Sensitivity of Aerodynamic Characteristics of Paraglider Wing to Properties of Covering Material

The paraglider wing is a flexible structure without stiffening elements of the elliptical contour in the top view and a cross-sectional airfoil profile during the flight. It acquires the aerodynamic shape due to the air pressure entering the vents on the leading edge of the wing. The covering is made of impregnated synthetic textiles, which (i) reduces the material’s permeability coefficient; (ii) influences the c_l/c_d ratio; (iii) creates the lift force by the advantageous pressure difference under dynamic conditions of the flight, i.e., the negative pressure on the upper plane and the overpressure on the lower surface of the wing.

The textile covering should be lightweight, shock- and ultraviolet (UV)-resistant, and waterproof. The impregnated synthetic textiles of reduced permeability coefficient are made of nylon PA 6.6 [1, 2], which results in an increased c_l/c_d ratio, i.e., better aerodynamic performance. The uniform impregnated layer of dimensional tolerance of 10⁻³ m improves the air permeability. Although its composition is not announced by manufacturers, the impregnant is usually based on polyurethane (PU). Fabrics are manufactured using the Ripstop technology, i.e., the reinforced threads are located at regular distances in the square form [3].

The problem of wing dynamics during the flight is defined by a state variable, which is the pressure. The fundamentals concerning paragliders and the mechanics of flight can be found elsewhere [4, 5]. The problem is solved using a geometrical model of the structure approximated by dimensionless coordinates of crucial points and smoothed by spline curves. The physical model is defined using the geometrical model, finite volume method, and accompanying phenomena. It is determined by the flight parameters (the lift force, the drag force, and the c_l/c_d ratio), the surrounding conditions, and so on. The mathematical model introduces a set of differential equations accompanied by the boundary conditions [6, 7, 8]. The problem is solved numerically by applying the wing model in Ansys program. The distribution of state variables can be visualized using any graphical program [9]. This paper is a continuation of previous work [3].

The main goal of the article is to determine the sensitivity of aerodynamic characteristics to the properties of the covering material of a paraglider wing. A set of different materials is introduced, ranging from the air-impermeable one to that subjected to hydrolytic–mechanical degradation. Optimization of the material properties improves the lift force and the aerodynamic characteristics of the paraglider.

The novel elements are the following. (i) The available literature does not introduce the effect of material permeability on the aerodynamic characteristics of the wing. (ii) A set of parameters determining the aerodynamic characteristics of the paraglider are introduced. (iii) The obtained pressure distributions explain the aerodynamic safety of the paraglider in dynamic conditions.

Let us first assume a universal paraglider wing of improved sliding capacity, and its total weight reduced to 5 kg. To determine the geometrical model, the wing contour and airfoil cross section of the real structure were measured. The initial step is to determine the 23 dimensionless coordinates creating the airfoil profile within the XZ plane (Figure 1). Next, the geometry of the wing contour is defined in the XY plane (Figure 2). The coordinates of the particular point in the 3D Cartesian coordinate system are calculated using the elliptic equation in the following form: (1) x=xiCj+12(Co−cj);y=(R+zjCj)sin(yjR);z=[(R+zjCj)cos(yjR)]−R x = {x_i}{C_j} + {1 \over 2}\left( {{C_o} - {c_j}} \right);y = \left( {R + {z_j}{C_j}} \right)\sin \left( {{{{y_j}} \over R}} \right);z = \left[ {\left( {R + {z_j}{C_j}} \right)\cos \left( {{{{y_j}} \over R}} \right)} \right] - R

Figure 1

Figure 2

The coordinates can be introduced into the simple numerical program in MatLab environment to create the coordinates of an optional point on the wing contour. These points are connected by the smoothing curves of the spline type to create the ribs’ profile. The final contour is obtained by incorporating the material surface for these points of assumed thickness of 2 × 10⁻³ m, which is the typical value for the paraglider (Figure 3).

Figure 3

Let us also assume a set of covering materials (Table 1). The basic material is always made of the polyamide PA 6.6 of plain weave using the Ripstop reinforcement. The air-impermeable material is a theoretical one, which limits the flight characteristics.

