Hyperloop, Elon Musk's dream to transport passengers at the speed of sound through vacuum tunnels between major cities, is going to cost much more than the billionaire industrialist first thought.

Musk proposed in 2013 that a hyperloop system, which is similar to a magnetic levitation (maglev) train but runs through a low-resistance tunnel with much of its air removed, would cost $11.5m (£9.4m) per mile to build.

But, leaked internal documents from Hyperloop One, one of two companies working to make Musk's dream a reality, reveal the estimated cost for a 107-mile route in the Bay Area, California is between $84m and $121m per mile.

Building a route between Abu Dhabi and Dubai would cost $52m per mile, the documents also claim.

In all, the two projects would cost Hyperloop One in the region of $11bn and $4.8bn respectively. Musk originally believed a hyperloop connecting Los Angeles to San Francisco would cost about $6bn, 10 times more than the $68bn the government is set to spend on a high-speed train line connecting the two cities.

Musk's argument in 2013 was that a hyperloop would cost far less while transporting passengers much more quickly. He criticised the government's train line, which is to open in 2019, describing it as "both one of the most expensive per mile and one of the slowest in the world".

Hyperloop One has chosen not to comment on the documents, which were obtained by Forbes and published on 25 October.

Of course, the original $6bn figure Musk came to was for one specific route. Musk reasoned that money could be saved by installing the hyperloop tunnel on pylons above an existing motorway, eliminating the need to purchase additional land or convince current owners to allow the hyperloop to pass through their fields.

The figures also demonstrate how much the cost of installing a hyperloop varies in different countries. The California hyperloop is projected to cost twice as much as the Abu Dhabi-Dubai route, despite Hyperloop One's plans for the latter to be built underwater.

Hyperloop One is not to be confused with Hyperloop Transportation Technologies, a second firm which is also working to make the 700mph train a reality, but is instead focusing on routes in Eastern Europe.