Heavy rider, very steep hills, not too expensive! Help please

MartsEbike

Well-Known Member
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Other
Other factors are strong enough wheels and height for 6"3". For weight the wheels are the most important factor, frames not so much. Is he mostly legs or mostly torso for height? Something like a Dutch Bikes would be strong and large.
All fair points!

Its the early hours of the morning in the UK, I shouldn't be awake myself :rolleyes:, I'm sure @Foffer will be back soon :)
 

m@Robertson

Well-Known Member
Region
USA
My geared hub motor climbs 15% grades with gross load 330 lb, no problem. Will start from a dead stop on that grade and that load with no pedaling without difficulty. Where geared hub motors reach their limits are lugging up long grades of an hour duration. They will overheat in the Rockies or Sierra mountains with a heavy rider. There is not one grade in England long enough to overheat a geared hub motor like my Mac12T. Pennines maybe but the grades there are hiking paths and I don't believe powered bikes are allowed on them.
Don't know how efficient UK customs is in keeping out 1000 W geared hub motors. I'm sure you can't buy a bicycle with more than the piddling 250 W useful in downtown London. Nobody in UK lives anywhere else, right? Stupid laws for city dwellers frightened of aggressive pizza deliverymen on sidewalks.
BIg myth about gearing on bikes is that it multiplies torque. That only happens on mountain bikes with rear sprockets the size of dinner plates, 36 or 42 teeth. $$$$ bikes. 99.9% of bikes sold have NO torque multiplication. Only speed multiplication. I can pedal my yubabike with 80 lb groceries up the 15% grade without power, using the 32:32 lowest range. Or even 32:28. Bike was designed for women with 2 children in car seats pedaling around hills of San Francisco without power.

I don't know what to say. thats just completely the opposite of any reality I have experienced, or heard other builders put forward. I started building geared hub bikes and only switched to mids when their weakness in hills became obvious by taking them up steep hills. Like this one.


The OP has already experienced the limitations of a hub firsthand. The fact that the hub drive is entirely independent of the drivetrain and provides no assistance thru it is a given. The fact that gears exist to more easily get up a hill is a given. The fact a mid drive provides power thru the drivetrain (gears) is a given.

And bike gears do multiply torque. Thats the nature of gears and what they do. Its called a 'mechanical advantage' and its the point of putting them on a bike. I don't know where to go with a statement like that other than to point to reference material.


Skip to page 3 for explanation with math:
 

m@Robertson

Well-Known Member
Region
USA
BIg myth about gearing on bikes is that it multiplies torque. That only happens on mountain bikes with rear sprockets the size of dinner plates, 36 or 42 teeth. $$$$ bikes. 99.9% of bikes sold have NO torque multiplication.
OK so to back up my comments on this being completely wrong, lets do the math by hand and show our work. If we figure wheel torque on a mid drive (or any pair of gears) by hand, the formula is

Motor Torque * Gear Ratio = Wheel Torque

Lets pick 80 Nm and ignore the fact that the geared hub is only capable of this momentarily (Bafang G060) and the mid drive can sustain this for longer periods (Bafang BBS02 in its 250w version) until it basically blows up. The purpose here is to demonstrate wheel torque is always multiplied by gears, not analyze the motor's efficacy (that can be done on the Grin Motor Simulator quite nicely, BTW, but its not easy to set up).

My front chainring is a 36T, which is an actual aftermarket ring available from Lekkie, and right in the ballpark for a typical emtb chainring size. You'll see why I picked it in a minute. For the singlespeed hub, gear ratio is 1:1 since the sprockets are irrelevant and power is delivered thru the axle. So

80Nm x 1 = 80Nm

No surprise there. And remember we're not commenting on whether that will work for the use case. We're figuring out if torque multiplication is a myth. Now for the mid drive: We have a 36T in front, lets use a Shimano HG-400-9 that I use on both my hub commuter bike and its mid-drive hill-climbing successor: whose cogs are 12-14-16-18-21-24-28-32-36. So our gear ratios are:

12T: 3.00 (36T / 12T)
14T: 2.57 (36T / 14T)
16T: 2.25 (etc. etc.)
18T: 2.00
21T: 1.71
24T: 1.50
28T: 1.29
32T: 1.13
36T: 1.00


Using the formula for wheel torque, the torque numbers for each gear are

12T: 80Nm * 3.00 = 240Nm
14T: 80Nm * 2.57 = 206Nm
16T: 80Nm * 2.25 = 180Nm
18T: 80Nm * 2.00 = 160Nm
21T: 80Nm * 1.71 = 137Nm
24T: 80Nm * 1.50 = 120Nm
28T: 80Nm * 1.29 = 103Nm
32T: 80Nm * 1.13 = 90Nm
36T: 80Nm * 1.00 = 80Nm


So... torque multiplication exists on every gear, and the multiplication is not only for sprockets the 'size of dinner plates'. In fact torque multiplication works in the opposite direction: The big cogs have less multiplication, which is what makes them easier to muscle thru when pedaling. Which makes them easier for the motor to turn fast, which makes you go up the hill more efficiently without making the mid drive work harder than its able, bog down and create heat vs. creating motion.

