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I hope it can be built one day because it uses only sustainable fuel- namely a combination of gravitational potential energy, solar, and geothermal.

It requires an underground tunnel, magnetic levitation in a vacuum, like the hyperloop, but uses a different form of propulsion, and the tunnel has to be deep.

In essence it's shaped like a giant underground skateboard ramp, with an electric motor that pushes off a moving water tank instead of the ground to go faster than an airplane.

I’ve done some back of the calculations to compare a Tesla Model S vs a land based oberth maneuver vehicle of the same mass & available energy. These are rough numbers just to give an idea of the potential performance and compare with an automobile.

Long story short with it’s lithium battery pack partially charged up with 45kWh of energy, at roughly 70mph the 2250kg Tesla can do 135 miles in about 115.2 minutes (3mi/kWh). At 13.3 cents per kWh, it costs $5.98 for the energy. The ratio of kinetic energy to total kWH consumed with the Tesla on this trip is about 0.67%. (2250kg @ 70mph has 0.306kWh kinetic energy vs 45kWh consumed on the trip)

The land based oberth maneuver vehicle also weighs 2250kg and has 45kWh energy and follows a ramp (maglev in vacuum) which is 4.412km deep (equivalent to 30 second freefall in vacuum on Earth). It consists of a 1350kg passenger section (16.22kWh gravitational potential energy), 750kg water (9.01kWh gravitational potential energy), and a 150kg tank (1.8kWh gravitational potential energy) and 18.03kWh of electromechanical potential stored in capacitors in the track. The vehicle coasts down the ramp reaching about 294m/s at the bottom (657mph). The water tank is ahead of the passenger section on a long tether. On the flat section at the bottom of the ramp, the passenger section "reels in" then releases the tank with the 18.03kWh electromechanical potential, bringing the tank to a halt on the tracks (from conservation of momentum), transferring all its kinetic energy plus the mechanical impulse to the passenger section. After the mechanical impulse at the bottom of the ramp between the tank and passenger section, the 1350kg passenger section is traveling 1096mph, can go 135 miles in 7.38 minutes (about 15.6x faster). At $0.004/gallon the water costed $0.79 (less than 1/7th the energy cost). The ratio of kinetic energy to total kWH consumed with the land based oberth maneuver vehicle is about 100% (~99.3% more of the vehicle's potential energy was converted to kinetic energy).

After traveling up a second ramp back to the surface, the passenger section still has 28.8kWh of kinetic energy (which is all the mechanical impulse + the kinetic energy the water tank had at the bottom of the ramp). The water is emptied from the tank at the bottom of the ramp and only the empty tank is lifted (the water is left to evaporate, and rock temp increases with depth). Factoring regen braking with 70% kinetic-to-kinetic efficiency at the destination, and using some of the recovered energy to recharge the capacitors, and some of the energy lift the empty tank, there is still a 0.36kWh excess of recovered energy from the regen above and beyond the energy used to push the vehicle at the ramp bottom. The excess energy comes from the lowered gravitational potential energy of the water left to evaporate at the bottom of the tunnel. It isn't perpetual motion because the vehicle requires gravitational potential energy to move itself forward, and geothermal and solar energy to lift the water out of the tunnel.

In summary the hypothetical land based oberth maneuver vehicle can theoretically go 15.6x faster, for less than 1/7th the energy cost, with the same amount of energy and mass as a Tesla Model S.

Suppose we compare the land based oberth maneuver to simply using a linear accelerator in a vacuum tunnel on the surface-- but using the same amount of water (750kg + 150kg tank) to move a heavier 40000kg passenger/freight section (shipping container) instead of 1350kg passenger section in the previous example.

In this case with more freight, from conservation of momentum, the mechanical impulse that stops the same mass water tank is only 11.06kWh instead of 18.03kWh in the original example. The gravitational potential energy of the water + tank at the surface is still the same - roughly 9.8kWh.

At the bottom of the 4.412km ramp after the mechanical impulse the 40000kg load has 502.7kWh of kinetic energy and is traveling 672.9mph. Compared to the push of 11.06kWh and the 9.8kWh gravitational potential of the water, most of the kinetic energy at the bottom of the ramp comes from the gravitational potential energy of the load itself.

To get the same load up to the same velocity with linear accelerators you'd need a lot more stored electrical energy-- at least 502.7kWh factoring 0 losses.

Factoring the 30% unrecoverable energy loss after regen braking the linear accelerated load at the same 70% kinetic to kinetic efficiency--

The energy irrecoverably lost using the linear acceleration would be about 150.81kWh.

With the land based oberth maneuver, if we factor capturing recovering 70% of the kinetic energy at the surface after the load climbs a second ramp to the surface, and using all of it to lift the empty trailer AND the water, then it takes an additional outside energy input of 6.56kWh to get the water out of the tunnel and recharge the capacitors.

So in the scenario with a 40000kg load, to get the same speed with linear accelerators requires electrical storage/loss of 502.7kWh/150.81kWh for the same performance vs 11.06kWh/6.56kWh storage/loss with the land based oberth maneuver (95.66% less energy lost per load).

The water at the bottom of the ramp would be emptied into and evaporate from a separate chamber connected to the surface at atmospheric pressure. In many places the heat of the rocks at 4.4km depth is more than sufficient to boil water & generate steam.

Since evaporation is proportional to surface area and temperature, I had imagined it being emptied into shallow but wide pools, at a depth where the rock temperature is significant.

As a side note, I've calculated the negative G's experienced by the passenger can be reduced to comfortable levels while still achieving the same top speed by using a less steep ramp to the same depth, and the acceleration G's during the pull can be reduced to comfortable levels by using a longer tether.

Where:

M_t = 240 = Trailer Tank + Water Mass ( K i l o g r a m s )

M_v = 10^3 = Passenger Vehicle Mass ( K i l o g r a m s )

T_d = 30 = Free Fall Duration ( S e c o n d s )

V_i = 0 = Initial Velocity Before Free Fall ( m / s )

G_e = 9.80 = Gravity Acceleration at Earth’s Surface ( m / s^2 )

W_i = 1.28 ∗ 10^7 = Mechanical Impulse Energy ( J o u l e s ) That Brings Trailer to 0 Velocity At Ramp Bottom

W_i = M_t * V_i * T_d * G_e + ( M_t * T_d^2 * G_e^2 + M_t * V_i^2 ) / 2 + ( M_t^2 * ( V_i + T_d * G_e )^2 ) / ( 2 * M_v )

W_i = 240*0*30*9.80665+(240*30^2*9.80665^2+240*0^2)/(2)+(240^2*(0+30*9.80665)^2)/(2*1000)

W_i = 1.28 ∗ 10^7 Joules

(this assumes vertical ramp, but as long as it is the same depth it works out the same energy regardless of slope)

The question is does the cost of digging the hole at such a depth justify the time and energy savings for long distance transit?