I have found a document with data for a 9-car pendolino at
http://www.rssb.co.uk/sitecollection.../T712_anxE.pdf.
The formula is:
Resistance (N) = 5311 + 21.696 v + 0.9097 v2
Resistance in N, V in km/h
This means that to run at a constant speed of 200 km/h (~125mph) the output energy per km would need to be: 46.0 MJ/km (12.8 kWh/km)
At 400 km/h (~250mph) it would be: 160 MJ/km (44.4 kWh/km)
If I use an 18 car pendolino to model your 400m train, I guess that the linear and constant forces will be directly proportional to the train lenght while the square component will remain constant (since it represents the air resistance, although it in reality it would incresase because their is a square component to friction force (High speeds are required to make it signinicant).
Using the 18-car pendolino model:
200 km/h (~125mph): 55.7 MJ/km (15.5 kWh/km)
400 km/h (~250mph): 174 MJ/km(48.2 kWh/km)
I could not find the price per kWh that the rail industry gets but I saw that the Manufacturing industry has to pay about 8p/kwh.
This means that for the distance from London to Birmingham (163km), ignroing acceleration and deccaleration, the energy costs are:
200 km/h (~125mph): £202 (881 seats and so 22.9p per passenger, assuming all seats used) (ignores motor inefficieny)
400 km/h (~250mph): £629 (881 seats and so 71.4p per passenger, assuming all seats used) (ignores motor inefficiency
People are welcome to check my figures to see if I have made a mistake somewhere. But figures appear to confirm that energy usage is not presently a financial issue with high speed rail
(I have forggotton to include electric motor and electrical tranmission losses these will increase the required input energy). Tempting people out of their cars would probably save more energy than the additional energy that the line would use. An issue left is how much will the 250mph stock cost?