first thought would be to put wheels between the tube an its supports (attached to the supports, not the tube).

[stcredzero]

But don't we have a window of minutes to shut down the system in case of an earthquake? I thought we could get advance warning from P waves. (This doesn't work if you're in the epicenter, unfortunately.)

If the car gets badly damaged, but the passenger stays alive, and the system can be fixed in a reasonable amount of time, then this is fine performance for a major earthquake event. High speed trains have similar performance in the same situation.

[dragonwriter]

> But don't we have a window of minutes to shut down the system in case of an earthquake?

No.

> I thought we could get advance warning from P waves. (This doesn't work if you're in the epicenter, unfortunately.)

Yes, but the advance warning is on the order of seconds, not minutes (per Wikipedia, for deep, distant, large earthquakes, 60-90 seconds is possible, but that's still at most a minute and a half.)

[stcredzero]

Even so, I thought that the failure mode for tube misalignment of hundredths or even tenths of an inch would result in stoppage, and perhaps damaged "track" and cars, with trapped passengers. This isn't so different from the performance of high speed rail during natural disasters.

[brenschluss]

I'd imagine that there's a great deal of prior work, research, and implementation detail on Maglev trains in Japan on this very issue. Not to say that you're not right, but that this test track is probably precisely what's needed for an initial test, since the other issues (commonly solved with expansion joints) are being actively tackled/solved by many different industries.

[rmxt]

According to Wikipedia [1], the only 3 passenger service operational Maglev lines have lengths of 18.95 miles, 5.5 miles, and 3.8 miles, which are in China, Japan and South Korea respectively. That would make it seem like it is far from a "solved" issue.

[1] https://en.wikipedia.org/wiki/Maglev#Operational_systems

[digikata]

It should be a pretty good step towards getting measurements on thermal issues to then spec the needed tolerances with better basis on reality...

You could also build segments with the intent of inducing displacements to study what's needed for seismic inputs.