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.
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:
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.
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.
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.
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!
@kryzsec