RE: Mathematically Breaking Down the Hyperloop (Math Warning) Part 1
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)