I happened to be searching the internet for this exact topic (using a chainsaw engine to power a moving vehicle).
WHY I'M DOING THIS:
1) I have a chainsaw engine that runs great
2) I have a 3 wheeler with good suspension and brakes but no engine
3) I've been watching too much Junkyard Wars
4) I'm a computer programmer by trade and want to see if I can do something completely different. That said - I have no business talking about any of this...
WHY THIS SHOULD WORK:
Vehicles based on this design (go karts, scooters, etc.) generally do not have a gear box. They have a single gear (ratio). Remember with any single geared vehicle, your top speed is basicaly based on ratios - ratio of the drive sprocket to the axle sprocket - factoring in rear wheel diameter and very importantly the rpms of the engine (or more specifically the output shaft) which determines how fast the chain can rotate. The horsepower of the engine and weight of the vehicle is only important in how fast you can get to your top speed. Remember your old single speed bicycle? You could turn the pedals as fast as you could but you would never seem to really get going that fast compared to your first multi-geared bike. What we're talking about doing with a chainsaw engine is very simple - like a single geared bike. Top speed probably only 20-25mph. If you want an ATV that will do 60+mph get one with a real ATV engine and gearbox.
Say you have a standard chain driven go-kart with a 12 tooth front sprocket and a 72 tooth rear axle sprocket. That's a 1:6 ratio. Almost all lawn mower (go kart) engines turn at 3600rpm at wide open throttle. Factor in standard go-kart sized tires and you're looking at a top speed of around 25mph give or take. (I'm not talking about racing karts!)
This is where the horsepower comes in. With our go-kart example you'll likely get to the top speed of about 25mph whether you have a 3.5hp engine or an 8hp engine. Obviously the 8hp engine will get you there faster with a much better sensation of speed (acceleration). But if the gearing is identical, your top speed will be basically the same with both engines.
So consider a chainsaw engine. The one I have is 58.2cc's and is rated somewhere between 2.9 and 3.9 horsepower depending on what website you look at. Interestingly, it revs much higher than a gokart engine - well over 10,000rpm. And because it is a 2 stroke engine it revs MUCH faster and is much more responsive to throttle than a 4 stroke lawn mower engine. Provided it has enough low end power to get me moving off the line without completely boging down and/or stalling, it should work fine. I have minimized the weight of my chassis and have relatively small ATV tires to try to deal with this concern.
HOW I'M PUTTING IT TOGETHER:
My 3 wheeler with chainsaw engine mounted and everything attached is expected to weigh in at 187lbs minus driver. I am having a machine shop remove the chainsaw sprocket from the clutch assembly. Remember a chainsaw has a built in clutch so at idle the chain doesn't turn (so your wheels won't try to turn when you are at idle). I got a 10 tooth sprocket from a local bearing shop that will be welded on in place of the chainsaw sprocket. I matched the chain pitch and roller diameter to that of the existing rear sprocket on the 3 wheeler so everything should match right up. (The chain should fit the chainsaw sprocket and rear axle sprocket perfectly).
HOW FAST IT SHOULD GO:
My frame will be heavier or at least a lot bulkier than a go kart with a lot more drag from being so high and having such wide and tall tires. But on the other hand I will have more of a top speed gear ratio and having taller ATV style tires also causes the top speed to increase. It may be a bit slow off the line, but possibly not with the higher rpms and better 2 stroke revs the chainsaw engine gives. My basic calculations come out to a top speed of right at 25mph reached in 7.8 seconds (with driver weight factored in). It will be interesting to see how this compares to real life if this thing even works at all. Since I'm using stuff I already have, my cost should be very low, basically just the sprocket making and chain.
THE FIRST SNAG I'VE THOUGHT OF SO FAR:
Since I have to start my chainsaw at full throttle, I think I am going to have to implement some sort of lift mechanism to raise the rear wheels every time I need to crank the engine so that they can spin freely. Once the engine is warmed up I can let it idle - the built in clutch will engage, the tires will stop turning, and I can let it down... ?
If anybody is interested in continuing discussing this idea I'll be glad to post more about it as I get to different steps in my project.