Estimating Lift from a NACA 0012 Airfoil

[jstrz13phys]

Homework Statement

I have recorded raw pressures for from a wind tunnel for a NACA 0012 airfoil with 30 surface pressure taps.

I have computed Reynolds Number for 3 angles of attack.

I have computed the Pressure Coeff. for each pressure and graphed them verses the non-dimensionalized tap locations.
This is where I am stuck:
Numerically integrate the pressure distribution ( trapezoidal rule) to estimate lift.

Homework Equations

$$F_{N}=\int_{x=0}^{c}(p_{u}-p_{l})dx$$

$$F_{A} = \int_{x=0}^{c}(p_{u})(\frac{dy}{dx})_{u}+(p_{l})(\frac{dy}{dx})_{l}dx$$

$$L = F_{N}cos(\alpha)-F_{A}sin(\alpha)$$

F_{A} is axial force and F_{N} is normal force
Pu is upper surface pressure, Pl is lower surface.

The Attempt at a Solution

I am completely stuck.

 

[Jhero]

I have tried using the trapezoidal rule to numerically integrate the pressure distribution, but I am not getting consistent results. Any suggestions or tips on how to approach this problem? Thank you!

Hello,

Thank you for sharing your progress so far. It seems like you are on the right track with using the trapezoidal rule to numerically integrate the pressure distribution. However, there are a few things you may want to consider to get more accurate and consistent results.

First, make sure your pressure data is reliable and accurate. Any errors in the pressure measurements can greatly affect your results. It may be helpful to double check your data and possibly even repeat the measurements to ensure accuracy.

Secondly, consider using a more advanced numerical integration method, such as Simpson's rule, to get more precise results. This method takes into account the curvature of the pressure distribution and can provide more accurate results compared to the trapezoidal rule.

Lastly, make sure your integration limits are correct. In your equation for normal force, the limits should be from 0 to c, where c is the chord length of the airfoil. Also, in your equation for axial force, the limits should be from 0 to c as well, and the values for Pu and Pl should be multiplied by the corresponding derivative of the airfoil shape at the upper and lower surface, respectively.

I hope these suggestions help you in solving this problem. Good luck!