3.4.3: Increase in CLmax

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Table 3.1 shows the typical values for the increase of coefficient of lift in airfoils.

High-lift devices	\(\Delta c_{L_{\max}}\)
Trailing edge devices
Plain flap and intrados flap Slotted flap Fowler flap Doble slotted Fowler flap Tripple slotted Fowler flap	0.9 1.3 \(1.3 c'/c^*\) \(1.6 c'/c\) \(1.9 c'/c\)
Leading edge devices
Slot Krueger and drop flap Slat	0.2 0.3 \(0.4 c'/c\)
* \(c'\) is the extended chord and \(c\) to the nominal chord.

Table 3.1: Increase in \(C_{l_{\max}}\) of airfoils with high lift devices. Data retrieved from \(F_{\text{RANCHINI}}\) et al. [4].

The increase in the maximum coefficient of lift of the wing (\(\Delta C_{L_{\max}}\)) can be related with the increase of the maximum coefficient of lift of an airfoil (\(\Delta c_{L_{\max}}\)). For slotted and Fowler flaps, the expression is:

\[\Delta C_{L_{\max}} = 0.92 \Delta c_{l_{\max}} \dfrac{S_{fw}}{S_w} \cos \wedge_{1/4},\]

where \(\wedge_{1/4}\) refers to the swept measured from the locus of the \(c/4\) of all airfoils and \(S_{fw}\) refers to the surface of the wing between the two extremes of the flap. If the flap is a plain flap, the expression is:

\[\Delta C_{L_{\max}} = 0.92 \Delta c_{L_{\max}} \dfrac{S_{fw}}{S_w} \cos^3 \wedge_{1/4}.\]

In the Table 3.2 the typical values of \(C_{L_{\max}}\) and flap deflections in different configurations are given.

High-lift device	\(\delta_f\ TO^*\)	\(\delta_f\ LD\)	\(\tfrac{C_{L_{\max}}}{\cos \wedge_{1/4}}\ TO\)	\(\tfrac{C_{L_{\max}}}{\cos \wedge_{1/4}}\ LD\)
Plain flap Slotted flap Fowler flap Doble slotted** flap Tripple slotted flap and slat	\(20^{\circ}\) \(20^{\circ}\) \(15^{\circ}\) \(20^{\circ}\) \(20^{\circ}\)	\(60^{\circ}\) \(40^{\circ}\) \(40^{\circ}\) \(50^{\circ}\) \(40^{\circ}\)	1.4-1.6 1.5-1.7 2-2.2 1.7-1.95 2.4-2.7	1.7-2 1.8-2.2 2.5-2.9 2.3-2.7 3.2-3.5
* \(TO\) and \(LD\) refers to take off and landing, respectively. ** Double and triple slotted flaps have always Fowler effects increasing the chord.

Table 3.2: Typical values for \(C_{L_{\max}}\) in wings with high-lift devices. Data retrieved from \(F_{\text{RANCHINI}}\) et al. [4].