We argue that light sails with nanometer-scale thicknesses that are rapidly accelerated to relativistic velocities by lasers must be significantly curved in order to reduce their intrafilm mechanical stresses and avoid tears. Using an integrated opto-thermo-mechanical model, we show that the diameter and radius of curvature of a circular light sail should be comparable in magnitude, both on the order of a few meters, in optimal designs for gram-scale payloads. Moreover, we demonstrate that, when sufficient laser power is available, a sail's acceleration length decreases as its curvature increases. Our findings provide critical guidance for emerging light sail design programs, which herald a new era of interstellar space exploration to destinations such as the Oort cloud, the Alpha Centauri system, and beyond.
Keywords: Laser propulsion; Membrane stress; Molybdenum disulfide; Photon pressure; Relativistic light sail.