Mach Number

[kijangnim]

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...

[john_tullamarine]

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

[Brian Abraham]

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

[john_tullamarine]

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 ...

[papa600]

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.

[Lightning Mate]

papa600,

Does this help?

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

[Microburst2002]

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.

[Keith.Williams.]

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.

[Mr Optimistic]

does this help ?

http://www.tscm.com/mach-as.pdf

[Pugilistic Animus]

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

PA

[papa600]

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

[Old Smokey]

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.

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.

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!

Regards,

Old Smokey

[Pugilistic Animus]

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...

[Pugilistic Animus]

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]

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],...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,...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

PA---I need to lie down

[Microburst2002]

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.

[Pugilistic Animus]

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

PA

[Microburst2002]

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.

[John Farley]

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.

[Mr Optimistic]

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 ) ?

[Pugilistic Animus]

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,

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

PA