# Mach Number

Thread Starter

Join Date: Jul 2008

Location: under papa 600

Posts: 55

**Mach Number**

Can someone please exlain why Mach Number is used to measure air speed at high altitude as opposed to IAS.

Also - is this measured directly by the pitot in the same way as IAS and how is it calibrated to read Mach number?

Also - is this measured directly by the pitot in the same way as IAS and how is it calibrated to read Mach number?

Join Date: Feb 2008

Location: Standby...call you back..

Posts: 210

Hello papa600,

mainly, because the IAS is not anymore a actuel figure of the A/C speed..

for exemple, you could fly in a climb at a constant IAS..but the MN is constantly increasing...furthermore the speed limitations of the A/C will be based on MN..let's say above FL300

For the instrument..I confess it's quite "long time ago" but I still remember that's quite simple in term of technology...Now using air data computer since a decade (at least)..everything is computed according to the different physic rules..starting with: speed of sound = 39 X square root T° (absolute in ° kelvin) and MN = TAS / Local speed of sound...finally this is simple math's..and glad to see this done by a silent pax...

Other advises will come up certainly..

Good evening

mainly, because the IAS is not anymore a actuel figure of the A/C speed..

for exemple, you could fly in a climb at a constant IAS..but the MN is constantly increasing...furthermore the speed limitations of the A/C will be based on MN..let's say above FL300

For the instrument..I confess it's quite "long time ago" but I still remember that's quite simple in term of technology...Now using air data computer since a decade (at least)..everything is computed according to the different physic rules..starting with: speed of sound = 39 X square root T° (absolute in ° kelvin) and MN = TAS / Local speed of sound...finally this is simple math's..and glad to see this done by a silent pax...

Other advises will come up certainly..

Good evening

Join Date: Jan 2000

Location: Long Beach

Posts: 336

I find it easier to think of a mach meter as being an ASI with an altimeter in it's workings, adjusting the speed (mach) readout according to altitude ...... and that is because it is exactly what a mach meter is! When you start with that in mind, it is easier to get your head around a technical description of the instrument (oh, the heady days of learning to fly! ) from a book.

Join Date: Aug 2001

Location: Dorset

Posts: 775

The maximum speed at which an aircraft may be routinely flown is limited by

the ability of the structure to support the resulting aerodynamic loads and by the compressibility effects encountered when flying close to the local speed of sound.

At low altitudes the calibrated airspeed producing limiting aerodynamic loads is the limiting value. This is called VMO.

The mach number at which compressibility effects become the limiting value is termed MMO. As altitude is increased, the local speed of sound decreases, thereby reducing the CAS equating to MMO. At high altitudes VMO is greater than MMO and at lower altitudes MMO is greater than VMO.

So VMO is the limiting speed at low altiude and MMO is the limiting speed at high altitude (as stated in two previous posts).

A mach meter produces an indication of mach number based on the ratio of dynamic pressure to static pressure. It does this by taking in pitot pressure and static pressure. An ASI differential capsule is then used to subtract static pressure from pitot pressure to leave dynamic pressure.

Movement of this capsule is then modified, using an altimeter aneroid capsule which senses static pressure. The mechanism is arranged such that the resultant output motion represents dynamic pressure divided by static pressure.

the ability of the structure to support the resulting aerodynamic loads and by the compressibility effects encountered when flying close to the local speed of sound.

At low altitudes the calibrated airspeed producing limiting aerodynamic loads is the limiting value. This is called VMO.

The mach number at which compressibility effects become the limiting value is termed MMO. As altitude is increased, the local speed of sound decreases, thereby reducing the CAS equating to MMO. At high altitudes VMO is greater than MMO and at lower altitudes MMO is greater than VMO.

So VMO is the limiting speed at low altiude and MMO is the limiting speed at high altitude (as stated in two previous posts).

A mach meter produces an indication of mach number based on the ratio of dynamic pressure to static pressure. It does this by taking in pitot pressure and static pressure. An ASI differential capsule is then used to subtract static pressure from pitot pressure to leave dynamic pressure.

Movement of this capsule is then modified, using an altimeter aneroid capsule which senses static pressure. The mechanism is arranged such that the resultant output motion represents dynamic pressure divided by static pressure.

Thread Starter

Join Date: Jul 2008

Location: under papa 600

Posts: 55

Thanks you very much for the replies!

The part I was struggling with is why we use Mach number at all. I understand the relationship between IAS, CAS, TAS, air density, altitude etc but did not understand why the transition from IAS to Mach number depending on altitude - I presume there is a straight relationship between altitude and IAS / TAS would hold so why bother with Mach number?

I'm not sure that particualr penny has dropped yet even after reading the excellent reply from Keith Williams several times (sorry Keith its more me than you).

The part I was struggling with is why we use Mach number at all. I understand the relationship between IAS, CAS, TAS, air density, altitude etc but did not understand why the transition from IAS to Mach number depending on altitude - I presume there is a straight relationship between altitude and IAS / TAS would hold so why bother with Mach number?

