# 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].

3.4.3: Increase in CLmax is shared under a CC BY-SA 3.0 license and was authored, remixed, and/or curated by Manuel Soler Arnedo via source content that was edited to conform to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.