How flat can an self supporting masonry elliptical arch be at 13' wide with virtually no load above it?

A self-supporting masonry elliptical arch can be designed to be relatively flat while maintaining structural integrity, particularly when there is minimal load above it. For a 13-foot wide arch, the rise can be reduced to about 1.5 to 2 feet to achieve a flatter profile, depending on the specific materials and construction techniques used. However, the flatter the arch, the more critical it becomes to ensure proper masonry bonding and alignment to prevent buckling or failure. Consulting with a structural engineer is advisable for precise calculations and safety considerations.