hill climbing? 750W hub versus 250W mid drive

who wants to do this bridge climb challenge?
IMG_3451.jpg
 
I'll argue you should ignore gear inches. Its a unit of measure everyone swore by... decades ago. In the modern world we have much better tools that give much more detailed performance answers. In particular when building a bike I would spend a lot of time with this table


and this one.


Using these you can give yourself a very near idea of how the bike will behave across a range of its gears, taking into account wheel and tire size. It is still not perfect, but its going to get you a whole lot closer to a correct result than trying to picture gear inches, which even if you master them which is not hard to do, will still not tell you speed at cadence, or cadence at speed which I would argue are actual end results and what you really want to know.
I find gear inches very useful — especially in conjunction with the formula

V = 0.0030 C G = 3 C G / 1000

where V = ground speed in MPH, C = cadence in RPM, and G = gear in gear-inches. For my preferred cadence of C = 85 RPM, this reduces to

V ≈ G / 4,

which I can do in my head. And since I'm now paying more attention to my hub-drive's wheel speed, thanks to this thread, here's another handy formula:

W = 336 V / D ≈ (1000 V) / (3 D),

where W = wheel speed in RPM, V = ground speed in MPH, and D = nominal tire diameter in inches. For my D = 27.5 inches, that reduces to

W ≈ 12 V,

which I can at least estimate in my head.
 
Last edited:
I find gear inches very useful — especially in conjunction with the formula

...

W = 336 V / D ≈ (1000 V) / (3 D),
Yeah. 1 mph is 336 gear inches a minute. On a hill, I'll find a comfortable gear. If I want to know the cadence, I divide 336 by my gear inches and multiply by the mph. If it's 74 gear inches, 336 is about 4.5. That would be a cadence of 67.5 at 15 mph. (That's kind of fast for me. Jacques Anquetil won the Tour De France 5 times at about 65. He sat his butt pretty far back, and if you can start pushing at TDC, you can get more torque without more muscle strain.) (I've read that modern Bosch mid drives are designed to work best at 50 to 80.)

Counting teeth on cassette wheels is beyond me. For gear inches, I drag a finger on the tire to keep it from freewheeling, turn the crank a revolution, and count the spokes (36ths) between the wheel's stopping point and the nearest complete revolution. If I know my gross weight and the percent grade, I know the thrust required. If I divide the gear inches by 14 (the pedaling diameter), I can multiply the result by the required thrust to see how much mean effective pressure I put on the pedals. It increased greatly three years ago, when I bent a post to move my seat back.
 
… If a dynamometer chart has torque and power, I don't know why engineers would have to calculate torque after looking at the power.

I don't understand why they would give the torque at peak power…

they don’t. peak torque and peak power are often produced at different rotational speed. there is absolutely no rule which says you must publish the torque figure at the rotational speed which corresponds to any particular power measurement, peak sustainable or peak legal or otherwise.

because the torque curves of electric motors are so flat, many of them produce peak power around the same spot, 60-70rpm, at which point torque starts dropping faster than increasing rotational speed makes up for it. because of this the relationship between published power and torque is pretty consistent, but there is absolutely no guarantee that they publish “torque at XX RPM” and it would in fact be unlikely that peak torque and power would be produced at exactly the same RPM.

only torque is measured directly. it is combined with speed to derive power.
 
they don’t. peak torque and peak power are often produced at different rotational speed. there is absolutely no rule which says you must publish the torque figure at the rotational speed which corresponds to any particular power measurement, peak sustainable or peak legal or otherwise.

because the torque curves of electric motors are so flat, many of them produce peak power around the same spot, 60-70rpm, at which point torque starts dropping faster than increasing rotational speed makes up for it. because of this the relationship between published power and torque is pretty consistent, but there is absolutely no guarantee that they publish “torque at XX RPM” and it would in fact be unlikely that peak torque and power would be produced at exactly the same RPM.

only torque is measured directly. it is combined with speed to derive power.
Here's what a DC permanent magnet motor would do without a controller, although a hub motor isn't wound to turn nearly so fast. At the low end, torque ( current ) would be so high that the motor would be wrecked in seconds.

Here are charts of a hub motor with two controllers. In both cases, maximum torque is about 3 times higher at 0 rpm than at max power; I've seen similar results with the two bikes I measured at different speeds. Note the knee in the torque at max power. That's where the controller quits restricting torque (amps) and lets back emf take over. If the controller didn't restrict current to the left of the knee, it would rise as steeply as it falls to the right of the knee, burning out the motor very quickly at low rpms.

A flat torque curve seems to be a feature of mid drive controllers. With a gearshift, a motor doesn't need extra torque to reach an efficient operating speed.
 
Here's what a DC permanent magnet motor would do without a controller, although a hub motor isn't wound to turn nearly so fast. At the low end, torque ( current ) would be so high that the motor would be wrecked in seconds.

