PARAGLIDER DESIGN HANDBOOK

CHAPTER 1. PLATFORM

1.1 Introduction

1.2. Geometric Definition

1.2.1 Analytical methods

1.2.2 Discrete method

1.3 Center of gravity

1.1. Introduction

The platform in a paralider is one of the most important elements involved in the design of it. Any design should begin with the picture of the platform.

Major elements:

We can distinguish the following basic elements of the platform:

- The leading edge

- The trailing edge

- The tips

- The trailing edge

- The tips

Of course, the designs are symmetrical in plan to maintain the same properties on one side and one wing.

Historically, have experimented with a variety of platforms: rectangular, trapezoidal, triangular, elliptical, rectangles truncated, arrow regressive, with Colita morros central or core, ... But now almost all forms designs tend to look an elliptical with tips slightly truncated.

The most important parameters of the platforms are as follows:

Parameter |
unit |
variable name |

Area |
m2 |
area |

Wingspan |
m |
span |

Max chord |
m |
maxch |

Medium chord |
m |
medch |

Minimum chord |
m |
minch |

Aspect ratio (flat) |
dimensionless |
AR |

Center of gravity |
m |
cdg |

1.2. Geometric Definition

1.2.1 Analytical methods

There are many possible methods for defining the plant. On that follows is one of mathematical methods possible.

In Cartesian coordinates the equation of the ellipse centre (0.0) is:

x ² / a ² + y

For a generic center in (x0, y0) is:

(x-x0) ² + (y-y0) ² = 1

clearing and function is obtained x: y = y0 +-b * sqrt (1 - ((x-x0) ²) / in ²)

Actually, it is not obliged to choose a form exactly elliptical for the leading edge or the edge of flight, why can change the equation by adding any other mathematically. To simplify linear add a variation to the tips such as:

if 0 <x <= kx and 0

if x> and xk = k * (x-xk) (k, xk parameters to choose)

Fig 1. Equation of the ellipse

Taking values x0 = 0 (x-axis centered ellipse), the shape of leading edge elliptical amended parameters elliptical a1, b1, k1 parameter linear, and focused on the point (0, y1) is:

Leading edge: y = y1 + b1 * sqrt (1 - (x ²) / a1 ²) + x * k1

Similarly, the shape of elliptical edge output parameters modified elliptical a2, b2, linear parameters k2, and focused on the point (0, y2) is:

Trailing edge: y = y2-b2 * sqrt (1 - (x ²) / a2 ²) + x * k2

With these equations and also choosing the correct parameters can be defined completely the platform of a modern glider.

Fig 2. Analytical platform definition

By way of example, shows the values of the parameters of a design: (in redaction)

1.2.2 Discrete method:

The discreet method is to give directly to each profile, coordinates "Y" of the leading edge (Ai) and coordinate "Y" of the trailing edge (Bi), forming the triplets:

(xi, Ai, Bi) for i = 1,2,3 ,.... N N being the number of profiles in a semi-wing

The coordinates Ai and Bi can be obtained from equations, of drawings by hand or with computer, other wings ... and allow maximum freedom to define the platform.

1.3 Center of gravity

The centre of gravity of the
platform, has no direct relationship
aerodynamics, but the knowledge is of interest, since some designers
get very interesting empirical relationships with the position of the
center of pressure.

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