For the explosion safety assessment in industrial setting, detonation dynamic parameters provide important information on the sensitivity and conditions whereby detonations can be favorably occurred. In this study, new measurement of the critical tube diameter and the critical energy for direct initiation of a detonation is reported for a number of hydrocarbon-oxygen mixtures. The simultaneous experimental measurement carried out in this work allows the investigation of the direct scaling between these two dynamic parameter quantities of gaseous detonations. Using the new set of data, this paper also assesses the validity of an existing semi-empirical initiation model, namely, the surface energy model by Lee, and a simplified work done model. Both phenomenological models provide a general relationship between the two dynamic detonation parameters and comparison shows a good agreement between the theoretical results and the experimental measurement. The scaling of critical tube diameter with detonation cell size in this study also confirms the results in the previous literature. (C) 2013 Elsevier Ltd. All rights reserved.