Why high aspect ratio

The aspect ratio of a wing is the ratio of its wingspan length to the chord width, or mean distance between the leading and trailing edges. A high aspect ratio wing is typically longer, thinner, faster, lower drag but lower lift; a low aspect ratio wing is shorter, fatter, and has higher lift but also higher drag.

High aspect ratio wings are often used in speed-oriented disciplines such as windfoil slalom and course racing, and Formula Kite racing. However, high aspect wings are also becoming more prevalent in the developing disciplines of big wave surf foiling, downwind paddling, and experimental wingfoil disciplines such as freestyle and racing.

High aspect ratio wings often have less surface area than low aspect ratio wings; a typical surface area range would fall in about cm2. A smaller surface area wing generates less lift, and gives the rider better control in higher wind and higher foiling speeds.

High aspect ratio front wings are usually designed to have a slimmer profile or leading edge for less drag. Aspects ratios and wing loading are combined for different flying capabilities.

For example, high aspect ratio combined with low wing loading is used for slow flight such as gliding or soaring. Add to collection. Activity ideas Continue the learning with your students with one or more of these activities Birds and planes — explore the importance of wing shape and size and how this determines the flight capabilities of birds and planes.

Aerofoils and paper planes — learn how to make an aerofoil and to make and fly paper planes. Making a glider — handcraft a glider from balsa wood and in the process learn about aerofoil wing shape, glider parts and terminology.

Then experiment with flight using variables of wind and nose weight. Observing wings for flight has suggestions on how to use the interactive Wings for flight graphic organiser. DLM has been employed to generate the steady and unsteady aerodynamics matrices needed to build the multibody strip theory aerodynamic model, as described previously.

As previously stated, the multibody structural model of the wing consists of rigid bodies interconnected by beam elements, which are defined by a 6-DOF stiffness matrix.

Starting from the 3D FE wing box model shown in Figure 2 , an equivalent stick model in the multibody environment is then generated. Since the beam stiffness matrix is fully defined by cross-sectional properties, these can be calculated analytically from a built-up 3D FE or CAD model of a wing box, as the geometric wing box height and width, skin and spar webs thickness, stringers, and spar caps area and material properties are known.

Bindolino et al. For more complex composite sections, where coupling terms between all the deformation components become important, specific cross-sectional analyses tools have been developed by Giavotto et al. A second approach consists of identifying the classical cross-sectional stiffness bending stiffness and torsional stiffness by loading the wing, assuming cantilever boundary condition, with unitary load cases and working out the stiffness, at each section of interest along the span, from the relative displacements and rotations.

Singh and Nichols [ 25 ] proposed a procedure to derive the elastic axis and the equivalent stiffness of a beam model from a built-up wing box Nastran model. Their procedure consists in applying unit moments at the free end of the cantilevered wing box structure and estimating the bending stiffness and torsional stiffness from the relative rotations between reference points along the wing box axis.

Recently, Jones and Cesnik [ 26 ] applied this technique to develop a nonlinear beam model of the XA Multi-Utility Demonstrator from a Nastran FE model to perform aeroelastic analysis.

Elsayed et al. Another category of methodologies includes mathematical reduction techniques, such as Guyan reduction [ 29 ] and Improved Reduced System [ 30 ]. In both methods, a set of master nodes of the FE model is selected and the mass and stiffness matrices reduced to this.

Guyan reduction, also known as static condensation, is well established in the aerospace industry and the reduced equations are developed using only the stiffness matrix, leading to an exact reduction of the stiffness, but only an approximate reduction of the mass matrix. IRS is an extension of the former methodology that includes mass effects in the development of the system reduction transformation matrix. Wang et al. A potential drawback of the reduction methodologies, compared to those previously described, is that the reduced mass and stiffness matrices are fully populated and lose the link to the physical distribution of the usual cross-sectional stiffness and mass.

In the present work, three approaches are investigated to build a multibody equivalent stick model from the 3D FEM of the high aspect ratio wing aircraft. These are as follows: A Cross-sectional analysis.

B Stiffness identification by unitary loadings. C Guyan reduction. The first method, cross-sectional analysis, applies the classical formula from thin walled structural analysis to calculate the sectional area and moments of area , , and. Knowing the geometry, thickness, and material properties of the structural elements and under the assumption of material isotropy, valid since the wing considered has a metallic construction, this procedure is straightforward and delivers the axial, bending, and torsional stiffness characterizing the beam at each span section.

A simplified cross-section representation of the wing box is assumed, shown in Figure 3 , made up of upper and lower skin, stringers, and spar caps and spar webs. With reference to Figure 3 , the formulas employed are presented hereafter. The sectional properties obtained are then directly input into the multibody beam stiffness matrices 7. The second method follows the procedure outlined by Elsayed et al.

The wing box is clamped at the root and unit tip moments along the wing reference -, -, and -axes are applied independently and linear static analyses are performed. The stiffness properties are extracted at each wing box section corresponding to the locations of the multibody beam elements, which have been described previously, from the relative rotations of each cross-section.

In order to retrieve these, interpolation elements RBE3 are introduced at the multibody beam locations and attached to the surrounding nodes lying on a cross-section. The interpolation element provides displacements and rotations of a dependent node by averaging the degrees of freedom to which it is connected. The above equations assume that the vertical and in-plane bending are coupled whereas the torsion i.

