Well here we have a 1000kg passenger section and 100kg trailer with 700kg water and a 17.3 kWh mechanical impulse between the passenger section and the trailer at the bottom of the ramp:
^Even after climbing back to the surface, the passenger vehicle is traveling 984mph. The passenger section on the surface has 26.9 kWh kinetic energy whereas the mechanical impulse was only 17.3 kWh. Even if only 70% of the passenger section kinetic energy is recovered at the surface destination and some that is used to lift the trailer after it was emptied at the bottom, 0.33 kWh more electrical energy remains from the regen braking than was utilized in the mechanical impulse, which I note is about enough to charge an electric skateboard.
Traveling from the San Francisco Bay Area to LA (a distance of roughly 380 miles) is about 6 hours in a car, 1-3 hours by plane factoring airport time, or about 23 minutes point to point at 984mph, so about 15 times faster than a car on the freeway and about 1.5 times faster than a commercial jet at cruising speed.
Okay so sounds like the idea is use extra gravitational potential energy from the water mass to get greater gravitational potential when at the peak so when it hits the slope you have higher kinetic energy at the bottom and dump the load then apply an impulse at peakish KE to take advantage of oberth effect? Then use geothermal energy to “lift” the water mass so really just looking at a different way of using geothermal power without going through the conversion to electricity using turbines? It still sounds like a lot of moving parts and complications so think the costs for constructing something like that in reality would likely outweigh the benefits, but again maybe some applications where it could make sense and get enough gain to be worthwhile. Also with passengers you need to take into account g forces applied if the max gain is achieved by minimizing the time and increasing the force of the impulse then this means increased g force and discomfort. Looks like .1-.3g added or removed is considered acceptable for commuter vehicles https://www.google.com/amp/s/www.pbs.org/newshour/amp/science/is-traveling-on-hyperloop-a-ticket-to-puke-city
The impulse is applied directly to the trailer WHILE “dumping the load” so to speak, rather than “pushing off” the ground…
I thought these posts from the physics forum are a helpful summary:
metastable (professor_shartsis) said: I’m still not very clear on understanding the difference between the passenger vehicle pushing off the tank or off the ground when at the bottom of the ramp.
jbriggs444 (physics forum moderator) said: That is a good starting point for a discussion that avoids the wall-of-numbers effect.
If one pushes off the ground the interaction requires energy. Part of the energy goes into the vehicle. Part of the energy goes into the ground. You can calculate how much by looking at the work done by the interaction force for each.
The ground does not move. Force applied times distance moved is zero. No work is done. The vehicle does move. Force applied times distance moved is non-zero. Work is done.
100% of the energy applied in the interaction goes into the vehicle.
If one pushes off from a 500 mile per hour trailer, things are roughly similar. Energy is still involved. Part goes into the trailer, part into the vehicle. We can look at work done.
The trailer moves in a direction opposite to the force applied on it. The work done on the trailer is negative. It loses kinetic energy as a result. The vehicle moves faster than before. Accordingly, the work done on the vehicle is increased relative to the push-off-from-the-ground case.
More than 100% of the energy applied in the interaction goes into the vehicle. The excess is deducted from the kinetic energy of the trailer.
There is no free lunch. Energy is conserved in either case. The total increase in kinetic energy from the push-off is equal to the energy provided (by piston, muscles, batteries, engine or whatever).
The important part to think about is this: jbriggs444 said: "More than 100% of the energy applied in the interaction goes into the vehicle. The excess is deducted from the kinetic energy of the trailer."
There’s a way to gain a high momentum turn, this would be a high speed arm like a lancer. Kinda similar to astronauts training G machine but made specially to deviate then release the vehicle.
Now talking about G, how are the ex-alive passengers going to exit the vehicle when they’ll have been crushed to puree by the G forces ?
During the first 30 seconds, the riders would actually feel 0 g’s even though they would be accelerating relative to the ground at 1 g.
The transition of the slope from vertical to horizontal can be very gradual limiting the g’s close to the bottom of the ramp. The important variable is the depth of the tunnel not necessarily the slope or sharpness of transition between different slope or horizontal sections. Think of a 2.5mile depth skateboard ramp with a very gradual change of slope at the bottom, flattening out at 2.5 miles.
The velocity of the trailer and passenger section at the bottom of the ramp before the mechanical impulse is 658mph, and accelerating from 658mph to 1184mph at 3g’s takes 8 seconds.
The rest of the ride can be a gradual climb to the surface (it doesn’t have to be a second vertical ramp- this is done only for simplicity of calculation but not strictly necessary in practice)
So at no point is it neceesary for the rider to experience anything greater than 3 g’s which is already done on some present day roller coasters.
Yah I’m not talking about what a person could physically endure before passing out but rather what is comfortable for Grandma and the kids on a commuter train also 0G means 1G less than we’re used to which is why people vomit in the vomit comet (generally gravity is holding the stuff in your stomach down with 1g force but in freefall you take this away). You could transport heavy material this way and maybe the extra complexity and maintenance might be worth it but need to keep it comfy if it’s meant to replace a business class seat on an airplane too.
@wafflejock Good points. If the initial ramp is 45 degrees or even 30 degrees, but still to a depth of 2.5 miles I believe the velocities at the bottom work out to be the same (but I have to double check on this point) and the passenger consequently shouldn’t ever need to experience full weightlessness (still assuming maglev in a vacuum). The vertical ramps with a flat section between mostly makes it easier to do the calculations but all that is really needed are more gradual ramps to a 2.5 mile depth, out of passenger comfort considerations.
it intuitively makes sense the velocity at the bottom of the frictionless ramp in vacuum will be the same with any slope as long as the depth is the same, but here’s the proof:
The depth of a 30 second vertical drop in 1 g vacuum is 4412.99 meters
a^2 + b^2 = c^2 can be rearranged c = sqrt(a^2 + b^2)
Guys I watched the marble video and I figured it out:
Instead of building roller-coasters for trains, we instead have heavy bolders roll down a short distance (lots of energy), that’ll hit a lightweight train, transfer all its energy to that, and send it off at high speed. Of course, the acceleration might destroy the train / kill passengers, so we put a long spring / liquid / gas chamber that will compress from the boulder and then decompress, sending the train flying, with hopefully minimal energy loss into heat.
At the other side the train hits another spring, which will launch up another bolder. lol
^at the point of lowest gravitational potential energy (highest kinetic energy), I push off the water in the tank instead of the ground, obtaining impulse not only from the energy of the push-off, but also from the kinetic energy the water had while at it’s lowest gravitational potential.
^ i was thinking the passenger section can use the water tank itself as the moving track for acceleration.
for example at the top left, both the magenta motorized passenger section and the blue tank are both traveling around ~650 mph close to the bottom of the 2.5 mile deep ramp
at the bottom right, the passenger section has accelerated to ~1000mph after pushing against the tank, bringing the tank to 0mph & transferring its kinetic energy to the passenger section, while being magnetically levitated in a vacuum.
