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In the bertin's Aerodynamics book It is written that reducing the wing chord increases the lift coefficient( decreases stall angle) and as a result, the wingtip stalls earlier than the wing root

how ?

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We know the definition of the aircraft lift coefficient in steady flight: $$C_L=\frac{W}{\frac{1}{2}\rho V^2 \cdot S}$$ We can now divide the entire wing (with area $S$) in tiny slices of area $dS$, each with width $dy$ and chord $c(y)$. $$ dS = c(y) \cdot dy$$ We can substitute the above equation to get the local lift equation: $$C_l(y)=\frac{ dW}{ \frac{1}{2}\rho V^2 \cdot c(y) \text{ } dy} $$

What happens to the to the local $C_l(y)$ when the chord is low or when it's high? How does $c$ vary for a typical wing from chord to root?

For a typical tapered wing, with an elliptical lift distribution the lift and the local lift distribution look like this: enter image description here

As you can see the outboard lift section is highest, meaning that section will stall first if all sections have the same definition.

Source: E. OBERT, Aerodynamic design of transport aircraft (IOS Press, 2009).

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  • $\begingroup$ thank you but what is happening in phisiycal point of view ? i mean when chord lenght reduced , reynolds number also reduced wich means lower stall angle and lower lift coefficient ! can you tell me what exactly happens in terms of reynolds number ? $\endgroup$
    – alireza
    Jun 16, 2023 at 11:55
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    $\begingroup$ The question that sophit refers to explains how Cl values change for varying Reynolds numbers $\endgroup$
    – ROIMaison
    Jun 16, 2023 at 11:58
  • $\begingroup$ Cl and stall angle both decreases with decreasing reynolds number but we know that higher Cl means stall earlier ! how can get higher Cl and lower stall angle with reduction in reynolds? $\endgroup$
    – alireza
    Jun 16, 2023 at 12:05
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    $\begingroup$ Local stall happens when the required $C_l$ ( $C_{l_{req}}$ ) exceeds the $C_l$ the airfoil can deliver ($C_{l_{max}}$). Decreasing the value of $c$ drives up the value of $C_{l_{req}}$ due to the reasons I mentioned above as well as reducing the value of $C_{l_{max}}$ due to the reynolds effects $\endgroup$
    – ROIMaison
    Jun 16, 2023 at 13:47
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    $\begingroup$ @alireza: $C_l$ does not decrease with Reynolds number rather with the AoA. $C_{l_{max}}$ decreases (and $C_d$ increases) at smaller Reynolds numbers. $\endgroup$
    – sophit
    Jun 16, 2023 at 15:44

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