Maybe I am not making my point clearly enough or have missed something. See below drawing:
Unless I have missed something, the ONLY factor that determines the value for the countershaft sprocket offset is the difference between the X Offset values for the old and new wheels measured at the rear wheel.
For example:
X(old) = Offset of old wheel measured from centerline of wheel to sprocket
X(new) = Offset of new wheel measured from centerline of wheel to sprocket
C0 = Countershaft offset difference
C0 = X(new) - X(old)
Please let me know if there is some fallacy in my reasoning. I can't see any but I'm not the smartest guy in the world by any means.
If my reasoning is correct the conclusion is that rim width plays no part whatsoever in the calculation for countershaft offset. Obviously, in practical application sufficient clearance to prevent chain to tire interference tire is required but for mathematical purposes rim width is irrelevant.
Thanks,
Joe
Joe,
I have attached a drawing to allow visualization of what otherwise might seem a jumble of verbal descriptions.
First it has been well established that a 5/8" offset is "nominally" the maximum offset you can run on a GS frame without pushing a 530 chain too far resulting in interference between chain and left hand side frame member. This is where Cf becomes too small for adequate chain clearance.
A 5/8" counter sprocket is the normal offset that anyone running a 5.5" 180/55-17 tire will use. The typical install is with the 2nd generation GSXR wheels and the GS sprocket carrier is used. Anyone that has accomplished this can pretty much tell you that this is a threading the needle undertaking; there is little leeway for making it work. In fact recently it seems to have become popular to drop down from a 180 to a 170 tire to improve the chain clearance.
I don't have numbers to quote, but properly done adequate clearance of both Cf and Ct can be accomplished which is probably about 2mm either side. I would defer to what ever numbers Katman could quote, but that is about 1/2 of the numbers that I have using my 4.5" wheel.
So no matter what this is the maximum offset you can run no matter what wheel tire combination you have. The chain can't be pushed any further into the frame and this is the offset required for a 5.5" wheel.
Now can you run this much offset with a smaller wheel? Well yes you can but then you have at least two drawbacks
1.) you are running more offset than required and putting additional strain on your output shaft
2.) You have not optimized the available space between the tire and frame for fitting your chain. You will see more chain to frame rub than necessary.
So it should be clear, that as long you have anything less than or equal to 5/8" offset you can avoid rubbing the chain against the frame. This probably explains why John's setup using a 4" wheel uses a 13mm offset and still have an aligned chain. In order to do that but he is running his chain 7mm closer to the frame than a "centered" chain. If he is more worried about tire rub than frame rub, then that is apparently OK.
On my GS1100ED, I know the chain is virtually perfectly centered within about 0.25mm as I have measured 4.0 and 4.5mm on either side (I don't remember which was which but it doesn't really matter). 4.0mm is still a little close but that is really all the space there is avaliable between the frame, chain and tire. I'm running a 3/8" offset counter sprocket with a 4.5" 1988 GSXR 1100 wheel with the sprocket carrier that goes with it with a 170/60-18" tire and 530 chain.
As described above, I could run a 5/8" counter sprocket, but then I would be reducing my chain to frame clearance and based on my final chain clearance measurements 3/8" is almost perfect (i.e. within 1/4mm).
So to my mind, 5/8" for 5.5" wheel and 3/8" for 4.5" wheels are established benchmarks for centering chains within the available space as measured on finished installs.
When Ray added in his 6mm number for a 4.0" wheel and you came up with a 4mm offset for a 3.5" these data points followed the simplified spacing model almost exactly and certainly within the likely measurement uncertainties.We need to ask Ray, but I would assume the 6mm is the correct number to center the chain?
By the time you get down to a skinny 3.5" wheel you are comparatively swimming in chain clearance room and so there is a lot more latitude on where your chain can be. The simplified model says that 1/8" will center the chain for a 3.5" wheel but there is much more leeway that that so depending upon your specifics on sprocket carrier and bearing spacing you can surely deviate from the idealized centering offset. You could go all the way to 5/8" as described above but then your chain is way off center within the available space.
Getting back to your figure, there is nothing wrong with it assuming you stay within the chain clearance constraints. What are the constraints? The upper constraint is always 5/8". The lower constraint is the ideal centering model less some margin that is growing the smaller your wheel is. For a 4.5" wheel clearances are small enough that I would still recommend something very close to 3/8" offset. Below that things get much easier as you are going to have more than 5mm on either side which is probably more than enough clearance either side of the ideal centering model.
There are enough variables here and difficulty in performing the measurements, that I think that anyone doing this should measure how well their wheels is centered in the frame (by measuring between wheel and the side frame side struts) as well as the chain clearance for tire,chain and frame. Those two measurements will likely explain any ambiguities between this idealized centering model and any particular specific install.
Jim