How does grain orientation effect the dimensional movement of wood?

Wood expands and shrinks depending on its moisture content.  The relative amount of change, expansion, or shrinkage differs for each of the three main grain directions.  Those directions are longitudinal, radial, and tangential.  Longitudinal is the direction a tree or its branches grows length-wise.  In most lumber, this is its length.  The change in this direction is very small.  That is why a wooden ruler can be used without changing its measurements when ambient moisture changes.  In almost all uses, longitudinal expansion and contraction are small enough not to be of concern.  Radial and tangential directional expansion and contraction are significant and different enough that they affect the dimensional stability of a piece of wood.  The relative amount of change in each direction is specific to the wood species.  Regardless of wood species, the change is greater in the tangential direction than in the radial direction.  The tangential direction is tangential to the growth rings in the wood, and the radial direction is perpendicular to the growth rings.  The T/R or ratio of tangential to radial change correlates to the dimensional stability of a wood species.  If you visualize a piece of lumber that is milled square and comes from a part of a log such that the rings are almost straight across in one direction, that is referred to as vertical grain or quarter sawn.  As the moisture content of the wood changes to come into equilibrium with its environment, it will move toward a diamond shape.  The closer the T/R ratio is to 1, the less the square dimension will distort. Dimensional stability and the direction of wood movement is important to plan for when cutting joinery in wood.  If two joined pieces are aligned so that they will not move in the same direction relative to the joint, the joint will be unstable when the ambient humidity changes and can cause the joint to fail.