Split sprockets work fine, you just need to buy a high quality brand and instal them correctly.
I always had good luck running Horstman brand split sprockets on my racekarts.
One side of each sprocket half will be labeled with a tooth count,
You need to instal both half's with this label pointing away from the sprocket hub.
Then instead of immediately tightening all the nuts/bolts, start with just barely snugging them up;
Instal your engine, clutch and chain, with the chain tension adjusted fairly tight,
Then jack up the back of your kart, and spin the axle around serveral times. This will allow the sprocket halves to better center themselves to each other & the hub before you do the final tightening.
Then as you tighten these bolts, take your time working your way around the 6 bolts and just gradually tighten each one just a little bit at a time until they're all fully tight. (but don't over-tighten these 6 bolts to the point of deforming things, just get-em snug and use a new set of lock-nuts so they won't loosen!)
Then spin the axle again to see if the sprocket halves are running true & perfectly aligned with each other or not, If not, loosen the 6 bolts and repeat this whole process again until you get it perfect !!!
Horstman split sprockets are available at most any racekart shop, including here:
http://out2win.com/catalog/sprkt_axle.html
Installing a sprocket guard on each side of the sprocket is a good Idea to help the chain stay on, they also help protect your chain and and axle sprockets making them last longer...
The "Part# '
KM 1081' Sprocket Guards 9" OD Nylon - 2 Sides" at this link works very good for reasonable price:
http://out2win.com/catalog/sprkt_acc.html
But you might need to buy 6 longer bolts when installing sprocket guards.
You can check out the pics on my old racekart thread to see what sprocket guards look like when installed, you'll find my pics at this link:
http://www.diygokarts.com/vb/showthread.php?t=6364
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Is your 13-tooth clutch made for the #35 pitch chain size?
If so, I'd suggest you start out with an axle sprocket somewhere in the 73 tooth range for a 245lb driver with a 13-tooth clutch and 11" tall rear tires. Most guys with racekarts end up owning serveral different sets of split sprockets, so they can change their gearing to better match wherever they'll be riding or racing...
Investing in a Chain Breaker tool makes it easy to shorten or lengthen your chain if necessary when swapping to different sized axle sprockets...
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PS:
Before you do the final alignment/tightening of your split sprockets:
You'll
first need to make sure your axle sprocket and clutch are
perfectly aligned with each other.
You can use a straight edge across the two sprockets.
Or, I think an even more accurate method is to start out by not installing (or tightening) your clutch retaining bolt: Then, (with the chain adjusted to around a 1/2" of slack, and the back of the kart jacked up), If you simply spin the axle you'll be able to easily see if they align with each other or not, by watching if the spinning axle sprocket & chain moves the clutch inward or outward on the engine. You'll want to align the axle sprocket hub and possibly also possibly your engine & motor mount in a way that spinning the axle moves the clutch (in or out) to the exact position that It'll need to stay when all the retaining bolts are fully tightened up.
Of course your clutch needs to easily slide (in and out) on your engine for this chain alignment method to work.
If your clutch doesnt have set screws, and only uses a retaining bolt/washer at the end of your engines output shaft, you might also discover you'll need to instal shims on the inside or outside of your clutch, so it will remain in the correct alignment to your axle sprocket... Some clutches need shims, and some don't...
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PPS:
I've never heard of a 1.5" diameter axle sprocket on a racekart.
I've got a feeling your axle is actually a 40 millimeter metric-sized diameter, that's a very common size
