True, I didn't even bother to show how much worse that made the prospect, chargers also typically 80 to 85% efficient.
The average car alternator should easily keep pace with charging current and losses when the engine is left ticking over though, but best to do a check of battery willingness to start the car after an hour or so when first trying this.
Maybe a dry run at home would be a good idea if trying out charging with engine ticking over.
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Probably rather worse than that. I have some info on the Wisper charger, which isn't wonderful:
Peak true wattage input is around 150 watts, though it doesn't hold that for long. The power factor is not good though - best case 0.58 to 0.6 when the charger is running at maximum power, dropping to around 0.52 when the battery is approaching a full charge.
This relates to a maximum VA of around 250, which would make an inverter work pretty hard considering that the charger output current limits at (I think) about 2.5 amps at 42 volts. That's around 105 watts coming out for 150 going in, or 70% efficient, even forgetting about the poor power factor.
Most inverters for 12V to mains use 'double conversion' which maximizes efficiency and you can get 80-85% efficiency towards full load. However, a poor power factor load will knock a big hole in this.
When rating computer power supplies, which are rather more complex switch-mode jobs than the Wisper charger, these days the manufacturers aim for better than 85% efficiency (to comply with one of the Euro directives) and a good power factor - as close to 1 as possible - and often 0.8 or better. So, the charger for an e-bike is probably cutting some corners in design and construction, though of course there will be some which are electrically better than others.
The bottom line here is that you'd probably need a large car battery in decent condition to recharge a much smaller ebike battery via a mains inverter and the official charger. The transfer taken as a whole could well be less than 50% efficient.
Rog.