Simple Gear Ratio calculation

[swbluto]

What's the gear ratio of the following picture?



My calculation may be wrong, but I think it's about 28. Is that actually not attainable in practice in the real world with bicycle chain for one reason or another? I'm thinking the highest torque the motor is going to put out is 10 NM (The motor is the small circle at the top), so I'm guessing the wheel will see 280 NM. The motor could put out more, but I have a feeling I'll be limiting it to keep everything within a "safe" rating.

I need to achieve a gear ratio of at least 16 on a 26-inch wheel for hill climbing.

 

[boostjuice]

(44/14) x (40/14) = 8.97:1 reduction

 

[swbluto]

(44/14) x (40/14) = 8.97:1 reduction

I really hope you're wrong.

But, I doubt my answer more than yours.

Now that I thought it through from a torque and RPM perspective, it seems like your answer is more likely to be correct. That kind of sucks. I guess I'll need a 60 tooth tall chain ring, a 12T motor sprocket, a 12t small chainring, and a... 50 tooth rear chain-ring? I have no idea how tall they get.

(60/12)*(50/12) = 20.8 That'd give me the gear ratio I'm seeking. I doubt the availability of 50T rear rings, though. I'd need a rear of at least 39T to get a gear ratio of 16.

EDIT: Shoot. It looks like the "most important gear" is the front chainring, but I can't find one that's even close to 12T. The smallest I've seen online is 22T. The largest "cheap" front chain ring was 56T (Otherwise, it was over a 100 and had questionable durability.). And the largest rear "chainring"/cassette was 34 teeth. That's definitely not going to be enough. Those numbers imply a largest "practical" ratio of (56/11)*(34/22) = 7.86 using a 11t motor sprocket

 

[REdiculous]

I rounded the numbers a little and got 8.94:1..he's right.

16:1 seems like a lot..what's the motor rpm? later

EDIT; 16t->48t, 16t->48t is 9:1 so 16t->60t, 16t->60t is 14:1...close.

 

[boostjuice]

For road bikes, the larger of the two front chainrings is often 52T (most often Shimano 5 x 130mm BCD, but sometimes campagnolo 5 x 135mm BCD), so no problems finding those cheap. You'll find them as off the shelf items up to about 60T. Recumpences Diskbrake>chainring adaptor is suitably sized with a 5 x 130mm BCD pattern should you want a non-at-wheel freewheeling LHD setup.

http://www.endless-sphere.com/forums/viewtopic.php?f=28&t=11690

Problems arise if you want >48T sizes in the various MTB BCD's (94mm, 100mm, 104mm, 110mm)

Not cheap, but this lot will make whatever you want in any BCD if your happy with 1/2" pitch bicycle chain.
http://www.cycleunderground.com.au/chainringdesigns.htm (They can make chainrings in tooth counts >56T despite what the webpage says)

Heres a USA based chainring company with competetive pricing, up to 60T in 130BCD & 110BCD
http://www.vueltausa.com/products/chainrings/flat-chainrings.htm

 

[RWP]

Maybe this will help...

 

[MitchJi]

Hi,

I guess I'll need a 60 tooth tall chain ring, a 12T motor sprocket, a 12t small chainring, and a... 50 tooth rear chain-ring? I have no idea how tall they get.

(60/12)*(50/12) = 20.8 That'd give me the gear ratio I'm seeking. I doubt the availability of 50T rear rings, though. I'd need a rear of at least 39T to get a gear ratio of 16.

EDIT: Shoot. It looks like the "most important gear" is the front chainring, but I can't find one that's even close to 12T.

A 12t motor sprocket is going to be noisy.

Do you plan to pedal because if you do a 12t chainring to a 39t rear won't work very well.

Why don't you use #25 or #219 for the first stage, something like 14t/78t (78t #219 is about 7.6" diameter) should work.

 

[swbluto]

Why don't you use #25 or #219 for the first stage, something like 14t/78t (78t #219 is about 7.6" diameter) should work.

I'm reviewing multiple possibilities now, and the current one seems to completely isolate the motor on the left from the pedaling on the right. So, in that scenario, 12t to 39t probably wouldn't be an issue.

