Many kits come without batteries and you can choose your own lower capacity battery pack. Many people use the scooter style battery packs on ebike projects. They are typically 180-270Wh capacity and have less sustained current output so only suitable for 250W/350W geared hub motors. This sort of thing.
https://www.aliexpress.com/item/1005002899628391.html
A 7Ah model from a reputable seller should contain 20x3500mAh cells. This one gives about 10A maximum continuous and probably and perhaps something like 15-20A peak current. A 250W controller should be 7A at 36V normal sustained output and maybe 11A peak so should be within the parameters of the battery. If you use the ebike in a lower power mode the current draw won't be as much.
7x36 is 252Wh. A quick look shows
Halfords do a ebike with a 24V battery with 4.8Ah capacity so 115Wh, less than half that capacity called the Assist bike. Many quite expensive lightweight ebikes come with batteries around 250Wh.
This would be a suitable kit.
https://yosepower.com/collections/u...-26-28-front-motor-kit?variant=39532573753479
You would also need a suitable charger and solder on a XT60 connector in place of its existing connector.
You could mount it all in a bag like below on the handlebars (a bit like Swytch) so the whole ebike kit doesn't have cables being stretched as you steer but instead everything turns together. Personally I would want to use a bike with steel forks for safety but you can probably get away with aluminium and maybe even carbon fibre if a light rider. I'd use hard foam dividers (maybe re-used from packaging) to keep the parts separate in the bag. That bag is big enough to hold the controller, battery and probably even the charger.
Amazon product ASIN B07ZZMZD5VView: https://www.amazon.co.uk/gp/product/B07ZZMZD5V/ref=ppx_yo_dt_b_search_asin_title?ie=UTF8&psc=1
Price for everything less than £300 and considerably better range than the newer Swytch kits with very low capacity batteries. If you use it only with the throttle only when you need assistance the battery could last quite a long range maybe 60-80 miles. If you use it like a pedelec type ebike so the motor is always assisting to a lesser or greater extent perhaps 25 mile on lower power levels.
It's perfectly legal to have a full function throttle on a converted bike to ebike project.
https://www.pedelecs.co.uk/dft-pedal-cycles-converted-twist-go-exempt-type-approval/
Many people prefer the safety and control of throttles (its the main way of controlling ebike power around the world on most ebikes).
I prefer front hub motors myself but if you want a rear hub motor then you could re-jig the layout with a saddle bag holding the battery and controller and just have the throttle and display cables along the top tube to the handlebars.
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