I don't know who could write a safety case to cover the operation of the tube or tunnel (once built). Just think of rescue arrangements in the Channel Tunnel then think of a tunnel thousands of miles long.....
The rescue arrangements for a transatlantic airliner involve a lot of pine boxes.
This is not significantly better than the ones available for a transatlantic tunnel - especially since buffer doors could be installed as required every couple of hundred kilometres.
If built and a safety case were to be achieved, any train running through a snaking, stayed, floating tube would cause the tube to flex so speed would not be likely to be very high.
The tube would remain in positive bouyancy at all times, otherwise it would sink. So the only snaking in the tube would be a result of the cables relaxing and stretching due to changes in load - as a train is relatively light this is sure to be a very minor effect.
Now, who's going to maintain the outside of the tunnel and inspect the stay cables in situ?
UUVs have come an awful long way in recent years.
Power transmission along the tube/tunnel would require many sub-stations to be spaced along the route.
That depends - if you used a standard 25kV supply system with conventional rails this would be so. But I doubt you would.
50kV-0-50kV AT would be the minimum, and I have heard talk that it would be feasible to build a 100kV pantograph if there was a need for it. At which point substation spacings will have reached the hundreds of miles. After all you would effectively be distributing power at 200kV AC.
You might only need two or three intermediate substations.
And since you will likely be using a conductor rail for reliability reasons - you have an enormous conductor cross section to use.
Volt drop would not be a major issue at 100-0-100kV and would be easily handled at 50-0-50kV (50kV is low risk as it is in operational use today)
To bring in another aspect, the Atlantic has currents which would try to move a stayed tube in various directions along its length and any change to these could potentially add stresses in cables and tube as would the various temperature gradients across the ocean. In the RN, we had to speed up and slow down condenser pumps whilst crossing the Gulf Stream so great was the difference in water temperature.
Definitely one for the fairy tales!
Yes, but the water temperature below the surface region does not tend to change much in the
same location. Annual variations below 30-40m in the Atlantic tend to be measured in single digit degrees.
Static temperature differences over the structure are nowhere near the issue that thermal cycling would be.
And the currents don't tend to change much either - they tend to run in broadly the same direction at the same speed for much of the year - especially since in the deep ocean we can neglect tidal effects.
These are all simple engineering problems - they could be overcome if it was required that they be overcome.