Here are charts of a hub motor with two controllers. In both cases, maximum torque is about 3 times higher at 0 rpm than at max power; I've seen similar results with the two bikes I measured at different speeds. Note the knee in the torque at max power. That's where the controller quits restricting torque (amps) and lets back emf take over. If the controller didn't restrict current to the left of the knee, it would rise as steeply as it falls to the right of the knee, burning out the motor very quickly at low rpms.

A flat torque curve seems to be a feature of mid drive controllers. With a gearshift, a motor doesn't need extra torque to reach an efficient operating speed.

that’s interesting. essentially, the controller can be tweaked to produce different amounts of torque at different speeds, resulting in power peaking at a different speed than torque except by coincidence.

the torque curve also explains why electric motors are so good for accelerating from a stop, although i am not sure the torque continually
decreases from a peak at 0 rpm as shown. probably an oversimplification or programming intended to illustrate a particular result.
 
the torque curve also explains why electric motors are so good for accelerating from a stop, although i am not sure the torque continually
decreases from a peak at 0 rpm as shown. probably an oversimplification or programming intended to illustrate a particular result.
I've worked with a lot of brushed permanent magnet DC motors as a hobbyist. Those torque and power curves are pretty accurate for real-world motors of this type — including those with internal gearing. Peak torque and no mechanical power at the shaft at 0 RPM. No useable torque or power at no-load shaft speed (NLS). And peak mechanical power and ~50% of stalled torque at ~50% of NLS.

Allowing for controller-induced distortions, brushless DC motors seem to follow similar curves.
 
Last edited:
Here's what a DC permanent magnet motor would do without a controller, although a hub motor isn't wound to turn nearly so fast. At the low end, torque ( current ) would be so high that the motor would be wrecked in seconds.

Here are charts of a hub motor with two controllers. In both cases, maximum torque is about 3 times higher at 0 rpm than at max power; I've seen similar results with the two bikes I measured at different speeds. Note the knee in the torque at max power. That's where the controller quits restricting torque (amps) and lets back emf take over. If the controller didn't restrict current to the left of the knee, it would rise as steeply as it falls to the right of the knee, burning out the motor very quickly at low rpms.
ats how fomoco
A flat torque curve seems to be a feature of mid drive controllers. With a gearshift, a motor doesn't need extra torque to reach an efficient operating speed.
with the proper controller an electric motor can serve as a variable transmission of sorts,i think thats how fomoco's mild hybrid system works in the escape and maverick( ford calls it a cvt i guess it is of sorts) i never considered an electromotive a hybrid,merely a compounded unit with an electric motor for a transmission and torque multiplier( study this a bit and you will see how" "an ant can move a rubber tree plant".still using diesel fuel as the energy source. funny factoid, years ago i suggested to cummins to make a nice gasoline engine,guess what ,now they are doing it,with a 6.7 litre version that can burn diesel,hydrogen and wait for it gasoline! basically requiring changes to the cylinder head, even the gas version is a torque monster with up tp 600#ft of torque( basically i believe hydrogen to be a "flash in the pan")
 
Last edited:
I've worked with a lot of brushed permanent magnet DC motors as a hobbyist. Those torque and power curves are pretty accurate for real-world motors of this type — including those with internal gearing. Peak torque and no mechanical power at the shaft at 0 RPM. No useable torque or power at no-load shaft speed (NLS). And peak mechanical power and ~50% of stalled torque at ~50% of NLS.

Allowing for controller-induced distortions, brushless DC motors seem to follow similar curves.
they are in a word"simply amazing"
 
I find gear inches very useful
Yeah there's nothing wrong with knowing what they mean. Especially as an academic exercise. But for comprehensive results, the tools we have available to us now are better suited to giving me a bigger picture at a glance.

Here's an example I just went thru over the last couple of days on my Big Fat Dummy. 36T front chainring and an 11-46T rear cluster. Because of the 2XL 5.05" tires I just put on, I have lost my two biggest cogs (the biggest one was already gone with the XL tires I had). This is an 11s so I am down to 9 speeds which is still good. Subtracting the two big cogs, this is what the bike's behavior is like.

ScrnShot_04-04-24_11.14 AM.JPG


So, that behemoth of a bike is still quite capable of being pedaled to 24-25 mph, and it should be throttleable to 26 or 28. The 36T largest cog in the back gives me 6 mph in the ballpark of my preferred cadence, which is about 70. I can probably get it up to 7-ish which is OK on a super steep road, and on the fast side for when the bike is really challenged in the woods where oftentimes there is no trail at all and I am going overland. So... room to improve at the low end. So what happens if I take a step up and change to a 11-51T cluster, where the biggest usable cog is still 3rd from the top, increasing to 39T?

ScrnShot_04-04-24_11.06 AM.JPG

No change on the high end of course, and on the low end we're closer to 4-6 mph, which is a little more like it on an unimproved hillside or forest floor, loaded with firewood in the back. But thats still a little fast, and riding the bike after the change, its working pretty hard on that lowest gear on the steepest stuff I can test it on. A mid drive is at its best when its never bogging. So... What if I went to the lowest front chainring I can put on this bike: A Lekkie 28T?

