The wing planform is the focus of the study and is performed on an elastic aircraft configuration. The starting configuration for this work is the demonstrator developed in the Flexop project including its flight mission and boundary conditions as presented in [
10,
11]. The UAV configuration has a span of 7 (m) and a MTOW of 65 (kg). The wing-fuselage arrangement is designed as a high wing aircraft with V-tail and is equipped with a jet engine. From the mission planning, the design flutter speed was specified to be
. The specified target flutter speed is the determined maximum speed at which the aircraft can be safely operated within the permissible flight pattern. Lower speeds would improve the operation of the demonstrator and are therefore preferred. Therefore the trade-off between wing planform and stiffness shall be investigated in the present work to favor lower flutter speeds.
Due to the coupled flight mechanics, a change in the wing planform also influences flight stability and dynamics of the aircraft’s rigid body motion. Since the flutter behavior is coupled with the rigid body dynamics, especially with more elastic wings, it is necessary to include this effect in the investigation, so that different configurations can be compared with each other. To achieve the same flight characteristics for each configuration the tail volume
is adjusted accordingly. The applied aircraft design approach is summarized in
Figure 1. Based on the six design parameters, wing area
, aspect ratio
, taper ratio
, wing sweep
and the two laminate thicknesses
and
, different wing layouts are created with a wing empennage/fuselage model adapted for each configuration. With the respective aircraft configurations, the properties required for the evaluation are then calculated and incorporated into a surrogate model. On last the optimization, the problem is finally solved.
The system requirements and details of the parametric aircraft design process are described in the following chapters.
2.1. Wing Planform Parameter and Structural Design
A parametric model of the wing and its internal structure is used to investigate several different wing planforms. The wing is defined with the parameters wing area , AR, TR and . The wing area is used to see the influence of the size scaling of the UAV configuration. The influence of different lift distribution is covered by the aspect and taper ratio. The wing sweep is used to study different bending-torsional coupling effects.
All four wing planform design parameters are indirectly influencing the structural layout and hence the wing stiffness. A larger aircraft generates more lift and therefore the structural components have to be dimensioned stronger. The same holds for the lift distribution, when it gets shifted more outwards, as it is the case with a rising aspect and taper ratios. Bending-torsion coupling tends to support a low flutter speed, but with higher sweep angles the torsional loading also increases, which is why the wing also has to be reinforced. In order to investigate these trade-offs, the adaptation of the structural sizing is also necessary.
The inner wing structure consists of a front spar, rear spar, ribs and is designed together with the wing shell in composite design. The highly stressed spars and ribs near the root consist of monolithic carbon fiber reinforced polymer (CFRP) with a Young’s modulus of in the fiber direction. Special considerations are necessary for the design of the wing shell. The construction of a flutter wing at very low airspeeds requires a tailor-made adjustment of the stiffness and naturally leads to a problem of material scalability. Due to the composite construction, the adaptation of the stiffness is restricted by:
Both restrictions have the effect that the stiffness of the wing shell cannot be reduced arbitrarily, even if other constructive constraints are not violated. The shell in the present study is made from a glas fiber reinforced polymer (GFRP) foam core sandwich, with the following advantages:
The GFRP plies have a Young’s modulus in the fiber direction of , and are therefore less stiff than CFRP.
Thin plies are prone to buckling. The foam core sandwich design increases bending stiffness significantly (parallel axis theorem) with a moderate growth in structural mass compared to a full monolithic design.
The structural components is shown in
Figure 2. The composite layup of the spars is chosen to maximize the bending stiffness while the wing shell is used to adjust the torsional stiffness. The wing shell is accordingly symmetrically designed with
layup. The wing shell has the same structure over the entire span, except at the wing root. In order to carry the high loads and to ensure a clean load transfer for the sandwich, the foam core is successively replaced by a monolithic design. To support the bending loads, front and rear spar are built up with
and
plies. The zero degree direction for spars and shell is determined by the sweep angle
. Since the highest loads occur at the wing root, the layup is thickest here and is reduced by
along the span over three steps. To achieve the necessary integrity for different wing planforms, the thickness of the individual plies is scaled accordingly. Therefore the thickness parameters
(mm) and thickness
(mm) are used to control the bending and torsional stiffness. With the presented structural design it is assumed that bending and torsion loads are carried separately via spar and shell. With increasing wing sweep, this approach is only possible to a limited extent, since typically torsion and bending are beared by both structural components. In addition, it is assumed that plies of any thickness are available. To avoid a discontinuous optimization task, the ply thickness is continuously adjusted between 0.01 and 2.0 (mm). For the conceptual design task this is considered justified and has to be converted to a discrete layup in the later detailed design. The remaining ribs are not included in the sizing process and therefore remain constant. For the evaluation of the structure integrity, only spar and the wing shell is used.
