Can a bird break an airplane windshield?
How do aircraft windshields not tear when flying through precipitation at supersonic speeds?
Because planes do not regularly fly at such altitudes at such speeds that this could be a problem.
The problem mentioned (hitting a drop of water faster than the speed of sound in water) becomes not seen from any real airplane . Even if there wasn't a windshield to withstand this impact due to the shock wave, it wouldn't be a problem as no Mach 4 aircraft flies at an altitude where it can hit rain.
In fact, no aircraft has ever been able to cruise at Mach 4. Aside from a few experimental prototypes, no aircraft could fly at Mach 4.
Even the handful of planes that can hit around Mach 3 can only do so in the stratosphere, where the air is much thinner and there is no rain.
Hence, hitting a raindrop at Mach 4 is not a problem as no airplane can fly that fast. In fact, no aircraft flies much faster than Mach 1 at altitudes where rain is possible. Even the planned future planes that will be able to fly above Mach 4 permanently will only fly at that speed if they are high are above the clouds as they couldn't fly as fast when the air is thicker.
Even if the problems occurred at Mach 1, planes regularly only fly supersonic in the non-raining stratosphere. In fact, very few planes fly supersonic: planes (with the exception of the Concorde) are all subsonic, and even the Concorde only went supersonic if it went high enough. Military aircraft, although many of them are capable of supersonic flight, rarely fly supersonic, and even then only for brief bursts.
So in summary:
Supersonic aircraft usually don't fly much above the speed of sound, so they can easily slow down to subsonic speed when it rains. (Perhaps someone can help whether there is anything in the Concorde flight manual about the maximum permissible speed in rain.)
Aircraft rarely (if ever) fly supersonic at altitudes where rain is a problem.
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