I said they don't use the bike's gears to assist in climbing hills.

This is where we keep having the communications breakdown, because you keep switching back and forth between two completely different proposals and terms:

A - What sounds like you're stating that a mid-drive doesn't provide any advantage at all over a hub drive and they are both equal when climbing hills with or without human power input.

and B - Insisting and conflating this with the stricter definition of mechanical advantage at less than 1:1 gearing is the only "real" assistance or advantage over a hub drive at all.

The part where we are disagreeing is that hub drives are mechanically exactly the same and providing the same assistance as a mid drive given the same gear range and drive train, and this isn't true at all due to the mechanical differences and torque band differences and how they overlap and work with or against the drivetrain.

To get the same power assist advantages as a mid-drive, the hub drive would have to be a powered IGH where you could change the ratios of the internal gearing on the hub.

Yes, you can get purely mechanical advantage with a hub drive by changing gears like on a normal bike and pedal power, but it's not the same range of mechanical advantage as a mid drive through a drivetrain due to the torque bands of the motor being able to be better matched to the drive train.

Side bar:

Sure, you can defeat it by lying about the size of your wheel (in the computer) or some other way.

Not all mid drives (or hub drives) have any kind of speed limiter, nor are they strictly class 1, 2 or 3 drives. Most of the DIY mid drive kits out there have zero limitations beyond total amps as defined and limited by the controller, BMS and battery cell ratings.

My 52V BBSHD has zero restrictions other than the safety cap of 29 amps on a 30 amp system to keep it from blowing up the controller, and the controller can actually handle some slight fudge factor greater than 30 amps. The battery and BMS is the real 30 amp bottleneck.

There's nothing to defeat or trick, here. The only limitations are the inverse square laws of aerodynamics and how they interface with motor efficiency and peak amps vs torque.

But the reality is, the power is such that it won't go much faster than about 30 mph for most hub drives. AFAIK, most, if not all are 750 watts or less. Regardless of gearing, it takes X amount of power to go Y speed.

Yes, and no. The difference between a hub and mid drive here is that given the same gear range and wheels, a mid drive can go Y speed for less power than a hub drive due to not running into field weakening problems at higher motor core speeds and the voltage/amperage limitations inherent in all brushless/PWM switched DC motors.

This ability to take advantage of RPM power bands should actually be seen as an electromechanical advantage, and I think this is where we're failing to communicate clearly.

I really and truly can go faster (or steeper!) per given rated watt because of the advantages of a mid-drive through gears because I can keep the RPMs in the power band.

Part of the issue here is that "watts" are actually a horrible way to measure ebike power at the wheel-road interface and are just a generally vague "this is how much power it can use over a given window of time" and not "this is actually how many volts/amps it is using right now".

This power limitation also limits your climbing speed regardless of mechanical advantage. What it will do by being in the right gear while climbing is keep the motor cool and efficiency higher.

This is true, but again, the power curves are different with mid vs hub drive due to being able to select the right gear range to match the efficiency/torque/power bands and zones of the motor core.

As a fellow old school analog cyclist that likes pedaling, I sure wish I could just let you ride my Bafang BBSHD build on a Surly Trucker up a steep hill and then directly compare it to hub drive with the same amount of watts and drive train, because it's a hugely and immediately noticeable difference in everything from acceleration from a stop to total speed climbing up hills with or without pedal input.

Not only is it faster and stronger per watt, it's also vastly more controllable than a hub drive bike especially since I can apply all that torque with the throttle alone without any pedaling required at all.

With my setup it's not speed limited at all. Throttle is free use, too.

I have the Eggrider v2 controller which stores two complete 0-9 PAS levels. One is the stock full power OEM settings, and the other one is totally detuned and dialed back for more chill (and legal) riding and lower speed torque and control. I'm driving that through a 11-50t 9 speed, so it's kind of like driving a semi truck in that I have an insane number of "virtual" gears with 18 power levels x 9 gears.

And those power levels on the "detuned" profile are dialed in to work with my drive train steps and jumps between gears, too.

I can actually tune my controller profiles to limit them to a lower total speed (or volts!), yet still draw higher amps for torque, or vice versa, and I can adjust all of this easily on the road with the bluetooth app to match my terrain for the day.

What this means in practice is that I can be riding slow, techy uphill single track with a totally insane amount of low speed, controllable torque that you won't ever get out of a hub drive because it has to run and "cold start" from a dead stop every time and has to faff about in the low end of it's power/torque band to get those low speeds, at the cost of a lot of torque per consumed watt.

With a mid drive I can start up from a cold stop pointed directly up a steep hill in the right low gear (just like an analog bike) and it's instantly within it's higher RPM power bands, and it'll do that all day long at nice, easy to control lower speeds that are very suitable for the terrain so I don't get thrown off my bike or trail due to being able to run high motor/pedal RPMs while maintaining full torque.

Hell, it'll burn straight up a hill in the wrong gear, too, and chug away at it dumping watts as heat just like a hub drive, but I don't do that because I want to protect both my motor and drivetrain. A BBSHD will strip the teeth right off a brand new 11t sprocket if you let it.

Try cold starts aimed up a steep hill on a hub drive and it's straining and dumping watts as wasted heat because it's running too slow to use it's power band.

I really, really wish you could try out my bike because it's a HUGE difference in controllable power, efficiency and ride-ability over hub drives. You'd basically have to have a 3k+ watt hub drive to do the things that my bike can do even without a 46x11-50t drive.

And it's a total blast for climbing rugged, techy trails. I can climb like 3000 feet in a couple of miles with basically zero sweat AND keeping the speed down below 5 MPH for precise torque control. But it'll also easily do 35+ on a smooth, flat road with or without pedaling at all.

It would easily do 40+ with someone smaller and lighter on the same bike, but I'm about as aerodynamic and light weight as a whole barn.

If I could actually run a 3x or 2x front derailleur and rings and go from like a 32t to a 44t to a 52t ring, it would easily get even my fat ass up to 40+ because it wouldn't run itself out of the power band so soon, and the HD has an insane 160nm of torque at the output shaft both due to the motor design and internal gearing.

The fact that it can haul my huge fat ass and two weeks of groceries up steep hills at 15+ MPH (without pedaling!) and do that kind of speed on a flat road all on the same bike is just phenomenal.

You could probably put the same stock 52V BBSHD kit on an aerodynamic, recumbent velocycle with a much bigger chainring and I wouldn't be surprised at all if it could do 70-80+ MPH with enough straight road to burn up because of the electromechanical advantage of power bands and RPMs.

Note: I don't generally go faster than 28 MPH with power. I do occasionally hit 40+ bombing down hills but that's just normal bike stuff and me falling like a brick.