Very old thread, I know, but I'm having real trouble with an ATPL Learning Objective in Instrumentation. For many years now, we've had the statement, "Explain why a Machmeter does not suffer from compressibility error." It's doing my head in, because I'm supposed to teach this to other people. I'm quite familiar with the workings of the Machmeter and understand that the density error in an ASI doesn't apply to the Machmeter, as the static capsule contained therein compensates for the change in density due to the change in altitude.
The problem I have is that the density also changes with speed. As the aircraft speeds up, the air compresses around the pitot tube, which would lead to an increase in dynamic pressure in an ASI. I cannot for the life of me understand how the Machmeter is able to detect this, unless it's somehow taken care of in the gearing or relationship between the ratio and ranging arms.
If anyone has an idea how this works, you would have my undying gratitude. I found the original reference but, other than a few lines about the temperature, nothing about compressibility.