as Leeds City station will likely be rebuilt again prior to the arrival of HS2, I prefer the route into central Leeds using the alignment of the current Wakefield line with the Wakefield traffic redirected through Cottingley using a relatively short cutting/cut and cover tunnel.
Leeds City would be completely rebuilt with a nice new almost entirely transparent ETFE roof with a new concourse above the platforms in a sort of reverse St Pancras, additional platforms would be added over the current car park, the current bays would be extended to full platforms (is the facade at Leeds listed?).
Additionally if more platforms were required they could be built above the lower ones, level with the new concourse.
The viaduct on the east approach would either be double decked (with High speed trains on top) or widened to four tracks depending on what ended up being cheaper. Additonally the platforms would be built to allow ~170kph through running to allow trains not actually stopping to run through the city centre, saving the expense of a bypass lines.
The HS2 lines would run alongside, or above, the current ones to the freight yard adjacent to East End Park where it would continue in a straight line and then loop around to escape to the North East by going between the city and Garforth.
Once you are that far east not going to York saves roughly 6km so is basically inconsequential.
As for York, you would approach to York along the alignment of the ECML from London, using the obsolete railway land and possibly sacrificing that new fourth approach line (since most of the Intercity traffic will be gone).
It would then climb onto a viaduct, cross over the York Avoiders and have a station with two platforms and two through roads over the current NRM car park, and then escape down the alignment of the line to Scarborough (which would be singled for a short distance) before looping back around to pass East of Haxby and return to a northerly direction.
EDIT:
As to the price of running fixed formation 400m trains rather than coupling 200m sets.
If we assume the maintenance of a TGV Duplex vehicle is roughly £1/mile (more than double a normal EMU) and that a High speed trainset's traction package has an overall 80% capacity factor (including regenerative braking) then the cost of 12 18m trailers (two powered but with maintenance free PMMs) running to Birmingham and back would be:-
Maintenance: ~120 miles in each direction -> ~240 x 12 vehicle miles -> ~2880 vehicle miles -> ~£2880
Electricity: ~45 minutes under power in each direction -> ~90 minutes under power -> 1.5hrs x 8800kW x 80% -> 10560kW.hr
10560kW.hr at ~6p/kWh is roughly £633 worth of electricity so the total costs are ~£3550.
(NOTE: Capital costs are irrelevant as this stock has already been purchased regardless and a 400m trainset likely costs as much as 2 200m trainsets largely made of the same components, likewise as trains are fitted with through corridors and all stations will be protected with barriers additional crew are not required, as for track access charges I'm having trouble calculating this as it seems to be chiefly based on price-per-path, so I'll just use my conservative maintenance estimate to cover it).
So a single TGV Duplex has 545 seats while a Grand Capacite trainset will have somewhere in the region of 1200, leading to roughly ~655 additional seats.
This means that roughly 655 additional passengers could be carried and this would be the lower bound for the additional ticket prices.
£3550/655 = ~£5.40 assuming every seat is full.
I doubt every seat would be full but additional off-peak Birmingham tickets could be sold for less than £10 quite easily in my estimation. With the additional Manchester and Leeds tickets coming in at less than £15.
And this is before we consider the extra crew and paths used for ECS moves to move the peak time sets around or the fact that the additional seats would be all standard class in all likelihood, increasing the additional seat count still further.
And as to having to keep more stock in for repair it is likely that the HS fleet will be sufficient large that failure rates will be easy to predict statistically, meaning that the total number of vehicles held in reserve should not change, just they will be formed into one set instead of two.
And in fantasyland that works. A few reasons why City won't be rebuilt like that...
1) It's on a viaduct, entirely brick arched (including the carpark), the structure is already at load bearing capacity, you'd have to do serious work to make is strong enough to hold even more infrastructure.
2) There's no space. The place 'on top of the carpark' you highlight is already needed for further western capacity on the Harrogate & Airedale/Wharfedale lines, especially if plans to increase frequency over the S&C & LNW, and to introduce through services to Glasgow via the S&C come to fruition.
Moreover, the area to the south of the station is highly built up, and construction is starting on new buildings. There's not enough capacity at City station now, without adding more requirements for longer trains. City House (the office block attack) is also not owned by NR, you'd have to buy out the entire space to demolish it, and you'd then not have a concourse to speak of for City station as a whole.
The viaduct on the eastern approach is also not strong enough to stand a second one on top of it, additionally accessing the site to start construction would be a nightmare given the constriction around City's eastern throat right through to Marsh Lane. Further to this, if you were running on top of the Eastern approach, you'd break all the overbridges, and either have to build new ones (humpbacks?) or drop the trackbed in EEP tunnnel to allow for 2 decks.
Then you've got to build a fairly significant viaduct over the Valley between Beeston & Cottingley, to bring extra classic trains onto the already congested Huddersfield lines, which will soon be handling up to 10tph through them.
In other words, HELL to the NO. This plan is STUPID.
Alternatively, in what I'll call 'sane world'
The southeastern approach (i.e. Methley Junction-Hunslet) is wide enough for 6 lines from Stourton, allowing for both a completely segregated HS approach, and potential 4-tracking of that line at a later date. No tunnelling, viaducting etc etc needed, just laying the line.
At Crown Point, you reach the approach to the old Crown Point goods station, which is still there & unused. The station site is a retail park, with low land values and no problematic infrastructure already there. You can uy & demolish relatively cheaply, and build the station on a gradient so that the line can duck under Hunslet Lane (road viaduct inset into the station Roof) and be at a level to pass under the Aire by the time it reaches the portals (I'd imagine just before Waterloo Street).
You'd then need a tunnel between 1.5 and 2 miles to go out to Killingbeck, where you could again have an isolated line before swinging north at Cross Gates.
This is beneficial for several reasons:
1) It's cheaper. As in ****eloads cheaper. One tunnel, one station, and additional tracks on existing corridors.
2) It requires no more infrastructure changes. Sending HS to city would require a huge extra redevelopment of City station, beyond the already planned Main concourse redevelopment & 3 new platforms. Given that's then City full, putting iron blocks on capacity enhancement is very silly indeed.
3) Well located station. Given the station building would be at the north end of a Crown Point station (i.e. on Waterloo Street/Meadow Lane junction), it would be just south of the river but still eminently within the city centre (you could see right up Briggate from the main entrance), and could be easily connected to city via a footbridge over the Aire and a southeastern entrance on Sovereign Street (which is also the prime site for relocating the long-distance Coach station). This is a site much preferred by everyone in Leeds, and would be a catalyst for development on the Southside, as well as being very handy for Holbeck Urban Village and Clarence Dock.
Altogether, anyone who thinks Leeds station will be at City is in dreamland, the cost of taking it there and the problems it incurs doing so is going to be way too expensive. The easiest option is Crown Point, the major battle is going to be ensuring it's build as a through station for connections to the north.
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