Constant Mach versus Constant IAS climb
 

To all those in the know...

My understanding (simple) is that if you climb at a constant IAS then the Mach No increases. Why? Because as you climb, the local speed of sound decreases (decreased temperature) and your TAS increases, therefore if Mach Number = TAS/Local Speed of sound then Mach Number increases.

The question is...what about your angle of attack? One might think that if you hold a constant IAS/CAS your angle of attack is constant (and Mach Number increases). Is this correct?

But what if you climb at a constant Mach Number. Would it be correct to say that:

To hold a constant Mach Number (considering that temperature is decreasing and TAS increasing thus MN increasing) you would have to raise the nose (reduce your IAS/CAS) and increase your angle of attack to climb at a constant Mach Number/hence IAS decreases?

Is this correct logic or am I off the planet.

Thanks Heaps

Essentially, all that you say is correct, but some qualification is required -

"My understanding (simple) is that if you climb at a constant IAS then the Mach No increases. Why? Because as you climb, the local speed of sound decreases (decreased temperature) and your TAS increases, therefore if Mach Number = TAS/Local Speed of sound then Mach Number increases."

Temperature has no effect upon CAS Vs Mach Number, only Pressure Height. Therefore the reducing speed of sound with climb at reducing temperature has no real effect. For Climb at constant IAS, compressibility increases due to decreasing Pressure (in isolation to temperature), and the degree of compressibility is directly related to Mach Number. Therefore, the Mach Number increases with increasing Pressure Height at the same CAS.

"The question is...what about your angle of attack? One might think that if you hold a constant IAS/CAS your angle of attack is constant (and Mach Number increases). Is this correct?"

With increasing Pressure Height, compressibility increases, thus the CAS over-reads, and EAS is constantly reducing. To fly at a reducing EAS (or CAS) requires an increasing Angle of Attack. Thus, AT A CONSTANT WEIGHT the angle of attack will slowly increase for a climb at constant CAS. To balance this, weight is not constant during climb, it is reducing because of Fuel Burn-Off, thus, if this is considered alone, AoA will be decreasing. At the end of the day, Angle of Attack change will depend upon your rate of climb (Fast climb = Low fuel use, and small rate of AoA decrease Vs AoA increase due to reducing EAS : Slow climb = High fuel use, and high rate of AoA decrease Vs AoA increase due to reducing EAS).

"To hold a constant Mach Number (considering that temperature is decreasing and TAS increasing thus MN increasing) you would have to raise the nose (reduce your IAS/CAS) and increase your angle of attack to climb at a constant Mach Number/hence IAS decreases?"

Again, temperature has no effect. At a constant Mach Number climb, both CAS and EAS are reducing, and increasing Angle of Attack is required. The logical extrapolation of this is that if you maintained a climb at constant Mach Number, assuming that you had a lot of excess thrust, you would climb all the way to where the AoA went all the way to the stall. (Airbus don't have this problem, they have barely enough excess thrust to taxy!).

Regards,

Old Smokey

Hey Old Smokey,
Thankyou so much for your reply!

Could you elaborate on what you were saying about:

"For Climb at constant IAS, compressibility increases due to decreasing Pressure (in isolation to temperature), and the degree of compressibility is directly related to Mach Number. Therefore, the Mach Number increases with increasing Pressure Height at the same CAS."

I have always thought of this relationship in relationship to temperature and TAS changes (from Mach No equation), not so much compressibility. How does this work? In simple terms how does compressibility increase due to decreasing pressure as we climb?

Regards
Katooie

katooie,

What you have to remember is that the Airspeed Indicator measures Impact Pressure, which is the total sum of Dynamic Pressure (related directly to EAS) and compressibility (related directly to Mach Number). It does not measure Density, which is related to Pressure and Temperature. In fact, all of the manometric instruments on your aircraft, the ASI, Mach-Meter, Altimeter, and VSI only sense Pressure. You, the pilot, have to apply Temperature to Pressure Height to find Density Height and True Altitude, and to CAS and/or Mach Number to find TAS.

During climb, with decreasing pressure, the aircraft must fly faster, i.e. a higher TAS, to achieve the same Impact Pressure, because you're at a constant CAS. This is so, even above the Tropopause where there is no change in temperature with change of Pressure Height. Because the aircraft is flying faster, compressibility increases, you are experiencing an increasing Mach Number. Note this - On a very hot day, your TAS will be higher due to the lower density AS WELL AS the lower Pressure, but this temperature factor puts you not one jot closer to the speed of sound, because at the higher temperature, the speed of sound (M1.0) is ALSO higher. Thus, the 'hot day effect' of a higher TAS than that due to pressure change alone, has no effect upon Mach Number whatsoever.

