Worked-Out Example: Configuring the Wing in Civil Aircraft
Continuing with the fuselage-design example outlined in Section 6.4, following are specifications required for wing design:
Maximum Cruise Speed: Mach 0.74 (HSC)
Initial Cruise Altitude: Above 40,000 ft (ceiling more than 50,000 ft)
Takeoff Field Length: 1,000 m at sea level (balanced field length)
Landing Distance from 50 ft: 1,000 m at maximum landing weight, as high as
0.95 MTOM at sea level
Initial Rate of Climb: 16 m/s
Unlike the fuselage, the approach to wing design starts with past statistics and is properly sized in Chapter 11. Following the considerations listed in Sections 6.3.2 and 6.5.2, a wing design could progress in a stepwise approach as suggested herein.
A worked-out example follows. Figure 6.10 is specifically for the aircraft class under consideration. Aircraft in the graphs are the Century, Cessna CJ2, Cessna Excel, Cessna 650, Lear 60, Cessna 750, and Challenger.
Step1: Decide the aerofoil section.
This is one of the most important aspects of aircraft design. Aircraft performance depends considerably on the type of aerofoil adopted. Today, most designers in the major aircraft industry design their own aerofoil and keep the profile “commercial in confidence.” There are also many industries that use the established NACA-type aerofoil. This book uses the established aerofoil section available in the public domain. Aerodynamicists prefer the aerofoil to be as thin as possible, whereas structural engineers prefer it to be as thick as possible. A compromise is reached based on the aircraft design Mach number and the chosen wing sweep.
Step 2: Establish the wing reference area.
Initially, the wing reference area must be estimated from previous statistics. First, estimate the aircraft MTOW from the payload-range capability (see Figure 4.5). Next, estimate the wing reference area, SW, from the MTOW (see Figure 6.10a); this gives the wing-loading. Both the SW and the MTOW are accurately sized in Chapter 11. Position the wing relative to the fuselage, considering the aerodynamic and structural features.
Step 3: Establish the aspect ratio, wing sweep, taper ratio, dihedral, and twist (see Section 3.16).
The wing planform is generally of but not restricted to a trapezoidal shape – it can be modified with a glove and/or a yehudi. The choices for the wing-aspect ratio, wing sweep, and taper ratio are interlinked to keep the compressibility drag increase within twenty drag counts at the high-speed design specification (see Section 3.18). The aspect ratio should be the highest that the structural integrity will permit for the aerofoil t/c ratio and the wing root chord based on the taper
ratio. At this stage, wing twist is empirically determined to improve stalling effects. The wing dihedral is decided from stability considerations. All these parameters are eventually fine tuned through CFD analysis and wind-tunnel testing, with the hope that flight-test results will not require further tweaking.
Step 4: Establish the control surfaces (e. g., aileron and spoilers).
Initially, these are approximated by reference to statistics and semiempirical data; the sizing could be postponed until more details are available. In this book, the control surfaces are not sized.
Step 5: Establish the high-lift devices (e. g., flap and slats).
The first task is to decide the type of high-lift device required to meet the maximum CL to satisfy the specified field performance requirements (i. e., takeoff and landing). Once established, the area and other geometrical parameters are initially approximated by reference to the statistics and semi-empirical data. The sizing can be postponed until more details are available. In this book, the high-lift devices are not sized.
To maintain component commonality, the wing should be the same for all three variants; obviously, it would be slightly larger for the smaller variant and slightly smaller for the larger variant. How this is determined satisfactorily is addressed in Chapter 11.
Maintaining the established design trends, the planform shape of the example is taken as trapezoidal and assembled as a low wing to the aircraft. The aerofoil for the aircraft is a NACA 65-410 (i. e., 10% t/c ratio; see Appendix C).
At this stage, the wing reference area and aircraft weight are not known. This is when the statistics of previous designs prove useful to initiate the starting point. Unfortunately, Figure 4.8 is very coarse; however, Figure 6.10 provides similar information in finer detail confined to the aircraft class. The author recommends that readers produce similar graphs in better resolution for the aircraft class under consideration.
Figure 6.10a indicates a MTOM of approximately 9,000 to 10,000 kg, corresponding to 10 passengers. An average value of 9,500 kg (21,000 lb) is used for the example. The corresponding wing area is «30 m2 (322.9 ft2) of trapezoidal wing planform, which gives a wing-loading of 316.67 kg/m2 (65 lb/ft2). These are preliminary values and are formally sized in Chapter 11. However, the aspect ratio is reduced to 7.5 to keep the OEW light (it will be iterated). A taper ratio of 0.4 is used, which reduces the wing span. With a relatively low LRC Mach of 0.65, the compressibility effect is low and a quarter-chord sweep angle of 14 deg (see Figure 3.36) would keep the wave drag to zero.
The wing span is worked out as b = V(AR x SW) = V225 = 15 m (49.2 ft). The wing root and tip chord (CR and CT) can now be worked out from the taper ratio of 0.4:
CT/CR = 0.4 and SW = 30 = b x (CT + CR)/2, solving the equations CR = 2.86m (9.38 ft) and Ct = 1.143 m (3.75 ft).
Using Equation 3.21, the wing MAC = | x [2.87 + 1.148 – (2.87 x 1.148)/ (2.87 + 1.148)] = 2.132 m (7 ft). Figure 6.11 gives the wing plan form geometry.
Figure 6.11. Example of wing design
It is interesting that most typical values of taper, twist, and dihedral are derived from statistics and are about the same for the aircraft class. From the statistics, a twist of -2 deg (i. e., washout) and a dihedral of 3 deg are typical for the class. Eventually, CFD and wind-tunnel testing will fine-tune the values. A wing-loading of 316.67 kg/m2 (3,106.5 N/m2) is a moderate value that would provide good field performances. A single-slotted Fowler flap without a LE slat would be sufficient, saving considerably on costs.
Control areas are provisional and are sized in Phase 2. Initially, a company’s statistical data of previous experience serve as a good guideline. Aileron, flaps, and spoilers are placed behind the wing rear spar, which typically runs straight (or piecewise straight) at about 60 to 66% of the chord. With a simple trapezoidal wing plan – form, the rear spar runs straight, which keeps manufacturing costs low and the operation simpler; therefore, it has a lower maintenance cost. With a third of the wing span exposed, the aileron area per side is about 1 m2 (10.764 ft2). Similarly, the flap area is 2.2 m2 (23.68 ft2) per side. Subsequent performance analysis would ascertain whether these assumptions satisfy field-performance specifications. If not, further iterations with improved flap design are carried out.
From the test data, the following maximum lift coefficients are given:
Flap deflection – deg 0 8 20 40
CLmax 1.5 1.7 1.9 2.1
For a small aircraft with limited ground clearance, the engines would be mounted on the rear fuselage. At this stage, the wing is placed just behind the middle of the fuselage. The wing location is subsequently fine-tuned when the CG and undercarriage positions are known. A smaller aircraft wing could be manufactured in one piece and placed under the fuselage floorboards, minimizing a “pregnant-looking” fairing (Figure 3.35 shows a generous fairing to smooth the hump; however, the example in this book has more streamlined fairing).