Longitudinal phugoid dynamics of aircraft/glider (2nd order ODE, simplified flight dynamics)

This video presents the modeling of the so-called "phugoid" flight mode of an aircraft, as an example of dynamic system modelling for aerospace and control engineeing students.
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 • Dynamics of planar mot... .
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" or "phugoid", depending on the source. Of course, this is a crude first approach, and more complex models are routinely developed in most flight dynamics textbooks (I'm not an aerospace engineer).
Note: engine thrust has been assumed to be a constant input force 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 • phugoid mode: simulati... (simulation), and • Phugoid mode dynamics:... (equilibrium points and linearization).
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#physics #flightdynamics #aerospaceengineering
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Antonio Sala
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