I have a range of hub kits with 13AH, 15AH and 17AH batteries that may suit your needs. http://wooshbikes.co.uk/?hubkits
They are slightly more expensive (about £50) than ebay offerings but you get better components, better pre-sale, installation and after sale support.
Ah (amp hours) is an expression of battery capacity. So a 10Ah battery can deliver 10 amps for 1 hour, or 1A for 10 hours.
The more useful expression is Watt/hours. To get this you multiply the Ah rating by the nominal voltage. So 10Ah*36V=360Wh. If you work on a ball park consumption of between 10 and 20Wh/mile, you'll get some idea of range. So a 10Ah (360Wh) battery will give you between 36 and 18 miles, depending on terrain, wind, rider effort, weight etc. etc.
My advice, buy the biggest battery you can afford, you won't regret it.
The voltage sag is an important consideration.
when you climb a hill or accelerate, the motor pulls a lot more power from your battery.
When your battery is fully charge, if you check its voltage with a voltmeter, it is 41.5V. When it's completely empty, 31.5V, 10V difference between a fully charged battery and a completely empty battery. The bike will feel less responsive when the voltage drops. When the voltage drops below about 33V, the electrics will start cutting out.
Cheap cells have higher internal resistance than more expensive cells, so batteries built with cheap cells sag more when you do that. Batteries with lower capacity has higher internal resistance. Its effect on the voltage sag is the same. Higher internal resistance also converts more energy into heat.
Yup, batteries is complex beasts my friend
Buy a cheap one and the cells could be a no name copy of a better cell. Their current rating could be low so giving a decreased range.
You need to look beyond headline statement figures.
What cells are they (manufacturer/type)?
What configuration are cells in?
What's the maximum draw of your bike's controller?
Will it fit the frame and where?
Look at post #3 from D8veh.
You need to :
1 - Get the bike
2 - Decide on the kit and show it to the guys, they'll let you know if it'll do what you want.
3 - Find/be guided to the right battery.
You may need to adjust your budget along the way, so as not to end up with something that disappoints so much, it ends up in the back of the shed.
The exact cells used aren't stated except being Samsung for the 14.5ah battery, it is possible that they are 29E cells.
Also you have to look at the rpm available as some kits vary with motor speed from 270 - 320 rpm.
Overall the kits are good value, hub wise they are a pretty much the same size to the Q128c though a few decibals louder. The 270/280rpm wound motor is comparable to the Q @36v, component wise you are getting the same 15A KT controllers, lcd3's etc available from BMSB or PSWP.