Effect of Annual Rings on Sawing Accuracy?

[kelLOGg]

I've read a lot on the FF about grain and knots contributing to rising and diving of a dull band but what about annual rings? I'm just trying to understand the forces at play on a dull band.

Let's say a sawmill is in ideal condition, blade flat and level, no curvature, roller guides aligned properly, everything is OK, etc., etc., and you start sawing and sawing on a sizeable clear log. Eventually the band begins to dull but you keep on sawing. You're still above the pith so the annual growth rings are arcing upward. Can this upward arc begin to control the band path and cause the blade to rise and produce crowned lumber? Likewise, if you don't flip the cant and you're sawing below the pith can the band dive causing crowning in the opposite direction? In my early years of sawing I have noticed both but I paid no attention to where in the log I was sawing. It seems to me that the alternate hard/soft parts of an annual ring could exert this control on a not-too-sharp band. 

[Brucer]

I've had the blade attempt to follow the rings at the interface between sapwood and heartwood. This only happened in frozen logs -- several degrees below freezing.

I've never had the blade follow the rings in mild weather.

[moodnacreek]

Most of what goes on while log sawing is the tension [ in the log] being released by removing one side more than the other. Knots and slanted grain will push the saw off line but you can see this. Squaring logs to saw boards can make worse lumber than leaving slabs on 2 [opposing sides] but all those flitch boards must be edged. A dull saw with good set would just take more power if both sides where equally dull but that's not how it goes.