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?

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

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! :ok:) from a book.

Greetings,
with the appropriate grid, with a TAT you can have the corresponding Mach :}

Hi
We use Mach because flying high and fast it is mach number that determines our limits and our performance, rather than IAS.

Thanks microburst..;this was already said in post # 2..:E

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.

Keith.Williams, well said, Sir.
A concise explanation.
ADC's started a loooong time ago...with the 707 fitted with KIFIS.
Considered rather crude now...but it worked.
Rather well, actually.

It is indeed an excellent example of an informative and to the point post. As the sage said: 'If I had had a little longer I would have sent you a shorter letter.'

Greetings,
Originally Designed by the Germans during WWII :eek: ans subsequently discovered by the British in a Messerschmidt :} (not sure of the spelling)

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).

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.

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!

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

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!

Aircraft separation by ATC is easier when planes fly a fixed mach. No complications as the temperature at same levels are equal.

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.

It's time for OS to reintroduce the Karman-Tsien 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;)

PA

Cesco, in a not-so-elegant manner

... Both 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

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.

Greetings
TAT(k)=SAT(k) (0.2(Mach^2)) normally there is a Coefficient representing sensor "precision" but for practicality we put it equal 1
so if you have grid then...:ok:

kijangnim .. you might need to revisit your temperature rise equation ? I suspect you've omitted a one and added a zero along the way.

Because of compressibility the measured IAT (Indicated Air Temp) is higher than the actual true OAT. Approximately

IAT=OAT+K*TAS^2/7592

The recovery factor K depends on installation and is usually in the range 0.95 to 1.0 but can be as low as 0.7

OAT =(IAT+273.15)/(1+0.2*K*M^2)-273.15

is usually in the range 0.95 to 1.0 but can be as low as 0.7

A long time ago, now .. but I recall that lumbering Queen of the Skies, the AW650, had a recovery factor about 0.55. Good, solid, British stuff, you know..... ah, the sound of four dogwhistles overhead in close formation at 0-dark-thirty in the morning when one had just nodded off to sleep ...

Excellent replies guys thank you. I don't wish to labour this too much but as a final point is Mach Number measured using the same instrumentation as IAS i.e. is it a direct measurment of dynamic pressure / static pressure converted to Mach number through calibration or is it "calculated" and displayed as Mach number.

Ta very much.

papa600,

Does this help?

The Machmeter is merely an ASI, the output of which is modified by an altimeter capsule.

http://i636.photobucket.com/albums/u.../Machmeter.jpg

Hi

Mach number and TAS relationship is dependent on temperature.
MN and EAS relationship depends solely on pressure altitude.
Therefore for a given MN and EAS, there is only one possible FL.
However we don't have any EAS indication available, just IAS, so I guess that the exact FL at which a given IAS reaches a given MN (or vice versa) can vary somewhat depending on the ISA deviation.

I have clearly been a little bit lazy in dealing with temperature in my second post.

Changes in temperature at a constant pressure level will not change the relationship between CAS and Mach Number.

But changes in altitude with change the realtionship between CAS and TAS (caused by changes in air density due mainly to changes in static pressure). So if we climb or descend at a constant CAS, the Mach Number will change.

The effects are illustrated in the attached diagrams.

As the bottom diagram shows, VMO is the most limiting speed at low altitude and MMO is the most limiting speed at high altitude.

As stated by JT, at high altitude it is far easier to monitor Mach number than it is to continue to monitor CAS and need to apply a constantly changing value for the speed limit.


http://i983.photobucket.com/albums/a...ASMachanda.jpg

does this help ?
 

The speed of sound and the TAS factors [in the mach equation are both dependent on temperature AND since they are both composite functions of temperature the changes that occur in temperature are only required for determine local 'FREE -STREAM conditions'


meaning,...with out any influnce of an aerodyamnic body impinging on the local freesteam,...i.e nothing possesing a TAS [dependent on temperature],...so instrument for calibration i.e the machmeter there's no T

Further, ram rise could be thought of as equally affected both terms of the mach number realation,....therefore there's no temperature differential,...


However, when dealing with supersonic flows the ram rise contributes to a temperature differential and dyanmic heating has to be taken into account in both terms ....

the Karman-Tsien relationship derived about 1926 by Von Karman and Hsue-Tsien just happens to be the most comonly used [at least in the US;)] for the subsonic regimes for correcting the q term in H,...H being Ps+q, for compressibility,... the relation fails miserably at supersonic speeds:8

PA:)

Thank you for your replies guys esecially the pictures / diagrams which make more sense to me than the equations. :ok:

Excellent responses from Keith Williams well supported by wise comment from John_T with respect to why Mach Number becomes the limiting speed of the aircraft at higher altitudes. Also wise comment from other posters with respect to EAS/CAS/DAS/TAS/Mach relationships.:ok:

The original poster asked why we use Mach Number in lieu of IAS at high altitudes, and the responses mentioned above correctly allude to ONE of the reasons, i.e. Aircraft Operating Limitations.

