0-15mph acceleration of 250W electric bicycle?

[Danidl]

Using our hypothetical man and bike at 100kg , it will take about 1000joules ( 1kJ) of energy to climb a vertical height of 1 m . Work = mgh Assuming the strictly legal motor is 250w ( not going into the testing methodology or other religious beliefs) , that means it will take 4 seconds to climb that. On a road with a 1:10 gradient, it will have traveled 10 metres . So forward travel is 2.5 m second. 9 km or 5 miles hr.
Assumptions made .. no wind , perfect power transfer of 250w from motor to wheel , no slippage.
Fortunately a 400whr battery pack contains 1.44 mega joules, so could in theory bring the guy up 1km. ...

 

[Woosh]

You would still have to take into account mechanical loss due to road surface, air resistance and voltage drop due to the internal resistance of the battery, low voltage cut off point of the controller. Typically, about 20% of the battery capacity can't be used if the assistance required is that high (250W or more).

- 25% loss due to motor yield
- 20% unreachable capacity reserve due to battery internal resistance
- 10% due to other mechanical losses

I reckon the maximum climb possible with a 400W battery is about 650m in elevation.

 

[anotherkiwi]

So I think we can safely say less than a week then?