Cognitive dissonance as it relates to the 9/11 attacks, and simplifying the lift-slope formula for a better understanding.

## 9/11 cognitive dissonance

I came across an interesting video today that presents all that we are supposed to believe as the official version of the 9/11 attacks in less than 5 minutes. No counter arguments are given, and even despite that it’s difficult to accept the official version due to how silly it sounds. Perhaps that’s why people just don’t care now about what occurred – the cognitive dissonance just becomes too much to handle as is mentioned in this global research article on cognitive dissonance.

## Lift-slope simplification

Today I was trying to figure out today why the formula for the lift-slope of a wing is:

$\pi^2/90$

The formula doesn’t seem to make much sense in the way that it’s presented, so this is a good opportunity to learn more about it.

After digging through lots of material that involved crazy equations, I finally stumbled across a beautiful simplification where I found that the formula is being converted from radians to degrees where we are representing a full turn of a circle.

The above formula can be better understood as:

$2\pi \cdot \frac{\tau}{360} \text{ or } 2\pi \cdot \frac{\pi}{180}$

And now it’s just a matter of figuring out where the 2 PI comes from. At first glance it was tempting to relate it to a full turn of a circle, so that I could use TAU once again for a better understanding. Further digging and thanks to an excellent PDF of Incompressible Flow over Airfoils, resulted in a better understanding, where it becomes clear that it’s due to an equation for the coefficient of lift:

$C_L=\frac{L}{\frac{1}{2}\rho v^2 S} \text{ which simplifies down to }\frac{\pi \alpha}{0.5}$

and after differentiating for the slope, we end up with:

$\frac{\mathrm{d}C_L}{\mathrm{d}\alpha}=\frac{\pi}{0.5}$

So a better understanding of the original formula is:

$\pi^2/90 = \frac{\pi}{0.5}\cdot\frac{\tau}{360}$

Is one formula better than the other? They both result in the same answer but my preference is for the latter of the two formulas, as it speaks more directly to an understanding of what it relates to.