And you can see why I picked a 36T front ring - thats a 1:1 gear ratio. So now lets say you shift from your 36T cog to your 24T cog. You've multiplied your rated torque (whatever the motor's true number is) by 50%. If the motor is strong enough to spin that cog, you've got your mechanical advantage. Thats why mid drives are used on bikes that live for hills.
 
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linklemming

Well-Known Member
You seem to have the torque multiplication backwards.

From your own reference (page 3):
gearing.PNG

So for an 80nm mid-drive with a 36t front chainring(motor shaft) and rear 12t(wheel axle)

WheelTorque = 80x(12/36) = 26.67 (yes I realize you are using nm and the pdf is using newtons)

As for the semantics of multiplier, you are technically correct since the equation has multiplication in it.

That being said, the term 'torque multiplier' is typically used to describe torque being increased
 
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Johnny

Well-Known Member
OK so to back up my comments on this being completely wrong, lets do the math by hand and show our work. If we figure wheel torque on a mid drive (or any pair of gears) by hand, the formula is

Motor Torque * Gear Ratio = Wheel Torque

Lets pick 80 Nm and ignore the fact that the geared hub is only capable of this momentarily (Bafang G060) and the mid drive can sustain this for longer periods (Bafang BBS02 in its 250w version) until it basically blows up. The purpose here is to demonstrate wheel torque is always multiplied by gears, not analyze the motor's efficacy (that can be done on the Grin Motor Simulator quite nicely, BTW, but its not easy to set up).

My front chainring is a 36T, which is an actual aftermarket ring available from Lekkie, and right in the ballpark for a typical emtb chainring size. You'll see why I picked it in a minute. For the singlespeed hub, gear ratio is 1:1 since the sprockets are irrelevant and power is delivered thru the axle. So

80Nm x 1 = 80Nm

No surprise there. And remember we're not commenting on whether that will work for the use case. We're figuring out if torque multiplication is a myth. Now for the mid drive: We have a 36T in front, lets use a Shimano HG-400-9 that I use on both my hub commuter bike and its mid-drive hill-climbing successor: whose cogs are 12-14-16-18-21-24-28-32-36. So our gear ratios are:

12T: 3.00 (36T / 12T)
14T: 2.57 (36T / 14T)
16T: 2.25 (etc. etc.)
18T: 2.00
21T: 1.71
24T: 1.50
28T: 1.29
32T: 1.13
36T: 1.00


Using the formula for wheel torque, the torque numbers for each gear are

12T: 80Nm * 3.00 = 240Nm
14T: 80Nm * 2.57 = 206Nm
16T: 80Nm * 2.25 = 180Nm
18T: 80Nm * 2.00 = 160Nm
21T: 80Nm * 1.71 = 137Nm
24T: 80Nm * 1.50 = 120Nm
28T: 80Nm * 1.29 = 103Nm
32T: 80Nm * 1.13 = 90Nm
36T: 80Nm * 1.00 = 80Nm


So... torque multiplication exists on every gear, and the multiplication is not only for sprockets the 'size of dinner plates'. In fact torque multiplication works in the opposite direction: The big cogs have less multiplication, which is what makes them easier to muscle thru when pedaling. Which makes them easier for the motor to turn fast, which makes you go up the hill more efficiently without making the mid drive work harder than its able, bog down and create heat vs. creating motion.

And you can see why I picked a 36T front ring - thats a 1:1 gear ratio. So now lets say you shift from your 36T cog to your 24T cog. You've multiplied your rated torque (whatever the motor's true number is) by 50%. If the motor is strong enough to spin that cog, you've got your mechanical advantage. Thats why mid drives are used on bikes that live for hills.

We can easily derive the needed equations, I hope this clears things up.

If Power was perfectly preserved(assuming no drivetrain losses),

(Torque at the crank) x (rotational speed of the chainring) = (Torque at the wheel) x (rotational speed of the wheel).

