I had a sudden thought. These Turnigy batteries are, it says, 14.8 volts, so with two in series, that's 29.6.
But they aren't really 14.8 volts. That's assuming that the cells are 3.7 volts, but when they're fully charged, they're 4.2. So the total voltage isn't 29.6, it's 33.6 volts. And can my 24 volt bike handle that?
Well, I know it can handle 29.2 volts, it's already doing that. So I did a bit of internet research. This is called "over-volting", and it seems that people have happily overvolted to 36 volts without problems. So I guess it will be OK - the proof of the pudding will, of course, be in the biking.
I've totalled it up. Four of the batteries I've chosen, plus a charger, plus a parallel charging board, plus a parallel balance lead, plus four voltage alarms (one of each Turnigy so that I don't run it down below the level that makes the battery stop working forever) is about £113 pounds.
Meanwhile, I just had an email from the folks in China where I tried to buy a 20AH, 24 volt LiFePo4 battery at 8.1 kg. The battery got to the UK, and then got bounced back by UK customs, who say that they can't send it by air mail (although I suspect what happened is that it never actually left Asia). So they're offering me a refund, which I'm going to accept. The cost of that would have been £138 (plus £80 for air shipping), for a 24v 20AH battery. Twice the capacity of the one I'm planning to cobble together, at about twice the price. If I cobbled a 20AH battery, that would be LiCoO2 (which has some disadvantages, but has more energy per kilogram) and cost me £190 (and weigh 4.2 kg). So DIY looks to be cheaper than air shipping it from China.
The charger I'm looking at is the imax B8plus. That can charge up to 8 cells in series at up to 7 amps, and 150 watts. Will that be enough? Suppose I want to fully charge the whole thing in 5 hours. Each Turnigy is 14.8 volts, 5 ah, so one will pull 1 amp, 15 watts, so the whole thing will want 4 amps, 60 watts, so the charger can cope easily. If I extended it to 10 hours, which I'd happily do, because I only ever charge overnight, I could charge a battery with twice the capacity.
The imax has a couple of extra ports. One, costing a couple of pounds, is a temperature sensor port; that means I can make it monitor the battery while charging, and take action if it gets too hot. The other is a USB port, so I can monitor things from a computer, although that doesn't sound enormously appealing, because I'm guessing it would have to run under Windows, and would need me to be fairly close to the charger (I couldn't do it from upstairs).