A Simple, correct pedagogical presentation of airplane longitudinal dynamics

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.