A 20Ah 36V LiFePO
4 pack delivering power a a rate of 1C should supply 20 amps continuous for a whole hour.
I am a bit puzzled by your 3 amp fuse, as this seems much too small for your 500 watt motor.
Supplying 500 watts at 36 volts would require almost 14 amps.
Drawing only 3 amps from a 36 volt pack would only allow 108 watts of power to be consumed by your motor
(Watts = Volts x Amps), which doesn't seem very much to me. After allowing for the inefficiencies of the motor, you would probably only receive around 90 watts of assistance, and your 20Ah pack should run for at least 6.5 hours at 3 amps continuous.
With a 36V pack, I would expect your top speed to be at least 30km/h. If it was possible to maintain this speed by using just 3 amps of current, you would have a range of around 200km.
20Ah/3A = 6.66hrs, 6.66hrs @ 30km/h = 199.8kms.
Pete, are you sure it's only a 3 amp fuse?
I am guessing in the dark here that the general idea Les was alluding to was to go easy on the battery for a couple of weeks. Does that mean not go too far? I should have a range of 43 kilometers at full speed on flat, so don't go that far?
As Les has already suggested, simply taking it easy on the throttle will greatly reduce the rate at which the current will be consumed, especially when accelerating away from a standstill or climbing steep hills.
I recommend 1C for 2 weeks, maybe 10-14 cycles. and no more than 1.5C after this time.
1C On your new pack = No more than 20 amps for 2 weeks then 30 amps should be sweet to ride for years.. So a little eazy on the throttle when it is new should be fine.
It's also beneficial for the longevity of the pack if you don't run the battery too low each time you use it, so if you can aim to use less than 70-80% of your pack's capacity, you should increase its life expectancy.
Alan