Agreed, about 3km out from Warrington at which I assume all trains would probably stop. The curve might be eased a little if the viaduct was reconstructed, which it might have to be anyway due to design or condition. The current viaduct is perfectly straight. A replacement might allow the curve to start a little to the east so the new structure is on the curve. 1200m radius might be possible in that case. What might that give? 120MPH under similar assumptions perhaps? Alternatively The new line could avoid the city centre and other rail connections entirely, or be in tunnel under it, in which case there is the considerable addition expense of an underground station perhaps.
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I reckon 1200 m should allow just under 110 mph. If all trains were stopping at Warrington, then it wouldn't matter. But surely the main purpose of a new route would be to connect the top-level centres by genuine fast services, i.e. Liverpool, Manchester, Sheffield, Leeds, Hull, and Newcastle, and such services would not stop in places like Warrington (or, if I dare say it, Bradford). There would clearly be other stations, like Warrington, and those would be served by second-level services, as with the Japanese pattern.
Though I must confess to being puzzled as to what the justification for this new line is if the best Liverpool-Manchester timing it can produce is 28 minutes, unless the argument is capacity rather than speed (or that if one is building the Liverpool connection to the south, then the short extra spur to connect to Manchester is not too desperately expensive an add-on). There are trains almost as fast now between Liverpool and Manchester Victoria, even if they are to be decelerated through an additional stop from May, and it does not seem impossible that four or five minutes could be shaved off their timings for vastly less cost than building the new line via Warrington. (Incidentally, can anyone explain why, when it is considered essential to get rid of stops at places like Stalybridge, Dewsbury, or Garforth east of Manchester, in order to speed things up, it is reasonable to add stops at Lea Green and Newton-le-Willows and so slow things down between Liverpool and Manchester?)