The other, and more common reason why we do so (because we rarely operate at the limiting speeds) is Aircraft Performance. After the aircraft speed has passed Mcrit, Wave Drag enters the picture, and severely modifies the Total Drag curve of the aircraft. Up until Mcrit, the conventional drag curves as we know them, are the sum total of Form Drag and Induced Drag. Thus, all performance is predicated upon EAS, which (unfortunately) is presented to the pilot as CAS.

Above Mcrit, Total Drag then becomes the sum total of Form Drag, Induced Drag, and Wave Drag. The "new" Drag Curve upon which we now predicate all aircraft performance is referenced to Mach Number. An Example - Maximum Range Cruise Speed is found by projecting a line from the 0/0 origin to a point tangential to the Drag Curve. For a given weight, this will always result in the same EAS for MRC UNTIL Mcrit is reached at that speed. After Mcrit the Drag curve then (after a small initial negligible effect) then curves up much more steeply than the original Drag Curve. The point of tangency then occurs on the Drag Curve at ...... a given Mach Number, EAS, CAS are irrelevant.

At increasing Altitudes, the EAS at which Mcrit occurs begins to 'slide' backwards down the curve, with typical operating speeds somewhat above Mcrit. (Except on low level short sectors, almost all jet aircraft Climb, Cruise, and Descend at a Mach Number except at lower altitudes, where Mcrit begins to 'slide' up the curve again).

Thus, at the normal operating levels for jet aircraft (High), almost all NORMAL performance is predicated upon Mach Number. For very high flying aircraft, Mcrit may descend to Vmd, and begin to creep upwards on the rear side of the conventional drag curve, and Vmd is no longer related to EAS, it too, is related to Mach Number (Mmd).

So, in short, there are 2 major reasons why jets operate at Mach Number at higher levels, namely -

.1. Mach Number defines the aerodynamic limiting speed of the aircraft, and

.2. Mach Number completely modifies the Total Drag Curve of the aircraft, thus all PERFORMANCE is predicated upon Mach. :ok:

In closing (because I felt like it), I reinforce earlier posters remarks that Temperature has NOTHING to do with the EAS/CAS to Mach Number relationship. PRESSURE HEIGHT is the determining factor for the EAS/CAS to Mach Number relationship.

As for DAS, throw it in the waste bin where it belongs!:ugh:

Regards,

Old Smokey

I seemed to have not stated in a clear manner and after careful reading of Old Smokey I'm led clarify what I meant,...I did not want to imply that temperature is used for mach measurement etc....so, in order to redeem myself I'm forced into a long post,..but first as a lamentation I'll briefly show mathematically why T will never appear then I must [unfortunately for me expound on some high speed aerodyanamics,...

1.proof of independence of Mach on T
since Mn = TAS/c [c = lss]

and TAS = eas *[d2/d1] [density ratio]--- no rho to keep down visual clutter
and lss =c0[T2/T1]

I can say thatM = Eas* [d2/d1] /c0*[t2/t1],...expressing TAS in terms of EAS and T ,..one obtains EAS *[p2*d1*T1/p1d2*T2]^.5/c0 [T2/T1],...it is thereby shown that T WILL cancel

ok...what about if I write c in terms of density, since density is a function T you end up as M= EAS[d2/d1]^.5/c0[p2*d1/p1*d2]^.5 again all like terms dependent on T disappear d1 an d2 cancel here...So wrt to this I've said my lamentations,...In the next post I will clarify what I meant to emphasize but apparently expressed badly,...in my defense I was thinking about work on supersonic flows,...but the actual text [engineering supersonic aerodynamics] is packed away like most of my books,...so I I tried with other physics and aerodyanic proofs to remember the basic jist of the arguments concerning supersonic flows and as a result of over simplication I wrongly and accidentally implied that M is a function of T

I'll try to get the next post right; this subject for me is a very tough topic... :uhoh:

Subsonic flow:

as stated above The karman-Tsien relation is the most common [perhaps only??] relation used for calibrating the mach meter camwork in order to correct for compressibilty that the basic transport propertiesthat the root means square velocity of molecules in a gas c =3RT/M for a perfect gas from this on can show [eventually--from Newtonian flows] that the speed of sound can be written thermodynamically as cs =gamma*[RT/M{molar mass}]^.5 further expansion shows that [gamma*pressure/d =cs]

*gamma is the ratio of heat capacity of a gas at constant p/heat capacity at constant v [1.4] 'air'

for an ideal gas for a body traveling at low to high subsonic speeds where the shape of the waveform travels like the speed of sound the airflow--traveling down a pipe placed in such a flow is compressed; this compression is then followed by rarefaction but the mass flow at a particular velocity remain the same from the fluid dynamic principle of continuity,... this is the compressibilty error,...when there are no molecular interactions ...the perfect gas equation is valid and those conditions were assumed by those two mentioned guys and the relation obviously worked,...


now supersonic flows:\ [I'll try to be 100% correct here]:bored:

when a body is traveling through a gas faster then the free airsteam several complications occur 1. ideal gas law do not apply, 2. the realtion of the free stream flows not continous 3. gamma is no longer a constant 4. the primary cause of all of these complication are intermolecular forces to further complicate matters air ahead of the pipe is at a different temperature than the air at the pipe,..the waves no longer move in an ordered manner they look like this <<...<<<,<<........>>>>,...etc.

