Thanks for the math, if I tried it, I'd screw it up. Your example shows why my dd motor( 7 count winding on 26") NEEDS to be going faster up the hill, and why I'd choose the gearmotor for a steeper hill, that would be climbed slower unless you were Dr Bass.
I did though, want to point out, that even a gearmotor needs more watts to climb the 5% hill at more than 10 mph. 10 mph up the hill is fantastic for most of us when newbies, but then we get used to 25 mph and want the same speed up the hills too.
But on 5% or less hills, I wouldn't sweat it about gearmotor or dd. Just get enough wattage to go a speed you like. Some people, actually want an ebike that is not faster than a regular bike, just easier to get up the hills. For them, a low watt gearmotor is perfection. But some of the gearmotor ad copy makes it sound like a direct drive sucks on any hill, and it simply isn't true if you have 500 watts or more. They, dd, just suck on hills above 10%, unless yer Dr Bass.
Another little known fact about a direct drive motor, is you can climb a very steep hill efficiently at low speeds. Again, pedaling plays a role, and you simply pedal at the bikes slowest comfortable cadence in the lowest gear you have. The apply only the smallest ammount of throttle it takes to make pedaling easier. Now you get up the hill with little heat produced, and very little wasted wattage from a stalled direct drive motor. We're talking 5 mph or less here, but you can climb 15% like this on a dd motor. This works by keeping the motor at low load, the reall inefficiency of a dd motor is high load at low speed, not just low speed alone. So low load low speed is not so bad.
This method is what I use when riding my fuji with the 5304 on it up really steep mt bike trails. Only on the really steep stuff, like short sections of 30% do I use full throttle, and I get range similar to cruising on flat ground at higher speeds. Sometimes less motor and more pedaling works great. And slowing down gets you there faster.