Something like a 14t to 78t might be nice. What are the particular advantages of #25 and #219 as opposed to bicycle chain? Is it quieter? I have some #25 laying around, but I associated them with small scooters, so I don't really know if they can handle the force. But now that I think of it, the first stage won't have as much force as it will speed, so maybe it won't be an issue. I'm guessing it'll have 100 to 300 newtons of force, and bicycle chain is rated at around 12,000.

If I want quietness, I'm probably going to want to slow down the chain speed. Since the fastest chain speed will be on the motor itself, I'll need to slow down the motor itself by going with a lower kV. I'm not sure what the best kV will be since it seems to require significantly more volts to get the desired performance, while keeping motor heating down when going with a lower kV. I have to rewind my 6 kW motor, so I get to choose the kV.

 

[MitchJi]

Something like a 14t to 78t might be nice. What are the particular advantages of #25 and #219 as opposed to bicycle chain? Is it quieter? I have some #25 laying around, but I associated them with small scooters, so I don't really know if they can handle the force.

The main advantage is smaller pitch:

  BICYCLE CHAIN    .5    1/2      inch Pitch (12.7mm)
  #35 chain        .375  3/8th    inch Pitch (9.525mm)
  #219             .306  2.45/8th inch Pitch (7.7724mm)
  #25 Chain        .25    1/4     inch Pitch (6.35mm)

Matt uses "extra heavy-duty" #25 for his second stage and his first stage with the 3220's (too much for 5mm pitch 15mm width belt). He said its quieter than #219 and while its not as quiet as a belt its OK in his opinion when using at least a 14t drive sprocket (even with very high rpm primary drives). D's #219 second stage didn't sound too noisy with an 11t drive sprocket.

http://endless-sphere.com/forums/viewtopic.php?f=28&t=15514&p=230744&hilit=+scooter#p230744

I run extra heavy-duty #25 chain from scooter parts.com. That chain is freaking DIRT CHEAP! I beat the crap out of that chain and in over 1,000 miles, have not worn one out, yet. But, it is so cheap, who cares!

Matt

He also said:

You would be surprised how long that #25 chain lasts. My recumbent has over 1,000 miles on it with the same #25 chain.

The PK Ripper has 500 miles of HARD abuse on it without any issues, no stretch, no tooth wear.

I just use light oil. I also neglect my recumbent chain because it is hard to get to. I lube it when the links start to bind. Even with that neglect, the chain is fine.

Plus, this chain is so inexpensive, it is no biggie to replace it every couple years or so.

Matt's #25 chain does have some great advantages though in sprocket size being available for dirt cheap everywhere. It's also pretty quiet. #219 is another fine pitched chain, and holds like 5-10x what #25 can handle, but sprocket options aren't as easy to find. Lots of advantages and disadvantages of various options.

If I want quietness, I'm probably going to want to slow down the chain speed.

Using a belt 1st stage will be best for quietness. Hard to get more than about 4:1 reduction.

 

[swbluto]

That's true about a belt drive being best for quietness. But, regular 5-15 HTD belts only have like a torque limit of 5 NM with a "tooth count" of 15 on the motor's timing pulley and as my experience suggests, the belt slips and breaks if you exceed that. So I'm just going to have to make a chain as quiet as possible. As long as it's not as noisy as a typical 2 stroke, I would be happy with it. If I really wanted quieted propulsion for "quiet areas" where higher speed isn't a priority, I'd probably just slap on a tiny front-wheel hub motor.

 

[swbluto]

Ok, so I found some ratings at wikipedia at http://en.wikipedia.org/wiki/Roller_chain.

#25 chain has a working load rating of 140 pounds.
Since I expect about ~200 NM at the backwheel(At max) and the distance from the center of 60 tooth sprocket to its edge is about 3 inches (.0762 meters), I'd expect the chain to carry about 200 newton-meters / .0762 meters = 2624 newtons. That's about 544 pounds. It looks like I'll need a larger chain, and it looks like the #40 / 1/2inch variety would be more appropriate according to the chart. Hey, that's a standard bicycle chain - or is it? ...

