Mach Crit for transport aircraft [Archive]

Crossunder

6th Mar 2003, 09:02

I've also tried posting this question a couple of times to no avail. No-one seems to know. I think Mcrit is somewhat lower than the normal cruising speed for most modern airliners. The Mach trim compensators on a B737 classic kicks in at about M .615 I think.

greengage22: does it really matter why people want to learn something?

Flamgat

6th Mar 2003, 13:58

Thanks for the comments

I believe Mach Crit must be at least equal to, or greater than MMO, otherwise the increase in drag from the shockwave formation, would make operation close to MMO un-economical.

The Mach trimmer is in effect only needed quite a bit after Mach Crit, but since some aircraft have a very slight pitch up just before Mach Crit, and the tuck under, and the fact that the system is available, most aircraft start to use it at a lower speed.

If I remember correctly, the 737 classic is limited to M0.74 if the Mach trimmer fails, so that must still be below Mach Crit.

I would guess Mach Crit to be at about M0.9 on most of the modern airliners.

Just for interest sake, the Spitfire had a Mach Crit of nearly M0.91. It was only because of the extremely effecient elliptical planform. It was not a specific design feature.

If you ask why a person wants to know a bit more about what keeps your aircraft flying, I guess you have not been flying for very long.

The first time you get an emergency that is not covered in any of the books, you will wish you knew a little more. And when you get back on the deck you will start to read up a bit more than the bare minimum required by law.

lucille

6th Mar 2003, 15:13

Next question (s)....

How is Mach Crit. defined?.....and do the different manufaturers define it differently? And while youre there, whats the Mach Crit of the Concorde?

BOAC

6th Mar 2003, 17:15

I'm sure one of the experts will be along shortly, but here is my understanding:

MCrit is the Mach number at which a shockwave first forms on a machine. It is largely of theoretical interest only. Small shocks form on the upper wing surface and leading faces first. The 'biggie' is the full bow wave shock which breaks greenhouses and frightens horses. Don't I know it! :( The BAC Lightning MCrit was around 0.95M (?canopy shock?) in S&L flight but a healthy boom could be dropped at 0.95M by pulling lots of 'g'. I seem to remember the bow shock passed the tip of the pitot probe at around 0.98M. Shockwave effects were virtually undetectable due to its EXCELLENT British design!:p A 'flicker' of the Mach indicator and reduced roll rate - that's all! (Oh, and not much endurance.....:eek: )

Hence 'Fat Albert' (737OG), being, well... fat.... has a low MCrit. I suspect 'Crossunder's' 0.615M is not far off the mark? Mmo is well above this, as this is the limit placed by the manufacturers at which shockwaves become a 'nuisance'. Mmo is a maximum of 0.82M on the 737OG, but adverse Mach effects will be felt well below that, down at 0.78 on a heavy aircraft if significant manoeuvre is made.

I supect MCrit for Concorde would be, at a guess, around 0.9M probably from the engine nacelles, but again I'm sure someone who knows will be along to correct me.

Crossunder

6th Mar 2003, 18:16

According to THIS (http://www.b737.org.uk/flightcontrols.htm) site I wasn't far off at all ;-)

Thunderball

6th Mar 2003, 19:14

Critical Mach Number
________________

At the risk of duplicating what has already been said;

As subsonic air flows over an airfoil (or wing), it accelerates, reaches a maximum speed and then decelerates toward the trailing edge. Thus, the Mach number of the flow increases and then decreases. The magnitude of this change depends on the airfoil shape and the angle of attack. Therefore as you increase the freestream Mach number, the highest local M on the wing surface may exceed 1 long before the freestream Mach number reaches 1. The value of M at which the highest M on the airfoil first reaches 1 is called the critical Mach number, or Mcr. Obviously Mcr is less than 1 for anything with any thickness at all.

Twenty years ago all transport aircraft in production were often defined by whether they had "supercritical wings" or not. The term had common currency in magazines like "Flight". The A300 did not, the A310 did (or was it only a semi-supercritical wing on the 310- anyone?). The Boeings from 75/767 onwards had supercit wings, characterised by having a "roof section" - an airfoil profile with a broad, flat upper surface without a clearly defined point of maximum camber, so no dramatic rise in local Mach number and no dramatic B47-style shock stall.

As to what the numbers are for different aircraft, I don't know. But logically there should be a small but significant jump in Mcr between the old generation and the new, by virtue of the supercritical sections now used.

lucille

7th Mar 2003, 12:46

Ah Ha.

