The main issue is that you get 7 rows of airline seats for every 6 rows of facing seat (assuming sensible leg room) so I can't see a workable solution.
Mark 1 was all bay seating, which makes the problem easier.
Sadly we don't have room for that on the modern railway, unless you'd like half your passengers to stand.
Indeed, having only bay seating would make it much easier;
if you persist with the idea that you get more airline seating in the same space than you would with bays. That's why the formula is
B = 2x
P, so that two rows of airline seats take up the same space as a bay. The population is getting taller, on average, so legroom in the airline-style seating needs to be increased anyway. For that reason we also need more carriages so that passengers don't have to stand.
One possible limitation is that it your formula doesn't consider whether the seats are aligned to the windows at the start of the carriage (in other words, whether the windows and seats are "in phase" or not). If the first seat has a pillar for a view, then following your formula will ensure that
every seat has a pillar for a view.
Good point! My intention is that the interior would be designed outwards from the window(s) nearest the centre of the coaches, where there would be bays of seating around tables with the airline-style seating towards (and facing) the carriage ends.
To my way of thinking many of the perceived issues with window spacing could be avoided if the deadlights between the window openings could be reduced in length. This may require some more expensive strengthening of the sides between the windows to maintain the body's rigidity and crash-worthiness while keeping the natural bending and twisting frequencies in a suitable range. But I am sure it would be possible.
Window pillars ('deadlights' as you call them) vary quite a bit in size on existing stock, with the class 195s at around 48cm exceeding the desirable maximum of 450mm given in the Rail Delivery Group's Key Train Requirements, so I imagine that there is some scope for improvement there.
Seating requirement change over time and some thing as simple as the extra legroom for the priority seats near the doors will completely throw everything.
No, the primary problem is priority seating, which I understand is required to be a certain percentage legroom increase. This is actually really stupid if you observe how people of limited mobility use train seating, and it means that most such people choose not to use priority seats - most such people want to lower themselves into their seat using the seat back in front or the table, which you can't do with extra legroom!
The most sensible thing to do with priority seats would be to give them the same legroom as other seats and position them near to the doors, the toilets and a large luggage rack provision. And to give all seats decent legroom like Class 80x.
Is the priority seating really required to have more legroom than the other seats, regardless of how much legroom is generally provided? If so, that is indeed really stupid as the logical solution otherwise is to give everyone priority seat levels of legroom (unless of course the requirement for priority seat minumum legroom is far more than required for able-bodied tall passengers).
In principle, B = 2P is a very convenient simplification, but different seats and tables are of different sizes.
Sorry, I'm not sure I understand. Are you saying the seats used in bays of four around tables are different to the ones used in airline-style arrangements, because I hadn't realised that if so (the Grammer seats one class 158s as refurbished by Arriva Trains Wales for example look the same whether they are around a table or not).
Your formula promotes lots of tiny windows, kind of like an aircraft, which would be very expensive to design and maintain.
How do you define tiny? It's
very possible I've written the formula out wrong, because if I've done it right
W +
D should always be larger than on a class 153 (which does have lots of fairly narrow windows and thus you cannot make bay seats align properly).
Looks good until you need to allow for things like luggage racks, doors, toilets. Then the added pressure to fill every available space with seating and that's why we end up with sub-optimal alignment.
Put all those things at the ends of the carriages and you don't have a problem, at least not with window alignment. Looking at
this picture (not mine) of a TPE mark 5 rake it would appear that TPE have decided to do just that and taken it a step further by not putting windows in the space the luggage racks occupy.