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What is your recommendation of motor and battery for lugging two units of children (1 X 10 and 1 X 5 years old) up and down SE London hills?
Chalfie-
Underslung/aftermarket mid drive ish type? Tongsheng 500w, in reality the big players from Shimano EP8/Bosch CX cargo 'rated at 250w' are actually more powerful and more torquey, its just the number they slap on it to make it sound good IME. They also do a 750 + 1000w versions but your definitely in 'illegal e bike' territory there. Not sure how LDN is doing with keeping tabs on them but in Glasgow police are much more interested in slightly dodgy e bikes than other more serious crime so beware, having something that says large numbers on the side of your bike could be an issue. Batteries, buy from anyone reputable, anything in the 500wH to 1000wH is plenty.
BrickMan
Seen/done a few +Bafang and Tongsheng conversions recently, both work absolutely fine. Defo not the same user experience as a proper mid drive, but actually for heavy loaded cargos, you just want torque, lots and lots of torque. Ability to change gear under power without backing off is a bonus (TBH only external gear systems really can do this without going bang) but not essential.
Difference in feel/experience between Bosch + Shimano in their most up to date models (gen4/e6100/ep8) are very small. choose one with the most torque if your a heavy user, you'll be happy with a performance line/E6100 if for family use. Older Gen 2/Gen 3 Bosch or Shimano E6000 yeah was some differences.
The supplied with/stock map on the Tongsheng is hopeless. Don't bother reading anyones reviews of it unless they bothered to flash another one onto it or at least made some rudimentary tweaks to it.