Which French companies are you talking about ?
LMX is one. Started off in endless-sphere forums, I believe.
There is a second one that has a left hand belt drive that I saw in a video, but I can't find it right now.
, i.e. typical offroad environment, it's clear that a hub motor, even with an excellent efficiency like the GMAC, cannot compete with a mid-drive motor on the right gear.
Well yes. That is what I said in my previous post. Slowly crawling up hill isn't a problem with e-MTB. If you have to go 10-15 kph on a street around other traffic then that is much more of a issue.
Also your graph is goofy. It should be more like this:
https://ebikes.ca/tools/simulator.html?motor=GMAC10T&batt=B5216_GA&cont=PR&wheel=26i&hp=300&mass=120&grade=16&autothrot=false&throt=100&autothrot_b=false&cont_b=PR&motor_b=MBBSHD&batt_b=B5216_GA&wheel_b=29i&mass_b=120&hp_b=300&throt_b=11.1&grade_b=16&mid_b=true&tr_b=50&tf_b=42&bopen=true&gear_b=1
The smallest front cog you can fit on a BBS** motor is 42 tooth. At least what I am aware of. Plus people are not going to run at 11% throttle. And they are going to be putting a lot of effort into pedaling. More then a 100 watts in most cases.
Of course the Mac motor still overheats after a few minutes and that is what I expect to happen. But it still will get you up 1-2 km before it does.
...
Anyways my contention is that you can design a single-speed motor to deal with these slopes.
Geared hub motors won't do as they are motors in a box and there is no direct cooling, so mentioning it was a bit of unfortunate red herring on my part. I was saying IF the cooling issue was addressed a motor of that size could work very well and be packaged very well to fit a typical bicycle. But that is a big IF and I don't see the cooling problem being solving any time soon.
Here is a very crude fantasy motor example to explain what I am talking about:
https://ebikes.ca/tools/simulator.html?motor=MSAW2013+SA&batt=B5211_PF&axis=mph&mid=true&tf=30&gear=7&kv=55&cont=PR&grade=16&cont_b=PR&motor_b=MSAW2013+SA&batt_b=B5211_PF&tf_b=30&mid_b=true&gear_b=7&grade_b=0&kv_b=55&bopen=true
It is a imaginary Crystlyte SAW 20 motor (small 3.4kg dd motor) that was re-wound for a 55 Kv that is injected with statorade to improve cooling. I don't know if that is possible to have that winding with that motor, but for the sake of argument lets pretend it is. The gear ratio is 7:1, which is actually something very reasonably obtained with a single stage 219 metric chain drive. Now this is a SPM outrunner motor.
If you fiddle around with the settings, such as using a imaginary controller with 100 amp limit and reduce the gear ratio you can get even better results. This style of setup loves amps, apparently.
And note that there actually exists motors like this, at least as far as I can tell:
https://store.tmotor.com/category.php?id=7
Those are big efficient outrunner SPM motors. I haven't figured out how to do all the math yet to figure out how feasible this all is, but on the surface it seems like it will work. They have Kv ratings down to the point were single stage reduction is possible.
Now a inrunner IPM motor with first stage planetary reduction drive in addition to a similarly sized chain reduction drive would be a lot lighter and a lot smaler. With a proper FOC controller that can do field weakening you can have a extremely massive usable RPM range. This means we can take advantage of this by providing extremely low gearing while still being able to reach good top speeds.
Like what you see with the CYC X1 Pro motors/gearbox setup. (although it is a outrunner SPM motor, it is very fast) I think that a huge potential for those motors is wasted by trying to tie it to the bicycle crank and there is no benefit to having multiple gears with these motors. If it was possible to turn the motor and gearbox around so it was reversed and then tie it to a 11 to 70 to 100 tooth rear sprocket with 219 chain then you would have a e-bike that is essentially unstoppable as far as slopes are concerned. Unfortunately you can't reverse the gearbox as it has a integrated clutch.
So this is still fantasy stuff. Like I said in my other post it's not really all that useful approach for 90% of us unless somebody produces custom frame around this sort of setup. Which I see as extremely unlikely unless you just go out and buy something like the LMX.