I guess I opened a can of worms with that comment. Goody, the debate is allways so educational!
I was refering to the battery energy, but yes, the total energy would be similar too, since the size of the hill doesn't change. The point I was trying to make was that at my bikes hill climbing speeds, that are generally under 15 mph, the effect of wind is less noticeable than when going say 25 mph on the flats.
At one point, I got the idea in my head than slowing down to climb a hill would extend my range. Normaly, on the flat, the slower you go, there is a noticable increase in range. But on a steep hill, the power used to lift the weight up it dwarfs any savings caused by riding slower, so the savings from riding slower is not very noticeable. On a steep hill, it will take x number of watthours to get up it, plus whatever watthours are needed to go a certain speed. In perhaps 300 trips up my hill on the way home now, I've tried all sorts of things, but only turning off the motor and pedaling up it seems to save any battery capacity that I can tell. It just costs you to lift weight up to a higher elevation no matter what.
As for going even slower, my lowest gear pedals at about 6 mph at a comfy cadence for me. Even slower most likely would get into the motors stalling range, which would create more heat. It's hard to balance that slow anyway, so I doubt I'll do any testing slower than 6 mph. My ususal strategy to get up my mile and a half of 5-6% grade is to drop a few gears, spin the pedals fast, and ride at about 15 mph. I could climb the hill faster in a higher gear, but I found I had to pedal too hard. Now I try to keep up 15 mph, and pedal fast, but with less power on each pedal stroke. On very long steep hills, then I go to the lowest gear, and use only as much trottle as I need to go 6 mph, trying to use the motor only as much as I need. The reason for this, is to lower the wattage, so the motor may get up the hill without overheating
On efficiency, I should have qualified my statement to incude only the commonly avaliable brushless bike motors. I understand that the guys using RC motors and such are exploring higher efficiency in interesting ways. And of course, anything brushed has horrible efficiency and will make more heat instead of motion than brushless hubmotors.
I just find the difference in efficiency between say a bmc 600 watt and a clyte 5305 to be not that much to be worried about. They may use widely different ammounts of watthours, but most likely that is due primarily to one motor being noticeably faster or faster to accelerate than the other. My killawatt tells me that my little bafang like gearmotor at 20 mph uses allmost exactly the same watthours to go a measured distance in the same weather as my dd aotema motor at 20 mph. Same thing with the 5304 at 20 mph. The fusin usually gets me home with less power used simply because I ride faster on the aotema. On a steep hill, the fusin heats up much faster, simply because it has less mass to be heated than the aotema. The clyte motor, at nearly twice the weight heats up the slowest, because it takes more heat to wam up 25 pounds of metal than 10 and it has more surface area to radiate. In my opinion, hubmotors need cooling fins.