Gearing question....

[ungeheuer]

G'Day Ducatters!

Stock gearing on my 09 M1100s is 15/39 and I'd like to lower the gearing.  Cheapest and easiest would be to go with 14/39 but I'd like to fit one of these >>



<< and run 15/42. 

So the question is this: If i go +3 at the rear sprocket am I gonna need a new chain too?

Thanks in advance for your thoughts......

[Ddan]

It kinda depends on where your wheel is in the range of adjustment.  You most likely won't need a new chain, but you may change the wheelbase enough that you notice it.

[stopintime]

Isn't this the perfect excuse to get a black or gold chain?

You'll probably need another link, so why hesitate

[ungeheuer]

Isn't this the perfect excuse to get a black or gold chain?

...lol... some help you are   

[stopintime]

ha ha .... and when you put on a gold chain and the ONE "connecting link is black - everything is ruined

until you buy this     
http://www.moto-racing.co.uk/item--DID-Chain-Links-525VM-X-Ring-Gold-RL525VM--DID+Link+RL525VM.html

[bigiain]

So the question is this: If i go +3 at the rear sprocket am I gonna need a new chain too?

If you go up 3 teeth on the rear, since the chain wraps (near enough for a first approximation) half way around the rear sprocket, the run around the sprocket will "use up" one and a half extra links. Since the chain has an upper and lower run, that means you'll be able to use the existing chain if you've got enough adjustment to move the axle 3/4ths of a link forward.

big

[Cloner]

The formula for determining the pitch diameter of a sprocket is (chain pitch)/sin (180/number of teeth)

For the 39t sprocket, and assuming 520, 525, or 530 chain (all have a 5/8" pitch) the pitch diameter is .625/sin(180/39), or 7.767".  For the 42t, it's .625/sin(180/42), or 8.363".

Now we have to compare the circumferences of the two sprockets.  The circumference at the pitch diameter is pi (3.1416, approximately) multiplied by the pitch diameter.  For the 39t it's 7.767 * 3.1416, or 24.401", and for the 42t it's 8.363 * 3.1416 or 26.273". 

The difference between the two is 26.273 - 24.401, or 1.872". 

We only have to wrap approximately half of the sprocket, so half of the difference is .936"...or about 15/16 of an inch. 

Now we have to remember that there are two strands of chain!  Since we take half of the difference from the top strand of chain, and half from the bottom one, we'll move the axle forward half of the .936", or .468"....just under a half inch....by changing from a 39t sprocket to a 42t one.

So....if you have 1/2 inch of adjustment to the front of the rear axle's present location you can install the new 42t sprocket without buying a new chain.

I knew that engineering degree would come in handy.

[ungeheuer]

The formula for determining the pitch diameter of a sprocket is (chain pitch)/sin (180/number of teeth)

For the 39t sprocket, and assuming 520, 525, or 530 chain (all have a 5/8" pitch) the pitch diameter is .625/sin(180/39), or 7.767".  For the 42t, it's .625/sin(180/42), or 8.363".

Now we have to compare the circumferences of the two sprockets.  The circumference at the pitch diameter is pi (3.1416, approximately) multiplied by the pitch diameter.  For the 39t it's 7.767 * 3.1416, or 24.401", and for the 42t it's 8.363 * 3.1416 or 26.273". 

The difference between the two is 26.273 - 24.401, or 1.872". 

We only have to wrap approximately half of the sprocket, so half of the difference is .936"...or about 15/16 of an inch. 

Now we have to remember that there are two strands of chain!  Since we take half of the difference from the top strand of chain, and half from the bottom one, we'll move the axle forward half of the .936", or .468"....just under a half inch....by changing from a 39t sprocket to a 42t one.

So....if you have 1/2 inch of adjustment to the front of the rear axle's present location you can install the new 42t sprocket without buying a new chain.

I knew that engineering degree would come in handy.

A mightily impressive effort there       
Love this place     Thanks everybody for the help. 

[Cloner]

You get the same answer by using bigiain's method....mine's just cooler 'cause it's more confusing.   

[bigiain]

You get the same answer by using bigiain's method....mine's just cooler 'cause it's more confusing.   

I was going to point that out - my calculation (3 quarters of a 5/8" link) comes out a little bit longer than yours, .468" vs .46875", so I was _almost_ a thou out... (if that's a problem feel free to file the swingarm slots out a thou or two...  )

big