Having completed the analysis of the wetted surface of the aircraft from a fluid dynamics perspective, attention next turns to the airframe structure. Assessing the strength and rigidity of an airframe is just as important as ensuring that its aerodynamic characteristics are as required. Moreover, building aircraft that are sufficiently but not overly strong is crucial in controlling airframe weight and thus the overall aircraft performance. In our experience, structural analysis can be somewhat of a Cinderella subject in small unmanned air vehicle (UAV) design; it is far from this in commercial aircraft work, and often more engineers will be found working on structures, loading, and weight control than on aerodynamics in large aerospace companies. While much of the work of designing the structure lies in the realm of detailed design, it is very important to have a preliminary structural model as soon as possible so as to better inform calculations on aircraft weight and center of gravity location, also so that any significant shortcomings can be identified before too much further design effort is expended. Essentially the structural design task during preliminary design is to establish the primary dimensions of the main structure that are needed to avoid overstressing the airframe during flight and to prevent any adverse aeroelastic effects stemming from an overly flexible structure. These can then be used to check against the available weight budget used when sizing the aircraft.

Given their low cost, light weight, and ready availability, we always build our main structural elements from carbon-fiber-reinforced tubes. We typically join these together with structural clamps made from 3D printed material (usually selective laser sintering (SLS) nylon) which, where possible, are integral to other parts of the airframe. We also pass them through 3D printed or laser-cut plywood elements to facilitate load transfer from other parts of the aircraft that either generate large forces or entail significant inertias, such as lifting surfaces, engine bearers, servo mountings, undercarriage elements, catapult launch bars, payload items, and heavy avionics components such as batteries. It is, of course, possible to opt for fully mono- coque structures that do not rely so heavily on spars, but since we tend to build our fuselages from fused deposition modeling acrylonitrile butadiene styrene (FDM ABS) or SLS nylon and these materials are not that structurally efficient, we incorporate spars or other reinforcements in our structures even when they are mainly monocoque in layout. Although it is then possible to use basic Euler-Bernoulli beam theory to assess the sizes of the elements involved, it is often simplest to build up an outline model in parametric CAD that is suitable for finite element

Small Unmanned Fixed-wing Aircraft Design: A Practical Approach, First Edition. Andrew J. Keane, Andras Sobester and James P. Scanlan.

analysis (FEA) in one of the many readily available analysis packages.^{[1]} Such a geometry definition can easily be set up with the AirCONICS code inside the Rhino environment.

The primary structural cases that need to be considered for small UAVs are the following:

• Maneuver and gust loads on the lifting surfaces;

• Aeroelastic checks (to establish the divergence, control reversal, and flutter onset speeds);

• Inertia and vibration loads, particularly for heavy elements or those near the engines (inertia loads during landing and takeoff can be very severe for small UAVs);

• Landing and take-off loads, which mostly affect the landing and launch bar gear and local supporting structure;

• Powerplant loads, essentially of thrust, torque, inertia, and gyroscopic effects, on the mounting structures.

Only the first two groups here really concern the overall structure and thus need addressing during preliminary analysis, with the other cases mostly being dealt with during detail design (weights for undercarriage, launch and engine mountings, and fittings being estimated by scaling from similar aircraft at this stage). The maneuver and gust load cases lead naturally to the so-called Vn diagram, which may be used to set out the aerodynamic loads on the airframe at various points in the operating envelope. Figure 14.1 shows a typical composite Vn diagram. The key features of this diagram are the positive and negative limits due to stall that set the maximum and minimum lift curves, the maximum and minimum maneuver and gust limits, and the maximum dive speed. These may be used to decide the operating points for which loads need calculating.

Figure 14.1 Typical composite Vn diagram for gust and maneuver loads on a small UAV (here for Decode-1 assuming maneuver load factors of +5 and -2, 9.1 m/s gust velocity, and a dive speed of 160% of the cruise speed).

