Directional bias of the lp-norm

This paper concerns the use of the lp-norm for estimating travel distances in a transportation network. In previous empirical studies, values of the parameter p>2 have been employed to characterize road networks. After a detailed study of the directional bias of the lp-norm, it is shown here that such values need never be considered, since the same degree of accuracy is obtained with a value of p in the interval (1,2) after rotating the axes 45°.