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I have the design lift coefficient of the plane during the cruise condition. Now, I want to calculate the lift coefficient required by the airfoil which makes up the wing, taking into account the Aspect Ratio, Sweep, etc. Is there a formula for that? I have seen formulas that give the slope of the lift curve for a wing using the slope of the lift curve of an airfoil.

I need the design lift coefficient of the airfoil for choosing an appropriate airfoil.

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  • $\begingroup$ Okay, that can be done. I had one more doubt. At each span location, will the lift coefficient (of the airfoil at that location) be different or will it be the same? As we move in the spanwise direction, the lift will decrease and the chord also decreases. Therefore, can we say that lift coefficient will be same cross the span? $\endgroup$ – Pavan Apr 27 at 14:43
  • $\begingroup$ Oh, I see. I forgot about the downwash and spanwise flow. Then how can one chose an airfoil if one has design lift coefficient of the wing? $\endgroup$ – Pavan Apr 27 at 14:47
  • $\begingroup$ Then, I will add another question. $\endgroup$ – Pavan Apr 27 at 14:51
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As far as your question on sectional lift given a wing geometry and total lift coefficient is concerned, there is no one single formula that estimates this. The sectional lift is affected by downwash and spanwise flow, which are in turn dictated by the wing geometry and airfoil themselves.

For straight tapered wing, you can use the lifting-line, which computes the downwash angle at the discrete spanwise locations, which you can use to easily back-out local $C_l$. For swept wing, your easiest solution is to use a vortex-lattice method, such as AVL. AVL directly outputs the section lift coefficient at the corresponding control points.

As far as selecting/designing an airfoil is concerned, it's much more involved than just looking at the cruise lift coefficient. You should consider:

  • Takeoff and landing requirements. What kind of performance do you need? What kind of trailing-edge and/or leading-edge devices can you fit with the airfoil?
  • Operating conditions. Is it a point-design? Or does it need to cater for large range of operating conditions?
  • Structural concerns. Can you actually manufacture a super thin trailing-edge, even if it gives the best stall characteristics? Can you actually fit a spar tall enough (and at the right location), even if it gives the best drag characteristics?
  • Space concerns. Can you actually fit fuel tanks in the wing if it's super thin?
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