This study presents numerical simulations of the maximum sensitivity to absolute rotation of a number of coupled resonator optical waveguide (CROW) gyroscopes consisting of a linear array of coupled ring resonators. It examines in particular the impact on the maximum sensitivity of the number of rings, of the relative spatial orientation of the rings (folded and unfolded), of various sequences of coupling ratios between the rings and various sequences of ring dimensions, and of the number of input/output waveguides (one or two) used to inject and collect the light. In all configurations the sensitivity is maximized by proper selection of the coupling ratio(s) and phase bias, and compared to the maximum sensitivity of a resonant waveguide optical gyroscope (RWOG) utilizing a single ring-resonator waveguide with the same radius and loss as each ring in the CROW. Simulations show that although some configurations are more sensitive than others, in spite of numerous claims to the contrary made in the literature, in all configurations the maximum sensitivity is independent of the number of rings, and does not exceed the maximum sensitivity of an RWOG. There are no sensitivity benefits to utilizing any of these linear CROWs for absolute rotation sensing. For equal total footprint, an RWOG is √N times more sensitive, and it is easier to fabricate and stabilize.