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circles with the bandsaw

I tried to cut circles on my band saw using a crude circle cutting setup. I tapped a short nail into a scrap and positioned the nail about 3 inches to the right of the blade. I fit a 6.5" square into the nail slightly off center so the edge of the scrap was right up against the blade. Blade is 1/2" which is supposed to be able to cut a 3" radius circle.

When I fire up the saw and start cutting, I systematically found that the cut would tend to spiral in, forming a spiral. When I got around back to the beginning and the "circle" could release I would see the bandsaw blade spring back to the left. I tried various things like positioning the nail in line with the gullets either along the direction perpendicular to my saw's lead line or just perpendicular to the blade. (The lead is about 3/8".) And the best I got was a circle where I only spiraled in 1/8" when I got all the way around. Again the blade was pulled off center by 1/8" by the jig setup.

What is the explanation for this spiraling behavior? How can I get an actual circle?

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