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II The Aircraft in More Detail

Wings

The most fundamental parts of any aircraft are the lifting surfaces that permit flight in the first place. For the UAVs being considered here, these are rigid wings, usually incorporating control surfaces such as ailerons and flaps. After more than 100 years of powered heavier-than-air flight, a great deal is known about the way the geometry of a wing impacts on its ability to generate lift with low drag. It is therefore useful to start by very briefly recapping the basics of wing theory before looking at how wings can be realized in practice at the size needed for UAVs of between 2 and 150 kg MTOW.

Simple Wing Theory and Aerodynamic Shape

The nonsymmetrical cross-section of a wing when presented to an oncoming airflow, caused either by using a cambered section or a symmetrical one inclined at some angle of incidence (attack) to the air, causes the air pressure on the upper surface of the wing to be lower than that on the lower one; the net imbalance in pressure generates the lift. For low-speed airfoils, the precise shape of the airfoils used does not make much difference to the amount of lift that can be produced with modest camber or low angles of incidence. In fact, a simple (two-dimensional - i.e., infinitely long span) flat plate inclined to the airflow will generate lift, and it is possible to show theoretically that if air was an inviscid fluid (i.e., it caused no losses due to friction, produced no boundary layer, and did not exhibit flow separation), the section lift coefficient for such a plate would be related to the angle of attack as Cl = 2ж sin a (where a is expressed in radians), which means that for small angles of attack the slope of the lift coefficient curve with angle of attack is just rad-1 (or ж[1]/90 ^ 0.11 deg-1). This is termed the classical lift slope; note that in this analysis the lift is not caused by the impact of the air on the surface of the plate, rather it is due to the air circulation around it.

Real airfoils, of course, have thickness and often camber - camber serves to increase the lift available at a given angle of incidence, while thickness allows for internal structure, and so on, and also permits the wing to operate over a range of angles of attack without separation. When suitable sections are used to form a three-dimensional wing, the issue of the flow around the wingtip then arises - this is because the pressure difference between the upper and lower surfaces of a simple straight wingtip will give rise to rotating flow and a vortex stemming from the tip and trailing backward into the flow. This rotating flow acts to alter the effective angle of attack of the wing and leads to so-called induced drag, which would be present even in an ideal fluid. A great many variations in geometry can be used to limit such losses; the four most common approaches are as follows:

  • 1. The use of large aspect ratios so that most of the lifting surface is distant from the vortex at the wing tip;
  • 2. Reduction in section chord toward the tip to reduce the pressure difference near the tip and hence lessen the tip vortex (as seen in the classical elliptical shape of the Spitfire fighter aircraft);
  • 3. Decambering or twisting of the wing to either reduce the local section lift coefficient or the local section angle of incidence near the tip, again reducing the strength of the tip vortex;
  • 4. The use of winglets or other wingtip shape modifications to control and position the tip vortex (a feature increasingly common on commercial aircraft over the last 10 years).

When deciding on wing sections and planform shape, a number of key aerodynamic aspects must be considered. Assuming the wing is large enough to lift the aircraft at sensible angles of attack, the designer must first consider the trade-off between aspect ratio and weight - a high aspect ratio wing will, in general, be more aerodynamically efficient than a low aspect ratio one because of the reduction in induced drag. However, as a wing is essentially a cantilever beam, the greater the aspect ratio, the larger the bending moments and the heavier it is likely to be for a given planform area and structural design approach. We find aspect ratios between 6 and 9 to be a sensible range to consider. For shorter wings, some form of taper becomes increasingly important to control induced drag.

The other important driver of wing drag is the section thickness to chord ratio. As the data collected together by Hoerner [9], and sketched in Figure 3.1, show, section aerodynamic drag is fundamentally driven by the thickness to chord ratio - thin sections have lower zero-lift drag (also once the flow is turbulent, the drag is not strongly impacted by the section Reynolds number). However, thin sections suffer from two main drawbacks: first, they limit the internal room within the wing for structural elements and control systems; second, they tend to stall at lower angles of attack because the leading edge radius is necessarily limited.

