Question for mathematical geniuses.

[pggg]

Here's 3 measurements I've done on 3 different sprockets I have.

16T and 17T radius difference is 3mm.
12T and 16T radius difference is 10mm.
12T and 17T radius difference is 13mm.

Here's the question. What's the radius difference between
1. a 13T and a 14T?
2. a 13T and a 15T?

Anyone know the correct formula to figure this?

[Geezer]

I need to know how many teeth on the rear sprocket to determine the ratio. You divide the number of teeth on the rear sprocket by the number of teeth on the front sprocket.

For example a bike with a 17 tooth front and a 42 tooth rear sprocket would have a ratio of 2.47 to 1.

Geezer

[winkel02]

I would not claim to be a maths genius, and i know even less about bikes but...

17T-16T = 3mm
16T-12T = 10mm
17T-12T = 13mm

Assuming they step down evenly in size, every T is worth ~2.5mm.

So the difference between a 13T and 14T will be 2.5mm and between 13T and 15T will be 5mm.

I'm assuming where you measured 3mm is actually more like 2.5, and 13mm is more like 12.5 - otherwise buggered if i know what hellish complex formula could work it out.

But then if you asked this to work out the drive ratio, then Geezer has already answered it!

Winkel.

[LoserShoes]

If you are asking what I think you are, measure the center to center distance between the pins in the chain, multiply by the number of teeth, which will give you an approximation to the circumfrence of the sprocket. Since circumfrence is PI (3.1416) X diameter, divide that by PI to get the diameter.
This gives you the diameter at the pin centers, so add the chain height to get the full diameter of the sprocket.
This wont be exact, but will get you in the ballpark.

Steve

[Street_Rat78]

values...

pggg,
With the actual radius values, I can write the equation to get you a fairily accurate answer. Just knowing that the difference between two is x amount doesn't help figure out the three unknowns you are trying to solve for.

Basically, what I'm asking is ...
Radius of 12T =
Radius of 16T =
Radius of 17T =

If you can get these to the closest tenth or hundredth of a mm, I can give you a fairly accurate estimate for the radius of the 13T, 14T, and 15T ... which would then provided the difference between each.

Overall, the equation is pretty simple once you have all the information.

[pggg]

It's not actually the ratio I'm after, thanks anyway - just trying to get an accurate dimension of a 14T and 15T sprocket. Winkel says 1 tooth should equal 2.5mm in a constant. Carefully re-measuring, the 13mm IS actually 12.5mm and the 3mm IS actually 2.5mm. So it looks like the tooth increases give an even radius increase after all. So, 1 tooth increase on a 5/8ths pitch sprocket equals 2.5mm increase in radius. (5mm increase in diameter). That means, with some dremelling of the gearbox case, a 14T sprocket will fit my chain unit comfortably. Thanks a lot fellas. Is there NOTHING the people on this site DONT know?

[DiverRay]

Not that we admit to!!

[Street_Rat78]

Well, you know what the say ...

2 heads are better than one ...
but
2,512 heads are better than 2.

Glad we could help.

[canned_heat]

How much accuracy do you want ?

exactly the radious ?

This could be a poor aproximation, but could do the trick


The radius is

R= (number of Teeth) * (diference between two consecutive sprockets radius )

illustrative:

Diference between 16 and 17 teeth is 3 mm

then 13 teeth has a radius of 39 mm ( aproximate)

v´sss

[canned_heat]

If you need more accuracy, I will need exact measures and the number of teeth. Then I will gladly help you.lol

v´ssss

[skids]

Re: Question for mathematical geniuses.

It comes down to two equations with two unknowns, Radius (R) and distance between teeth (t).

The first condition gives t = 18.85mm
The second condition gives t=15.71mm
The third condition gives t=16.34mm
I would throw out the first condition because the differences are too small to lead to any accuracy and average the second two outcomes for t=16mm.

Using circumference = Pi x 2R and Circumference = 16mm x (No. of teeth), the following is the result:

1. a 13T and a 14T? =====>> difference is 2.6mm
2. a 13T and a 15T? =====>> difference is 5.1 mm

Originally posted by pggg
Here's 3 measurements I've done on 3 different sprockets I have.

16T and 17T radius difference is 3mm.
12T and 16T radius difference is 10mm.
12T and 17T radius difference is 13mm.

Here's the question. What's the radius difference between
1. a 13T and a 14T?
2. a 13T and a 15T?

Anyone know the correct formula to figure this?

[pggg]

Hey heat, my measurements are only to about 1mm, so aren't super accurate but I've enough info to know a 14T size close enough. Just curious Skids, what's the radius difference between, say, 300T and 301T? I assume it's not actually a constant 2.5mm change for one extra tooth then?

[canned_heat]

well, if you have the exact measurements of an 14 teeth sprocket, then we can focus the problem as a poligon of 14 sides.

I will asume that the radius measure is the smaller one, I mean it has been measured in the inner part of the teeth ( the gap betweeen two teeth)

The exact lenth of the sprocket T, measured on the base of the aproximate triangle that it forms is:


T= 2 * Rft * tan (2 * PI / 28)

and is constant to all our sprockets

where:

Rft = the radius of the 14 teeth sprocket
PI = 3,141591...

Angles in radians !

And the the radius of a sprocket with n teeth Rn will be:

Rn = (2 * Rft * tan( 2 * PI / 28)) / ( tan( 2 * PI /(2 * n))

hope this helps you to short it out

v´ssssss

[skids]

First, let me clarify that when if did the figurin' before, the "radius" is from the center of the sprocket to the circumference created by the pins in the chain. It is not from the center to the ends of the teeth.

Second, I am assuming that you are asking about differences between radiuses (radii?) of 300-tooth and a 301-tooth sprockets?? Those would be BIG sprockets, no?

OK, if that is what you are after (theoretically),

R2-R1 = {301(16mm)-300(16mm)}/{pi(2)}
R2-R2 = 2.5mm

I guess it does boil down to a constant:

R2-R1 = (T2-T1)16/(pi x 2)
R2-R1 = (T2 - T1) x 2.55

Winter sets-in, we all go out of our minds, eh?

Originally posted by pggg
Hey heat, my measurements are only to about 1mm, so aren't super accurate but I've enough info to know a 14T size close enough. Just curious Skids, what's the radius difference between, say, 300T and 301T? I assume it's not actually a constant 2.5mm change for one extra tooth then?

[pggg]

Rn = (2 * Rft * tan( 2 * PI / 28)) / ( tan( 2 * PI /(2 * n)) - yeah...aaahhh...ummm...wellll... O.K! I believe it!