The sectional area is instead directly calculated from the cross-section geometry Guyan reduction is chosen as the technique to derive the reduced stiffness matrix from the 3D FEM.

Regarding the mass distribution of the multibody model, both the structural distributed and concentrated masses are first discretized along the span, considering wing segments between each reference point of the equivalent multibody stick model, and subsequently lumped to these locations, taking into account proper CG offsets and moments and products of inertia.

In this way, there is no need to use the mass matrix obtained by Guyan reduction, which is known to be inaccurate [ 30 ]. To reduce the size of the 3D FEM, the degrees of freedom are first divided into two subsets, those retained in the reduced model set and those omitted set , such that Then perform the following transformation on the stiffness matrix: where the transformation matrix is given by As previously mentioned, this methodology is purely a mathematical reduction and the reduced stiffness matrix does not provide information about the physical distribution of the cross-sectional properties along the wingspan.

Three stick multibody models of the high aspect ratio wing aircraft have been generated from the 3D FEM employing the three presented methodologies.

Nonlinear static analyses have been carried out in Nastran and in the multibody environment to validate the structural modelling. Figures 4 and 5 present the wing deflected shape for these two load cases. For the tip force load case, little difference is evident between the linear and nonlinear 3D FEM results; in the nonlinear solution there is, as expected, a wing lateral shortening.

Regarding the multibody results, the model obtained by the stiffness identification technique is the one delivering the most accurate results with respect to the reference 3D FEM. It is interesting to note that the multibody model obtained by cross-sectional analysis, despite being nonlinear, is still overpredicting the vertical displacement. This result suggests that the cross-sectional analysis approach, which is based on approximate formulas, is not accurate for complex geometries and structural layouts.

The wing deflected shape for the 2. The stick model generated by cross-sectional analysis overestimates the displacements and bending curvature. Similarly, the model generated by Guyan reduction shows higher displacements than the reference solution for both load cases. The best agreement with the reference nonlinear 3D FEM is again obtained with the multibody model generated by the stiffness identification procedure. Following the static analyses, a normal modes analysis of the 3D FEM RHS wing with free-free boundary conditions has been carried out and the natural frequencies compared to those obtained with the three multibody models.

In the multibody environment natural frequencies and mode shapes are computed by performing a linearization of the equations, through the finite differences method, about the undeformed configuration. Table 3 reports the first five natural frequencies and the relative errors between the 3D FEM and the three multibody models.

These results confirm the trend shown by the static analyses. The cross-sectional analysis method exhibits the largest differences, underpredicting both the bending and torsional natural frequencies, which confirms that the stiffness is underestimated.

Likewise, Guyan reduction, though more accurate, leads to lower natural frequencies whereas the model created by stiffness identification shows the best agreement.

Anyhow, for all the three methods the greatest discrepancy is in the 1st torsional frequency, which is to be expected since the torsional behavior of a complex built-up structure is difficult to predict accurately with a stick model. In the light of the structural validation of the three multibody models, the equivalent stick model generated by stiffness identification Method B is deemed the most accurate and it is the one selected for the nonlinear static and dynamic aeroelastic analyses presented in the following.

The model is shown in Figure 6. These results confirm the good agreement of the multibody modelling selected and also illustrate that a stiffening effect occurs on the bending frequencies when the wing is loaded and deformed.

For instance, in the 2. Nonlinear aeroelastic trim analyses have been performed with the multibody stick model of the high aspect ratio wing aircraft.

The results of such analyses are compared to those obtained by standard linear trim analyses carried out in Nastran SOL using the 3D FEM, with the purpose of highlighting the effects of structural nonlinearities on flight loads prediction.

In the multibody approach, the trim solution is sought by performing a dynamic settling simulation with the implementation of controllers in order to achieve a steady trimmed state.

Details of the trim methodology developed are provided by Castellani et al. The 2. Table 5 reports the trim angle of attack and the computational time resulting from the linear FEM and the multibody trim analyses. This latter predicts slightly higher trim angles of attack, the reason being that, in the nonlinear approach, the follower force effect of the lift is accounted for and thus, as the wing bends upwards, the lift is progressively tilted inboard and its vertical component, the one balancing the weight, is reduced.

As a result the angle of attack required to balance the aircraft must be increased compared to a linear solution and the greater is the load factor, since the bending on the wing increases with it. In order to gain further insights about the effects of structural geometric nonlinearities, the lift distribution is plotted in Figure 7 versus the undeformed for linear analysis and the deformed for nonlinear analysis wing coordinate, together with its lateral, , and vertical, , components in aircraft body axes.

Due to the significant wing bending at 2. As previously mentioned, this force is neglected by the linear analysis. Furthermore, the lift in the nonlinear solution is shifted inboard because of the wing tip shortening, a second-order effect not captured by a linear structural formulation. Load control systems may prove essential to the feasibility of very high aspect ratio designs. Optimal wing span may lead to the need for folding outer wing sections.

This topic aims to provide a preliminary design study involving the capture of the current state of the art, an analysis of potential gains through the use of very high aspect ratio wings in the various transport aircraft market segments [regional, short-medium and long range]. Different design concepts should be analysed, paying particular attention to design constraints such as those mentioned above.