The Finite Element Method (FEM), as implemented in MSC NASTRAN, is used to investigate the flexible wing characteristics such as structural deformation, integrity and stability. The flutter solutions are calculated using the pk-method as provided by NASTRAN. The first 15 elastic eigenmodes of the free-flying aircraft are used to represent its dynamics. To model the composite layup, shell elements as shown in
Figure 2, in combination with the classical laminate theory is used as stiffness modeling approach. To investigate several different configurations, a parametric geometry model was implemented and passed to the FE pre-processor for meshing. In pre-processing, the system masses are modelled using lumped masses, boundary conditions are defined and the aerodynamic interface is created. Fuselage and empennage are treated as rigid body, so that no structural dimensioning is necessary. Elastic wing, rigid fuselage, empannage are connected by rigid body elements in the aircraft’s center of gravity.
2.2. Parametric Empennage and Fuselage Design Process
The rigid body dynamics of the entire aircraft cannot be neglected for reasonable investigations on flexible wings. Therefore, the flexible wing model is extended by a rigid fuselage and a tail to a complete aircraft model. Different wing planforms require different centers of gravity (C.G.) and neutral point (N.P.) positions for a stable configuration. Therefore, the empennage and sub-components are arranged in such a way that the natural static and dynamic flight stability of the aircraft is the same in every configuration.
Before the actual investigations begin, an aircraft pre-design loop is carried out. Based on the wing plan form, the aircraft tail and fuselage are designed in such a way that each configuration fulfils the following characteristics.:
Both criteria are based on experience with UAVs flown by hand and are therefore rather conservative. In case the dynamic behaviour is supported by a flight controller or the UAV is completely controlled by an autopilot, the corresponding constraints have to be reassessed. In order to meet these requirements, the position of the neutral point and center of gravity as well as the size of the empennage cannot be selected independently of each other. The used reference point definitions are presented in
Figure 3, with the aircraft reference coordinate system located at the wing leading edge.
As the wings Neutral Point and Center of Gravity are defined by the wing planform, the remaining design variables are
: lever arm of the tail.
: Empennage Volume, defined as , where the empennage reference area is.
: Center of Gravity full aircraft.
These three size parameters are non-linearly dependent on each other, and in order to find a solution so that the static and dynamic flight stability conditions are fulfilled, the computational fixed-point iteration method is used for solving. Because there is more than one mathematical solution, the additional constraint that forces the tail volume
to create a minimal wetted surface area is added. This restricts the solution space and separates mathematically correct but physically unreasonable designs from meaningful ones. The approach, in which the fuselage wetted surface is approximated by a truncated cone depending on
is, e.g., presented in Gudmundsson [
14].
The empennage design is defined as a V-Tail configuration and has for all configurations the same form parameters. Therefore, the only remaining design variable is the size. With the tail surface
and the leverage
, the aircraft neutral point
is calculated from Equation (
1) as shown in Schlichting [
15].
The aerodynamic derivative
as well as
of the wing is calculated in a previous initialization run. For this case, the wing is clamped and an aerodynamic model based on the vortex-lattice-methode (VLM), as implemented in NASTRAN [
16], is used.
The Area Ratio parameter in Equation (
1) is defined as
. The down-wash parameter
as well as the dynamic pressure correction
are two remaining parameters to determine. Schlichting [
15] gives some estimations of those correction terms, which are based on an elliptical lift distribution on an unswept wing. Schlichting [
15] further differentiates between a single furled and unfurled wing vortex layer, which interacts with the empennage. These assumptions and unknown correction parameters cause significant deviations in the final aircraft configuration, especially for higher swept wings. The two correction parameters are therefore combined to one empennage correction factor
, which is identified by a computational aerodynamic evaluation via the VLM of the combined wing-empennage configuration.
To evaluate the relative pitch damping of the aircraft configuration, the absolute damping factor
and the natural frequency
is calculated according to Equations (
2) and (
3).
The aerodynamic derivatives
and
are approximated, according to Schlichting [
15], with the wing and tail lift slope derivatives
,
and the introduced correction term
.
To evaluate the dynamic behaviour of the aircraft configuration, an inertia model for Equations (
2) and (
3) as well as for the FE model is required. The inertia data of the wing are directly derived from the FE model. The empennage mass is modeled by taking the existing FLEXOP tail unit as reference value and scaling it with the reference surface
. The empennage is further treated as a point mass, so the inertia contribution can be described simply by
.
The fuselage inertia is assembled by discrete mass points of the subcomponents such as batteries, receiver, flight control devices and their relative position. The internal component arrangement is assumed to be equal for each configuration and is based on the FLEXOP arrangement. The tail boom is the only component taken into account that depends on the size. The cross-section of the tail boom is considered constant and is scaled accordingly with the length
. The fuselage mass is thus calculated
. The total mass model is obtained by adding up the three main components and can be specified as follows.