Well, this is obviously a lot more interesting than debating whether 6 turns of a 10t sprocket will produce anything other than exactly one turn of a 60t sprocket !
Have you done your test? Maybe not yet since you say: "proposed". I'll be interested in hearing your results.
Along those lines... as you have probably discovered: no two companies seems to make chain sprockets exactly the same way (especially noticeable on small tooth-count sprockets). If you've ever dug through Machinery Handbook and gone through all the formulas to design a sprocket, you may discover (like I did) that there some "art" to it... it's not an absolute science.
Many years ago (early 90's) I was doing a lot of playing and testing running a direct drive Yamaha on a sprint track. A company in karting approached me about making higher quality (more durable) engine sprockets vs. what was available at the time (mostly from Europe, though I recall there was one from Japan). These were all 10t sprockets for 219 chain. The readily available parts had a fairly short lifespan, as you can probably imagine with a 10t sprocket running 17,000+ rpm.
At the time, my dad owned a company that made gear cutting tools, and I had both a gear hobbing machine and a gear shaper in my own shop. My first step was to just design a sprocket using the basic formulas in Machinery Handbook, and make the sprockets out of 9310 instead of 8620. My dad's company made the shaper cutter for me, and I knocked out a couple dozen or so for testing. The sprockets looked quite different from what was on the market at the time, but worked well. As a matter of fact, if you set the sprocket I made side by side with an Italian one, it was surprising how different they were, yet both got the kart around the track just fine. At the track, I started paying attention to how they ran at different tension (slack in the chain), and how much the chain would vibrate on the top side. They definitely "acted" different watching them run.
As a next step, I designed a sprocket "geometrically" in CAD following pure math on how a chain would wrap around a sprocket (that part is pretty much what the Machinery Handbook shows), but used my ideas for how much clearance the teeth needed on entry/exit (the "art" portion of the design). Had another cutter made, and the results were sprockets that looked a bit different yet again. This design seemed to show less chain vibration than the others I had run. The wear also looked good in this design, though I "suspect" that my own design would have been less tolerant of a well-worn chain since I gave it less "leeway" for increased chain pitch spacing (chain stretch).
The project ended up getting dropped simply because it was too expensive to produce sprockets with the methods I had in my shop at the time, and the material and heat treat were fairly expensive.
The results were something that, at the time, got me to thinking quite a bit about chain and sprockets, since it's somewhat obvious watching a chain that the crankshaft is not rotating a steady rate. (much easier to see what happens through the rev range on a direct-drive kart). I experiment with a couple of different mounting angles of the engine as well (to shift the point of max/min crank speed around a bit relative to the chain angle). There was no clear-cut answers or winners/losers, but it was an interesting time.
As another point of interest -- (not sure how long you've been in karting) -- back in the mid-70's there was a fairly quick transition to belt drive in enduro racing. Even though a belt (toothed belt) is not quite as efficient at transferring power as a straight-running lubricated chain, we all went faster with belt drives. My "gut feeling" is that the drive system with a belt is just much smoother. Also, since the fibers in the belt don't stretch or compress, they are (by definition) running at or very, very close to the pitch diameter. The teeth on the belt can stretch/compress to fit the teeth in the pulleys (very unlike a chain). Interestingly at the time, someone even brought out a Poly-V belt drive system (no "teeth", rather just a few grooves running around the engine pulley just like the serpentine belt on a modern car). The rear axle pulleys where completely smooth, as I recall. Gear ratio was set by diameters. The whole system worked pretty much like running a flat belt on a smooth pulley when it came to selecting gear ratios, but of course the Poly-V had a bit more "traction" on the engine pulley where it was needed. The system "felt" nice on the track, but it never caught on -- I suspect because it was just so much simpler to select a ratio based on tooth count rather than diameters. Interesting side-note on this: I seem to recall that they made only a few sizes of axle pulleys. The gear ratio was adjusted by running *slightly* different diameter engine pulleys (which were of course super easy to make). I'd probably revisit this idea if I was racing vintage enduros nowadays.
Ah well... enough history and nostalgia.
I'll have to do a bit of digging on some ancient computer backups, and see if I can find my original 10t sprocket designs.
More as I remember it. ;-) .
PM