=> (Torque at the crank) x (rotational speed of the chainring)/(rotational speed of the wheel) = (Torque at the wheel)

The chain travels the same distance at the cog and chainring hence you have a second equation:

(rotational speed of the chainring) x (Number of teeth on the chainring) = (rotational speed of the wheel) x (number of teeth at the cog that the chain sits on the cassette)

Combine them together:

(rotational speed of the chainring)/(rotational speed of the wheel) = (number of teeth at the cog that the chain sits on the cassette)/ (Number of teeth on the chainring)

Hence

(Torque at the crank) x (number of teeth at the cog that the chain sits on the cassette)/ (Number of teeth on the chainring) = Torque at the wheel


Now an example:

Suppose you generate 85nm at the crank, chainring has 44T and you are on the 11T cog on the cassette:

Torque generated at the wheel = 85x11/44= 21.25 nm


Of course this is assuming no drivetrain losses, expect to have %3-8 ( a bit more on the smallest cog) losses. In that case you can just multiply your result with %92-%97 to get the torque after losses.


In your examples it is reversed. The correct calculation should be:

At 12t you will have 80/3 = 26.6nm and so on.


Edit: Seems linklemming already supplied a nice pdf (My only problem is the pdf erroneously uses newton instead of newton-meter as the unit of measurement of torque).
 
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Stefan Mikes

Well-Known Member
Region
Europe
City
Brwinów (PL)
Love these zero to hero posters with one bike experience.
I own three, and live in Europe. Yet I won't take part in this thread, as "not too expensive" (but street legal) eliminates my need to be here. Good/legal doesn't come cheap. And I wouldn't indeed try really climbing on my 250 W hub-drive motor e-bike. I own a Specialized Vado and a Giant e-MTB that are excellent climbers. Neither of them came cheap.

Art Deco, retiredNH, and MatsEbike said wise things. Especially Marts as a Briton can give practical advices.
 

m@Robertson

Well-Known Member
Region
USA
You seem to have the torque multiplication backwards.

From your own reference (page 3):
View attachment 90485
So for an 80nm mid-drive with a 36t front chainring(motor shaft) and rear 12t(wheel axle)

WheelTorque = 80x(12/36) = 26.67 (yes I realize you are using nm and the pdf is using newtons)

As for the semantics of multiplier, you are technically correct since the equation has multiplication in it.

That being said, the term 'torque multiplier' is typically used to describe torque being increased

Are you sure about that? I used the second formula since gear ratio was easy to obtain and lets you check my method with an outside source, which I linked.

So if

gearRatios.png


and I use the formula exactly as its written:

WheelTorque=MotorTorque×GR

Then the numbers I posted remain correct:
240 = 80 * 3 (12T)
80 = 80 * 1.00 (36T)

And so on. Where did I go wrong given the above? Is the source wrong?

EDIT: Here's another one. Displays the same result using different terms:

gearRatios2.png


EDITEDIT: A third source:

Let’s say you’ve got a Shimano XT 11-46 cassette and a 32T chainring. With this configuration, the lowest gear has a ratio of 32/46 = 0.696 and the highest gear has a ratio of 32/11 = 2.909.
The method I illustrated and the other sources all use Front Gear Divided By Back Gear. So I'm not seeing a mistake in the math or the method here.

Or is the formula WheelTorque=MotorTorque×GR whats wrong? It doesn't seem to be on its face as a 1:1 gear ratio of the inner cog *should* have less torque than the 3:1 of the 12T cog
 
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Rás Cnoic

Well-Known Member
Halfords are pretty good for "value for money" bikes, they might not be the latest and greatest in every way but they're normally pretty rock solid, and have a decent warranty should anything go wrong. Plus they have stores all over the country so you maybe able to view before you purchase.

The Raleigh Felix+ comes with the bosch activeline plus motor... and is similar in style to your current bike. £2149


There's a few others on that link, all mid-drive bikes.
Halfords is a good shout, carrera? I think is their popular e bike model. Also Decathlon, very good e bikes at around the same price as Halfords. They do seem to sell out but equally re stock - you might get lucky. Also ask if they'll swap out the rear cassette for something bigger for the steep hills you mentioned. Both reliable with warranties and back up etc.
 

PedalUma

Well-Known Member
Region
USA
Halfords is a good shout, carrera? I think is their popular e bike model. Also Decathlon, very good e bikes at around the same price as Halfords. They do seem to sell out but equally re stock - you might get lucky. Also ask if they'll swap out the rear cassette for something bigger for the steep hills you mentioned. Both reliable with warranties and back up etc.
What motor does it have? It does come in XL and has a mountain range of gears. A comfy saddle and stem riser are in order. The price comes in on budget. Good job spotting it.
 

