How much power does an e-bike(or any vehicle) need?
In Australia the limit for e-bikes is now set at 250Watts for pedalec and only 200Watts for electric-assisted bikes, previously it was only 200Watts. This brings Australia into line with Europe and Singapore. Some countries allow 500W and in the US some states allow 750W. Part of the Pedalec standards state that the electric assist can only work while the rider is pedaling, which is a good idea, and also state that the electric assist must cutout above 25kph or sooner if the rider stops pedaling. Both are good conditions to keep them as bicycles and not crossing over into the Moped/Motorcycle class of vehicle although I would argue that 25kph is a bit low if we want to see more people using them as an alternative mode of transport. In Australia bicycles are still seen as just for leisure or hobby.
Now back to the question, “How much power does an ebike need?”
For my formula I will use the speed of 10kph, just above walking speed, low enough to disregard most wind resistance and still well within the Pedalec category. The weight is 80kg for the rider and 20kg for the bike to give a nice round 100kg. And gravity as 9.8ms-2 .
Speed = 10kph = 2.8ms-1
Power = Work / Time
Work = Force x Distance
so Power = Force x Distance / Time
Force = 100kg x 9.8ms-2 (gravity)
Then to work out the power required, if I ignore friction and wind resistance, use the vertical velocity to get the distance traveled times the force(due to gravity) over the time period of 1 second.
Vertical velocity = speed x sinα
α = angle of incline
|Angle of Incline||5°||10°||15°|
|Power Required (Watts)||239||476||710|
As can be seen from the table 250 Watts isn’t that much. In a hilly place like Sydney more power at lower speeds would be a big help. Maybe the laws could allow more power but have it reduce at 25kph and cutout at 30kph. That way if you could keep your average speed up a lot more people would use it to get to work.
Links to Pedelec laws for different states
Western Australia – Has not yet adopted the Pedalec laws [Oct 2014] Coming in early 2015, hopefully.