pfh.glidersim.paraglider_harness#

Models of paraglider harnesses.

Classes

ParagliderHarness(*args, **kwargs)

Interface for classes that implement a ParagliderHarness model.

Spherical(mass, z_riser, S, CD, kappa_w)

Model a harness as a uniform density sphere.
class pfh.glidersim.paraglider_harness.ParagliderHarness(*args, **kwargs)#

Bases: Protocol

Interface for classes that implement a ParagliderHarness model.

Methods

mass_properties(delta_w, r_R2RM)

Compute inertia-related properties about a reference point.

r_CP2RM(delta_w)

Compute the control points for the harness model dynamics.

resultant_force(delta_w, v_W2h, rho_air, g, ...)

Calculate the net force and moment applied to the harness (and pilot).
abstract r_CP2RM(delta_w)#

Compute the control points for the harness model dynamics.

Parameters
delta_wfloat [percentage]

The fraction of weight shift, from -1 (left) to +1 (right)

Returns
ndarray of float, shape (K,3) [m]

Control points relative to the riser midpoint RM. Coordinates are in payload frd, and K is the number of control points for the harness model.

abstract mass_properties(delta_w: float, r_R2RM)#

Compute inertia-related properties about a reference point.

Parameters
delta_wfloat [percentage]

The fraction of weight shift, from -1 (left) to +1 (right)

r_R2RMarray of float, shape (3,) [m]

The reference point in harness frd

Returns
dictionary
m_pfloat [kg]

The solid mass of the harness (and pilot)

J_p2Parray of float, shape (3,3) [kg m^2]

The moment of inertia matrix of the harness about its cm

J_p2Rarray of float, shape (3,3) [kg m^2]

The moment of inertia matrix of the harness about R

r_P2Rarray of float, shape (3,) [m]

The position of the harness cm relative to the reference point

r_P2RMarray of float, shape (3,) [m]

The position of the harness cm relative to the riser midpoint

abstract resultant_force(delta_w: float, v_W2h, rho_air: float, g, r_R2RM, mp: Optional[dict] = None)#

Calculate the net force and moment applied to the harness (and pilot).

The moment is calculated with respect to a reference point R at some position relative to the harness origin RM.

Parameters
delta_wfloat [percentage]

The fraction of weight shift, from -1 (left) to +1 (right)

v_W2harray of float, shape (K,3) [m/s]

The wind velocity at each control point in harness frd.

rho_airfloat [kg/m^3]

Air density

garray of float, shape (3,) [m/s^s]

The gravity vector in harness frd

r_R2RMarray of float, shape (3,) [m]

The reference point in harness frd about which the moment is calculated.

mpdictionary, optional

The mass properties associated with the specified control inputs and reference point. Used to avoid recomputation.

Returns
f_h, g_h2Rarray of float, shape (K,3) [N, N m]

Net force and moment about the reference point R.

__init__(*args, **kwargs)#
class pfh.glidersim.paraglider_harness.Spherical(mass: float, z_riser: float, S: float, CD: float, kappa_w: float)#

Bases: pfh.glidersim.paraglider_harness.ParagliderHarness

Model a harness as a uniform density sphere.

Coordinates use the front-right-down (frd) convention, with the origin at the midpoint of the two riser connections.

Parameters
massfloat [kg]

The mass of the harness

z_riserfloat [m]

The vertical distance from RM to the harness center.

Sfloat [m^2]

The projected area of the sphere (ie, the area of a circle)

Typical values for pilot + harness ([1]):

  • <80kg: 0.5

  • 80kg to 100kg: 0.6

  • >100kg: 0.7

CDfloat

The isotropic drag coefficient.

Typical values for pilot + harness ([1]):

  • Conventional: 0.8

  • Performance: 0.4

kappa_wfloat [m]

The maximum weight shift distance

Notes

The spherical assumption has several effects:

  • Isotropic drag: the aerodynamic force is the same in all directions, so the drag coefficient is a single number. This implies that using the drag coefficient for a performance harness (shaped to minimize drag in the forward direction) will also reduce the drag from crosswind.

    Also, the aerodynamic moment for a sphere is zero, and since the aerodynamic force is computed at the center of mass, the net moment about the center of mass is always zero.

  • Isotropic inertia: neglects the fact that pilot will often extend their legs forward for aerodynamic efficiency, which should increase the pitch and yaw inertia.

References

1(1,2)

Benedetti, Diego Muniz. “Paragliders Flight Dynamics”. 2012. pg 85

2

Babinsky, Holger. “The aerodynamic performance of paragliders”. 1999. pg 422

Methods

mass_properties(delta_w, r_R2RM)

Compute inertia-related properties about a reference point.

r_CP2RM([delta_w])

Compute the control points for the harness model dynamics.

resultant_force(delta_w, v_W2h, rho_air, g, ...)

Calculate the net force and moment applied to the harness (and pilot).
__init__(mass: float, z_riser: float, S: float, CD: float, kappa_w: float) → None#
r_CP2RM(delta_w=0)#

Compute the control points for the harness model dynamics.

Parameters
delta_wfloat [percentage]

The fraction of weight shift, from -1 (left) to +1 (right)

Returns
ndarray of float, shape (K,3) [m]

Control points relative to the riser midpoint RM. Coordinates are in payload frd, and K is the number of control points for the harness model.

mass_properties(delta_w, r_R2RM)#

Compute inertia-related properties about a reference point.

Parameters
delta_wfloat [percentage]

The fraction of weight shift, from -1 (left) to +1 (right)

r_R2RMarray of float, shape (3,) [m]

The reference point in harness frd

Returns
dictionary
m_pfloat [kg]

The solid mass of the harness (and pilot)

J_p2Parray of float, shape (3,3) [kg m^2]

The moment of inertia matrix of the harness about its cm

J_p2Rarray of float, shape (3,3) [kg m^2]

The moment of inertia matrix of the harness about R

r_P2Rarray of float, shape (3,) [m]

The position of the harness cm relative to the reference point

r_P2RMarray of float, shape (3,) [m]

The position of the harness cm relative to the riser midpoint

resultant_force(delta_w, v_W2h, rho_air, g, r_R2RM, mp=None)#

Calculate the net force and moment applied to the harness (and pilot).

The moment is calculated with respect to a reference point R at some position relative to the harness origin RM.

Parameters
delta_wfloat [percentage]

The fraction of weight shift, from -1 (left) to +1 (right)

v_W2harray of float, shape (K,3) [m/s]

The wind velocity at each control point in harness frd.

rho_airfloat [kg/m^3]

Air density

garray of float, shape (3,) [m/s^s]

The gravity vector in harness frd

r_R2RMarray of float, shape (3,) [m]

The reference point in harness frd about which the moment is calculated.

mpdictionary, optional

The mass properties associated with the specified control inputs and reference point. Used to avoid recomputation.

Returns
f_h, g_h2Rarray of float, shape (K,3) [N, N m]

Net force and moment about the reference point R.