Vertically curved monochromator crystals are commonly used to increase the intensity on the sample in thermal neutron scattering applications. Such devices are found on spectrometers installed both at nonreflecting beam tubes and at totally reflecting guide tubes. We present an analysis of the performance of vertically curved monochromators located at instruments of both types. The acceptance diagram approach gives considerable insight into the behaviour of vertically curved monochromators. The analysis can be extended to more complicated systems, which closely represent what is actually found at a neutron scattering installation.