Solve Equilibrium Equations

Definition of the initial basic parameters used to solve the longitudinal equilibrium of the paraglider. This section is informative and is used by the designer, to study the values of the forces involved in the balance of the wing, the flight speed, the angles, and the glide coefficient. To find realistic values, it is necessary to do the study simultaneously with the XFLR5 program or CFD programs, and perform several iterations until satisfactory values are obtained. Currently, it is not yet possible to fully automate this calculation. The designer must apply his criteria according to the type of wing under study.

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Raw data:

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*       35. SOLVE EQUILIBRIUM EQUATIONS
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1
g        9.807  m/s2 gravity of Earth
ro       1.225  kg/m3 air mass density
mu       18.46  muPa·s air dynamic viscosity (microPascals)
V        12.4   m/s  estimated flow speed
Alpha    9.45    deg  estimated wing angle of attact at trim speed
Cl       0.67913       wing lift coefficient
cle      1.0         lift correction coefficient
Cd       0.03790     wing drag coefficient
cde      1.1        drag correction coefficient
Cm       0.0         wing moment coefficient
Spilot       0.438  m2   pilot+harness frontal surface
Cdpilot  0.6         pilot+harness drag coefficient
Mw       4.0    kg   wing mass
Mp       70   kg   pilot mass included harness and instruments
Pmc      0.2    m    pilot mass center below main karabiners
Mql      8.0    g    one quick link mass (riser-lines)
Ycp      0.575  m   y-coordinate center of pressure
Zcp      0.395  m   z-coordinate center of pressure

g Gravity of Earth (9.80665 m/s2 standard gravity)

ro Air mas density kg/m3

mu Air dynamic viscosity microPascals·s

V Estimated initial flow speed m/s, used for first Cl, Cd, Cm values

Alpha Estimated ideal angle of attack deg. Max glide ratio according wing aerodynamic analysis

Cl Wing lift coefficient, obtained by analysis with individual profiles, XFLR5, or CFD

Cle Multiplier coefficient of Cl, to consider non-modeled geometries, use 1.0 in case of doubt

Cd Wing drag coefficient, obtained by analysis with individual profiles, XFLR5, or CFD

Cde Multiplier coefficient of Cd, to consider non-modeled geometries, use 1.15 in case of doubt. If the Cd data comes from CFD this coefficient can be very close to 1.0. Currently studying how this Leparagliding 3.20V Notes and changes over previous versions 9 coefficient affects the results. Probably by adjusting through Cde the expected GR, the rest of the parameters will be very close to reality.

Cm Wing moment coefficient, obtained by analysis with individual profiles XFLR5, or CFD

Spilot Pilot + harness frontal surface (m2)

Cdpilot Pilot+harness drag coefficient (depends on the type of harness, especially if have fairings)

Mw Wing mass (kg) without lines and risers

Mp Pilot+harness+instruments mass (kg)

Pmc Pilot+harness mass center distance from main carabiners (m)

Mql Mass of one quicklink used to connect riser with lines (kg)

Ycp Y-coordinate of center of pressure (m), obtained by analysis with individual profiles, XFLR5, or CFD

Zcp Z-coordinate of center of pressure (m), obtained by analysis with individual profiles, XFLR5, or CFD

Remember that the axes used in LEparagliding are:

  • Origin (0,0,0)= at the nose of the central profile section.

  • X-axis horizontal and in the span direction

  • Y-axis along the central chord

  • Z-axis perpendicular to the XY plane and pointing down (not coincides with gravity axis)

A more detailed description you can find here Laboratori d'envol website.