So maybe a 90/14 reduction on the first one (7.5), and then a 24 / 56 reduction on the second stage. That assumes that a 56 could clear the chainstays on a disc-brake mount. If I wanted at least a gear ratio of 10, it looks like I'd need a back ring size of at least 38.

Now let's see if the first stage could use a #25 chain. A 14 tooth would have a radius of approximately 1.7 cm. If the motor's torque was 20 NM, that'd imply first stage tension of 20/.017 = 117 newtons = 26.3 pounds. That's within rating.

 

[boostjuice]

Ok, so I found some ratings at wikipedia at http://en.wikipedia.org/wiki/Roller_chain.

#25 chain has a working load rating of 140 pounds.
Since I expect about ~200 NM at the backwheel(At max) and the distance from the center of 60 tooth sprocket to its edge is about 3 inches (.0762 meters), I'd expect the chain to carry about 200 newton-meters / .0762 meters = 2624 newtons. That's about 544 pounds. It looks like I'll need a larger chain, and it looks like the #40 / 1/2inch variety would be more appropriate according to the chart. Hey, that's a standard bicycle chain - or is it? ...

So maybe a 90/14 reduction on the first one (7.5), and then a 24 / 56 reduction on the second stage. That assumes that a 56 could clear the chainstays on a disc-brake mount. If I wanted at least a gear ratio of 10, it looks like I'd need a back ring size of at least 38.

Now let's see if the first stage could use a #25 chain. A 14 tooth would have a radius of approximately 1.7 cm. If the motor's torque was 20 NM, that'd imply first stage tension of 20/.017 = 117 newtons = 26.3 pounds. That's within rating.

Yes #40 is bicycle chain, and it would be silly to use it for your first reduction stage as it is overkill strength wise as well as overly noisy at high speed.

If you follow Miles' suggestion of using a Pawl-removed freewheel as a jack-shaft bearing mounted to your left side crank (actually a RHS freewheel crank mounted on the LHS), then there is another advantage of using #25 chain for your first reduction stage. Most large tooth count #25 sprockets suit small BCD's as they are often designed to be bolted to wheel hubs or freewheels. This means you still have material left close to the sprockets centre for which to drill through and mount directly to the freewheel. Bicycle chain-rings most often have this central material cutaway to save weight as it is unnecessary with large diameter BCD's. Basically it would save you having to make a chain-ring > freewheel adapter plate.

How about this scenario;
First stage reduction; 14T > 90T #25 Chain = 6.43:1 reduction (90T #25 sprocket is only 7-1/4" OD, about the same as a 44T bicycle chainring)
Second stage; 20T > 52T #40 Chain = 2.6:1 reduction
Total reduction = 16.72:1

In order to mount the 90T #25 sprocket directly to the freewheel so as to not interfere with the #40 teeth/chain, you need >= 20T in order to have enough radial distance between the chain wrap path and the bearing/ratchet&pawl housing to mount standoff spacers. A picture describes this best....

Obviously the standoff spacers allow lateral space for the #40 chain to clear the #25 sprocket.

Here's the common 90T #25 sprocket. You would have to remove the welded on threaded cup to use it as described.

 

[amberwolf]

An example of what a #25 chainring looks like mounted to a 16T #40 BMX freewheel, by bolting between the sprocket teeth (opposite of how you'd want to do it, which would actually be like the pic boostjuice shows above):



In my case it's this #25 chainring:


like this:



On yours, it would be spaced away from the actual freewheel sprocket teeth, (presumably an 18T or 20T rather than 16T to give enough space under the tooth tip for the spacers and bolts) far enough for the bike chain to fit on the freewheel teeth.

 

[Miles]

Tensile (Onza) do/did a 20t freewheel. That would be a good one to use, sans pawls.......

I would have thought that a heavy duty BMX chain, run directly on the freewheel teeth, would be strong enough....

http://www.connexchain.com/Bicycle-chains/BMX/1_342.html

 

[John in CR]

TNC has different drive and driven sprockets for #25 chain, and freewheels that bolt to the sprockets. Check here about 1.3 way down the list. http://tncscooters.com/partsdb.php?type=ALL. I've bought stuff from them several times without issue.

John