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flyingdream
24th Jan 2003, 19:09
Can someone or some of you "big guys" explain some Mach theory for a simple propdriver like me.

Why are you not using MACH at low altitude, I know why you do it at high altitude.

Please give my some facts to grab on and give me a hint of the reality.

thanks

FD

john_tullamarine
24th Jan 2003, 22:49
At lower levels, the limiting consideration is airloads on the aircraft ... EAS things, so the pilot has an IAS limit.

As the altitude increases, for a given climbing IAS, TAS increases, OAT and speed of sound decrease .. so the Mach Number increases. At some particular height/IAS combination the Mach Number is high enough so that, for the particular aircraft, compressibility considerations become more limiting than airloads.

Below this height, IAS reigns, above Mach Number.

Too Few Stripes
25th Jan 2003, 12:36
Vne is a structural limit, Mne is a limit to stop the airflow over the top surface of the wing becoming supersonic. As you climb the local speed of sound decreases (speed of sound in air being solely(well almost) dependant on temp) at some point the Mme limit will become more limiting than the Vne limit which remains the same throughout.

HTH,

TFS ;)

just re-read johns post, i think ive probably repeated exactly what he's said, oh well never mind................

atco-matic
25th Jan 2003, 20:48
I thought speed of sound was dependant on air pressure? Hence as you go upwards pressure decreases with altitude hence speed of sound decreases... or was I not listening properly in that lecture?? :D

flyingdream
25th Jan 2003, 21:10
Too Few
Even if you repeted JT:s post, I really appriciate that you took your time time to answer me.

Thanks

fd

Fat Dog
26th Jan 2003, 12:39
atco-matic

The speed of sound only changes with the temperature of the air in which it is travelling.

Cheers
Fat Dog

john_tullamarine
27th Jan 2003, 01:08
Normal consideration for sonic velocity

a/a0 = sqrt(T/T0)

for
temp in absolute (Kelvin or Rankin)
subscript 0 indicates standard SL values

timzsta
3rd Feb 2003, 21:09
Speed of sound is only dependant on temperature. The reason airliners fly at IAS up to about FL260 and mach numbers above is so as not to get supersonic flow of air over aircraft or the aerofoils which would cause loss of lift and buffet over the horizontal stabiliser, all of which is not good!

The change over from constant IAS to mach in the climb takes a little explaining, here goes.

First you must understand when we talk about flow velocities over the aircraft becoming supersonic we are expressing their speed in TAS not IAS. As we climb at constant IAS our TAS is increasing. Also as you climb because the temperature is decreasing the local speed of sound is decreasing (mach number = TAS/local speed of sound)

There are two speeds that we have to consider so as no to run into problems. Vmo and Mmo. As we climb at constant IAS (say about 300 kIAS for a 737-300) our TAS is building and so we are approaching the local speed of sound problems. Due to the fact that air accelerates as it passes over the wing it is possible to achieve supersonic local flow velocities at mach numbers of about M0.8 over a typical airliner wing.

So at some point in the climb the flow velocities over the wing are going to start getting to close to the speed of sound so we could exceed Mmo. Usually the changeover point for IAS to Mach is at FL260. At this point we climb at constant mach, usually the aircrafts cruising mach number, so about M0.74 for the 737.

The autopilot mode for the vertical path/speed control engaged at this point would be the VNAV mode. Here the FMC will command the auto-thrust to climb at contanst mach number at the climb power setting. The ROC will be dependant on the excess of thrust available over that required to climb at the commanded mach number. Hence we have no longer a worry about getting a supersonic airflow over the wing as cruise speed will be below the speed this can happen. When changing over from constant IAS to constant Mach the rate of climb will initially increase and then decrease as the excess thrust decreases because the air is getting less dense.

Conversly in the descent as we descend the local speed of sound is increasing and the danger is you could exceed Vmo in the descent. So a descent is at constant mach again until FL260 then at constant IAS. Typical descent profile for a 737 would be descend at M.074, then around 300 kIAS, then at about FL120 decel to 250 kIAS to meet the speed restriction. Downwind would be about 220 knots, 180 on base, then approach speed (Vref = and must not be less than 1.3 x Vs) would be around 130 knots.

I am only ATPL student who just did PoF exam. Big jet drivers please correct me if I am wrong!

Max Angle
4th Feb 2003, 10:59
I am only ATPL student who just did PoF exam. Big jet drivers please correct me if I am wrong! Which makes you far better placed to answer the question than most of us, nice reply and good luck with your career.

TOPBUG
4th Feb 2003, 13:40
Mach number is actually dependent on air density, which is generally a function of temperature.

Mach number can be worked out from the temperature this way:

38.94 times sqrt of the absolute temperature

Ie at sea level (15C) = 38.94 times 288
= 660 kts

FIRESYSOK
4th Feb 2003, 15:43
Did you mean the speed of sound is dependent on air density? From everything I have read, it is directly related to temperature. Which of course is related to air density. Nowhere though, does any text say it directly. Why?

Captain Stable
4th Feb 2003, 15:46
Sorry, Topbug, but incorrect.

Mach# is solely dependent upon absolute temperature, and is not related to density.

togabutton
4th Feb 2003, 16:10
Have to commend timzsta's reply. Your grasp of the theory is impressive for someone who has not flown airline jets.

