The info below is distilled from my prior research on this exact question – the choice of sail cloth and panel layout can be confusing, and I find that the marketing material does not do so much to make things clear. But it comes down to cost versus strength, stability and longevity.
Hope this helps,
Sail Fabrics & Construction
Laminate sails are made of taffeta (or other thin film material) sandwiching load-path fibres such as carbon-fibre. These sails provide great aerodynamic shape giving great performance, and hold their shape well (unless their structural integrity is compromised). Laminate sails can be easily repaired with glue (e.g. 3M Fast Cure 5200). However, issues have been seen with the structural integrity of laminate sails in the cruising use-case, particularly after a few seasons in the tropics, or with less than perfect care in use (such as flapping or flogging sails, to which laminate sails are particularly susceptible). Due to less-than-perfect use-and-care cruising environment, meaning shorter than wished-for life-span in the context of initial cost, laminate sails are not further considered in this discussion.
The basic sail-cloth, suitable for seasonal or day-sailing, is made of woven polyester (Dacron). All other things being equal, when compared to other sail cloth, Dacron sails have greater stretch, least shape stability, the least resistance to UV, and least cost per unit area.
Dacron sail cloths may be augmented by various strength and longevity enhancers, such as additional yarns incorporated into the weave (for example, extra yarns woven diagonally across the fabric). Or, further strength can be built-in by increasing the density of the weave, or by hot or cold rolling the fabric, or by impregnating the fabric with resin. Resin impregnation or other coatings may be used to improve resistance to UV-induced degradation.
The so-called “hybrid fabrics” (such as HydraNet, made by Dimension-Polyant), incorporate high-modulus (low-stretch) polyethylene yarns (such as Dyneema) into a polyester weave. The alignment of the hi-mod yarns will determine the axis of best load-bearing and dimensional stability. Some hi-mod yarns are woven into the fabric in the lengthwise or longitudinal direction (that is, along the warp); some sail cloth is manufactured with the hi-mod yarns woven in the transverse direction (along the weft, that is, across the fabric, e.g. Nautosphere Voyager). The alignment of the hi-mod yarns will determine the whether the fabric is best suited for TriRadial or Crosscut panel layout construction. (Nautosphere Voyager is, for example, good for cross-cut panel layout, but not for TriRadial construction.)
One further thing to note with any of the so-called ‘hybrid’ sail cloths, those that have Dyneema (or other polyethylene yarns) woven into them. Because of the structural attributes of Dyneema (such as resistance to stretch, cutting and abrasion), these fabrics cannot be easily or accurately cut by the metal cutting wheel on a conventional CAD/CAM cutting table. Automated cutting of hybrid fabrics is best facilitated by laser cutting — not all sail-lofts have laser-cutting facilities. The alternative is hand-cutting, which is less accurate than an automated machine cutting. Hand-cutting increases the time (and cost of production compared to automated cutting.
Cross-cut layout comprises long panels, roughly the width of the bolt of sail-cloth, laid horizontally (that is, roughly fore-aft in the finished sail). The lengthwise or longitudinal yarns (the warp yarns) are aligned roughly horizontally along the sail, with the transverse weft yarns aligned roughly vertically in the sail.
The lesser shape-holding and shape-stability of the cross-cut panel layout can be offset to some extent by incorporating additional yarns into the weave of the fabric, for example, diagonal yarns, or hi-mod yarns more closely aligned to the load-paths. For example, some dpHydranet is specified for cross-cut panel layout (this fabric should not be used for TriRadial panel construction).
Apart from the cost of sail cloth, the cost-of-construction of sails is driven mainly by the length of the seams to be sewn. Because Cross-cut sails have less seams for a given sail-area, Cross-cut sails are less expensive to make than an equivalent sail made using Tri-Radial panel layout.
Tri-Radial panel layout comprises narrow roughly triangular panels radiating from the three corners of the sail.
The narrower the panel, the better the shape-holding and shape-stability (because the seams can support the panel-shape, and accommodate load-bearing). Shape stability of TriRadial sails is better than Cross-cut sails, all other things being equal.
Narrower panels, however, means more panels. More panels means more seams.
In-mast furling: more seams, of which more overlap in Tri-Radial, compared to Cross-cut, means more bulk in a TriRadial sail when furled compared to an equivalent cross-cut sail. This can present problems, especially when slab-reefed (cross-cut) sails are changed to TriRadial sails with retro-fitted in-mast furling; especially when the mast profile was not designed for in-mast furling. For mast profiles designed specifically for Tri-radial sails and in-mast furling, this can be less of an issue.
Cost-of-fabric and hourly-rate aside, the Cost-of-construction is driven mainly by the length of the seams to be sewn. Because TriRadial sails have more seams than Cross-cut sails of a given area, TriRadial sails will be more expensive to make than an equivalent sail made using a Cross-cut panel layout.
Load-bearing strength and shape-stability of TriRadial panels can be augmented by incorporating hi-mod yarns aligned to the load-paths, with the panels being oriented such that the strongest yarns are aligned along the primary load-path/s, which emanate mainly from the three corners. For example, some dpHydranet is specified for TriRadial panel layout (this fabric should not be used for Cross-cut panel construction).