Longitudinal phugoid mode dynamics of an aircraft/glider (simplified 2nd order ODE)

Antonio Sala, UPV

Difficulty: *** ,       Relevance: ,      Duration: 16:13

*Enlace a Spanish version

Summary:

This video presents the modeling of the so-called “phugoid” flight mode of an aircraft. Under certain assumptions (planar motion, negligible rotational inertia, large radius of curvature of the CoG trajectory), the plane can be considered as a point mass subject to tangential and normal forces; thus, we may write the equations of motion in intrinsic coordinates, discussed in the video  videorefintrid1EN.

Once these equations of motion are taken into account, it is simply a question of substituting in said equations the thrust of the engine and the aerodynamic resistance in the tangential direction, the lift in the normal direction, and of breaking down the weight into its tangential and normal components.

With these ideas, it is possible to write the so-called Zhukovski/Lanchester equations that approximate this mode of flight dynamics called “fugoid”. Of course, this is a crude first approach, and more complex models are routinely developed in most flight dynamics textbooks.

Note: engine thrust has been assumed to be a constant input but depending on the propulsion system, it may have airspeeed-dependent terms (for instance in constant-power propeller engines); these issues (and many others) have not been considered here, for simplicity.

The study of fugoid dynamics continues in video [fugsimEN] (simulation), and [fugeqlinEN] (equilibrium points and linearization).

*Link to my [ whole collection] of videos in English. Link to larger [ Colección completa] in Spanish.