MartsEbike
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- United Kingdom
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- Dunstable
All fair points!
Its the early hours of the morning in the UK, I shouldn't be awake myself
, I'm sure @Foffer will be back soon Heavy rider, very steep hills, not too expensive! Help please
- Thread starter Foffer
- Start date
Its the early hours of the morning in the UK, I shouldn't be awake myself
, I'm sure @Foffer will be back soon Comfortably Numb
Well-Known Member
....or Ignore in the name of sanity. CN
m@Robertson
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- USA
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.
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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
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- USA
I like this one for telling me what gears to plug in to a bike vs. my intended use. This screen in particular.
Bicycle Gear Speed Cadence Table | BikeCalc
Calculate cycling speeds at a specified cadence given chainring, sprocket, tire and wheel sizes.
www.bikecalc.com
m@Robertson
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- USA
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):
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
From your own reference (page 3):
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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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
Gravel e-biker
- Region
- Europe
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- Mazovia, PL
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
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- USA
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
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:
EDITEDIT: A third source:
How to find the perfect gear ratios for your MTB drivetrain
For many riders, working out gear ratios seems like a Gordian knot; there continues to be a fear of not having enough gear range when switching over to a 1x drivetrain. With a little mental arithmetic, however, you’ll quickly be able to bring light into the dark. We’ll show you, step by step...
enduro-mtb.com
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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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.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
Electric Bikes | E-Bikes | Halfords UK
Shop our Electric Mountain Bikes with interest free finance. We stock an excellent range of e-bikes suitable for all budgets, have it built and delivered.www.halfords.com
There's a few others on that link, all mid-drive bikes.
PedalUma
Well-Known Member
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- USA
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- Petaluma, CA
27.5 Inch Electric Mountain Bike E-ST 520 - Grey/Yellow ROCKRIDER | Decathlon
With the E-ST 520 electric mountain bike, you can tackle any climb. With the help of its built-in motor (70 Nm torque), even the most difficult of…
Brose T motor it says. Looks nice.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.27.5 Inch Electric Mountain Bike E-ST 520 - Grey/Yellow ROCKRIDER | Decathlon
With the E-ST 520 electric mountain bike, you can tackle any climb. With the help of its built-in motor (70 Nm torque), even the most difficult of…www.decathlon.co.uk
MartsEbike
Well-Known Member
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- United Kingdom
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- Dunstable
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...
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:
How to find the perfect gear ratios for your MTB drivetrain
For many riders, working out gear ratios seems like a Gordian knot; there continues to be a fear of not having enough gear range when switching over to a 1x drivetrain. With a little mental arithmetic, however, you’ll quickly be able to bring light into the dark. We’ll show you, step by step...
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.
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.
m@Robertson
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- USA
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
Thank again
Foffer
New Member
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- United Kingdom
Thanks, I really like the look of the DecathlonWhat 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.27.5 Inch Electric Mountain Bike E-ST 520 - Grey/Yellow ROCKRIDER | Decathlon
With the E-ST 520 electric mountain bike, you can tackle any climb. With the help of its built-in motor (70 Nm torque), even the most difficult of…
PedalUma
Well-Known Member
- Region
- USA
- City
- Petaluma, CA
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.
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