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A method for modeling the fabrication of capillary tubes is developed that includes the effects of preform rotation, and is used to reduce or remove polarization mode dispersion and fiber birefringence. The model is solved numerically, making use of extensive experimental investigations into furnace temperature profiles and silica glass viscosities, without the use of fitting parameters. Accurate predictions of the geometry of spun capillary tubes are made and compared directly with experimental results, showing remarkable agreement and demonstrating that the mathematical modeling of fiber drawing promises to be an accurate predictive tool for experimenters. Finally, a discussion of how this model impacts on the rotation of more general microstructured optical fiber preforms is given.