What’s with the watts?

I sent an email to the Bosch help desk asking about optimum cadence. I noticed the motor did not increase its power contribution above 105 revs of the pedals per minute. Generally they recommend a cadence of between 60 and 90 which is fine for me.

I have other queries which I will send to them in due course. One is to do with the maximum watts the motor can deliver. It is stated as 250 watts and I assume this puts a limit on what it can contribute at any particular moment for maximum efficiency for my and the motor’s power output.. Whatever I produce and whatever the percentage increment is theoretically, if the motor’s contribution reaches 250 then it can’t give me any more.

For instance if 40% = 250 then I would have to generate 625 watts myself to get the motor to provide its max 250. If this was possible, then our combined output would be 625+250=875. This would be eco mode.

If 100% (tourist mode) = 250 then I would generate 250 myself, a total of 500 watts.

If 180% (sport mode) = 250 then I would have to generate 139 watts, a total of 399.

If 270% (turbo) = 250 then I would have to generate 92 watts myself, a total of 342 watts.

To get the full 250 watts assistance realistically I could only do this in sport and turbo modes. According to Zwift my FTP is 170 .In addition I’m sure these figures would be complicated due to each mode offering different levels of torque in Nms.

So using real world figures, let’s say I can produce and sustain 120 watts.

In eco mode the increment would be 48 and the combined total 168 watts.
In tourist mode the increment would be another 120 and the combined total 240 watts.
In sport mode the increment would be 216 watts making 336 watts in all.
In turbo mode the increment would be 324 but the motor is not capable of this so would give me the max of 250 and a total of 370 watts. In fact I could produce as little as 92 watts in turbo mode to take the motor up ti its full 250 watts contribution.

I assume in practice the variable Nms of torque available in each mode would also put a limit on the power available.

It would also be interesting to know how different power figures from me impact on battery life. I assume that in any given mode if my power level is lower and requires less power from the motor, below its max of 250, then there is less demand on the battery. However this may not make much difference to the available range, only the overall average speed.