# Whats the derivation of a low speed ratio for stall warning?

I've seen an equation related to stall and angle of attack in a few places like this patent that goes more or less:

$$\frac{CAS_{alert}}{CAS_{current}} = \sqrt{\frac{C_{L,current}}{C_{L,alert}}}$$

Where CAS is your airspeed and C_l is the coefficient of lift at certain angle of attack.

It seems intuitive, for example if you are in unaccelerated flight and using 90% of your available lift then you are about 5% over your alert speed. However I'm confused about a few details like why there's a square root in the equation, or whether there are scenarios where this is just an approximation and it breaks down. Where does this speed ratio come from?

• $\rho$ times $\text{TAS}^2$ is approximately $\text{CAS}^2$. (More accurately it's equivalent airspeed squared). Commented May 17 at 21:28
It's a simple scaling law. The lift is proportional to $$C_L$$ times the square of the equivalent airspeed. In other words, for a given load factor, $$C_L(\text{EAS})^2$$ is a constant. So $$\frac{\text{EAS}_1}{\text{EAS}_2}=\sqrt{\frac{C_{L,2}}{C_{L,1}}}$$ is true for any two flight conditions at the same load factor.