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Icaro Laminar 13 MRX: Difference between revisions
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→The moment diagram for hang gliders
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==== The moment diagram | ==== The unique moment diagram of hang gliders ==== | ||
In the moment diagram, the moment coefficient is shown as a function of the angle of attack. A positive moment indicates a nose-up tendency (pitching up), while a negative moment indicates a nose-down tendency (pitching down). Steady flight is therefore characterized by CM = 0. | |||
[[File:Pitching moment depending on the pilot position.jpg|none|thumb|800px|Influence of pilot deflection on pitching moment]] | |||
For conventional aircraft, the diagram consists of a single curve. However, since the pitching moment depends strongly on the center of gravity position - and hang gliders are controlled by shifting the center of gravity - there are practically an infinite number of moment curves for hang gliders. The following diagram (Figure 3) shows the curves for trimmed flight, slow flight, and high speed flight. | |||
The moment curves shown are based on measurement data for a modern topless flexible hang glider at an airspeed of 40 km/h. | |||
The differing shapes of the curves depending on the center of gravity respectively pilot deflection are clearly visible. The range of angles of attack for steady flight extends from approx. α = 12° (maximum flight speed) to about α = 37° for minimum flight speed (stall limit). However, during unsteady flight conditions, any angle of attack may occur, ranging from –180° < α < +180°. | |||
All the moment curves intersect at CM<sub>0</sub> (CM<sub>0</sub> refers to the moment coefficient at α<sub>0</sub>, the angle of attack at which lift is zero). This must be the case, because without lift, the total moment is independent of pilot displacement (see Figure 2). No lift means no moment - regardless of the moment arm (i.e., the pilot's displacement). Therefore, CM<sub>0</sub> must be the same for all pilot positions. Since aerodynamic lift increases linearly with angle of attack, the '''moment curves pivot around CM<sub>0</sub>'''. | |||
This behavior is a '''unique characteristic of weight-shift-controlled hang gliders'''. | |||
Also clearly visible is the previously mentioned control reversal for α < α<sub>0</sub>. In this range, pushing out (i.e., shifting the pilot's weight backward) leads to a dramatic reduction in moment, even resulting in negative moments. Every hang glider pilot must be aware of this! '''Understanding control reversal is essential for preventing tuck accidents'''.<br> | |||
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[[File:Pitching moment depending on the pilot position.jpg|none|thumb|800px|Figure 3: Influence of pilot deflection on pitching moment]] | |||
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Another interesting aspect is the moment curve during trimmed flight. | |||
Trimmed flight is characterized by the absence of bar pressure, meaning it makes no difference whether the pilot grips the base bar or flies hands-free. For this reason, the diagram also includes the moment about the hang point (shown as an orange dashed line), which serves as a measure of bar pressure. The angle of attack for trimmed flight (α<sub>Trim</sub>) is where both the moment about the overall center of gravity and the moment about the hang point are zero (CM<sub>Total</sub> = CM<sub>HP</sub> = 0). | |||
The hang glider can be trimmed by slightly shifting the hang point (🟠). Just like the total moment curve, the hang point moment curve also rotates around CM<sub>0</sub>. Shifting the hang point rearward flattens the curve and shifts CM = 0 to a higher angle of attack, resulting in a lower trim speed. Shifting it forward, on the other hand, steepens the curve and moves CM = 0 to a lower angle of attack, increasing the trim speed. This fine-tuning is a key tool for adapting flight characteristics to the pilot's preferences or conditions. | |||
The moment curves around the reference point for hands-free flight (<big>▼</big>) as well as for the glider alone (without the pilot; 🟦) differ only marginally from the curve about the hang point, since the respective moment reference points are located very close to each other. To keep the diagram clear and readable, these additional curves were omitted. | |||
One more interesting point: Every hang glider pilot knows that the glider flies much less stable when flying hands-free compared to holding the base bar. This behavior is easy to interpret using the moment diagram. Longitudinal (pitch) stability is characterized by the slope of the pitching moment coefficient curve at CM = 0. The steeper (more negative) the slope, the greater the stability. When the control bar is held, the blue moment curve applies. For hands-free flight, the orange dashed curve applies, which has a significantly flatter negative slope than the blue one. So, in trimmed flight (and unfortunately ''only'' there), the pilot holds the power to choose the level of stability by either gripping the bar or not. Cool, isn't it? | |||
=== Tuck avoidance === | === Tuck avoidance === | ||