Rás Cnoic

Well-Known Member
What motor does it have? It does come in XL and has a mountain range of gears. A comfy saddle and stem riser are in order. The price comes in on budget. Good job spotting it.
Brose T motor it says. Looks nice.
 

MartsEbike

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Region
Other
Halfords is a good shout, carrera? I think is their popular e bike model. Also Decathlon, very good e bikes at around the same price as Halfords. They do seem to sell out but equally re stock - you might get lucky. Also ask if they'll swap out the rear cassette for something bigger for the steep hills you mentioned. Both reliable with warranties and back up etc.
Yeah Decathlon is another good shop for bargains, I forgot about them! Although like you say its much of it is "while stocks last" so you have to be lucky sometimes... But certainly worth checking out. Good shout 👍

Halfords Carrera line of bikes are great value IMO, but they've also been selling these VooDoo branded emtb's (Shimano Steps motor) that have had some favourable reviews, and are well priced too. Maybe worth shortlisting.

I think the OP maybe looking for a Step-Through style bike though...
 

Johnny

Well-Known Member
Are you sure about that? I used the second formula since gear ratio was easy to obtain and lets you check my method with an outside source, which I linked.

So if

View attachment 90502

and I use the formula exactly as its written:

WheelTorque=MotorTorque×GR

Then the numbers I posted remain correct:
240 = 80 * 3 (12T)
80 = 80 * 1.00 (36T)

And so on. Where did I go wrong given the above? Is the source wrong?

EDIT: Here's another one. Displays the same result using different terms:

View attachment 90505

EDITEDIT: A third source:


The method I illustrated and the other sources all use Front Gear Divided By Back Gear. So I'm not seeing a mistake in the math or the method here.

Or is the formula WheelTorque=MotorTorque×GR whats wrong? It doesn't seem to be on its face as a 1:1 gear ratio of the inner cog *should* have less torque than the 3:1 of the 12T cog

Linklemming's formula is correct. You are taking the ratio in the wrong direction.

In my post I have derived the formula in case you are interested.

Your driver is your chainring and the cog on the wheel is driven.
 

drewberz

Active Member
That being said, the term 'torque multiplier' is typically used to describe torque being increased

I think this is the source of confusion/disagreement. Perhaps call it a torque divider for <1, and a torque multiplier for >1 (Cog teeth/Chainring teeth)? And before anyone points it out, yes you can multiply the inverse to divide.

Per indianajo's point, my own mid-drive has a stock setup with a 42T chainring and largest cog is 42T, so no torque multiplication takes place at that step of the drive.
 

PedalUma

Well-Known Member
Region
USA
Are you implying that if I had two fifty-cent pieces I would then be able to multiply them together? 🤣
 
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m@Robertson

Well-Known Member
Region
USA
Linklemming's formula is correct. You are taking the ratio in the wrong direction.

In my post I have derived the formula in case you are interested.

Your driver is your chainring and the cog on the wheel is driven.
OK thx. It sounds like the gear ratios in the tables are correct, and torque delivered does change with every single cog change, but that formula WheelTorque=MotorTorque×GR does not work to find the specific output from gear to gear as GR as defined in the formula is not the same as the GR used in the BikeCalc etc. calculators. Thats where I went wrong.
 

Foffer

New Member
Region
United Kingdom
Thanks to everyone for the advice. I have now realised that probably due to the pandemic e-bike sales here in the UK have gone through the roof and there is a lot of nil stock! However, on the other side of the coin, it looks like I'll get a decent price on eBay for my Pendleton. I think I will be going for a Bosch mid drive, maybe full suspension as well so I can go a bit more off-road! I now realise that I will probably have to spend more than I thought I would, and I'll definitely insist on a proper test ride before I buy.

Thank again
 

Foffer

New Member
Region
United Kingdom
What motor does it have? It does come in XL and has a mountain range of gears. A comfy saddle and stem riser are in order. The price comes in on budget. Good job spotting it.
Thanks, I really like the look of the Decathlon
 

PedalUma

Well-Known Member
Region
USA
Thanks, I really like the look of the Decathlon
I would love to see an image of a cycling group of kitted-out riders, as the camera zooms out we realize they on an open flat bed lorry riding through the rolling hills on Pelotons. 🤣
That would be very Python with violins and French horns playing. But after the lovely part they would then need to be chased or set upon a quest.
In the US Peloton investing $400,000,000 in a new Ohio plant. I wish they would retool to produce electric bikes for the same money.
I have had fun as part of the team helping you. Good discussion everyone.