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3.4.3: Increase in CLmax

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    78114
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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.

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