# Sprockets Figuring out Gear Ratio?

Discussion in 'Transmission / Drivetrain' started by RocketPenguin, Jun 9, 2015.

1. ### RocketPenguinNew Member

All I have been able to find is how to calculate the ratio of two gears, but near to nothing on more. I saw one thread where a guy kinda explained how it's done, involving multiplying one number by another, but i found that very confusing.
Kept looking for a little bit, and either found nothing, calculators that were way too complicated for me, or very vague explanations on how its done.

Could someone care to elaborate/point me in the right direction?
That, and i need to find a variable for such a situation:
I have 6 teeth on my engine sprocket, which goes to a jack shaft that has X amount of teeth. From the jack shaft, i have a sprocket with 13 teeth, which leads to a tire of 24" that has a sprocket with 47 teeth. How many teeth do i need for sprocket X to achieve a ratio of 1:13~1:16 (Or whatever is recommended for a chainsaw bicycle. I heard some say 1:14-1:15, others as low as 1:18, and others as high as 1:10)
Thanks!

2. ### SloggerMember

With 6/24, to 13/47 on a 24" = 14.46/1 drive ratio. X= 24 tooth
With X=22, you'd have a 13.26/1 ratio.
Make X=26, you get 15.67/1.
This is according to the downloadable and cool "ratio calculator" program somewhere on the forum. I kept it.
If your engine could pull 6000 RPM at these ratios, your top speed would be either 27.3, 29.6 or 32.3.
~Regards

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3. ### LR JerryWell-Known Member

Here a few factors need to be known. Engine size and power rating, your weight and primary riding terrain. The larger you are and the steeper the hills and the smaller the engine the greater the reduction will need to be. I'm 250 lbs; there's lots of 20%+ grade hills where I live. The engine is a 33 cc. I use a shift kit. The reduction range is 49.21-18.82:1. Without the lowest reduction there's no way I'd be able to get up the hills here.

To get the ratios you want sprocket x=22-27.

Last edited: Jun 10, 2015
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4. ### RocketPenguinNew Member

Thanks! So there is a calculator somewhere on this forum for it? I'll look around for that. How do you calculate this stuff on paper, in case I change sprockets and need to calculate again without a calculator? The engine I have can pull around 10k to 13k at full throttle.
EDIT: Found the calculator. Thanks!

Last edited: Jun 10, 2015
5. ### RocketPenguinNew Member

I weigh 170lbs, the bike and me in total would be around 200lbs. Depending on where I drive it, I will anything from minor hills all the way to 40° inclines. Probably won't be riding it on those steep hills though. Engine I am using is 42cc, has between 2-4 HP.

Last edited by a moderator: Dec 18, 2015

7. ### The_AlemanActive Member

I have a Huasheng 49CC with a 5:1 4G, SBP shift kit, and a 5-speed Sturmey-Archer (X-RD5)

I've drawn up a couple pics to demonstrate how to use Jim Sitton's ratiocalc program with jackshaft and gears (in this case, an internally geared hub or IGH).

Pic 1 is the basic figuring of overall reduction with the jackshaft.

Pic 2 is the speed with each gear at my Huasheng's HP peak. Since the 5-speed is an IGH, one must use the percentage values of reduction.
In my case, Sturmey-Archer claims my X-RD5 has percentages of 66/75/100/133/160%.

Whether you have an IGH or standard gears with a derailleur, it is not difficult to figure what your ratios are using this program.
IGH reductions are posted by the manufacturer and gear clusters can be manually counted or looked up online.

Hope this helps!

8. ### LR JerryWell-Known Member

You must be planning to do some extreme off roading going up a 40° incline. That's an 89% grade. The two steepest streets in the world are a 37% grade. Which is a 16.65° incline. Your weight and the size of engine will probably need at least an 18:1 reduction. Which means sprocket X will need to be a 30t.

Last edited by a moderator: Dec 18, 2015
9. ### RocketPenguinNew Member

My bad, over estimation. 35° Is probably the steepest I have, everything else is under that.

Last edited by a moderator: Dec 18, 2015
10. ### RocketPenguinNew Member

Kinda confused about your pictures... Mainly 1st step and 2nd step. With a jackshaft, wouldn't I just calculate as the first Drive Gear/Sprocket Teeth being the amount of teeth on the clutch (6), the Driven Gear/Sprocket Teeth being the amount of teeth it leads to on the jackshaft, and the second set of Drive/Driven Gear/Sprocket Teeth being from the jackshaft to the tire?

