Yes I have. The low noise is due to several factors including traction motor cooling using external blower motors rather than motor shaft end fans (this also reduces the escape of traction motor noise from other sources e.g. magnetoresitive) which no other EMU manufacturers have done in the UK, enclosing the traction electronics in "sound proof" boxes, much quieter compressors etc.
Bombardier put a lot of though into making them quiet rather than just sound proofing as the former is a much lighter way of doing things!
At typical UK train speeds (e.g Crossrail and LO with Aventra so far) there isn't much improvement to be had with better aerodynamics over the previous generation of stock)
As neat an idea as that is, it hasn't really worked. The Aventra traction kit is much quieter than the Electrostars that went before them, but that's mainly in the high frequency controller, not the motors and gearing itself - something that itself has been somewhat undone with the 710s and 720s which are a much more audible pitch than the 345. Sitting above a powered bogie, there is still more traction motor noise audible in the cabin than, for example, a Desiro UK like a 360, and that's not because the Desiro has better soundproofing (though it does a little), there is simply less electrical noise to begin with, once the interference suppression ceases above 30-40mph. The overall experience on the Aventra is good from a noise perspective, but 345s certainly still have the rattling bogies, perhaps they fixed that with the 710s, I haven't ridden one yet. Or, perhaps on the Goblin they just don't reach the sort of speeds where it becomes an issue.
Getting back to the orginal discussion point, power usage of rolling stock has come down considerably but that's already being considered because the example we're using is a 345 (Simply because it's a figure I know, kwH/km figures for other stock aren't easy to come by). The only thing that will really differ between the high speed unit used on EMR and the 345 is the speed, I imagine efficiency will otherwise be very similar, and as stated, if you want to be able to recover all the energy used to run from Leicester to Derby at over 100mph in the 3 minute dwell at Derby, you're looking at a minimum of 1.6MWh, so 32MW for 3 minutes. I can't see the battery voltage in a train much exceeding 1500V DC before causing issues, so that's what, 21kA? It's a ludicrous amount of power - not something better technology will solve, this is in the area of 'not permitted by the laws of physics'. Transferring that amount of power in that space of time reliably just isn't feasible.
If you take a five-car 125 mph battery-electric train it will hold around 430 passengers.
The train could weigh around 200 tonnes empty.
Add the passengers at 90 Kg each, with buggies, bikes and baggage gives a train weight of 218.7 tonnes.
Running at 125 mph gives a kinetic energy of 94.9 kWh for the train.
Hybrid bus-sized batteries like the one from a new Routemaster are around 50-70 kWh. If you put two in each car, that would be a total of 600 kWh.
Suppose, you were approaching Leicester at 125 mph, after stopping probably 80% of the 94.9 kWh (76 wWh) would be transferred to the batteries. To get back up to 125 mph after Leicester would need 94.9 kWh, unless a lot of Leicester rugby players had joined, which would mean a bit more.
So charging at Leicester would need to add perhaps 20 kWh for the stop and whatever has been used in the high speed run from Market Harborough. At 4 kWh per car per mile, it will use about 320 kWh.
I think it is all possible, especially, as my 4 kWh is a very rough figure. I'd love to know the figure for an Aventra at 100 mph for starters.
Hybrid battery packs are smaller for just that reason, they are hybrids, only intended to normalise combustion engine use into efficient cycles, the routemaster etc. are not plug-in hybrids, so the size of their battery packs is largely irrelevant (other than knowing what size battery pack you can fit in a bus chassis) - a far more suitable comparison would be the size of the batteries in the BYD full electric city buses. I can't easily find a figure for this but Magtec's Repower system offers 266kWh, I have seen other estimates of 300kWh as a maximum, so that probably gives you an idea what you're looking at.
Your calculation does not consider losses of keeping the train at 125mph during the journey - that is where most of the energy is lost. 24kWh per train km is for a 9-car (200m) 345 at "up to" 90mph. In reality, the figure is probably higher than that for continuous 90mph operation as the figure was devised for Crossrail over the length of the route where top speed doesn't exceed 60mph for more than half of the entire route length. It also includes the regenerative braking effect, so more than 24kWh will be used until the train regens some of it back as it comes to a stop. Even if the 24kWh figure is accurate at 90mph, then that trip from Leicester to Derby would be 1.14MW. Given we're aiming for closer to 125mph, I've used 1.6MWh in my example above, which I think is probably quite generous - I suspect it'll be more in practice, maybe closer to 2MW. Enough battery packs could be used to achieve this (though probably not all under the floor, I expect some cabin space would be lost) but it's the fast charge part of your idea that doesn't work. To use a realistic amount of current and charging speeds, these trains would need to be sitting for at least 45 minutes at each end to recharge that much, which isn't workable in practice without extra platforms for them to occupy.