Is Mach Crit best defined when local flow first becomes sonic anywhere on the wing or over the fuselage?...remembering that camber is not constant, this may well first occur over a very small region and at a surprisingly low free stream Mach.

Or is it better defined as when the pilot is first aware of it's effects?...which of course opens up a whole new can of worms.

Perhaps, with modern aerofoil design resulting in innocuous behaviour at the classic definition of MachCrit, these numbers are no longer quoted in their sales brochures and Mmo is the primary number of interest.

BOAC

7th Mar 2003, 16:46

Well, 'lucille', all getting a bit esoteric now for a simple question!:eek:

99.99% of the time that 'M'crit' is 'used' it refers to a wing, as that is where the shock induced drag-rise is most significant (just above Mcrit) and the largest trim changes will occur.

I believe, however, that in purist terms it refers to ANY part of a moving body (including that well-known Aerodynamics student's nightmare, a 'right cylinder in supersonic flow'), and in my defence, your honour, submit

<10. The critical Mach number is precisely defined as that freestream Mach number at which sonic flow is first encountered on the surface of a body. The large drag rise due to compressibility effects normally occurs at a freestream Mach number slightly above the critical Mach number; this is called the drag-divergence Mach number. In reality, Caldwell and Fales had reached and exceeded the drag-divergence Mach number in their experiments. But their introduction of the word "critical" in conjunction with this speed was eventually the inspiration for its rise in later coining the term "critical Mach number." >

from the comprehensive NASA background document to supersonic flight by
John D. Anderson (http://history.nasa.gov/SP-4219/Chapter3.html).

However, all of very little interest/relevance to the initial questioner!

<Or is it better defined as when the pilot is first aware of it's effects?> Certainly if the canopy reaches Mcrit first on a swept thin wing aircraft, the pilot may indeed notice 'buzz' on the rudder.

In pure transport operating terms, as you say, MMO is relevant, and the extra power needed to cruise above Mcrit shows on your fuel flow gauges!

Reckon 'Flamgat' will have passed out by now?:D

flyer4life

8th Mar 2003, 14:01

I'm not flying jets yet but here's what I remember of my ATPL course...

MCRIT is where the local flow reaches M1.0 over some part of the aircraft. Drag due to shockwaves starts to increase but only becomes significant at MCDR (critical drag rise).

The Operating Manual should give a figure of MRANGE which is the high altitude speed for best range determined by test flights: this MRANGE speed is usually slightly higher than MCRIT.

Going above MCRIT allows you to fly higher for better engine efficiency without the EAS falling below VMD. The increase of engine efficiency and reduction of profile drag at VMD outweighs the slight increase of shockwave drag above MCRIT.

Modern transports operating in the "transonic" regime are by definition in the speed range between MCRIT and MDET.

So I would say cruise speeds are between MCRIT and MMO, although of course some types may vary.

timzsta

9th Mar 2003, 00:32

I recently sat ATPL PoF exam. Mcrit is the point at which airflow over the aircraft at some point reaches speed of sound. Operationally its on a day to day basis of not much significance. The important limits are Vmo and Mmo. Hence the change from constant IAS to constant Mach in the climb around FL260 and vice versa on a descent.
737 max cruise is about 0.74 as above this you get problems if the mach trimmer fails (got this from the IAS/TAS discussion (see my excellent post!)) earlier on the Tech log section.

NW1

9th Mar 2003, 12:57

The only help I could offer about the Concorde is that Mach crit is not a published number in the manuals (well not that I've noticed!!). If we have to cruise subsonically we do it at M0.93 (M0.95 if the autopilot is engaged in alt. hold). The latter is interesting because approaching M1.0 and over the transonic speed ranges the elevons are kept very busy by the active fly-by-wire system due to the shockwaves "dancing" around, often assymetrically (sp?) across the ship. The autopilot in alt. hold is considered smoother and therefore the increase to 0.95. Hand flying through the accel. highlights the constant changes in pitch and roll trim for this reason until about M1.4ish (although the handling is always precise and accurate at any speed - a joy, in fact). Once above M1.7, reheats turned off, it is like a train on a track. As to mach crit by the above definitions - I would guess something above M0.9 but I don't know.....

lucille

9th Mar 2003, 20:32

NW1...thanks for the Concorde insight - most interesting...it serves to highlight the irrelevance of the Mach Crit value for simple drivers such as us.
BOAC...thanks for the esoterica, this is, after all the reason why we visit this forum.
My observation of most ATPL level aerodynamic models is that they are, in the main, 2 dimensional - and thank god for that!. Great for teaching but risky business to extrapolate to real world cases.

Personally, I prefer the definition of Mach Crit to be when the pilot first becomes aware of its effects thus placing its value above Mmo in most (1G) cases - which may be why poor old flamgat will probably never learn the answer to his question.

Thunderball

10th Mar 2003, 15:23

NW1's post is fascinating, esp "dancing shockwaves" (and asymmetrical too)..

I once sat over the wing in a window seat on a KT (Caledonian) B757-200 en route back from Eilat to Gatwick. From memory we were at either FL380 or 390. The only thing that kept my mind off the horrendous 28/29" pitch and the steamed rodent main course was the mesmerizing sight of an incipient shockwave hovering around the area of maximum camber from root to tip, looking like a sharply-defined transparent tube. I was very tempted to wander up to the flight deck, but fearing being made to look a complete plonker I convinced myself that we were way below a shock stall, and that even if it happened I was well insured.

I must have sat by a window with a reasonable view of the wing a thousand times, but that's my only sighting. No better place than the anonymity of a pprune forum to be rumbled as a plonker, so is this in fact rare/unusual/commonplace, or should I being seeking professional help?

:confused: :confused:

BOAC

10th Mar 2003, 18:58

TB - perhaps 'unusual' would be a better description of what you saw? In certain atmospheric conditions shock waves ARE visible to the naked eye - normally 'Schlieren' photography is required in a wind tunnel to visualise them. I'm not sure whether it is humidity or what that determines their appearance, but I have seen probably 5 occasions in my 'passengering' times, the MOST remarkable being a real 'lambda foot' (http://www.imp.gda.pl/struktura/o2/z2/fig.gif)shock on a wing. (Left-hand pic shows it best). That I think is a rare thing to see. There is that famous picture (on Pprune somewhere, no doubt!) of a just subsonic fly-by by an ?F-14? of a US carrier, where the shock forming on the canopy can clearly be seen.

" They're coming to take me away, ha-ha!"

Crossunder

11th Mar 2003, 11:15

The SWs are visible because as the density across the SW changes, so does the refractive index. Light is then spread (refracted) in an "uneven" manner, thus making it visible to the naked eye!

Thunderball

11th Mar 2003, 16:29

Tks BOAC, I believe the picture you mentioned was an F18, looked for it but without success. A stunning picture.

As you say, Crossunder, it's a question of refraction. But what was so fascinating was the extraordinarily fine definition of the shock front, and the compactness of it. Almost looked like a large diameter transparent washing line laid out along the wing. Was KT experimenting with a stealth HF aerial?.....

Thunderball

16th Mar 2003, 18:26

Mcr

If you go to;

http://www.airliners.net/open.file/252881/M/

you'll get a superb picture of a B1-B airframe enrobed in a just a tad of supersonic airflow here and there....

Apologies to Airliners.net. I read your section on copyright, but I didn't expect this cut-and-paste to work as a hyperlink. I'm out-of-my depth with all this stuff. Bring back the Amstrad 8256.

DrSyn

18th Mar 2003, 03:24

BOAC, whilst I am familiar with the lambda foot, I only seem to see the rear end of one who is very dear to me in the picture you have linked. Could you, perhaps, explain further for the benefit of those less acquainted with the subject?

BOAC

19th Mar 2003, 17:51

Hmm! I'm glad I don't have a twisted mind like you, good Dr!:eek:

Thing us a thong:D

Does your friend have any similar friends..........?

..........and just to clarify - are we to be less acquainted with lamda feet or your friend's.................?

D120A

19th Mar 2003, 19:42

I can echo Thunderball's experience of having seen a shockwave dancing on a 737 wing en-route from LAX to Las Vegas many years ago.

The wing was up-sun, and I was perched (as usual) right over the point of maximum camber with little to look at but metal. The key seemed to be the polaroid sunglasses I was wearing, because these produced the image of a shock wave about 3 feet away, as clear as any Schlieren picture that I ever produced in a lab (BOAC will vouch for that). Took off the glasses - gone - put them back on again for the show of a lifetime.

