**Re: (JeffKoch)**

Jeff, I’m sorry for not responding earlier and not giving a complete explanation. No disrespect intended, I have the highest regard for your posts.

So here goes ...

Let:

T = torque output of the engine at any given RPM

R14 = radius of a 14-tooth front sprocket

R15 = radius of a 15-tooth front sprocket

F14 = chain tension using a 14-tooth speocket

F15 = chain tension using a 15-tooth sprocket

Sprocket circumference is proportional to the number of teeth, so from the geometry,

R15/R14 = 15/14 (Eq. 1)

From a free body diagram of the front sprockets,

T = R14 X F14

and

T = R15 X F15

or

R14 X F14 = R15 X F15

Solving for F15, and substituting using Eq. 1 we get,

F14 = (R15/R14) x F15 = (15/14) F15 (Eq. 2)

Therefore, the chain tension using a 14-tooth sprocket is 7% higher than the chain tension using a 15-tooth sprocket for any given applied torque.

This result can also be shown by considering the rear sprocket:

Consider the following near-identical final drive set-ups:

Case 1: 14-tooth front, 38-tooth rear sprocket. Ratio; 38/14 = 2.71

Case 2: 15-tooth front, 41-tooth rear sprocket. Ratio; 41/15 = 2.73

For simplicity, assume that they’re equal such that:

38/14 = 41/15

or,

41/38 = 15/14 (Eq. 3)

T1 = torque applied to the rear wheel for Case 1

T2 = torque applied to the rear wheel for Case 2

R38 = radius of a 38-tooth rear sprocket

R41 = radius of a 41-tooth rear sprocket

F14 = chain tension for Case 1

F15 = chain tension for Case 2

Again from the geometry,

R41/R38 = 41/38 (Eq. 4)

From a free body diagram of the rear sprockets,

T1 = R38 X F14 (Eq. 5)

and

T2 = R41 X F15 (Eq. 6)

The final drive gear ratios for Case 1 and Case 2 are the same - which means that the torque multiplication is the same, so the torque applied to the rear wheel is the same at any given engine torque output level and RPM.

Therefore,

T1 = T2

substituting from (Eq. 5) and (Eq. 6),

R38 X F14 = R41 X F15

or,

F14 = (R41/R38) X F15

from (Eq. 3) and (Eq. 4)

R41/R38 = 41/38 = 15/14

Substituting,

F14 = (15/14) X F15

Which is the same result as (Eq.2)

So here is an example where you have two setups having the same gear ratio, one with a 15 tooth front, the other with a 14 tooth front. As I said, the chain tension will be greater in the 14 tooth setup.