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Question: How will the machmeter behave in a constant CAS climb if the static source becomes blocked?
Answer: The machmeter reading will decrease.

Why? I couldn't find any logical reason for the machmeter reading to decrease. My understanding is that when CAS is constant during a climb, the TAS should increase. If the static source is blocked, this will only increase the TAS further to maintain same CAS because the static pressure outside is less than the pressure in the blocked static source.

I fail to understand how the local speed of sound (LSS) is related to a blocked static source. Because LSS is related to temperature only, so it decreases during a climb.

That means that Mach speed = TAS (increasing) / LSS (decreasing) = overall increase in Mach speed

What am I missing?

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    $\begingroup$ If you have a constant speed climb, the total pressure measured by the pitot tube would drop, thus the indicated speed would decrease, not increase. Could it be a misinterpretation that "constant CAS climb" means an autopilot constant speed climb (not an actual constant CAS climb)? $\endgroup$ – falstro Dec 11 '16 at 18:58
  • $\begingroup$ If your static port is blocked, you have bigger problems than the behaviour of your machmeter. $\endgroup$ – Sean Sep 18 at 21:09
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A Machmeter doesn't use the true airspeed (TAS) or the local speed of sound for its readings since the TAS measurement can't be obtained without getting the Mach number first.

The calibrated airspeed (CAS) shown to the pilot is also used by the Machmeter, it measures the speed based on the pressure differential between the pitot tube and the static port.

  1. If $P(pitot)$ $>$ $P(static)$, then the speed reading will be positive.

The bigger the difference, the faster the speed.

  1. If $P(pitot)$ $<$ $P(static)$, then the speed will read zero since the speed indicator doesn't allow negative speeds.

A blocked static in a climb will cause (2.), and it would require an extremely fast flying to get the gauge to show any speed reading above zero, probably even faster than the plane can handle.

The blocked static will also freeze the altimeter and show zero vertical speed. Glossing over how such a climb can be maintained, let's assume there are different pitot-static sources, one for flying and one for the Machmeter.

Answer:

After the static-port is blocked in a climb, the Machmeter will within minutes (or seconds if it's a fast climb) drop to zero, just like its CAS reading.

Do note:

Aircraft flight instruments use pressure differential, not temperature, to compute the Mach number.

Wikipedia

and

The true airspeed is calculated by the Air Data Computer from the Mach number and the outside air temperature.

Is the Mach number shown by an Air Data Computer considered a "true" Mach number?

As you can see, it is the Mach number that is used to know the TAS, not the other way around.

enter image description here

Pre climb and blocking.

enter image description here

Blocked, then climbed at same speed.

(Source)

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A pneumatic airspeed indicator relies on the differential pressure between the pitot tube and the static port. If the static port ices over, as an example, the altimeter will read constant, and VSI will become zero.

Assuming the pitot tube is operational, an increase in altitude will result in a decrease in ram air pressure measured at the pitot tube. This will result in decreasing IAS. Since most machmeters use air data from the static and pitot system, the machmeter will also show a decreasing mach number. Practically speaking, the IAS and machmeter will become rapidly unusable with an obscured static port.

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