Typical maximum and minimum maneuver load factors for UAVs are range from 4g to 5g positive and -1.5g to -2g negative, although these values will depend on the aircraft mission and the regulations being designed to. Combat and aerobatic aircraft are typically designed to higher load factors, and acceptable designs can be built with lower ones. For example, the Federal Aviation Agency (FAA) regulations^{[2]} (FARs 14, CFR, part 23^{[3]} and part 25^{[4]}) state things such as that the maximum maneuver load factor is normally to be 2.5 but that if the airplane weighs less than 50 000 lbs, the load factor is to be given by n = 2.1 + 24 000/ (W + 10 000), though n need not be greater than 3.8. Loads caused by flying through gusts can be significant drivers in aircraft design. Appropriate load factors can be calculated from the

k„ UgE VE a pS

various formulae such as those in FARs 14, CFR, part 23, which states that n = 1 ± — g- - ,

2 W

0.88^„

where k„ the gust alleviation factor is given by k„ =^{g}, and the aircraft mass ratio given

^{g g} 5.3+^g ^{g}

by ^_{g} = p2Wg. Here, U_{gE} is the equivalent gust velocity and a = dC_{L}/da is the slope of the lift curve in radians. A gust velocity of 9.1 m/s has commonly been used for small aircraft up to their cruise speeds, dropping linearly to 4.6 m/s at dive speeds; the FAA regulations use a maximum of 15.2 m/s. For the Decode-1 aircraft with a cruise speed of 30 m/s, the FAA maneuver equation gives n = 4.49 and the gust equation gives n = 1 ± 3.68 with a gust velocity of

9.1 m/s; thus a maximum load factor of 5 is quite appropriate and the slightly more modest value of 4 would suffice for many purposes.

The load factors can be taken from the Vn diagram and applied in a number of ways: most obviously by scaling the normal flight loads and applying to the wing spar, for example. Alternatively, elevator and fin loads may be calculated by using maximum C_{L} values and applying equivalent loads since in small UAVs the structures supporting these elements are less severely loaded by maneuvers and gusts. Note that the angle of attack will influence the direction of aerodynamic loads.

To establish the distribution of loads on the aerodynamic surfaces, a number of approaches can be taken. The simplest and most pessimistic is to apply the full lift and drag forces falling on each surface to the tip of that surface as a point load. This is a very pessimistic approach but one that can be very quickly utilized, particularly if the main structural elements of the aircraft are made up from beam-like elements. Then the simple Euler-Bernoulli beam theory results (found in all standard texts) will allow deflections and stresses to be rapidly and directly calculated. Less pessimistic and only slightly more difficult to apply are uniformly distributed loads (UDLs) of the same total magnitude. More sophisticated approaches seek to distribute the lift and drag forces more accurately, sometimes in both spanwise and chordwise directions. There are a number of semiempirical methods for doing this such as the Schrenk approximation, where the total loading is taken to be an average of a pure elliptical distribution and one that apportions the pressure pro rata to the planform area. If chordwise distributions of loading are to be used with beam models, then local torque distributions will be needed as well. If, however, an XFLR5 analysis has been carried out for the lifting surfaces, it is more sensible to take the pressures calculated there and scale them by the desired load factor to arrive at a load distribution. In either case, the resulting loads can then be broken down into equivalent point or short-span uniform loads and torques and a total load case built by superposing these.

Alternatively, the load distribution can be carried into a structural FEA code such as Abaqus®^{[5]}, either of a spar-based model or of more complete representations of the airframe. If using a relatively complete FEA model, this loading can be applied directly in the form of pressure maps onto the lifting surfaces, which can then provide appropriate force and torque loads on any embedded spars using contact analysis. Our normal practice is to begin with simple, uniform loading calculations on the main spars followed by progressively more detailed FEA models.

[1] Note, that although many CAD packages now include a built-in FEA system, we prefer not to use such tools as theyrarely have the degree of mesh control and part to part interaction capabilities that we often need.

[3] Airworthiness standards: normal, utility, acrobatic, and commuter category airplanes.

[4] Airworthiness standards: transport category airplanes.

[5] http://www.3ds.com/products-services/simulia/. Abaqus® is a registered trademark of Dassault Systemes or its subsidiaries in the US and/or other countries.