The geometrical model of a paraglider is introduced into the finite volume mesh of cuboid elements. Due to its symmetry, only a half of the structure is considered using the condition Symmetry. The dimensions of the control volume are 20 m in front of the wing and 40 m in other directions. The external surfaces of the cuboid control volume are defined by the boundary condition Pressure Far-Field, which is the undisturbed flow of the prescribed values of velocity, pressure, and temperature of the surrounding air. The finite volume mesh is created by standard procedures.

3.2

Tetrahedron patch conforming method

The procedure creates a finite volume mesh for the medium (the air) in the surrounding space.

3.2.1

Edge sizing

This method of mesh dimensioning introduces the prescribed number of nodes on the selected edges/segments. Each part of the upper and lower profiles is divided into 30 parts, whereas the short profile of air inlet is divided into three parts.

3.2.2

Face sizing

This method of mesh dimensioning incorporates the prescribed dimensions of each element on the selected surfaces. The procedure is applied to model the air inside the paraglider in the plane of symmetry.

The finite volume mesh of 474264 elements is generated using the Ansys Meshing program (Figure 4). The mesh quality is relatively good because the mean value of the parameter Orthogonal Quality is equal to 0.7629 (the perfect mesh has Orthogonal Quality = 1) and Skewness is 0.2463 (the perfect mesh has Skewness = 0). The deviations are absolutely acceptable for the considered number of the finite volume mesh.

Figure 4

The problem was solved in the Ansys Fluent environment applying the Spalart–Allmaras turbulence model. The fluid filling the computational volume is air, which is determined by the procedure Materials; air → ideal gas. Thus, the boundary condition Pressure Far-Field can be applied on each surface of the cuboid (except the plane of symmetry). The outer surfaces are at sufficient distance from the examined object; therefore, they might present a state of undisturbed flow. Thus, the parameters of the surroundings are the following: temperature T = 300 K; pressure p = 101325 Pa; velocity v = 0.037 Ma; and angle of attack a = 6°. The plane of symmetry is described by the condition Symmetry. The boundary condition given to the walls creating the wing surface is Interior; this condition enabled the use of the model Porous Media (Cell Zone Conditions → Porous Media) for the cells creating the paraglider wing geometry. Therefore, the materials are introduced into the numerical model using the effective air permeability. The corresponding condition Porous Resistance has the following form: (2) 1α=−Δptμvm {1 \over \alpha } = - {{\Delta p} \over {t\mu {v_m}}}

The parameter Porous Resistance is determined in Table 2, for porous materials transmitting air according to Table 1, except for the air-impermeable covering.

The dynamics of air motion is defined by the conservation equations of mass, momentum, and energy in vector form, which can be simplified to the set of equivalent scalar equations. The corresponding differential equations are accompanied by the boundary conditions, i.e., the environmental conditions. (3) ∭V∂ρ∂tdV+∬AρvndA=0ddt∭Vρv→dV=∬Ap→ndA+∭VF→mρdVddt∭Vρ(cwT+v22)dV=∬Ap→n⋅v→dA+∭VρF→m⋅v→dV+∬Aq˙nρA+∭Vq˙mρdV \matrix{ {\mathop{\int\!\!\!\int\!\!\!\int}\limits_{\kern-5.5pt V} {{{{\partial _\rho }} \over {{\partial _t}}}dV + \int\!\!\!\int\limits_A {\rho {v_n}dA = 0} } } \hfill \cr {{d \over {dt}}\mathop{\int\!\!\!\int\!\!\!\int}\limits_{\kern-5.5pt V} {\rho \vec vdV} = \int\!\!\!\int\limits_A {{{\vec p}_n}dA} + \mathop{\int\!\!\!\int\!\!\!\int}\limits_{\kern-5.5pt V} {{{\vec F}_m}\rho dV} } \hfill \cr {{d \over {dt}}\mathop{\int\!\!\!\int\!\!\!\int}\limits_{\kern-5.5pt V} {\rho \left( {{c_w}T + {{{v^2}} \over 2}} \right)dV = \int\!\!\!\int\limits_A {{{\vec p}_n} \cdot \vec vdA} + \mathop{\int\!\!\!\int\!\!\!\int}\limits_{\kern-5.5pt V} {\rho {{\vec F}_m} \cdot \vec vdV} + \int\!\!\!\int\limits_A {{{\dot q}_n}dA} + } \int\!\!\!\int\!\!\!\int_V {{{\dot q}_m}\rho dV} } \hfill }