A key problem in aircraft design is achieving adequate lift at the low speeds desirable during landing and takeoff. Since lift is proportional to speed squared, it is common to size the wings of an aircraft to be much larger than needed while flying at cruise speeds so that the angles of attack needed at low speed can be accommodated. On simple UAVs that lack high lift systems of slats and multipart flaps, this can be a particularly important part of the wing design. Again, a compromise is needed - if the wing has to be oversized to provided adequate lift at low speed, it is important that the wing drag be low at the shallow angles of attack used during cruise - implying the use of thin sections. However, to maximize lift at low speed, a high angle of attack will be needed, where a thicker section is less likely to stall. The location of where stall begins along the wing is also an important aspect for handling - if the wing stalls at the root before the tip, the aircraft is likely to have more benign flight

Variation of airfoil section drag at zero lift with section Reynolds number and thickness-to-chord ratio. After Hoerner [9]

Figure 3.1 Variation of airfoil section drag at zero lift with section Reynolds number and thickness-to-chord ratio. After Hoerner [9].

characteristics - thus wings are commonly twisted (have washout) or have reduced camber toward the tip.

A brief consultation of any of the widely available airfoil section libraries on the Web will reveal that there are literally thousands of potential sections that can be adopted. The section lift, drag, and moment coefficients for the more popular sections are widely available - most will lift perfectly adequately up to 10° angle of attack where, as predicted by the classical wing theory noted earlier, they typically have lift coefficients of 1.1. Their zero-lift drags basically follow the data presented in Figure 3.1, varying quadratically away from this as angle of attack increases. Where significant differences do reveal themselves is in the maximum lift coefficients achieved at stall and the way the lift and drag vary once stall has begun.

This leads to the final key consideration in wing design - the behavior of the wing as lift starts to break down at high angles of attack. Unless the UAV under consideration is likely to fly at very high speeds where drag minimization is crucial, adopting very thin wing sections is likely to be counterproductive, especially if complicated and expensive leading-edge high-lift devices cannot be used. We generally see little point in adopting thickness to chord ratios below 15%. In our experience, the precise choice of the section geometry and camber matters rather less in slow to moderate speed UAV design than accurate manufacture of the wing so that the sections chosen are realized in practice - there is little point adopting a highly optimized airfoil section if the build process is unable to follow the prescribed section data over its entire surface.

A UAV with significant FDM ABS winglets (this aircraft also has Custer ducted fans)

Figure 3.2 A UAV with significant FDM ABS winglets (this aircraft also has Custer ducted fans).

When building small UAVs, it is also very convenient to have a straight main spar and simple two-dimensional curvature of the lifting surfaces, so we have generally opted for tapered wings of fixed camber but often with suitable winglets mounted at the tips, see, for example, Figure 3.2. To ensure that the wings have the correct aerodynamic shape, we now rely on precision-cut closed-cell foam cores for all our wings (and tail surfaces). We have access to several digitally controlled hot-wire foam cutters of various sizes and capabilities, which is why we prefer to use straight-line generators to loft the wing surfaces where possible. These foam cores are typically hollow but also have a circular spar hole or load transfer region cut into them to aid transfer of aerodynamic loads to the spars, see Figures 3.3 and 3.4. We will return to more detailed considerations of aerodynamics in subsequent chapters.

Wing foam core prior to covering or rib insertion - note strengthened section in way of main wing spar

Figure 3.3 Wing foam core prior to covering or rib insertion - note strengthened section in way of main wing spar.

Covered wing with spar and rib - in this case, the rib just acts to transfer the wing twisting moment while the spar is bonded directly to the foam without additional strengthening

Figure 3.4 Covered wing with spar and rib - in this case, the rib just acts to transfer the wing twisting moment while the spar is bonded directly to the foam without additional strengthening.

  • [1] Small Unmanned Fixed-wing Aircraft Design: A Practical Approach, First Edition.Andrew J. Keane, Andras Sobester and James P. Scanlan. ©2017 John Wiley & Sons Ltd. Published 2017 by John Wiley & Sons Ltd.
 
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