From our friends at Challenge Sailcloth
A crosscut sail uses fabric that is woven such that the fill yarn is stronger than the warp yarn. A Tri-Radial sail uses fabric where the warp yarn is stronger than a fill yarn. Traditionally, tri-radial sails were only made with laminate or membrane cloth, because it is extremely hard to weave a warp-oriented cloth.
A crosscut sail uses cloth that has straight fill yarns and crimped warp yarns. It aligns the strength of the fill yarn with the load bearing direction of the sail.
A tri-radial sail uses Warp-Drive cloth that has straight warp yarns and crimped fill yarns. It aligns the strength of the warp in the load bearing direction of the sail.
How do the yarn strengths differ between a Crosscut sail and a Tri-Radial sail?
A crosscut sail aligns the straight fill yarn with the load direction. A Tri-Radial sail aligns the straight warp yarn with the load direction.