My old papers (!) reveal that I subsequently asked the crew the cruise Mach No. - it was 0.76. When a light chop was encountered, the shock wave moved fore and aft by an inch or so, co-ordinated exactly with the "g" of the chop. When the chop turned more severe the aircraft decelerated (Rough Air Speed on a 737-200?) and the shock simultaneously reduced in intensity, slid forward towards the leading edge and disappeared.

I hope I successfully hid my excitement but, belatedly, thank you Western Airlines.

BOAC

19th Mar 2003, 19:48

"BOAC will vouch for that" - nay, some of the finest!
I thought that was one of yours I had linked to (erhmm - shockwave, old chap, of course):D

OneDotLow

21st Mar 2003, 09:03

Thunderball!!
I, too have seen what you have seen. I was sitting in window seat right neat the no.1 eng of a UAL DC10. It appeared over the engine, and I would best describe it as having the appearance of a very hot jet of air blowing in a straight line (as we were moving about M0.8x, obvioulsy any air escaping would've had a curved appearance). The "jet" would have only been around 5 mm in diameter. Truly amazing stuff to see! I have not seen it since.
ODL
P.S. Very different to the enveloping cloud of mist seen in many photos, as it was the very first are of supersonic flow {Mcrit}. Therefore I can only assume that Mcrit on a DC10 is below crusiing speed.

Basil

23rd Mar 2003, 16:48

Thunderball,
In conditions of high humidity but where condensation into water droplets has not taken place in free air, any small drop in pressure will cause local cooling below dewpoint and visible condensation will take place.
You can see the resulting water droplets in the wingtip vortices, flap edge vortices, and spanwise in the area of reduced pressure above the wings.
I wonder if this is what you saw?

ps: what was the date of your flight Ovda - Gatwick?

pps: Inadvertently replied before readind p2 of postings. All v interesting esp observation by D120A.

Flamgat

24th Mar 2003, 12:42

Basil. I agree with you! I have seen the same halo of condensation around a Buccaneer in flight and that was definately not at Mcrit.

Remember that the point of minimum pressure will also condense the water vapour under the crrrect conditions, and although that is where the shock waves will eventually form, they have not necessarily formed just because there is condensation.

Thunderball

29th Mar 2003, 03:08

Basil, OneDotLow,

Thanks. The date of the KT B757 flight from Ovda to LGW, by the way, was Monday 22nd March, 1993. How do I remember that? Don't ask.

But I must emphasize that what I saw on that B757 was very clearly a refraction phenomenon, related to a dramatic and highly-localised change of air density (presumably), rather than any hint of condensation. As I mentioned before, it looked almost like a transparent plastic washing line stretched between the tip the root of the wing which constantly moved chord-wise, forward and aft, but only a few inches.

I'd had one small bottle of red wine, maybe two at the most.

OneDotLow

1st Apr 2003, 15:47

Ok guys! The crew rest was U/S the other day so i went to sit down in C Zone (B744). I was sitting on the right hand side watching a movie ("The Hot Chick"....dont bother!), when i decided to open the shade and take a look outside. As we were in light chop, the wing was bending and I could see the refraction (appearance as i described in my post above as "hot jet of air" like apperance) moving inboard then outboard with the bending of the wing.
I had not had any bottles of wine...:D

Hope you all get to see it... truly amazing.

ODL

Flamgat

15th Apr 2003, 16:40

Just for interest. I eventually got an answer from Boeing.

Critical Mach number is a term aerodynamicists use to quickly compare the "drag rise" or "compressibility drag" of several wing design alternatives. At Boeing, we define critical Mach number as the Mach number, at a constant lift coefficient, where the drag coefficient is 20 counts greater than the drag coefficient at the incompressible Mach number.

Typically, a wing does not have a critical Mach number. Rather, critical Mach number of a wing varies with lift coefficient. Generally, as lift coefficient increases, critical mach number decreases.

Wing designers can change critical Mach number by changing wing sweep, airfoil thickness or airfoil technology.

There are two other speeds that characterize the integrated airplane (as opposed to just the wing). These speeds are "Max Range Cruise speed" and "Long Range Cruise speed".

They continue on about the calculations for Max range cruise speed and LRC speed. Basically they are more worried about MCDR as that affects their economy, and as you see they refer to that as “critical Mach number” As they allow a margin of safety when they calculate their Max range cruise speed, which is calculated at a given weight and therefore lift co-efficient, I would estimate the “aerodynamic” MCRIT to be in the vicinity of M 0.80 under the same conditions on a B737.

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