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Icaro Laminar 13 MRX: Difference between revisions
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→Basics of pitching moment and longitudinal stability
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=== Basics of pitching moment and longitudinal stability === | === Basics of pitching moment and longitudinal stability === | ||
The | The moment curve plays a central role in analyzing the static and dynamic longitudinal stability of an aircraft. It describes how the moment (i.e. the torque) acting on the aircraft varies with changes in the angle of attack and over time. | ||
Here are the key points about the moment curve and its importance: | |||
# '''Definition of Moment''': The moment is a measure of how a force causes an object to rotate around a pivot point (in this case, the aircraft’s center of gravity). In the context of static longitudinal stability, the moment refers to the pitching behavior of the aircraft. | |||
# '''Moment Curve and Angle of Attack''': The moment curve shows how the moment about the center of gravity of an aircraft varies as a function of the angle of attack (α). The angle of attack is the angle between the wing and the airflow. When the angle of attack changes, it affects the lift and the moment acting on the aircraft. | |||
# '''Stability Criterion''': An aircraft is statically stable if the moment about the center of gravity produces a negative value when the angle of attack increases (i.e., the moment acts against the deviation). Therefore, the moment curve should have a negative slope as the angle of attack increases up to a certain point. The steeper the negative gradient, the higher the restoring forces. The gradient of the moment curve is also known as the longitudinal stability margin. | |||
In summary, the moment curve is an important tool for evaluating and understanding the static and dynamic longitudinal stability of an aircraft and how changes in the angle of attack affect its flight behavior. | |||
In order to assess the longitudinal stability of hang gliders, it must first be clarified where the moment reference point for hang gliders actually is located. | |||
For conventional aircraft, it is the aircraft's center of gravity. Unfortunately, there are many different centers of gravity for weight-shift controlled hang gliders with flexible main suspension. The following slide provides an overview: | |||
[[File:Moment reference points, center of gravity positions and their meaning for pitch stability.jpg|left|thumb|800px|Moment reference points, center of gravity positions and their meaning for pitch stability]] | [[File:Moment reference points, center of gravity positions and their meaning for pitch stability.jpg|left|thumb|800px|Moment reference points, center of gravity positions and their meaning for pitch stability]] | ||
<div style="clear:both"></div> | |||
The diagram shows that the moment reference point can change considerably depending on the configuration. Basically, a distinction can be made between three different flight configurations: | |||
<br> | |||
Configuration 1 corresponds to the '''usual flight condition''': | |||
* hands are at the control bar | |||
* main suspension is tight | |||
The moment reference point is the '''overall center of gravity''' of the system consisting of the hang glider and the pilot (green triangle in the diagram <big>▲</big>). | |||
<br> | |||
Configuration 2 corresponds to '''hands-free flying''': | |||
* no contact between pilot and base bar | |||
* no contact from the pilot to any other part of the hang glider | |||
* the only connection from the pilot to the glider is via the main suspension to the hang point (HP) | |||
* tight (!) main suspension | |||
For this configuration, the moment reference point is in the “'''common center of gravity of glider and pilot, whereby the entire pilot mass is to be assumed at the hang point'''” (green gradient symbol <big>▼</big>). This point is much closer to the wing. | |||
<br> | |||
''Comment: For this configuration only, it can be shown (e.g. Horst Altmann dissertation, 1997; Michael Schönherr,, 1977-1979) that the (mathematically difficult to describe) 2-body hang glider-pilot system can be regarded as a 1-body system (simple mathematical description).'' | |||
<br> | |||
In configuration 3, | |||
* the main suspension is loose and there is | |||
* no contact between the pilot and the hang glider (pilot is falling aside the hang glider). | |||
Consequently, the '''center of gravity of the hang glider''' (🟦) must be selected as the moment reference point. During this phase of flight, the hang glider does not even 'know' that there is a pilot next to it. The hang glider must recover on its own. However, this flight condition usually only occurs for an extremely short time. The practical relevance is therefore low. | |||
<br> | |||
Another important moment reference point - although this is not a center of gravity - is the '''suspension point (HP)''' (🟠). The moment around this point '''describes the control forces'''. | |||
<br> | <br> | ||
In the prevailing discussions on longitudinal stability, these four moment reference points are often mistaken and mixed up in the argumentation. | |||
<br> | <br> | ||
[[File:Composition of the total moment (Glider + Pilot).jpg|left|thumb|800px|Explaining the mechanism of control reversal]] | [[File:Composition of the total moment (Glider + Pilot).jpg|left|thumb|800px|Explaining the mechanism of control reversal]] | ||
<div style="clear:both"></div> | |||
<br> | <br> | ||
[[File:Pitching moment depending on the pilot position.jpg|none|thumb|800px|Influence of pilot deflection on pitching moment]] | [[File:Pitching moment depending on the pilot position.jpg|none|thumb|800px|Influence of pilot deflection on pitching moment]] | ||