I am trying to convert 2d Cl data obtained from javafoil for a NACA 4412 into 3d data to be used for analysis of the airfoil, but cant find any equations online

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    $\begingroup$ It's unclear what you're asking. By "convert into 3D data" you mean you want to determine the lift or lift distribution of an entire wing that uses the NACA 4412 airfoil? Because the airfoil by definition is only two-dimensional. $\endgroup$ Apr 7 at 13:26

1 Answer 1


3D data, as in the third dimension is the wing span: the performance of the whole wing is the integral of the wing sections from root to tip. For the local 2D lift l of the section: $$\frac{dL}{db} = c_l \cdot \frac{1}{2} \rho V^2 \cdot c$$ with $c$ = chord length of the profile and $b$ the wing span. For the complete wing:

$$L = \int_{root}^{tip} c_l \cdot \frac{1}{2} \rho V^2 \cdot c \cdot db = C_L \frac{1}{2} \rho V^2 \cdot S$$ with $C_L$ the average lift coefficient, S the wing area.

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Local $c_l$ is a function of local angle of attack $\alpha$. Along the integral, the local $\alpha$ and therefore the local $c_l$ will vary because of:

  • Wing twist (washout).
  • Interference effects from the fuselage
  • Vortex generation around the wing tip

with the last two effects most noticeable on swept wings, as depicted in fig 7-19 of Torenbeek. Also, the local chord $c$ changes due to the taper ratio of the wing, and the local stream velocity V will change as a function of interference with other bits of the aeroplane. So in order to compute the 3D wing data, the wing configuration must be known. The integral can be solved mathematically if the functions of $c_l$ and $c$ and V along the wing span are known.

Even then there are issues with the local streamline fields that are hard to capture in an equation, and comparison with statistical data of existing aircraft wings is useful. So are Computed Fluid Dynamics and wind tunnel measurements


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