I believe it is a function of the volume of material involved in the shrinkage process which is obviously more in the tangential direction than the radial. You see this by taking the shrinkage in a unit volume of the timber. The final shrinkage in any direction should be the integral of the total volume involved in the particular direction.

I also believe the ray cells that are oriented to 90 degrees to the other cells helps to restrict the shrinkage/swelling in the radial direction.

Paper in support of Brian's suggestion:

https://www.fpl.fs.fed.us/documnts/pdf1957/peck57a.pdf

I totally agre with Joseph, once in tagential direction we have an higher proportion of latewood than in radial direction. In this way, is important to remember that in latewood we have thicker fibers and shrinkage is correlated with the microfibril aproximation of secondary wall (i explanned o little of that in my thesis rsrsrsrs)

It's because of the cell wall on the tangential direction is thicker (in direction) than radial. Cell wall have ability to bond water, the thicker cell wall, the higher its bonded moisture content which lead to shrinkage in drying condition.

So, when the shrinkage happened, cell wall (which have much moisture) will shrink in all direction, especially higher in the tangential.

Dear Dr. Hein:

I believe that although the proportion of latewood is actually greater in the tangential direction (which causes a greater percentage of shrinkage in such a direction), the presence of the medullar rays (in radial direction) also contributes to the fact that shrinkage in the tangential direction be systematically superior.

Dear Paulo Ricardo Gherardi,

Based on the wood physics and macroscopic scale it can relate to shrinkage coefficient and density of wood. In the microscopic scale, wood ray and microfibril angle have the main role in higher shrinkage of wood in the tangential direction.

B.R.

Saman

In tangential section, microfibril orientation is parallel to the axis of cell wall in where radial section the microfibril angle is perpendicular to the cell wall axis.

So, parallel angle that means more energy is needed to change its dimensions so shrinkage will be higher than the radial section.

Well, I suppose it is due to the volume of material involved in the shrinkage process, which is obviously greater in the tangential than in the radial direction. This may be seen by calculating the shrinkage of the timber as a unit volume. In any direction, the final shrinkage should be the integral of the whole volume involved in that direction.so the volume weather its small or great has a significant impact on shrinking