Various shortcomings and inaccuracies in the existing approach and presentation of airplane flight dynamics in pedagogy have been identified. An improved pedagogical presentation is offered which is clean - uses the two timescales in longitudinal dynamics to derive short period and phugoid mode parameters, simple - starts with the longitudinal dynamics equations rather than the complete six degree of freedom formulation, and correct - uses a physically correct model of the dynamic (rate) derivatives and employs the concept of a static residual in deriving the slower (phugoid) mode approximations. The redundant and confusing concepts of dimensional derivatives and static stability are junked. A companion paper presents a similar approach to the lateral-directional dynamics.