Relativistic light sails need to billow.

We argue that light sails that are rapidly accelerated to relativistic velocities by lasers must be significantly curved in order to reduce their 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, when sufficient laser power is available, a sail's acceleration length decreases and its chip payload capacity increases as its curvature increases. Our findings provide guidance for emerging light sail design programs, which herald a new era of interstellar space exploration.