Hi all:
Try marking out the radius of your cut on both sides of the timber, then cut down to nearly the line about every 3 or 4 inches--knock the blocks away and then clean up the surface up with a carpenters adze, this is a very simple chore, and leaves a nice undulating surface on the timber.
I just finished the inside surface of a pressure box constructed with 10 by 12 oak timbers, and found that this worked quite well. The diameter of the circle was 36" and from this you can see that the circle was real tight as far as the arc goes.
Nothing seems to work as good on inside curved surfaces as a carpenters flat edged adze, even in this modern era I had to resort back to the original tools to do the job.
good luck
NH