By my understanding, the Mach Number at a given altitude is calculated by dividing IAS by the speed of sound at that altitude. So how is this speed of sound calculated to display the Mach Number on the Mach Meter? Does the Mach Meter share the same pitot tube used to calculate airspeed?
Most modern jets use an Air Data Computer (ADC) to calculate (among other things) Mach Number.
An ADC is simply a computer which accepts measurements of atmospheric data to calculate various flight related data.
A typical ADC may be connected to1:
Each of the inputs and outputs may be analog or digital depending on the design of the system, and are used for many purposes throughout the airplane. Each output is a purely calculated value based on the various input measurements and data stored within the unit.
To answer your question about the pitot source for the Mach Meter: Yes, they use the same pitot and static sources as the airspeed indicator.
In the case of mechanical instruments, they are both connected directly to the pitot static system.
In the case of an ADC, the pitot static system is connected directly to the ADC and then electrical signals communicate the airspeed and mach number to the electric airspeed indicator and mach meter (or EFIS), which no longer require actual pitot static connections.
A simplified example for the Mach Number calculation2 would be based on the pressure inputs:
The actual calculation makes corrections to the pressure data to compensate for installation errors and nonlinear sensor readings.
Note that it doesn't actually calculate the (local) speed of sound (LSS) in order to determine the current mach number, but with the TAT input and the calculated mach number, it could calculate it by calculating the outside air temperature (OAT/SAT) first:
Again, these are simplified formulas because the actual ones would consider sensor error, etc.
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A (analog) machmeter looks something like this:
So it's more like an more complex version of the airspeed indicator, in this case correcting for the altitude in the process. That being said, I found this extract apparently from an FAA publication:
Most systems today use more detailed data from sensors to give a correct value through a variety of (complex) calculations.
A little more discussion is available on PPruNe.
Side note: Speed of sound (a) itself is solely determined by temperature (that being said, you are able to determine it from pressure, as pressure is a function of temprature) hence the problem with the analog system above.
For air: a=sqrt(R*ɣ*T) [m/s] where:
Remember that you're reading of indicated airspeed [IAS] in knots in the cockpit, which is not the same as True airspeed [TAS] converted to m/s, in case you're trying to work out your mach speed manually (M=TAS/a. ))
For use without knowledge of airspeed & temprature, Wikipedia gives the following formula for subsonic flows:
A Machmeter does not determine the speed of sound. It doesn't even need to:
Mach number is simply the ratio between total pressure minus static pressure, divided by the static pressure.
Here is why:
mach nr is true air speed versus local speed of sound
converting indicated speed to true speed, we need to multiply with the sqrt of absolute temperature (in degrees K btw)
also the local speed of sound is directly proportional with the square root of absolute temperature (in K)
If you divide (2) by (3) the sqrt(T) will cancel each other out
IAS we already have, it's dynamic pressure minus static pressure, and, well, P , it's just static pressure, or, like I said in the beginning:
see, no thermometer.. only dynamic and static pressure.