there is a discontinuity of form,...
however the funny wave form impinging on a body as well as those traveling throgh the pipe have an 'unpredictable' complex form....that concept was what I meant to convey [not DAS:ouch:],...but the mass flow through the pipe is constant [again from continuity] so in order to describe both the affects of compressibilty and molecular forces the state variable defining them have to be corrected,...I'll try to keep this simple,...in general these intermolecular interactions are highly dependent on T,...the corrections for gamma and the coorection for the defining state variables [rather than attempting to define the wave in the tube] it is better to redifine the state variables [and gamma] in termes of the molecular interactions,...generally the best correction involve writing the ideal equation and the gamma value in terms of a Taylor expansion,...from that expansion the effects of the waveform ican then be corrected for at sonic and supersonic flows,..lastly I'm not going to try and derive the final form from my head:eek:,...but using 'Poiseulle's formula' for a fluid moving throgh a tube of radius 'r' that dV/dt =[p1^2-P2^2]*pi^4/16l(nu)p0 where p1 and p2 are the pressures at the ends of the tube.....

by combining...that with corrected state variables as appropriate a similar but much more complex formula than the K_Ts is obtained for mach meter calibarion also completly independent of T as shown in the prior post and beacuse of the same reasoning it will cancel

OS---it IS true you don't flame:O

PA---I need to lie down:uhoh:

Amen, Old Smokey

I said the same in my post (not so brilliantly, however) and was accused of repeating rolljoe's post, though I cant' see why.

To the original post:

I prefer to consider the airspeed indicator as a dynamic pressure indicator.
EAS is not an airspeed. As a matter of fact is not a speed at all. TAS is the speed of the airplane relative to the air mass. Ground speed is the speed of the airplane relative to the ground. And EAS is the speed relative to... nothing. It is the speed that an airplane would have in the ISA at sea level if it had the same dynamic pressure that the airplane has.
All aerodynamic forces depend on dynamic pressure. That's why we don't refer to TAS when flying, except for navigation purposes. We use IAS, which is the closest to EAS that we have available.
When compressibility effects become noticeable and affect limitations and performance, dynamic pressure alone will not determine the aerodynamic behaviour of the airplane. Since Mach number is an indicator of compressibility, we will have to refer to it when it becomes high enough.

In civil airplanes this occurs at high levels. In military jets it can occur at sea level, where they have to be careful with both dynamic pressure and compressibility effects.

Hope this way of looking at this speeds thing helps.

Microburst2002
'q' dynamic pressure is dependent on TAS in rho*V^2Scl/2; 'V' is in terms of TAS

PA

Hi PA

Actually, q as such is dependent on TAS squared and density, only. It has units of pressure and could be considered as kinetic energy per volume unit of air. The more, the greater the aerodynamic forces.
TAS alone won't tell me how the aerodynamic behaviour of my airplane will be if I pull the controlwheel during the take off roll, if it will become airborne or it will strike the runway with the tail, and so many other aspects of airplane handling and performance. It is q which determines those, so I need a measure of q when flying.
The ASI measures q by sensing total pressure and static pressure, as you know. Instead of expressing q in psi or Hpa, the concept of EAS allows us to express q in knots, but these knots are not "real" knots. For each value of q there is only one value of EAS. The same is not true for TAS.
EAS is a convention. It is, by definition, TAS times the square root of relative density. Someone "invented" it (I wonder who) for convenience.
TAS has an influence in manoeuvring stability and other aspects. It is also useful for checking airframe/engine performance in cruise. It is required for navigation, either to calculate GS or wind component. It is a real speed. EAS is not, it's "better" that TAS.

Why use Mach number at high altitude and not IAS
 

May I suggest your friend could be satisfied by you saying that for aircraft types not specifically designed to fly at supersonic speeds:

There is a Mach number above which you may loose control (very often in pitch but can include roll).

There is a Mach number above which your range performance drops dramatically.

Further more:

At low levels you always reach IAS limits before Mach ones

At high levels you always reach Mach limits before IAS ones.

PS

An explanation of these simple facts is another matter entirely.

forgive me if I have missed it
 

Back to the original post, do the instruments which indicate mach number do so by direct or indirect reference to the standard atmosphere (ie is it calibrated in from a model of the world as opposed to being directly measured?). Didn't quite get an understanding of this before the discussion zoomed off in search of the missing 'T'.

In terms of 'why mach number', isn't it just that at low alt the margin between TAS and LSS is large enough you can ignore compressibility but as altitude increases and TAS converges on the decreasing LSS you have to do things more rigourously (ie take into account local variation in flow speeds, transient shock formation etc ) ?

Eas* [d2/d1] /c0*[t2/t1],...


TAS =Eas* [d2/d1]

q=1/2 rho *[Eas* [d2/d1]^2 [scl] = d2 Eas^2 * (d2/d1)= (EAS^2 d2^2 /d1 *scl) /2 ...so,