What is the "compression ratio" of air hitting the nose?
I think what you seek is called the stagnation pressure, which is the pressure rise experienced in a given parcel of air if all the kinetic energy associated with that parcel's velocity were to be converted without losses into potential energy (stored work) of compression according to the ideal gas law. The equation for stagnation pressure is

$$ \frac{P_\text{stagnation}}{P_\text{static}} = \left( 1 + \frac{\gamma - 1}{2} \times M^2 \right) ^ \left( \frac{\gamma}{\gamma - 1} \right) $$

where $\gamma$ is the ratio of specific heats for air and $M$ is the Mach number.