The aerodynamic force is generated by an advantageous pressure distribution, i.e., negative pressure on the upper plane and overpressure on the lower surface, and it has the following form: (4) F=clSρv22 F = {c_l}S\rho {{{v^2}} \over 2}

The resultant aerodynamic force during the flight can be decomposed into the advantageous lift force L and the drag force D. The greater the lift force compared to the drag force, the greater is the c_l/c_d ratio, according to the following formula [3]: (5) cl/cd=LD {c_l}/{c_d} = {L \over D}

The paper is theoretically oriented. Modeling and optimization of aerodynamic characteristics and properties of the covering material are significant for a paraglider structure, being more beneficial and efficient than prototype tests. The wing of considerable dimensions and complicated structure is designed without stiffening and is manufactured in specialized factories. The costs of the materials, finishing procedures, production, and amount of work are significant.

The validation of results for the complete paraglider is impossible because of the expensive manufacturing process of the prototype. The tests are implementable inside a large-size wind tunnel, which is inaccessible in Poland. The dynamic conditions of flight will be now extremely dangerous for the pilot.

Modeling on a reduced scale is unrealizable because of the nonexistence of manufacturing technology for reduced dimensions and due to the high manufacturing costs. The price of the scaled-down prototype is much higher than the paraglider on a 1:1 scale. The structure of reduced dimensions has stiffness during the flight uncompared to the real object and is hard to operate (the pilot has standard dimensions).

Thus, only a theoretical model enables the analysis of the global sensitivity of the paraglider characteristics to different materials, optimization of the pressure distribution inside and outside the contour, and optimization of the structural shape. Some parameters can be partially verified, e.g., the air permeability and creation of the single airfoil profile. However, the problem is complicated and beyond the scope of the paper presented and will be discussed in a consecutive article.

Numerical analysis considers five different covering materials and a few parameters determining the aerodynamic characteristics, viz., the mean pressure inside the wing profile, the mass flow rate, the aerodynamic force, the lift force, the drag force, the c_l/c_d ratio, the pressure distributions in the plane of symmetry, and the pressure distribution on the upper and lower wing surfaces.

The best aerodynamic characteristics are presented by the paraglider made of air-impermeable covering (the comparative material). The pressure inside the wing contour is 101415.83 Pa; and aerodynamic excellence is 13.1687. However, the paraglider made of material of higher air permeability (3 L/m²/min) presents comparable properties. Its aerodynamic excellence decreased by only 0.3979. That is, assuming a starting height of 1 km, the wing of better characteristics reaches a distance longer by 388 m during the gliding flight. The analysis does not include the additional resistance of the rigging and the pilot attached in the harness.

The paraglider made of Porcher Marine 9017 PU E38A material (used approximately 20 years ago) has much worse parameters than the previous two structures. Its c_l/c_d ratio reaches 11.6253, although the wing still generates sufficient aerodynamic force. Based on the pressure distribution, the wing covered by this material is safe and stable during the flight.

The last two materials are degraded and show the worst characteristics. The paraglider made of Skytex 27 Classic material after seven washes is usable but dangerous. The wing covered by Skytex 36 fabric subjected to hydrolytic–mechanical degradation is probably unfit for flight. A very high pressure at the leading edge disturbs and creates overpressure inside the wing and forms an aerodynamic shape. The flight is extremely dangerous.

Summarizing, the aerodynamic characteristics of paragliders covered by the currently used fabrics are comparable with those of paragliders covered by air-impermeable material. The technological progress yields adequate wing covering; the materials have improved air permeability and lower surface masses.

The textile covering can be also optimized with respect to the reduced surface mass of acceptable strength. The air permeability, material strength, and susceptibility to permanent deformation should be improved. The other question is the resistance to damage caused by fabric aging and finishing procedures. These characteristics can be next optimized in terms of the coupled heat and moisture transport within the covering material [7, 10, 11].