Safe, I don't know how to say this more clearly but

**you are wrong, flat wrong, plain wrong, simply wrong, and almost completely wrong.** I've shown you your mistakes and will show you new ones as they arrive. I also think you have a lot of gall, saying my calculations don't feel right without working through them yourself to see I have made no error.

Tell me, why do you insist in repeatedly coming back with your bad assumptions and incorrect calculations? This time, the first mistake I caught was dividing by 0.7 to account for generator inefficiency, instead of multiplying. I stopped there, because I have given you all the information you need to get it right. Please check my calculations before suggesting new scenarios as an attempt at refutation. You will find my work is correct (to within a significant figure or two).

**Think** ...

**carefully** ... about what we have been discussion before coming back with more bad conclusions derived from faulty logic.

By the way, PLEASE use correct units if you are going to bother writing them. I was mislead by your use of the term "746 watt", where you should have had "746 watt/HP". Also, I hardly need a lecture on the use of appropriate units. As I explained, expressing energy in kilocalories simplified my presentation because that is the unit the bicycle calculator presents as its result. I even showed you the conversion to watt hours the first time I used the unit, to help eliminate any possibility of confusion. Apparently to no avail. Maybe next time I'll present my calculations in the FFF system of units in protest of your pickiness.

Another factor is gears... are we to allow gears with regen? How does one implement it? We know that with a freewheel you can use multispeed gearing that's critical to getting your efficiency up higher.

There are several solution to this problem. An internally geared (ala rohloff's speedub) hub motor could be possible, as could a secondary chain driving the motor through a completely separate path when using regeneration. The simplest solution might be fitting the bike with a separate generator (say, a small, high efficiency outrunner) driven directly by friction on the wheel and disconnected when not in use. Perhaps you can think of some solutions if you try.

So would we want to explore more "real" situations that involve actual hub motors using regen and compare them to multispeed freewheel bikes on the same track?

**No, no, no!** Not until you are able to understand the simple case.

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Regarding your "real world" race scenario. You suggest a strategy that leaves some charge in the battery at the end of the race. That's simply a bad strategy. No rational competitor will choose to end the race with charge left in the battery. For short races with limits on motor wattage, it probably pays to load up with enough battery to run flat out the whole way.

Last, please understand I bear you no ill will. One of the things I get a personal reward from is tutoring people in math and physics, as I am trying to do here. I very much enjoy applying physics to athletic activities like cycling, so this topic is right up my alley. However, I can only help you if you are willing to listen.