Consider the formula for CAS calibration -

Vc = SQR ((Y/(Y-1)) * Po/Qc * [(Qc/Po+1) ^ ((Y-1)/Y)-1]) * SQR (2 Qc / Rho0)

Where –
Vc = Calibrated Airspeed in ft/sec,
Qc = Impact Pressure in Lb/ft^2,
Rho0 = Sea Level Air Density = .0023769 slugs/ft^3,
Po = Sea Level Air Pressure = 2116.2 Lb/ft^2,
Y = A constant for air = 1.4, being the ratio of the Specific Heat of Air at constant pressure to that at constant volume (Y = Gamma, I don’t have a Greek key-board)

The Left-most portion of the equation is the ‘f’ factor, the compressibility effect –

F = SQR ((Y/(Y-1)) * Po/Qc * [(Qc/Po+1) ^ ((Y-1)/Y)-1])

At altitude, the Static Pressure, P, is substituted for Po in the left-most radical.

Temperature does not even get a mention (except in establishing standard Sea Level Density for calibration purposes, and then it's a constant)!!!!!

Regards,

Old Smokey

Whilst compressibility is a factor in the relation between CAS and Mach number, I think the main contributor to this is simply the static pressure.

If we consider EAS the relationship is simple: The ratio EAS / Mach number is directly proportional to the square root of the relative pressure.

I find the best way to get a handle on this is to put the equations relating Mach, CAS, EAS, TAS etc in a spreadsheet and play with some numbers. I posted some equations I have used in spreadsheets on a previous thread.

http://www.pprune.org/forums/showthread.php?t=204260

As for angle of attack the situation is quite complex. Even if we work from EAS (to avoid compressibility error) and ignore fuel burn, we still find that the coeficient of lift is a (inverse) function of Mach number as well as of angle of attack.

god,oldsmokey..have you missed your call to be an aerodynamicist instead? :D :ok: imo,it's rather uncommon to have a pilot possessing such intimate knowledge of flight..line pilots that i've known so far hardly know this in such detail..but sufficient for the safety of a flight nonetheless.;)

All these calculations put me off being an airline pilot- doesn't matter though as i want to be a flying instructor:)


Consider the formula for CAS calibration -

Vc = SQR ((Y/(Y-1)) * Po/Qc * [(Qc/Po+1) ^ ((Y-1)/Y)-1]) * SQR (2 Qc / Rho0)

Where –
Vc = Calibrated Airspeed in ft/sec,
Qc = Impact Pressure in Lb/ft^2,
Rho0 = Sea Level Air Density = .0023769 slugs/ft^3,
Po = Sea Level Air Pressure = 2116.2 Lb/ft^2,
Y = A constant for air = 1.4, being the ratio of the Specific Heat of Air at constant pressure to that at constant volume (Y = Gamma, I don’t have a Greek key-board)

The Left-most portion of the equation is the ‘f’ factor, the compressibility effect –

F = SQR ((Y/(Y-1)) * Po/Qc * [(Qc/Po+1) ^ ((Y-1)/Y)-1])

At altitude, the Static Pressure, P, is substituted for Po in the left-most radical.

Temperature does not even get a mention (except in establishing standard Sea Level Density for calibration purposes, and then it's a constant)!!!!!

Regards,

Old Smokey[/quote]

babyboeing400: I don't think Old Smokey missed his calling at all --- He's a Practicing - Polymath - Pilot :D

Hey Old Smokey,

Thanks so much for the detail. I will have to go and think about this further. Got asked this in an interview recently - gave the correct answer but with (I think) incorrect logic.

You are a legend.

Cheers
Katooie

Don't be too hard on yourself katooie, although Temperature and TAS don't figure in the discussion here, TAS is a convenient 'anchor' in CAS/EAS/Mach Number calculations and discussions. For a given EAS, CAS or Mach Number, you can use any 'phoney' temperature that you like (the correct temperature is best of course) to calculate an 'anchor' TAS, and work back to find the appropriate equivalents. The effects of the phoney (or real) temperature just cancel themselves out on the way!:ok:

Some lazy computer programmers (like yours truly) use just such a technique, saves working out a lot of new algorithms:E

Regards,

Old Smokey

Hey A330ismylittlebaby, I dont think you'll find the CAS calibration formula in any of the ATPL exams and I don't expect many airline pilots would know it.

Besides if you ever did want to calibrate an ASI, there are simpler versions of the CAS formula (see my post on the other thread) and a spreadsheet will make light work of the number crunching.

