Airspeed is more accurate when displayed by a Machmeter than when displayed by an airspeed indicator. It isn't affected by ambient temperature / density changes. It is still affected by position error, hence it must indicate something between IAS and CAS.

enter image description here enter image description here
Source, source

What does prevent to have a Machmeter scale both in knots and Mach numbers, and use the Machmeter in place of the airspeed indicator, as the standard airspeed instrument?

Such instruments exist:

enter image description here
Source (From FAA Airplane Flying Handbook)

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    $\begingroup$ I assume you're asking about larger turbine aircraft? Being 10 knots too fast is significant when landing a light aircraft, but it's only about M0.01 and I'd hate to have to try to tell the difference between M0.1 and M0.11 on that Machmeter in your question :-) $\endgroup$ – Pondlife Jul 5 '17 at 13:29
  • $\begingroup$ @Pondlife: No, I'm asking in general. The problem you point out isn't a problem of unit or instrument, just a problem of difference between low/high values which is more large in high-speed aircraft. You would have the same problem with an ASI without a moving scale. $\endgroup$ – mins Jul 5 '17 at 13:32
  • $\begingroup$ Yes, it was mostly a tongue-in-cheek comment. But practically speaking, dealing with hundredths of a unit in flight plans, documentation etc. seems like it would be rather awkward, even if the instrument shows it clearly on an appropriate scale. $\endgroup$ – Pondlife Jul 5 '17 at 13:43
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    $\begingroup$ "It isn't affected by ambient temperature / density changes." - I question this assertion, given that the speed of sound itself varies with both temperature and altitude. So you tend to gain nothing accuracy-wise, as the mach number still won't accurately tell you how fast you're traveling unless you manually correct for ambient factors. $\endgroup$ – aroth Jul 5 '17 at 23:21
  • $\begingroup$ @aroth, I took into account a Mach meter shows ${EAS} / {k\sqrt {P_s}}$, and EAS isn't dependent on local density or local temperature. Is this wrong? If not, wouldn't that mean, given M is proportional to EAS, a Mach meter is more useful for the pilot than an ASI, at subsonic speed (e.g. at 300 kt)? I agree it's not more accurate, but more useful. I used more accurate because some measuring biases had been removed. $\endgroup$ – mins Jul 6 '17 at 12:00

Machmeter-based tachometer would not indicate something between IAS and CAS, it would indicate TAS but for the same¹ instrument and position errors the normal airspeed indicator has.

However, airspeed indicator does not indicate true airspeed and this is intentional.

The EAS, that the airspeed indicator is aiming to show, is a measure of dynamic pressure. Since lift, which also includes effectiveness of control surfaces, is proportional to dynamic pressure and drag is also a function of dynamic pressure, most handling characteristics depend on the dynamic pressure. Therefore the value indicated by the airspeed indicator is exactly what the pilot wants to know.

The only effects that depend on other speeds are aeroelastic flutter, which depends on true airspeed, and compressibility effects, that depend on Mach number. Both limit the maximum safe speed. That is why fast aircraft also need Machmeter. But they still need the indicated² airspeed.

¹ Both instruments use the same two raw values obtained from the pitot-static system: total and static pressure. The airspeed indicator shows square root of the difference (because dynamic pressure is proportional to square of speed), the Machmeter shows the ratio to some fractional exponent. So all the errors affect both the same way, and in electronic instruments, they are compensated² to the same extent.

² Electronic systems in modern airliners say to show CAS, correcting all errors they can reasonably estimate.

