Yes, and no, Mark.
Yes, the cutter is (evidently) designed for a flatter plane of travel. I believe you'd see the in-action cutters lift off the bar and get snatched back toward it, much like a group of dolphins popping out of the water momentarily as they swim at speed. Around the tip of the bar, naturally, there is less slack available for that action.
As the cutters round the tip the depth gauge is disproportionately exposed, the more-so the tighter the radius the chain is bending around. This opens up the cutting edge to greater exposure as well but the effect of the more-protruding depth gauge is predominant.
For homeowner use the chains often have an additional bumper on the tie-strap between the cutters (or on the driver itself). When the chain is running along the body of the bar the bumper is relatively unobtrusive but when circling the nose the bumper tip swings farther above the centerline of the chain rivets, pretty much preventing any meaningful cutting surface contact. This effect is greater the smaller the radius of the circle the chain is running around.
Kevin is correct that smaller-radius noses are less prone to kickback and for the general populace this is a good thing. The tradeoff is poorer performance. A professional sawyer just might be more interested in performance than "idiotproofness" (taking the concept to the extreme).
I wish at this moment that I had a digital camera. I've got a piece of paper here on which I'd (some time ago) traced in different colors the outlines of three Stihl 20" sprocket-nose bars. The laminated 10T nose, the solid 11T nose, and the solid 13T nose. On the largest, the top and bottom are nearly parallel as they blend into the nose, so let's call it 180° of sprocket exposure. The middle size has the rails meeting the nose at somewhat less than that, and the smallest appears to have about 150° (maybe less) of the nose sprocket "exposed". Lets call it 180/360, 165/360, and 150/360 exposures (0.50, 0.46, and 0.42 factors).
10T × 0.75" × 0.42 = 3.15" exposed nose circumference
11T × 0.75" × 0.46 = 3.80" exposed nose circumference
13T × 0.75" × 0.50 = 4.88" exposed nose circumference
It might be interesting to note (if you could) that the transition to the nose also occurs almost a full inch further back from the tip on the largest nose than on the smallest.
For the rotational form of kickback you'll note the smallest nose exposes about 5/8 the amount of chain than the largest to that possibility, as well lessening the effect by kicking the depth gauges (and safety bumpers) furthest above the plane of the chain rivets. This is undoubtedly a good thing for Harry/Harriet Homeowner and I wholeheartedly applaud it.
The straight-back-at-ya form of kickback is also lessened with it by virtue of the fact that the top and bottom of the bar are at a greater angle to the centerline of the bar (they're less parallel) so force would be redirected somewhat upward on the smallest-nosed bar. On the largest, the top and bottom are nearly parallel with each other and with the centerline of the bar so the careless operator will note a much greater tendency to get the saw shoved straight back at them with it.
Why don't I think all noses should be reduced to the smallest size possible? Better question: why do I prefer the largest/"unsafest" size available? Because all things being equal (as in being done "right") the smallest nose requires the operator to lean into the saw while boring and the largest nose practically pulls itself in. I hate to force a tool to do its job. With the smallest nose of the three and with a "safety" chain (Stihl's version with the tie-strap bumpers) it's nigh unto impossible to push the tip of the bar into a cut or to swing a fully-buried bar through.
If you consider reducing the time actually running the saw to also be a safety factor, that's the one I choose over the other.
Thank you; it's been great; I'll be here all week!