ScrnShot_04-04-24_11.08 AM.JPG


I've lost some of my top end this time and realistically this is an 18 mph street bike on flat pavement. Maybe 22 on throttle. Thats fine. More importantly at the super low end, when I need torque the most, I'm given what amounts to a wider available power band, both for pedaling and for throttling. Heck... with 4 36 paks of soda on the bike (about 125 lbs) on pavement... 8 mph is too much. Going 4-6 on forest floor is plenty.

So that told me to spend the $75 on the 28T cog and hopefully it will be here soon.

Fussing with gear inches just doesn't give a big picture like this. Again... nothing wrong with using them and knowing them but for me their use is no longer practical.
 
Last edited:
For those who have ridden up hills on both a hub and a mid drive, how do they compare in terms of how easy and quick they are to make it up the hill? I have a 750W geared rear hub with (IIRC) 90 Nm torque, and torque sensor at the crank. Thinking of getting a Bosch mid drive with 250W, 65 Nm torque. Assuming the same gear inches for the gearing (and let's suppose we use the peak PAS since it's a really steep hill), which one will pedal easier up the hill? TIA. Mainly I just want to make sure I don't buy the mid drive and then regret it, which I would do if it made life harder on the inclines.

I enjoy bicycling, but if I wanted to work my tail off during the climbs 😝 I'd just ride an acoustic!
Mid drive any day of the week with decent gearing
 
Fussing with gear inches just doesn't give a big picture like this. Again... nothing wrong with using them and knowing them but for me their use is no longer practical.
You have to count and input the number of teeth on each of 10 sprockets. I just count revolutions. You have to input the rim diameter and tire width. I just measure the height of the axle.

If I count chainwheel teeth, a spreadsheet can show the cassette teeth in each speed without the fuss of counting all those sprocket teeth.

Circadian rhythm has a big effect on my cadence, which I don't want to count with a stopwatch. If I sometimes jot down a gear and speed, a spreadsheet can use gear inches to generate a list of recorded cadences. Then gear inches can be used for a spreadsheet with a potentially useful speed range for each gear. I think a little picture of 14 speeds is better than a big picture of 117 cadences.
 
You have to count and input the number of teeth on each of 10 sprockets. I just count revolutions. You have to input the rim diameter and tire width. I just measure the height of the axle.

If I count chainwheel teeth, a spreadsheet can show the cassette teeth in each speed without the fuss of counting all those sprocket teeth.
Many ways to skin this cat. All I really to need to tweak an existing drivetrain for my knees and riding conditions are the teeth on the chainring and the largest and smallest cassette cogs. All that's known from readily available specs. No counting involved.

Once I calculate the existing top and bottom gear-inches, I do many varied test rides with those 2 figures in mind. If the bottom gear isn't low enough, or the top isn't high enough, I can then make reasonable guesses as to the top and bottom gear-inches to try next.

If you're not too picky about cadence, you could probably get by with pedal feel in the testing phase. But my knees are very picky, and a real-time cadence readout on the handlebars helps me know just what they'll tolerate. I use a cheap Bluetooth sensor strapped to my left crank. RideWithGPS on my phone provides the readout.

Back home, I put the guesses into my gearing spreadsheet and predict the top and bottom speeds they'd give at acceptable cadences. The tables @m@Robertson linked would also work well here. This step prevents glaring errors, but as he pointed out, you still have to confirm in the saddle.

As for the cogs in between, I've been happy to let Shimano space them. From the online cassette data I've checked, they do it pretty much exponentially to give an evenly spaced feel at the pedals. Within rounding error, that means a 16% jump in teeth from one cog to the next larger on my 11-42t Deore cassette.
 
If you gear a bike like a tractor it will clime any hill easily able it very slowly. That is where a transmission comes int play.
 
You have to count and input the number of teeth on each of 10 sprockets.
No you don't. You just cut and paste from the specs. Since the exercise described is shopping for clusters you'll already have them in front of you. Like this:

I just count revolutions. You have to input the rim diameter and tire width. I just measure the height of the axle.
I click on "26" and 2.0" from the dropdowns on the page (I will also say I have to click Enter so you don't have to make another post saying I left out that additional step).

Once again like earlier in this very same thread, you are bending over backwards to make things up that you pretend are significant so you can start and then continue a meaningless argument.
I think a little picture of 14 speeds is better than a big picture of 117 cadences.
Thats nice. I think everyone else knows implicitly they can ignore the stuff in those tables that isn't relevant, like most all of the boxes that show cadences that are not humanly possible (or so low they are undesirable). I wouldn't try to reach 26 mph on the big cog so I don't have to burden my dim intellect with wondering what the consequences of a cadence of 383 are.

But by all means, as I already took great pains to say more than once, there's nothing wrong with using these if thats what you want.
 
As long as I'm noting results-oriented stuff here, this is the Sheldon Brown gear-inch calculator I used for years before leaving them behind.


and BikeCalc has one too.


You will have to type into the form or pick from some drop-downs, and press Enter.
 
Back