@LaidBack: Just to clarify... The UA uses a standard Bosch 250W motor with a battery capacity of 400W or 500W.
Sorry to be picky, but battery capacity is measured in watt hours, not watts. It's a measure of the amount of energy that can be stored in the battery, not the battery's power output.
The SI unit of energy is the joule, which is the amount of energy required to move one metre against a resisting force of one newton. It's roughly the amount of energy required to lift a normal-sized apple through a height of one metre. Or two apples half a metre. Or half an apple two metres. You get the idea.
The watt is the unit of power, which is the rate at which energy is expended, in joules per second. Thus, to lift one apple through one metre in one second requires one watt of power. To lift the same apple the same distance in half a second requires two watts. Do it in two seconds and you only need half a watt of power. Either way, though, it still uses one joule of energy.
The watt hour is a non-SI-sanctioned unit of energy. Simply put, it's the amount of energy expended in an hour by a system with a constant power consumption of one watt. Since a watt is one joule per second, a watt hour is 3600 joules.
The normal symbol for the watt hour is "Wh". (Again, this goes against the SI sanctioned form, which requires either a non-breaking space or a centre dot between the two 'base' units. Note also that the symbol for the watt - which is correctly written with a lower case "w" - is upper case "W". This is because the unit is named after a person. Hence also the symbol for joules is J, and for newtons it's N.)
So, to cut to the chase: a 500 Wh battery can, theoretically, provide energy to a motor producing a continuous 250 W of power for two hours. (More SI pedantry there: the number and the unit should also be separated by a space.)
Interestingly, the Bosch eBike range assistant does indicate that my eMTB should have a range of ~50 km if ridden in the highest assistance "turbo" mode at an average speed of 25 kph - ie, in two hours. More interestingly, if you make the terrain more hilly, the surface rougher or the headwind stronger the range goes down. That might seem obvious, but it does suggest that the Bosch controller is actually able to let the motor run at more than 250 W output some of the time - as suggested by the link provided by greenroofer (albeit that is to a web site which seems to be oriented more towards DIY ebikes than off-the-shelf pedelecs which are supposed to be compliant with EU directive 2002/24/EC.)
It's almost enough to tempt me to try to put an ammeter on the circuit which supplies power to the motor of my eMTB, just to see what it can can be persuaded to draw...
250 watts delivered to pedals can give torque values of up to 75nm. (ie quite enough to do a loaded hill start).
Firstly, with my annoying pedant's hat on again, "nm" is the symbol for nanometres (there is no space between the prefix and unit symbol). The symbol for the SI derived unit for torque, the newton metre, is "N m".
Secondly, another way to calculate power is as the product of torque and rotational speed (in radians per second). If a motor is producing 75 N m of torque at a power output of 250 W, that means that the output shaft is rotating at ~30 rpm. You'd need to know your ebike's gearing and wheel size to turn that in to a road speed but I think on my eMTB it's about 2.5mph. My calculations were complicated by the unexpected discovery that the chainwheel on my eMTB is not directly connected to the pedals - there seems to be some kind of epicyclic gear in there which means that the chainwheel turns roughly three to four times faster than the pedals (which explains why the chainwheel is so small). I think it's like this in order to allow the motor to spin at a reasonable speed even at a low pedalling cadence/low speed - and possibly also to keep the low speed torque down to a controllable level, since electric motors produce more torque the slower they run.
posts