I'm not sure that particualr penny has dropped yet even after reading the excellent reply from Keith Williams several times (sorry Keith its more me than you).

Join Date: Oct 2009

Location: UK

Posts: 1,270

Hi Papa600,

It may help to think of it like this:

Your minimum speed is always IAS.

Your Maximum speed is either VMO (IAS) at low Alt: or MMO (Mach) at high Alt.

For economy (fuel & engineering flying costs) we fly at a Mach speed at high Alt and at an IAS at low Alt.

e.g. During the climb - say we use 300 kts IAS until we reach Mach Number 0.8 then continue climbing to cruise at 0.8 Mach. Depending on FL, this may be say 250 kts IAS.

It may help to think of it like this:

Your minimum speed is always IAS.

Your Maximum speed is either VMO (IAS) at low Alt: or MMO (Mach) at high Alt.

For economy (fuel & engineering flying costs) we fly at a Mach speed at high Alt and at an IAS at low Alt.

e.g. During the climb - say we use 300 kts IAS until we reach Mach Number 0.8 then continue climbing to cruise at 0.8 Mach. Depending on FL, this may be say 250 kts IAS.

*Last edited by rudderrudderrat; 1st Dec 2009 at 11:49. Reason: finger trouble with preview and save*

Join Date: Aug 2001

Location: Dorset

Posts: 775

To avoid unnecessary complications with isothermal layers and such, let's consider the ISA below the tropopause.

Consider a graph with altitude increasing upwards on the vertical scale and speeds increasing from left to right on the horizontal scale.

The EAS, CAS, TAS and Mach Number can be represented by straight(ish) lines in that order (ECTM) from left to right. The lines fan outwards as altitude increase.

If we rotate the fan slightly so that any one of the lines is vertical, this will show the effect of climbing with that speed constant. For example in constant Mach climb, all of the other speeds decrease as we climb.

VMO is the CAS at which aerodynamic forces start to damage the structure.

Let's consider VMO to be a constant CAS (not quite true but close enough our purposes today).

MMO is the Mach number at which compressibility causes control problems such as Mach Tuck Under. MMO is a constant(ish) Mach Number.

If we fly faster than VMO we damage the structure and if we fly faster than MMO we suffer control problems. So we must never fly faster than either of them

Now lets draw a graph to represent the CAS values equating to VMO and MMO. Our graph will have altitude on the vertical scale and CAS on the horizontal scale.

Because VMO is a constant(ish) CAS we can show it as a straight vertical line.

If we look back at our earlier graph we can see that in a constant Mach climb CAS decreases. So to represent our CAS value for MMO we need a line that is sloping to the left as we move upwards. But where should we locate it on our graph?

At low level the CAS equating to MMO is greater that the CAS equating to VMO. But the speed of sound is related to temperature, so it gradually decreases as altitude increases. So the CAS value for MMO does the same.

This means that MMO is greater than VMO at low altitude, but less than VMO at higher altitude.

So our MMO line should be to the right of the VMO line at the bottom of the graph, but cross over the VMO lone part way up. Our graph should look like an X with the left leg vertical.

Now consider the effects of accelerating from zero at different altitudes. To do this we simply move horizontally from left to right across the graph. At low altitude we will hit VMO before we hit MMO, so we need to watch our CAS.

At the altitude where the two line scross we will hit VMO and MMO simultaneously.

But at high altitude we hit MMO before we hit VMO. So we need to watch our mach Number.

This would all be much easier (and shorter) if I could figure out how to post diagrams, but I have not yet done so!

Consider a graph with altitude increasing upwards on the vertical scale and speeds increasing from left to right on the horizontal scale.

The EAS, CAS, TAS and Mach Number can be represented by straight(ish) lines in that order (ECTM) from left to right. The lines fan outwards as altitude increase.

If we rotate the fan slightly so that any one of the lines is vertical, this will show the effect of climbing with that speed constant. For example in constant Mach climb, all of the other speeds decrease as we climb.

VMO is the CAS at which aerodynamic forces start to damage the structure.

Let's consider VMO to be a constant CAS (not quite true but close enough our purposes today).

MMO is the Mach number at which compressibility causes control problems such as Mach Tuck Under. MMO is a constant(ish) Mach Number.

If we fly faster than VMO we damage the structure and if we fly faster than MMO we suffer control problems. So we must never fly faster than either of them

Now lets draw a graph to represent the CAS values equating to VMO and MMO. Our graph will have altitude on the vertical scale and CAS on the horizontal scale.

Because VMO is a constant(ish) CAS we can show it as a straight vertical line.

If we look back at our earlier graph we can see that in a constant Mach climb CAS decreases. So to represent our CAS value for MMO we need a line that is sloping to the left as we move upwards. But where should we locate it on our graph?

