When pedalling a Bosch e-bike when its motor/electricity is off, how many watts are lost compared to non-ebike drivetrain?
If it differs, let's assume a Bosch Performance CX and 250 watts input power at 90 rpm.
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In theory - none because the motor has a freewheeling clutch that is completely disconnected when it is not providing assistance. That is when you're travelling over 25 km/h (location-dependent) or have not engaged the assistance.
However you're dragging around a heavier frame, with a motor and wiring, and maybe the battery pack too. All this extra mass will take energy to get to speed, and have an increased cross section to affect aero.
Also the tyres will be selected to suit the total weight of bike+rider, so they will not be as light/supple as a non-ebike and will have more loss.
The answer by Criggie excellently explains that the motor doesn't add any pedaling resistance. I find the claim true especially on by Bosch Active Line Plus system -- I have never observed any pedaling resistance above 25 km/h.
However, there's a bit of extra weight. Around 5 kilograms to be precise.
If riding at 23 km/h average speed on varying terrain including hills, my power simulator shows that a 15kg bike plus 70kg rider requires 129.6 watts. Add 5 kilograms of weight and the required power increases to 134.3 watts. So about 4.7 watts more power needed. I'd say this is so significant that you don't want to use an e-bike without assist.
I know this isn't 250 watt input power but I find sustained 250 watts unrealistic except for athletes that surely won't use an e-bike.
I think the two answers are not strictly correct as the 2nd generation Bosch motors use a gear ratio between the pedal input and sprocket output that is something like 2.5*; hence the small sprocket on these systems. There is inherent loss within these systems but to measure it in the real world you would want to use a calibrated pedal wattmeter (or crank) and a rear hub powermeter like the Powertap to see what has been lost in translation.
It may be that the newer system with the large sprocket is directly connected to the pedals and the motor is fully disconnected, but not everyone rides this. Also, we can say that the losses are "minimal" but they still exist in any transmission component.