Abstract: Collective phenomenona are found in every branch of science; the behavior of the whole differs strongly from the behavior of the individual elements. In quantum optics, a hallmark example is Dicke superradiance. Here, a fully inverted ensemble of atoms emits a short and bright light pulse, known as the superradiant burst, that initially grows in intensity. This is in stark contrast to independent atoms which decay exponentially, emitting a pulse that monotonically decreases in time. Experiments in dense disordered systems have observed the superradiant burst, but there, inhomogeneous broadening plays a large role, making the systems hard to model or control. In contrast, ordered arrays have much lower inhomogeneity - atoms in the bulk all see the same set of neighbors - making them an ideal platform to study dissipative many-body physics. Here, we show the conditions under which such systems produce a superradiant burst. We go beyond two-level approximations, and demonstrate that long-wavelength transitions from ytterbium and strontium atoms can be used to observe such physics. Our work represents an important step in harnessing such systems to build quantum optical sources and as dissipative generators of entanglement.