I think your explaination provided the best answer to the question asked on this thread. I have flown B737-200s for a while and your numbers were spot on. Our company used 0.74M for our cruise (this is also the speed limit for a mach trimmer failure so a good choice). We climbed at 300 IAS till cross over and then 0.74M. Normal descent was at 0.74M then 280IAS. We would use 300IAS only if we needed to expidite the descent or were high. Of course as you stated, we would slow down to meet ATC speeds.

I enjoyed the question posed - nice example to illustrate the complexities of jet flight.

Max Angle
4th Feb 2003, 16:43
Looks like everyone is partly right, to quote from "Mechanics of Flight" by AC Kermode (a worthy tome but pretty hard going)


"People are often suprised that the speed of sound in the air depends on temperature alone. As a matter of fact it doesn't! But the other properties, such as air density, on which it also depends, are so related that temperature is the controlling factor"

timzsta
4th Feb 2003, 20:56
Max angle is correct. When we learn about speed of sound etc as pilots we are taught is is dependant on temperature alone, I believe, because this is the answer to the question in the CAA question bank!

Temperature/pressure/density are all related off course, but temperature has the greatest effect on the speed of sound for us as pilots, so for the purpose of simplification we say "speed of sound is dependant on temperature alone", when it actually isnt at simple as that.

Let us consider sonar (being ex Navy myself, but not aircrew). Now lets take a look at say a cold bit of north atlantic water at about 4 deg c. This equates to an altitude in ISA conditions of about 5000 feet. But the speed that our sonar "ping" is much faster than the speed of sound of in the air (seem to remember from my Oceanography course speed of sound in water is of the order of 790 metres per second). Why? Because the water is much more dense.

Whilst we are speed of sound etc here is an interesting thing about compressibility effect and mach cone angle. When you stand on the platform at an underground station and the train is approaching you know its coming because there is a rush of air. At the very low mach number of the train the cone angle is almost 90 degrees. Now lets suppose London Underground built a tube train that could go at mach one. Would you get an onrush of air ahead of it? You would not.

BEagle
5th Feb 2003, 05:14
I vaguely remember from my university days 30 years ago that the velocity of sound was equal to the square root of the product of gamma (the ratio of specific heats of gas at const. pressure and const. volume), Boltzmann's constant and the absolute air temperature?

Oktas8
5th Feb 2003, 06:27
Like BEagle said. Also, inversely proportional to the square root of the mass of the molecule of gas in question, since we are getting picky. :p

That must be the first time I've ever actually used that particular textbook... You're better than most of us if you can remember that stuff Beagle.

dexter256
27th Apr 2003, 01:47
That's right, the speed of sound is given by rt(gamma * R<a> * T)

Where gamma is the ratio of the specific heats, R<a> is the gas constant for air, and T is temperature absolute. Bear in mind that the unit for length here depends on that used in R.

Under SI:
Gamma for air is 1.4, R for air is 287.05 m^2/(s^2 K) and ISA T 288.15 Kelvin.

Under Imperial:
R for air would be 3,089.8136 ft^2/(second^2 K)

If you were to use a value of 1084.6391 for R<air> then the dimentions would be nm^2/(hour^2 K) and thus the above would yield a speed in knots.

All of this nicely assumes that we are dealing with an ideal gas, which for the normal pilot's application is fine. One last point while I'm beating the issue to death, the speed of sound at sea level under ISA is referred to by the Greek letter alpha with a subscript 0. a<0> * rt(theta) yields, as stated, a local speed of sound. theta being T/T<0>. Again, this subscript 0 indicates the ISA MSL value (288.15 Kelvin.)

A wonderful article may be found here, http://www.jeminas.com/aviation/pdf/Aircraft_Performance_Flight_Testing.pdf and section 4.3 would be relevant.

ft
28th Apr 2003, 19:08
...and gamma is what will vary a bit with air density and so on, making the "varies only with temperature" only almost spot on.

Cheers,
Fred

Notso Fantastic
28th Apr 2003, 20:58
The simple formula is Sp of Sound=(644 + 1.2T) knots where T= temp deg C. More rule of thumb, but shows temperature is main controlling factor.

Avi8tor
28th Apr 2003, 21:13
I would hate to challange the learned AC K, as his 'Mechanics of Flight' is the basic repository for most aviation knowledge. BUT...

As the density of air at FL390 at -56 is NOT the same as the density at FL450 at -56, I think that we all agree. However, we all agree that the LSS is equal at both atltitudes, by the formula.

Has the basic formula been simplified for the 'not so clever guys that drive the buses'?

HotBus
1st May 2003, 02:20
As I understand it, the local speed of sound is defind by:

a = sqrt(gRT/M)

Where:

g(Gamma on a UK keyboard!) = Ratio of specific heats, also known as the adiabatic constant
R = Universal Gas Constant
T = Absolute Temperature
M = Molecular mass of gas

Certainly R and M are independant of pressure. I thought g (Gamma) was as well. If that's the case, the the local speed of sound, and therefore Mach No, are only affected by temperature.
I guess that if pressure does have an effect, it must be that gamma varies with pressure...


Looks like I've just managed to repeat dexter:rolleyes: