So my focus on the hyperloop is whether it would be more efficient to either constantly supply energy to a train to maintain its velocity in an environment with air resistance (like seen with modern maglev trains) or if it would be more efficient to continuously pump out any potential air that might leak into a near-0 pressure environment. This will look at a hypothetical situation deemed as "The Ideal Environment" and then look at a real life example to see how the two compare.
The Ideal Environment
Since we know that we are working against the pressure of the ambient air (we are ignoring the friction between the plug and container) we know that the energy required will be proportional to the pressure. Now using dimensional analysis we know that the nit for pressure (pascal) is also J/m3 and since energy is measured in Joules we know that we just need to multiply by m3 (or Volume) to get the required energy. Therefore:
E = PV
E=PAd
Now assuming our container has a cross sectional area of 1 cm by 1 cm (or 1 cm2 which is also 0.0001 m2) then we can calculate the ideal energy required to pull the plug up any defined distance.
For instance, lets calculate the energy required to pull the plug 1 cm (0.01 meters) with an atmospheric pressure of 1 atm (like found at sea level):
1 atm = 101325 pascals
E = PAd
E = 101325 p * (0.0001 m2) * 0.01 m
E = 0.101325 J
E = 1.0 * 10-1 J
So now that we know that, lets just give a simple calculation for approximating the energy (for an ideal system) to empty out the tunnel for the hyperloop to travel from Los Angeles to San Fransisco (approximated at 560 km). According to The Verge the hyperloop tubing would be 11 ft in diameter (3.3528 meters, for fuck sakes America, this is science so use the god damn metric system). Anyways using this we can find that the volume of the entire tube would be, approximately, 4944167.82485 m3 which has a (in an ideal environment) required energy of 500.967804852 GJ (109 J) to turn into a vacuum. Now one ton of TNT is considered to be 4.184 GJ (109 J) which is roughly 0.8% of the energy released from the nuclear bomb dropped on Hiroshima. Now these numbers look impressive and large.
Anyways now that we have seen that we will form a general equation used for any distance of hyperloop to calculate the energy requirements for making it a vacuum, under ideal circumstances.
E=Pπr2d
Energy Usage of Maglev Trains
Now for this I had to grab the information from other sources and will be using something closer to actual data. Anyways what I found was a table that had the energy consumption of the train in a form of watt hours per area of usable space inside for each kilometer it needed to travel. So using the values from the Nasa Research Center to find the size of the hyperloop pods we can calculate the energy consumption of the maglev train for a similar distance at similar speeds. Using the proposed numbers of 4.0m2 of passenger/cargo space and another 6.0 m2 of non-usable space we can deduce a 10 m2 of usable space. Using the transrapid maglev train as our basis we can calculate that it would require 263.2 MWh (at ~35 minutes suggested time given the speed would actually half it bt we are going to approximate it takes 1 hour) which puts it at 263.2 MJ which means for the same trip (approximately) the energy consumption is 0.000417777% of the energy released by the Little Boy nuclear explosion. Not only that but the hyperloop itself would also require the usage of some energy for actually running and not just the energy required for making the vacuum.
References
The references present are in no particular order
Jeffrey C. Chin, Justin S. Gray, Scott M. Jones, Jeffrey J. Berton. 2015. Open-Source Conceptual Sizing Models for the Hyperloop Passenger Pod. NASA Glenn Research Center, Cleveland, OH. [1]
Stathis Ilonidis. 2010. Maglev Energy Budget. Stanford University. [2]
Russell Brandom. 2017. A real hyperloop is almost here — and it’s not what Elon Musk envisioned. The Verge. [3]
Part two will hold another argument (looking at the vacuum time) and my conclusion. The reason why I don't want to make it 1 post is because the simulation isn't complete yet and I want to call out the users whom have made a post so that we as a community can go support them.
As of posting this there have been 3 posts submitted by @tfcoates
So go read these posts. Maybe go give them a vote, comment on their post, or even write up a response specifically to their response. You can do that to mine as well. Lets be a community and lets support each other!
As a chemist trained in engineering I can only raise my hat for this first part, as well as for the other three contributions. They really provide a well thought-out introduction and argumentation. But one question rises especially for me. Since I worked a lot with vacuum technologies down to the range of Ultra-High-Vacuum I am wondering, why the actual final pressure is never stated or taken into account. Is it just for simplification reasons? Because if you do so, you will allow for significant deviations between the calculated estimation and potentially relevant usable technology. - I just read this post as my bedtime story, so I can not provide a calculation right away, but from my own experience I know that the effort to produce vacuum does not rise linear with the quality of the vacuum, and this also accounts for the maintenance.
Hence the assumption of p = 0.0000000 mbar or the perfect vacuum may be not realistic or purposeful and thus unfair.
(Although I doubt that it turns the facts and the results shown in the mentioned posts and leads to a totally different conclusion.)
Best,
mountain.phil28
So mainly it is for simplicity but it also provides us a lower limit of the energy required. As for the setting of the pressure to 0 I have read many sources that have put the pressure inside the tubes at around 100 pascals with the first publication setting the internal pressure at 100, some of them went <1 pascal as well. I could easily change the formula to handle an ending pressure to E = ΔPV however it still assumes a linear relationship between the amount of energy required. Anyways since this assumes 100% efficiency (basically) and is optimal it will act as if its the lower limit of the energy required to pump out the tube and can give us an idea of the total energy required to run the hyperloop.
I hope this answered your question.
Ok in that regime (1-100 Pa) there is not a big difference in needed pumping technology, so thank you for the answer. 😀
(Since perfect vacuum is harder to achieve than the mentioned ones, that assumption provides the maximum needed energy, not the lowest. But the lower the pressure, the more efficient ist the transportation, hence there must be a realistic - technologically and economically feasable - optimum in pressure.)
I <3 my turbo-molecular pump for EPR :)
Which one do you use?
Bruker Elexsys E580 and E500, casual CW and Pulsed Spectrometers (X-band and L-Band)
And the pump is Alcatel, of course (Vive la France) :)
I meant the pump. :) We use Pfeiffer Vacuum HiPace TM-Pumps, German of course. :P
So it is actually the minimum energy required as it assumed a 100% efficient vacuum. The difference of 100 pascals (sing the linear calculation) has a difference in the final answer of around 1% but the final answer would still be that it would take around 500 GJ.
An upper limit would be imposed by assuming a low efficiency pump of an exponential difficulty increase with non-linear efficiency (meaning the efficiency will decrease as the volume of gas left in the tube decreases) and that will end up being a much higher energy requirement total.
Yeah ist gives the minimum (ideal) energy for the assumed state (p = absolute zero pressure), but the state itself is unrealistic and poses the maximal necessary energy required to achieve that state (compared to realistic ones with some mbar).
More Work has to be done if you pump out 100% rather than <100%.
The statement on the pumping efficiency is correct.
Well the energy to pump down to 1 mbar (for the tube that size) is around 0.5 TJ when using a linear formula
The energy required to pump to 0 mbar (again when using that formula) is considered 0.5 TJ, however realistically it would require an infinite amount of energy.
I do understand where you are coming from but for the vast majority of the population, I would like to keep it somewhat simplistic. I am not trying to argue with you, just stating why I stated it was a lower limit (as an approximation)
Ok so i read the other posts and i understand the concept but as you all have different approaches i figured i would reply to you @kryzsec. As yours centers around the general mathematics of the issue i wanted to address that. As temperature and pressure are linked, pump stations (as suggested in this entire theory) would be following the length of the tunnel. As its being built above ground the tubes would be subjected to environmental stress and temperatures, some sections may be warmer than others and therefore would have different air pressures and densities inside the tube. Ok you may ask WHY is this being built above ground?? Well 2 issues, California's governor has a pet project of high speed rail and is draining the tax coffers to cover that, on the other hand the hyperloop is payed for by Elon. So the hyperloop project has no backing from local government. Secondly i think its being built above ground to allow for fault movement. Underground tunnels have less flex, but the hyperloop could be built upon supports that may have dampeners. the problem is this becomes one giant long target for anyone wanting to cause chaos, so i would assume an outer "shell " would be needed to prevent sabotage. I hope im on the right track in my theories.
You should make a post on it covering your arguments and stuff as these are all very valid points I have seen others bring up. This post doesn't cover the why I am making this (this one does) but please make a post and a contribution responding!
They evacuated the Large Hadron Collider so it likes like an energetically feasible idea. And you only have to do it once (plus vacuum maintenance energy of course).
I wonder if the Hyperloop will recover the energy to accelerate their train with regenerative braking. Get back most of what you put in?
If you compare the energy costs of the Hyperloop to the energy costs of the airline industry it might come out quite favourable.
The LHC is a 26-27 km tube that is about 7 cm in diameter, the hyperloop is suggested to be around 560 km and around 4m in diameter. As well since you will have the air pressure on the entire external surface of the structure and next to no internal pressure acting as support the structure which will cause many major structural problems as not many materials will be able to handle the sheer force that will be acting upon it in such a hot climate.
As for getting back what they put in, sure they could get back some of what they put in for actually accelerating the passenger pod (which as shown above will be nothing compared to the energy requirements to empty the tube.... which they are planning on repressurizing the entire thing when people get in and out of the pod and then depressurizing it again, as linked in the paper) meaning our lower limit estimation on energy required to operate the hyperloop is around 1675 times that of the Transrapid maglev train in Germany, remember that is lower limit.
Now one could say that solar panels will make up the energy difference but if we were to cover the entire top half of the hyperloop with around 20% efficient solar panels (that is about average when looking on the market) we will produce around 571.7 MW (MJ/s) which means it would take roughly 1000 seconds to just produce the energy to operate the hypothetical 100% efficient pumps and power the track along with take care of colling the track... oh and solar panels decrease in efficiency (exponentially) as they heat up, same with conductors and funny enough, pumps.
Now sure a jumbo jet making the same trip (using rough estimates) will take about 2-3 times the energy as what was used to just evacuate the air... but the plans for the hyperloop is to have the damn thing on a track (meaning there is still friction) like a normal train, they aren't even planning on using maglev in a lot of the plans... So viable... no, it will be an expensive train ticket (like super expensive). Assuming they do go maglev then the expected operating energy costs will be similar to that of regular maglevs but slightly more feasable.
Will it ever be a cheap way to travel? Maybe, but the more I look into this the more I see an engineering nightmare
Do you remember that scam-idea to use Maglev style levitation to levitate the buildings in case of an earthquake :D
http://www.dailymail.co.uk/sciencetech/article-3119169/Could-hover-houses-protect-California-big-one-Firm-reveals-plans-raise-homes-giant-magnets-event-quake.html
Buildings... During the Earthquake...
Yeah I remember seeing the headlines. I never actually read it because I thought it was stupid... It wasn't until recently that I started actually reading 'stupid science' and started looking at the problems
Reading stupid science is addictive, be aware :D
Quick thought... if it costs lots of energy to vacuum the system, surely a lot of energy could be harnessed when it's re-pressurised? Could this be harnessed to ofset the overall cost of going back and forth?
It could to a point as long as people are okay with pressurization times to increase (because you will have to limit the air going into the tube to some extent) or else they would have to have more sites for the pressurization to happen but that also means A) more Single Point of Failure's will exist (i.e. any point that if they fail has the potential to cause the entire system to fail) and B) you will have more problems with leakage which will mean higher energy consumption. You could also have some of these points work as both an intake and have a pump and have it generate energy but you will still need to limit the air flow at those points because if they are out of sync with each other then it becomes very difficult to convert it to DC to charge a battery system, if they are going at different frequencies then it will be very difficult to have an electronics system that can handle the wide array of frequencies, and more. Basically, if the turbines aren't spinning within a specific frequency range then it has the potential to ruin the electronics.
I might be making this more confusing. Anyways they could do that to allow for energy production but it would add a lot of complexity to a system that already isn't very thought out (it would be better to have a loading bay and then the evacuated tunnel and have only the loading bay get pressurized and depressurized with an air tight seal between that and the tunnel and only when the loading bay is depressurized will the air sealed door open, however this too is very complex)
So I think the best argument that can be made about this entire situation is K.I.S.S.
Keep It Simple Stupid
I think the take-home from all these arguments is really that the system just has so many ways to fail and failure in the case of a system like this is going to be catastrophic!
Oh yeah, I mean if there is a catastrophic failure then you have almost 1 GJ of energy being released per kilometer of vacuum, so like a quarter of a ton of TNT which basically means if something catastrophic happened it would be like there was a line of dynamite the length of the tube that would go off (doesn't sound like a lot but if you are in the tube or at a loading zone then things can be violent and if there are battery arrays for the solar panels then you just increase the potential energy in those locations)
Not to mention that the sudden re-pressurization would result in the whole system gaining a whole lot of thermal energy, probably burning everyone inside.
Your theory is a bit complex and advance to comprehend. Am taking my time to really study and understand this energy of a train theory...