# effect of wing chord length on lift coefficient

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 ?

• Does this answer your question? How would you adjust C_l airfoil values for different Reynolds numbers? Jun 16, 2023 at 7:50
• What do you mean by reducing wing chord? Keep the same overall area and increasing the aspect ratio of the wing, OR Keep the same wing span and change chord length so that also the wing area is smaller Jun 18, 2023 at 11:43

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:

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).

• 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 ? Jun 16, 2023 at 11:55
• The question that sophit refers to explains how Cl values change for varying Reynolds numbers Jun 16, 2023 at 11:58
• 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? Jun 16, 2023 at 12:05
• 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 Jun 16, 2023 at 13:47
• @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. Jun 16, 2023 at 15:44