At low level the CAS equating to MMO is greater that the CAS equating to VMO. But the speed of sound is related to temperature, so it gradually decreases as altitude increases. So the CAS value for MMO does the same.

This means that MMO is greater than VMO at low altitude, but less than VMO at higher altitude.

So our MMO line should be to the right of the VMO line at the bottom of the graph, but cross over the VMO lone part way up. Our graph should look like an X with the left leg vertical.

Now consider the effects of accelerating from zero at different altitudes. To do this we simply move horizontally from left to right across the graph. At low altitude we will hit VMO before we hit MMO, so we need to watch our CAS.

At the altitude where the two line scross we will hit VMO and MMO simultaneously.

But at high altitude we hit MMO before we hit VMO. So we need to watch our mach Number.

This would all be much easier (and shorter) if I could figure out how to post diagrams, but I have not yet done so!

Join Date: Feb 2008

Location: Standby...call you back..

Posts: 210

Hi Keith,

great explanation...to join a picture (scanned doc..for exemple) use the "Insert picture" function (small yellow square on top)..but your pictures should be hosted on a specific web site..;(plenty around)..then you just have to replicate the url adress..and your picture will be available to all while clicking on the links..

Hope this help you

Have a good day..

Roljoe

great explanation...to join a picture (scanned doc..for exemple) use the "Insert picture" function (small yellow square on top)..but your pictures should be hosted on a specific web site..;(plenty around)..then you just have to replicate the url adress..and your picture will be available to all while clicking on the links..

Hope this help you

Have a good day..

Roljoe

Thread Starter

Join Date: Jul 2008

Location: under papa 600

Posts: 55

Keith - if you could draw that you would be my saviour! I've tried to sketch what I think you are saying but am getting a bit muddled.

Alternatively is there a reference book to explain this?

By the way I am a PPL and was asked this question from a friend of mine with an interest in aviation. I couldn't answer why Mach number replaced IAS at high altitude given the IAS will always give you a reading of some fashion changing with altitude and that IAS will have an equivalent Mach Number at any altitude (is this true?)

I can tell you even a jet pilot I know couldn't answer though that was maybe because he didn't know how to explain it properly.

Its a bit sad the things that keep you awake at night!

Alternatively is there a reference book to explain this?

By the way I am a PPL and was asked this question from a friend of mine with an interest in aviation. I couldn't answer why Mach number replaced IAS at high altitude given the IAS will always give you a reading of some fashion changing with altitude and that IAS will have an equivalent Mach Number at any altitude (is this true?)

I can tell you even a jet pilot I know couldn't answer though that was maybe because he didn't know how to explain it properly.

Its a bit sad the things that keep you awake at night!

Moderator

Join Date: Apr 2001

Location: various places .....

Posts: 6,789

*I couldn't answer why Mach number replaced IAS at high altitude given the IAS will always give you a reading of some fashion*

Quite correct and you could operate with reference to IAS if you wished. However, that would involve having a cheat sheet alongside so that you could keep track of a constantly changing IAS limit with height .. so, to make life easier for the pilot (and that's the only reason we prefer to use the machmeter at height) we fly Mach rather than IAS.

*Alternatively is there a reference book to explain this?*

Any of the undergraduate aerodynamics/performance texts (eg

*Aircraft Performance, Austyn Mair and David Birdsall, Cambridge Aerospace Series*) are useful but probably a bit too much into the mathematics for the typical pilot (who really doesn't need the esoteric detail .. unless one derives a masochistic pleasure from that sort of stuff).

For pilot use, probably one of the more useful texts is Hurt's

*Aerodynamics for Naval Aviators.*This has the usual pilot relevant equations for note but is a very easy simplified read on the story. Readily available in just about every technical bookstore flogging aeroplane stuff.

A number of the posts above have referred to temperature - not relevant to Mach.

Join Date: Dec 2006

Location: The No Transgression Zone

Posts: 2,470

It's time for

PA

**OS**to reintroduce the*relation to PPRuNe as well as explain some more in instrument calibration,...it seem the measurement of mach no. gets confused with local free stream qualities quite often***Karman-Tsien**PA

Join Date: Dec 2006

Location: The No Transgression Zone

Posts: 2,470

**Cesco**, in a not-so-elegant manner

... B

**oth**Ps,..and LSS,...these quantities are both dependent on temperature as a result it cancels,... pressure is a function of temperature, as well as lss,...so in measurement of mach no. it is disregarded,...now we all await a much more elegant expansion

PA

Moderator

Join Date: Apr 2001

Location: various places .....

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*Karman-Tsien*

OS does like to play with mathematics .. me, I prefer a well aged Port of noble colour and bouquet.

*isn't temperature a factor in Mach Number?*

Confuses a lot of folk. Temperature is tied up with speed of sound. Mach, however, can be expressed as an equation involving pressures only. The equation comes out something along the lines of

M = (5((qc/ps+1)^0.286-1))^0.5

which I've lifted from an old thread on machmeters .. and ... if I have counted brackets etc., correctly.