You didn't answer my question about ow many of those 47 trains are outside of the key 7am to 7pm "day" when the vast majority of people travel.
Also I assume to get your figure of more than 9 million seats (so that 3 million passengers is less than 1/3 of the total number of seats) you have used the same 47 trains a day for each and every day of the year. Which would be a little off, given that the number of trains is less on a Sunday (and most bank holidays), non existent on Christmas Day and Boxing day and have limited appeal when there is engineering works.
Based on a letter published here:
http://www.parliament.uk/documents/...ic-case-for-HS2/McLoughlin-hollick-141208.pdf
The AM peak (3 hour) loading was 57% from Manchester to Euston, if we were to reduce the frequency from 4tph to 3tph (peak hour frequency) this would reduce spare capacity from 43% to 24% (even allowing for all seats being standard class). If we then assume 3 years of growth (to when the new service is due to start) at 2.5% that spare capacity falls to less than 19%.
Therefore if we didn't want lots of empty seats we should have left all the 390's as 9 coach trains; as then a train which is 57% full (11 coaches) would be 76% full (9 coaches), rather than increasing seating capacity by about a third. However, if passenger growth continues at the 5% that it has been running at in recent years that spare capacity is used up (even allowing for the trains being 60% full) in 10 years (remembering that we've had 3 of those years since the 390's were finished being extended in 2012), even if growth starts to fall and runs at an average of 3% for 15 years it will use up all that new capacity.
Just out of intrest 15 years from 2012 is 2027 which is a year after phase 1 of HS2 is due to open, a coincidence? I don't think so.