Look at the image attached. It illustrates an aircraft in uniform airflow. As the aircraft pitches down, the airflow at nose and rear of the aircraft would bend and squeeze. Since air is assumed analogous to an elastic medium, as it bends, due to its elasticity, it (air) tends to unbend and get undeformed. As the air (streamline) unbends, it generates restoring reaction force over nose and rear of the aircraft, producing a restoring pitching-moment to stabilize and restore the aircraft to its initial level attitude. This is simply an empirical model for aerodynamic stability modeled through assuming resilience of fluid flow.
Notice that, for zero velocity v=0, where v is velocity of aircraft relative to wind, air is like water with no elastic restoring force, hence an inert body inside still air, would experience a freefall if no other auxiliary force as buoyancy is present. When the velocity is increased, air would get more elastic, making the aircraft in fluid flow become more stable. But if again velocity is increased more and more (extreme state), air would get a state near a solid with less resilience and no deformability, hence aircraft dynamic response would get less smooth (less resilient and more damped).
Modeling such pitch response as second order dynamics with an associated frequency and damping would be consequential.
How do you think about that? Is aerodynamic damping and stiffness depending only on fluid properties as viscosity and density and fluid relative velocity? Does shape affect achieved velocity and velocity affect aerodynamic characteristics (as a dual interaction)? Is the Reynolds number a good criteria for evaluation of elasticity and resilience of fluid flow? Let me know your ideas.
To tell the true, I don't see the analogy to an elastic medium... Consider a volume of air, you can apply normal or tangential stress and there is not elastic force that can do resistence in the changing of shape of the air volume due to displacement as it happens in an elastic medium. To restore the initial shape you need to convert the stress but when you apply tangential stress this is associated to a loss of kinetic energy due to entropy production.
Maybe I am not understanding your question?
@Filippo Maria Denaro. Thank you for the comment. You are explaining fluid dynamics through a mechanical standpoint, whereas I am trying to model fluid motion through an aerodynamics viewpoint for stability analysis of an aerospace vehicle. What I am aiming at to describe is solid-fluid interaction in hope of revealing an empirical aerodynamic model. What you described is with regard of a lumped amount of fluid. We are separated through our assumption. You exemplify fluid through its mechanical sense, while I am exemplifying fluid dynamics through an aerodynamics viewpoint to build an empirical model for aerodynamic stability analysis.
You did this assumption that in my opinion is not true:
" Since air is assumed analogous to an elastic medium, as it bends, due to its elasticity, "
Your opinion is honorably respected. I am looking for pros and cons, and further discussion.
@Filippo Maria Denaro.
It is probably the distinction between fluid mechanics and flight mechanics.
Honestly I am not an expert of flight mechanics but I doubt that the assumption of air as an elastic medium can be assumed. You cannot change the physical assumption depending on the discipline but I could be wrong.
I am sure someone more experienced can give his opinion.
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