Determining technique for optimal rigging angle and aspect ratio of the soft wing with sling support

Aeronautical and Space-Rocket Engineering

Aerodynamics and heat-exchange processes in flying vehicles


Shved Y. V.



While developing paragliders and gliding parachutes many issues on the optimal selection of the airfoil, its relative thickness and twist over the span, the law of the wing arc distribution and its shape in the sweep, length and slinging arise. Selection criteria for of some of these parameters may be transferred practically without changing the methods, rather explicitly elaborated for the historically earlier appeared aerial vehicles with balancing by the payload weight (hang-gliders). However, the paraglider, also related to the flying vehicles balanced by the load, has some specifics, since it employs momentless carrying shell.

The parameters estimates of the aerial vehicles with the soft wing and sling support with various working-out degree are presented in [5-19]. However, the issue of working-out the simple and vivid analytical technique for obtaining optimal characteristics of the above said aerial vehicles, which does not employ iteration approximating and general empirical assumptions, still remains open. The article is devoted to the study of some aspects of this technique.

author proposes to perform the calculation in the following sequence:

  1. It is assumed, that in the assigned flight mode, the wing has the required angle of attack. Aerodynamic coefficients of the airfoil Cxp and Cya for the specified mode are being elected.

  2. Based of the obtained coefficients, the glading angle is calculated according to the expression proposed in the article. Then, with account for the obtained gliding angle, the gliding speed is calculated using the following expression.

  3. After selecting several options of the wing profiles and aspect ratio the comparative calculation of the flight quality is performed. With too small values of the wing lift coefficient, the main contribution to the resistance is brought by the air-dropped cargo and slings. If the Cya is too large, the inductive resistance becomes prevalent. Consequently, for each wing aspect ratio, the system slings and cargo type it is possible to determine the optimum carrying capacity of the designed wing profile. Conversely, it is possible to determine the optimal aspect ratio with given the remaining design characteristics.

  4. After the final selection of the profile, by the center of pressure on the wing MAC (middle aerodynamic chord) is determined. Further, with account for the obtained coordinates of the center of pressure on the MAC, the coordinate of the wing suspension relative to the load center of gravity is determined by the proposed formula.

The article demonstrates also the independence of the of self-balancing wings angle of attack from the thrust magnitude. This conclusion is based on the fact, that for the angle of the slant of the slings relative to the center of the pressure of the MAC in the horizontal flight mode under thrust and in the gliding mode, identical equations were obtained.

In [1] the algorithm for static parameters calculation of the motor flight vehicle with a soft wing is presented. In the presented article it was expanded for the gliding descent mode.


paraglider, gliding parachute, soft wing, aspect ratio of the wing, wingspan, lift-drag ratio, airfoil


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