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battery watt hours vs motor watts


wilson_smyth

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Is there a rough formula to work out how long certain Wh capacity battery will last with a certain watt motor?
 

e.g. battery is 100Wh, will it power a 10Watt motor for 10 hours, all other things being equal?


I know gearing, wheel size, rider weight etc will all have an effect so am i just better in relying on manufacturer specified ranges?

 

 

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No, the actual wattage you're using at any moment in time is dependant on many factors, your weight, speed, acceleration/deceleration, going up and down hills, air drag... You can't calculate your "battery consumption" from the motor nominal or max power. On a level flat road at steady speed, you use a lot less power than accelerating or going up hill, when braking or going down a hill, you're actually (slightly) charging the battery. A stronger motor will help climbing hills, maintaining higher speeds and accelerating faster, and for heavier riders is a must, as for example climbing hills, the power requirements go up fast with rider weight. For "typical" numbers, I'd say the average consumption is somewhere between 10-25Wh/km or 16-40Wh/mile (more weight and/or higher speed & accelerations = more consumption), depending on your riding style, environmental factors and terrain.

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35 minutes ago, wilson_smyth said:

Is there a rough formula to work out how long certain Wh capacity battery will last with a certain watt motor?

Errrrrr....... No. what the rated power of a motor is, and what the power the rider is consuming are two very different things.This is more than slightly confused by the questionable power ratings some manufacturers give their motors, some quote maximum power, others the power the motor can give continuously, some are more optimistic than others!

35 minutes ago, wilson_smyth said:

E.g. battery is 100Wh, will it power a 10Watt motor for 10 hours, all other things being equal?

Yes, the above is true if you totally flatten the battery and you pull 10 Watts continuously - both of those things will not happen in real life.

A much better, but still fairly flawed, yardstick is the Wh/km or Wh/mile an electric vehicle will consume, but that is still very, very variable depending, for EUC's, on:

  1. The rider weight - this can make a massive (pun intended) difference.
  2. the average speed- higher power motors will allow you to go faster, power consumption goes up much faster than speed, air resistance increases as the square of the speed
  3. How hilly it is, regen braking will put some power back but it is a small fraction of the extra power consumed 
  4. Temperature - doesn't directly effect power, but low temperature very much impacts battery capacity.
  5. How low the battery empty voltage is set to in the software on a particular wheel.

I'm sure there are lots more. You can probably reckon on an average weight person on an average EUC burning 12-18Wh/km or 20-30Wh/mile.

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38 minutes ago, wilson_smyth said:

am i just better in relying on manufacturer specified ranges?

No, that is the very very last thing to rely on!

EUC manufacturers seem to quote range with a baby chimpanzee riding the wheel downhill with the wind behind it. My EUC has a range that is pretty much half or less of what it theoretically (or is that fictionally) should achieve and I'm only 11 stone (154lb). That is close to what most other western riders find.

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You can greatly extend he range of your EUC by not climbing the same hill twice, as going up and down hills uses the most energy.

Imagine a stream of water starting and ending on you and your destination. By following this imaginary stream you can avoid repeatedly climbing the same hill; you are being much more energy-efficient even though you might need to travel further.

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