I will be investigating the NACA 0012 symmetric airfoil to determine the sound levels produced by it as air flows across its surface and produces lift. To do this I will use a linear regression model to see if there is a relationship between noise levels, velocity and angle of attack which will be further explained in the next paragraphs.

Here we have Frequency in Hz that the sound produced is generating, Alpha in degrees which is the angle between the chord line of the airfoil in relation to the oncoming flow of air, Delta in m which is suction side displacement or how much airflow is displaced due to velocity, SSPL in dB which is scaled sound pressure levels which is the amount of noise generated as the airfoil passes through the air, and U_infinity in m/s which is the free stream velocity of oncoming air just before it interacts with the airfoil and the velocity the airfoil will experience at the point of contact.

ggplot(foildata, aes(x = U_infinity,y = SSPL, color = factor(alpha))) + 
  geom_point(alpha = 1) +
  geom_smooth(method="lm", se=F, formula=y~x, color= "red")

  #facet_wrap(~alpha)

Using linear regression we see an increasing trend of sound pressure levels increasing as the free stream velocity is increased with different angles of attack. There seems to be a direct relationship between airspeed and noise levels produced aerodynamically.

ggplot(foildata, aes(x = factor(alpha),y = SSPL, color = factor(alpha))) + 
  geom_boxplot()+
  labs(title = "Sound Pressure Level vs. Angle of Attack")

Exploring changes in angle of attack, there looks to be considerable variation by noise levels that are produced with each increasing angles of attack.

fig <- plot_ly(foildata, x = ~U_infinity, y = ~SSPL, z = ~alpha,color=~alpha, width=500, height=300, type="scatter3d",  mode = "markers")
fig

Here we get a 3D view of the relationship between angle of attack, sound pressure levels and the free stream velocity.

Model: \(\text{Y} = \beta_0 + \beta_1 \cdot \text{x}+\varepsilon\)

Fitted: \(\text{SSPL} = \beta_0 + \beta_1 \cdot U_\infty\)

This shows the standard linear regression equation alongside the regression equation for this case.

Model: \(\ R^2 = \frac{\sum( \hat{y}_i- \bar{y})^2}{\sum(y_i- \bar{y})^2}\)

The coefficient of Determination shows how well the regression fits the data, and this case y is SSPL.