  This contribution compares several different approaches allowing one to
derive macroscopic traffic equation directly from microscopic car-following
models. While it is shown that some conventional approaches lead to theoretical
problems, it is proposed to use a smooth particle hydrodynamic approach and to
avoid gradient expansions. The derivation circumvents approximations and,
therefore, demonstrates the large range of validity of macroscopic traffic
equations, without the need of averaging over many vehicles. It also gives an
expression for the ``traffic pressure'', which generalizes previously used
formulas. Furthermore, the method avoids theoretical inconsistencies of
macroscopic traffic models, which have been criticized in the past by Daganzo
and others.
