In a Vehicular Ad hoc NETwork (VANET), vehicles broadcast safety messages disclosing their trajectory information in order to warn drivers of impending accidents. Precise location information needed for these safety applications, combined with the need to exclude attackers through the use of authentication, creates a significant privacy risk. One method proposed to improve privacy is the use of many pseudonyms, and changing pseudonyms while in a mix zone where all other vehicles also change pseudonyms. Previous work has evaluated the effectiveness of mix zones using traces generated based on traffic theory. In this paper, we analyze the privacy obtainable from using mix zones in VANETs based on actual recordings of vehicle movements. We choose rank instead of entropy as our privacy metric because, as we will show, entropy is difficult to measure in our scenarios.