250w (from motor) plus a third of 250 w from rider. ( an highest setting mine is roughly 3 times rider contribution) gives 330 w ( or so) which is adequate to climb any hill. The bike doesn't need to draw 700 on steep climbs.
Let me put a few things straight Flud. First you greatly underrate rider power, an averagely fit rider can maintain a steady 200 watts, the third of 250 watts you suggest is quite puny at 83 watts. We consume 50 watts just sitting still in an armchair.
The 330 watts that you suggest is sufficient to climb any hill is well short of that required by legal wheel hub motors which, unlike crank drive units, can gain no gearchange advantage. They require very much more power on many steeper hills.
On your prior comments that companies such as Bosch would not knowingly break the law, that shows a misunderstanding of the law. A company can supply an e-bike/pedelec with any power they wish and many do. For a example, one, a long term member of this forum, supplies machines with around 2 kilowatts of motor power. There is no law forbidding companies from doing this, an offence is only committed in the public use of such machines, the liability falling entirely on the consumer.
To illustrate this, our UK EAPC law restricted all e-bikes/pedelecs to 200 watts of continuous maximum power from 1983 to 6th April 2015. But from 1999 Yamaha supplied 250 watt rated pedelecs throughout that period and from 2001 Giant did also. From 10th November 2003 to that 2015 date almost all companies did also, and after a warning notice issued by the DfT in 2005, almost all of the companies continued to
knowingly supply 250 watt machines which could not be used legally in the UK. The late entrant Bosch joined in that knowingly for more than four years.
In essence, there is no such thing as an illegal pedelec, there is only illegal usage.
Finally a practical example since you asked for one. From 1999 for over a decade Powabyke, one of the longer established companies, supplied their e-bikes with a legal 200 watt rated wheel hub motor. At one point published data on one of their popular models showed it consumed a stable continuous 600 watts at 7 mph climbing with around 60% efficiency at that point. That means its net power output was around 360 watts continuous, near to double it's nominal legal rating. It's prodigious hill climb ability supported that.
I have other practical examples, including two on the Bosch unit.
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