Development of a 6-DoF simulator for analysis and evaluation of autonomous parafoil systems

Gliding parachutes offer considerable scope for a large number of civil, humanitarian and military applications due to their ability to cover large horizontal distances from the drop point and their excellent controllability. A concept in the gliding-parachute category which has received attention since mid 60’s is the ram-air inflated fabric wing (also known as Jalbert parafoil or simply parafoil). Parafoils consist of a flexible fabric wing with rectangular planform and a streamlined cross-section which is opened at the leading edge to allow air to enter and inflate the wing to a specified shape. The payload is suspended on lines below the wing. Some of the earliest projects involving the usage of parafoilbased systems are discussed by Nikolaides and Knapp.1-7 and comprehensive bibliography up to 1980 is provided by Lingard8. Moreover, some definitions that in the last quarter of the twentieth century have become a sort of standard and discussion on modern parafoil design are given by Poynter9.
As it is possible to observe in the works mentioned above but also in more recent publications, parachute’s design and analysis rely mostly on empirical methods. An up-to-date example of this is a survey about the use of computational tools in the design and evaluation of parachute systems which was carried out with 15 worldwide parachute manufacturers10. All of ten responses received deny the employment of simulation software with the exception of computer assisted design (CAD) tools. This is a clear indication that, despite the growing relevance parachute systems have today in many application fields, computational mechanics is still hardly applied to their design and analysis.
With the objective of addressing this shortcoming, a series of computational tools have been developed at CIMNE in recent times. Most of them are integrated in a simulation code intended for the unsteady simulation of ram-air type parachute-payload systems11 which is based on an unsteady low-order panel method12 coupled with a membrane finite element explicit technique13 (including cords and ribbons models). In addition, the development of a set of complementary tools aimed at studying in an integrated manner the flight performance of guided parafoil-payload systems was undertaken. This software package consists of a 6 degree-of-freedom (DoF) dynamic simulator, based on aerodynamic derivatives, and an autonomous guidance, navigation and control system (GNC) implemented by means of a proportional-integral-derivative (PID) algorithm. Briefly, dynamic models based on derivatives offer a simple mathematical way of describing the flight dynamics of an aerodynamic system by means of linearized equations written in terms of suitable non-dimensional (constant) coefficients known as aerodynamic derivatives. These coefficients, which define, for example, how the aerodynamic forces and moments change with the angle of attack, yaw or brake deflections, determine the response of the system to small deviations from the equilibrium conditions at which it is linearized. The fidelity of the model depends on the number and accuracy of the derivatives employed. In this way, the behaviour of a particular parafoil-payload system can be modelled up to a desired degree of fidelity by defining a proper set of aerodynamic derivatives and also mass and inertial parameters. Given these characteristics through experimental
or numerical means, the model allows predicting the behaviour of the system subject to different flight and environmental conditions with a very low computational cost, making feasible parachute and mission real-time analyses. The main aspects underlying the 6-DoF simulator and the GNC model are described in this document.
The work is organized as follows. Section 2 briefly reviews some of the most important experiences in the modelling of parafoil vehicles. The 6 DoF dynamic model and the GNC strategy implemented are presented in Sections 3 and 4 and a first application example is provided in Section 5. Next, an advanced procedure for estimating aerodynamic derivatives from numerical data computed with CIMNE’s parachute code11 is presented in Section 6 and an application test case is given in Section 7. Finally, some relevant conclusions and future lines of research are drawn in Section 8. Moreover, with the objective of summarizing current airdrop technology, some of the most relevant parafoil systems are described in Appendix A at the end of this document.