Two recently proposed experiments by Kolen and Torr (K-T), designed to detect possible failures of Einstein's special relativity (SR) are analyzed. Imprecisions in these papers are pointed out. Computation in Lorentz aether theory (LAT), with the K-T violation of SR, of the theoretical prediction for the proposed K-T clock experiment prove their results to be incorrect. Analytical computation of the proposed K-T rotor Doppler experiment using LAT confirms the order of magnitude of their prediction by numerical computation. For LAT in (...) the K-T form, this experiment, using a turntable, is shown to give results which could be detected with the technology of 20 years ago. Another LAT model is considered which leads to deviations of SR smaller than in the K-T model. The central point of the approach adopted in this paper is the use of Einstein's coordinates in the comoving frame, even when SR is violated, leading always to isotropic propagation of light in vacuum; the anisotropy usually obtained in LAT is only a coordinate effect. (shrink)