A330ismylittlebaby,

As the author of the post that sparked your concern, I feel an obligation to echo the wise words of Rivet gun in stating that an airline pilot need not be familiar with the fairly complex mathematics and physics of manometry.

What is necessary, is to possess a good understanding of the relationships between CAS / EAS / Mach Number / TAS / TAT etc., and to be able to make day to day conventional conversions between them using conventional means such as Pilot Computers and/or tables.

As an ATPL student, a practicing airline pilot, an ATPL instructor, and in preparing ATPL examination papers, not once did I ever see the need for discussion of or examination upon the 'deeper' mathematics and physics involved. In studying Aeronautical Engineering and in lecturing to University students on the subject, much emphasis was made upon these aspects.

It's only necessary to be practical, understand the relationships, and be proficient in the day to day conventional application of the conversions involved.:ok:

Some people understand the 'why' better if they understand the 'how', which is why I sometimes go a bit to excess with the physics and mathematics involved. I, for one, cannot accept anything unless I understand HOW, but that's only me.:}

Regards,

Old Smokey

Me too Old Smokey, I'm very hard to please in certain subjects :} :confused: :}

Old smokey. Amazing there are some clever people still in this game. If u are that is. 38.94*SQR( absolute temp) is the only thing you practically need to know to impress fellow aviators.
To quote detailed ias/eas/cas/mach is useless and just proves you are not a real pilot.
Great if you are an engineer.

All the best

.. you forget that some pilots are engineers .. or is it vice versa ? .. and, thus, have a constant personality conflict trying to speak engineer to pilots and pilot to engineers (unless they be TP/FTEs, in which case, usually, they are fluent in both dialects).

As my brother-in-law, a chemical engineer, used to put it .. other discipline engineers he could confuse with chemistry, chemists with engineering .. but amongst his own, they would generally discuss women ..

"Old smokey. Amazing there are some clever people still in this game. If u are that is. 38.94*SQR( absolute temp) is the only thing you practically need to know to impress fellow aviators.
To quote detailed ias/eas/cas/mach is useless and just proves you are not a real pilot.
Great if you are an engineer.

All the best"

Re-entry are you :mad:ing on crack!!! we all don't go to fancy flying schools for self-esteem class- some pilots are MDs, Ph.Ds Engineers read again John Tullamarines post above... it not good to be closed-minded as an aviator... y'could end up closed-COFFIN:= := :=

oh no rhov my a12 lead is disconnec\t with the athero 1/2/3 lodge embard within the RBB oblique. But basic bounce is within A2/A2 leads limits if you consider asymmetric (pelio) ventricular palp. As it were.

Ok. where did you go to fancy flight school?

I never as of yet required a class room just a CFI, we'd talk it out. for the other nonsense I spill out well it comes from Nassau Community College, AS biology then SUNY Purchase, BS biology- concentration biochemistry, BS chemistry-ACS certified curriculum:
N.B Ground school for my level [I don't think any level] isn't required under the FARs

now, really I have nothing against university based flight schools for an aeronautical degree My CFI was from one excellent and VERY KNOWLWEGDEABLE dood(Sorry, if i had inadvertantly offended some :oh: ).

be more open minded, admittedly my first post here to you was born out of sheer disbelief of the folly in your statements... HAVE YOU EVER READ ANY OF HIS PRIOR POSTS !!!...this is the TECH LOG :ugh:

TO ALL OF THE :8 :8 :8 ON TECH LOG WHO CONTRIBUTE SUCH ENLIGHTENED POST :ok: AND CLEAR UP MOST :confused: AND THOSE WHO ASK THE VERY INTELLEGENT QUESTIONS, THAT MAYBE WE ALL WERE THINKING ABOUT, BUT WERE AFRAID TO ASK :\ ...MY :D :D :D

OK RE-ENTRY want a REAL TOUNGUE TWISTER
Adult onset Non-familial hypophosphatemic vitamin D resistant osteomalacia.:} :} :}

but no more crazier to a non-pilot/lay preson considering aviation there are plenty of confusing terms doesn't mean they cant be explained but it WOULD TAKE A LONG TIME TO EXPLAIN, Very high frequency Omni-directional Range beacons or a Holding side and A Non-holding side, or a localizer type directional aid, or Procedure turns, WAT limits, Altimeter setting, AFD, BUT THESE TERMS ARE EASY for YOU, BECAUSE YOU'VE SOUGHT A DEEPER UNDERSTANDING i hope !!! AND...you get my point, I HOPE !!!