Relativistic Rotation in the Large Radius, Small Angular Velocity Limit
Relativistic rotation is considered in the limit of angular velocity approaching zero and radial distance approaching infinity, such that centrifugal acceleration is immeasurably small while tangent velocity remains close to the speed of light. For this case, the predictions of the traditional approach to relativistic rotation using local co-moving Lorentz frames are compared and contrasted with those of the differential geometry based non-time-orthogonal analysis approach. Different predictions by the two approaches imply that only the non-time-orthogonal approach is valid.
Toward a Consistent Theory of Relativistic Rotation. Chapter 6 in Relativity in Rotating Frames
Part 1. Conundrums in the Traditional Analysis of Rotating Frames. Part 2. Resolution of the Conundrums: Differential Geometry and Non-time-orthogonality. Part 3. Experiment and Non-time-orthogonal Analysis. 
Part 3 contains a tabular history of the experiments performed since 1887 to test special relativity theory. It notes that the Brillet and Hall experiment in 1978 stands alone as a true, and sufficiently accurate, test of light speed in a rotating frame. Anomalous data (considered "spurious" at the time) from that experiment support the conclusions drawn herein.
Sensitive fiber‐optic gyroscopes
Special relativity teaches us that no contrivance, mechanical or electromagnetic, confined in a closed vehicle, can detect the uniform rectilinear motion of that vehicle. But anyone who suffers from motion sickness can attest to the fact that nonuniform motion (acceleration or rotation) is a different story. Thus it is possible to direct ships, aircraft or missiles by inertial navigation systems, once an initial direction is established, without reference to magnetic compasses or radio beams.