Tangential and radial shrinkages are much larger. Worse, they are often quite different. In a spruce log, for instance, the radial shrinkage on complete drying is about three percent, while the tangential shrinkage is more than twice that much. The circumference of a circle is an exact multiple of its radius, so if the fractional shrinkage of the circumference is more than that of the radius, something gives, and the circumference develops gaps. If we apply this to house logs, where the situation is made worse by the outside of the log drying faster than the inside, the result is cracks.
Cut boards have slightly different problems.
A board which is cut so that the growth rings, looked at from the end of the board, show as little curvature as possible is unlikely to warp if the drying process is properly controlled. However, if a board is cut nearly parallel to the bark, so that the growth rings appear to curve on the board end, the differential shrinkage on drying will have the same effect as if the growth rings were shrinking rubber bands. The growth rings will try to straighten out, and the board will tend to curl in the opposite direction from the curve of the growth rings. Knots will also cause problems, as their diameters will shrink more than will the surrounding wood, which is oriented so that shrinkage is in the tangential and lengthwise directions. Regardless of how well the wood is cut, lumber will expand and contract to some extent as the humidity changes.