There is an important way that planes measure their true airspeed, and that is with pitot tubes. Pitot tubes use the principles from Bernoulli's equation to derive the current airspeed of aircraft. The way it works is it compares the static and stagnation pressure about the aircraft.
As a side note, static pressure is the measure of purely random motion of molecules in a gas. This would be the pressure felt as you travel with gas at the local flow velocity. As for stagnation pressure, denoted by $ P_o $, this is the pressure at a stagnation point where velocity is equal to zero. Stagnation pressure is also often called the total pressure. A pitot tube would actually be a stagnation point where velocity would equal zero. We can see this in Fig. 1.
Fig. 1 - Image of a pitot-static probe.
At the entrance of the pitot tube, there is a stagnation point where the airflow velocity is zero, hence, we can use the pressure value at that point to be our total pressure, or $ P_o $. It was mentioned before that pitot tubes used Bernoulli's equation. Let's write out the equation for our entrance being one focus of the equation and the static pressure inlet, point 1, being the other focus.
[ 1 ]
$$ P_1 + \frac{1}{2} \rho v_1^2 = P_2 + \frac{1}{2} \rho v_2^2 $$ $$ \Rightarrow P_1 + \frac{1}{2} \rho v_1^2 = P_o $$
Notice how in the last part of Eq. (1), $ v_2 = 0 $, so that term dropped out. This is because point 2 is at the stagnation point where velocity is equal to zero, hence we are only left with the total pressure at that point, $ P_o $. On the left-hand side of Eq. (1), we have point 1, which is the static pressure point in Fig. 1.
We can then rearrange Eq. (1) to solve for $ v_1 $.
[ 2 ]
$$ v_1 = \sqrt{ \frac{2(P_o - P_1)}{\rho} } $$
Now using the static and total pressure, we can solve for our aircraft's velocity!
We have talked about static pressure and stagnation pressure. Now it is time to talk about dynamic pressure, or the pressure caused by movement. We can denote dynamic pressure as $ q $, where
[ 3 ]
$$ q = \frac{1}{2} \rho v^2 $$
We can also define a relation using dynamic and static pressure to get total pressure where
[ 4 ]
$$ P_1 + q = P_o $$
Here, $ P_1 $ is the static pressure, $ q $ is the dynamic pressure, and $ P_o $ is the stagnation pressure. This makes sense because if we were to be static in a given gas volume, we would feel the static pressure of the air molecules impacting our bodies. However, if we started to run forward, we would feel a larger pressure than before because of the dynamic pressure. And with these two pressure added together, we get our total, or stagnation, pressure.