High-Lift Devices#
This section talks about sizing of high-lift (HL) devices to meet maximum \(C_L\) requirements for the example airplane. Typically, the goal of a HL device is to modified wing camber and area to enhance the lift generated by the wing. There are various types of HL devices and can be located at leading or trailing edge. Some common types of trailing edge HL devices consists of plain flap, split flap, slotted flap, and fowler flaps. Note that control surfaces (aileron, elevator, and rudder) are usually plain flaps. Some leading edge HL devices include LE slot, LE flap, slats, and kruger flap. Refer to lecture notes and section 12.4.6 in Raymer for a detailed discussion about HL devices and how they modify the lift generated by the wing.
For the example airplane, slotted flaps are used due to its ability to provide adequate increase in \(C_{L_{max}}\) while being simple. Only trailing edge devices are used since there is no need of LE devices. Sizing method consists of a simplified analysis using empirical data and extrapolation from 2D airfoil test data. The first step is to determine spanwise location of the flaps. This can be estimated based on the amount of span occupied by the fuselage at root and the aileron towards the tip of the wing. For the example airplane, fuselage occupies 15% of the half span from the root.
To determine the aileron size and location, Table 8.3b in Roskam Part 2 is used. The start and end location for aileron is set to 65% and 95% of the wing half span, respectively. The chord ratio for the aileron is set to 25%, note that the chord value can be changed later based on stability analysis. Based on these values, the start and end location of the flaps is set to 20% and 60% of wing half span, respectively. The chord ratio (\(c_f/c\)) for the flaps is set to 25%.
Once flap size is determined, one can proceed to compute the amount of flap deflection required for producing a requried amount of \(C_{L_{max}}\). In this section, procedure described in chapter 7 of Roskam Part 2 is followed. First step is to determine the required change in \(C_{L_{max}}\) using
where \(C_{L_{max_{req}}}\) is the required maximum lift coefficient and \(C_{L_{max}}\) refers to the maximum lift coefficient in clean configuration (already known). The factor of 1.05 is to account for trimming the airplane. The computed \(\Delta C_{L_{max}}\) can be linked to the change in maximum lift coefficient for an airfoil using
where \(S_f\) is the area of the wing between the starting and ending spanwise location of flaps (refer to figure 12.21 in Raymer for a visual representation of \(S_f\)). Note that above equation can be corrected for the wing sweep but it is not used here since example airplane does not have sweep. The \(S_f\) can be estimated based on the wing planform geometry. For the example airplane, flaps starting from 20% half span location and ending at 60% half span location results in \(S_f\) of 58.1 \(\text{ft}^2\).
During initial design stages, the computed \(\Delta C_{l_{max}}\) is further refined to compute the required change in section lift coefficient using
where factor \(K\) depends on the flap type and \(c_f/c\), and is obtained from figure 7.4 in Roskam Part 2. For a single slotted flap with \(c_f/c = 0.25\), the value of \(K\) is set to 0.93. The \(\Delta C_l\) can be computed based on deflection of a single slotted flap using
where \(C_{l_\alpha}\) is the airfoil lift curve slope, \(\alpha_{\delta_f}\) is the lift effectiveness for a single slotted flap and it depends on the flap deflection. Using Figure 7.8 in Roskam Part 2, appropriate flap deflection, and corresponding \(\alpha_{\delta_f}\), can be determined so that required \(\Delta C_l\) is obtained.
The change in zero lift angle of attack, \(\Delta\alpha_{L=0}\), can be computed using
Based on the recommendations provided in Raymer section 12.4.6, \((\Delta\alpha_{L=0})_{airfoil}\) is set to \(-9^{\circ}\) and \(-18^{\circ}\) for takeoff and landing, respectively.
Furthermore, change in zero-lift drag coefficient, \(\Delta C_{D_0}\), due to flap deflection can be computed using (Raymer equation 12.61)
where \(F_f\) is 0.0074 for slotted flaps. Note that in above equation, sweep effects are not included since example airplane has minimal sweep. This concludes the process for sizing the HL devices. Next subsection applies this process for the example airplane in takeoff and landing configuration. The corresponding drag polar are also plotted, along with estimating the maximum \(L/D\).