It sounds as though you have an agenda about which you are not informing us. What do you think will the case if those 'controls' aren't needed?
It sounds like you have a clear pro-'Schengen' agenda which you are not informing us of...
However, even without the controls, there's not enough demand between
London (you know, the very large place that is the economic hub of Europe and the one of two Alpha++ cities in the world - if anywhere can generate demand it's there) and the continent for any meaningful reduction in Euston terminating services by a through station at Euston St Pancras - you lose 3tph max (given there's less than 2tph now, and you've opened up a couple of trains per day to the north), and I got shot down for pairing up the classic-compatibles with Javelins to make it a handful more...
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For a start, I still can't imagine what the rail network is going to look like once Phase 2 is completed. All I can see is what services will use or partially use HS2. Also, the length of the captive trains. If, say, Manchester has three trains to London per hour, then three 400m long ones is a hell of a lot more seats than with three 200m ones but it seems likely that many if not most will be 200m outside of the peak. Also, entirely classic services just aren't mentioned.
Look about a page back - I link to a sample timetable that HS2 Ltd used for modelling, published by the DfT.
So what happens to Stoke then, for example? I'm assuming there'll still be a service from Piccadilly to Euston via the existing WCML but again, there's nothing that says for sure.
Stoke fast trains to London will be 1tph, not 2 and will stop at Milton Keynes Central and a Trent Valley stop, but they will go through Manchester to Scotland, providing the service for Oxenholme, Penrith, etc - who can, if they want, change at Preston or Piccadilly for a faster journey to London.
I've read somewhere that Chester won't be getting a service at all, which is strange and surely can't be right.
You've read wrong. Chester trains will pick up a couple of stops (after all, change at Crewe and you can cut lots of time off), but will still be fast and with no loss of frequency (as only 1tph anyway)
Also, what's going to happen to CrossCountry services? I assume Manchester & Leeds are still going to have these run on the classic lines via New Street, on top of the captives into Curzon Street, which will be a bit odd having the two Birmingham stations offering the same destinations.
Some diversions and more stops n of Birmingham as end-to-end journey time of the Birmingham - Manchester or Birmingham - Newcastle leg doesn't matter - Stafford, Congleton, Water Orton, etc will see better service to Birmingham.
Another weird thing is that Centro seem to think that classic compatible services to Bristol and Cardiff from Birmingham will happen once the line is electrified but I've always assumed Curzon Street was going to be designed as a terminus, unless the idea would be to reverse back out of the station.
A chord onto the classic lines in the Curzon Street throat, I'm guessing. Not planned, but possible. The trains wouldn't stop at Curzon Street (but will at New Street), but join the line NE of there.
In terms of capacity of the line, all I seem to know for sure is that the southern section can take a maximum of 18tph. What about the two branches and the spurs into Birmingham, Manchester and Leeds?
IIRC, the branches and spurs have a similar capacity, though with the spurs the terminus area is the limiting factor and they won't be able to turn anywhere near 18tph (save Euston).
Also, if Heathrow doesn't happen, as seems likely, what will happen to the two paths allocated to it from Manchester and Leeds? Will they just go to Euston instead?
I'd imagine that the Liverpool via Stafford/Birmingham train will take up one of those paths so as not to have to split/join at Birmingham Interchange, and the other will probably be a Manchester/Leeds - Euston splitter, or just a Manchester - Euston service.