  • $\begingroup$ Could the indicated mach number be calibrated at sea level pressure, similar to IAS? $\endgroup$ – Koyovis Jul 7 '17 at 9:14
  • $\begingroup$ "Therefore the value indicated by the airspeed indicator is exactly what the pilot wants to know." Wants to know or needs to know? $\endgroup$ – FreeMan Jul 7 '17 at 12:50
  • $\begingroup$ @FreeMan, I would stick with wants, because there are workarounds for when he does not, so it's not an absolute necessity, just very, very useful. $\endgroup$ – Jan Hudec Jul 7 '17 at 18:24
  • $\begingroup$ Just making sure! $\endgroup$ – FreeMan Jul 7 '17 at 18:57

...Machmeter scale both in knots and Mach numbers

The simple answer is that unlike say (MPH vs KTS) the equivalents change with altitude so one scale would have to move. For example at sea level Mach 1 is roughly 661 Kts. by comparison at 35,000 ft its 574 Kts. Even though an air speed indicator also suffers from similar corrections the MPH/KTS scales are always in line. The IAS/TAS calibration creates a similar issue but generally its acceptable to correct once cruise altitude has been reached (or you are at least in a cruise climb situation and free to handle such correction). The truth is that most modern glass cockpit units handle this for you.

One other thing to consider is units. Mach Number, strictly speaking is unit-less while speed is measured as Distance/Time many might say these two things cant be on the same instrument.

The fact remains that you, could, potentially print them on the same instrument as long as one scale was constantly adjusted for. I presume (based on the picture) that Mach gauges may have an issue with low readings which could be a problem for things like stall labeling etc.

You may also want to take a look at the example outlined here.

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    $\begingroup$ "at sea level Mach 1 is roughly 661 Kts. by comparison at 35,000 ft its 574 Kts", this is a comparison of Mach number and TAS, IAS and TAS conversion has the same problem, still we use IAS. $\endgroup$ – mins Jul 5 '17 at 13:30
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    $\begingroup$ I have added some more to possibly clarify $\endgroup$ – Dave Jul 5 '17 at 13:37
  • $\begingroup$ The dual ASI/Machmeter shown in the OP appears to have a movable Mach scale, so that may be exactly what's done on these dual gauges. $\endgroup$ – FreeMan Jul 7 '17 at 12:54
  • $\begingroup$ I noticed that as well I need to do some research on how they work and what they are as I have never seen one before. $\endgroup$ – Dave Jul 7 '17 at 13:08

The needle would move very little at lower airspeeds and would be subject to non-linearity. Velocity follows directly from $p_{total} - p_{static} $, while Mach number is a fraction. From Wikipedia:

$$M = \sqrt{5\left[\left(\frac{p_t}{p_s}\right)^\frac{2}{7}-1\right]}$$

At the beginning of the scale, there is very little relative change and very little movement of the needle, and as the speed picks up there is more needle movement per knot.

enter image description here

A plot of $\Delta$ dynamic pressure as a fraction of static pressure (at sea level in ISO atmosphere) shows this. At 200 knots, the dynamic pressure is only 6% of the static pressure. Any friction in the measuring equipment will have large effects on the accuracy and linearity of the speed reading up to this point. Only at speeds of > 200 knots does the gradient start to be reasonably useable.

  • $\begingroup$ @JanHudec I could not find a fault in this answer $\endgroup$ – Koyovis Jul 6 '17 at 6:39
  • $\begingroup$ Hm, WP says $M = \sqrt{5\left[\left(\frac{p_t}{p_s}\right)^\frac{2}{7}-1\right]}$. And so does the other answer. $\endgroup$ – Jan Hudec Jul 6 '17 at 10:36
  • $\begingroup$ Yes, perhaps a better source, hey? I'll update. $\endgroup$ – Koyovis Jul 6 '17 at 15:19
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    $\begingroup$ Unfortunately I don't know where they got it from and while I know quite a bit of physics, fluid thermodynamics involving $\gamma$ seriously confuses me. $\endgroup$ – Jan Hudec Jul 7 '17 at 10:41
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    $\begingroup$ @JanHudec I posted a question on physics SE, the answer turns out to be pretty simple. Have also placed a comment at the wrong answer referenced above. $\endgroup$ – Koyovis Jul 7 '17 at 11:30

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