11. ### LR JerryWell-Known Member

You seem to be confusing degree with grade. A 35° hill would be close to a 78% grade. Still way steeper than any paved street in the world. If you meant 35% grade not likely either. San Fransisco steepest street is a little over a 31% grade. Here in the mountains we have some close to a 30% grade. What you've probably got at best is between a 15-25% grade.

Here is a good way to understand it, say from axle to axle is 45". If you lift the bottom of your front tire 15" off of the ground that's approximately how steep a 33% grade hill would be.

The 18:1 reduction is more of a level ground or no greater than 10% grade hills. If you do have steep hills between 15-25% grades, a 25:1 reduction may be more of what you need meaning a bigger gear on the rear wheel. Of course a shift kit could solve the issues all together.

For a 25:1 reduction you'd need 6t engine to jackshaft 30t; 9t jackshaft to rear wheel 45t.

Last edited by a moderator: Dec 18, 2015
12. ### RocketPenguinNew Member

Yea, I meant a 33% grade hill. They are pretty steep, most vehicles have issues getting over them.
Probably won't be riding on them if its that much of an issue.
Mk, I'll aim for something around there. Thanks!

Last edited by a moderator: Dec 18, 2015
13. ### butreWell-Known Member

calculating compound gear reductions is elementary school level math
it's easiest if you can reduce the second number all the way down to 1 rather than reducing them both to whole numbers, ie. if you have a 44 tooth driven side and a 12 tooth drive side you would reduce it to 3.66:1 rather than 11:3. reducing the second number down to 1 means you don't have to do any math for the second number. it's as simple as putting 44/12 into your calculator and adding :1 to the end of your result.

lets say you've got 3 sets of gears, first is 30 tooth driven side and 10 tooth drive side, second is 40 tooth and 10 tooth, third is 50 tooth and 10 tooth.
that means you have a 3:1 reduction, followed by a 4:1 reduction, followed by a 5:1 reduction. From there it's basic third grade level math, the ratio is (3*4*5):1. so you multiply 3*4*5 and you get 60, meaning the overall reduction is 60:1

In the case of a china girl engine, you have an internal 4:1 reduction and an external 3.66:1 reduction if you use the sprocket that comes with the kits giving you an overall reduction of 14.6:1, which without compound reductions would require a sprocket as big as your wheel.

I like to use this website to calculate potential top speed, you can punch in the first number into the teeth on axle field and the second number into the teeth on clutch field. http://www.csgnetwork.com/minibikepotentialspeedcalc.html

using that you can find out that the absolute fastest an unmodified kit china girl bike can go is 34 miles per hour. puts a big hole in a lot of sellers claims

14. ### LR JerryWell-Known Member

If I'm understanding you correctly Rocket Penguin you already had the following gears a 6t for the engine, a 47t on the rear wheel and a 13t for the jack shaft you wanted to know what other gear to use on the jackshaft. For your weight, engine size and the steep hills where you live you'll need a 25:1 reduction for 24" wheels. Keep the 6t for the engine and the 47t for the rear wheel. Order a 9t and a 30t for the jackshaft. Not much use for the 13t keep it as a back up. Then 6t engine to 30t jackshaft. Followed by 9t jackshaft to 47t rear wheel. This will give you a little over a 26:1 reduction. You should be able to pull any of the hills with a little assistance at the most. Without a shift kit its a compromise in steep hill country.

15. ### RocketPenguinNew Member

A little bit has changed since the post, I currently have not purchased either of the sprockets that will be going on the jackshaft. I have also decided I am not modifying the rear hub, as I have more leeway because I am not purchasing two sprockets instead of one. The goal is to have the rear shifter also work after I am all done, to provide a method of shifting.
With that said, I have the 6t on the engine, nothing yet on the jackshaft for either direction, and the rear hub has 28t, 24t, 20t, 17t, and 14t.
Doing some calculations, if I have the engine sprocket (6t) go to a 54t sprocket on a jackshaft, leading to a 10t sprocket that goes to the 28t sprocket on the tire, I should be within 25:1.