View Full Version : Mach Crit, Mach Number Buffet, Mach Tuck, and Mach Trimmers

Panama Jack
22nd May 2004, 20:41
I think I understand the concepts individually.

However, I am having a bit of trouble trying to visualize them in interelationship to each other.

I understand that Mach Crit is where the relative flow initially reaches the speed of sound. However, if I understand it correctly, this does not necessarily result in a Mach Buffet (or does it). Instead, the aircraft becomes longitudinally unstable and tends to pitch nose down. For this we have Mach Trimmers, to allow for higher speed cruise by providing artificial inputs to compensate for the longitudinal instability. Am I right so far???

So then, where does Mach Buffet come into play?

Also, do modern jet transports regularly cruise at speeds above Mach Crit? Do all jet transports have Mach Trimmers or do some of them have good longitudinal stability above Mach Crit?

Thanks in advance for all helpful answers and discussion.

23rd May 2004, 05:10
If I've got it right, Mach crit is that mach number above which supersonic flow will appear over a part of the wing, where depends on the wing profile. When this happens, you will get Mach buffet caused by flow separation at that point.
One of the aerodynamic effects experienced at high Mach numbers is the aftwards movement of the Centre of Pressure, causing the nose to dip, Airspeed to increase and therefore, Mcrit to be exceeded leading to buffet, increased drag and, possibly, unusual control effects. The Mach trimmers counter this dip to avoid this exceedance.
Hope that explains the basics.

23rd May 2004, 05:21
Higher speeds do indeed result in poor aerodynamic effects resulting in undesirable mach tuck.
The B707, especially early models, were rather severe in this regard.
Oddly enough, the Lockheed TriStar had no descernable untoward effects, in this area.
Lockheed got it right.
Suspect later Boeing aircraft are likewise.

Panama Jack
23rd May 2004, 08:44
OK, so Mach Buffet is associated with Mach Crit?

If I had read it right, Mach Trimmers were explained to allow stable flight in this range (allowing higher cruising speeds). Perhaps this is what confuses me. Do jet transports cruise below their respective Mach Crit's (Vmo or Mmo is below Mach Crit)?

23rd May 2004, 14:03
Is this something I've just dream-ed of or is it real?

I understood that Mach Tuck was also, in part, caused when the lift over the wing started to fail but the lift in the tail plane continued thus causing the tail to lift and the nose to 'tuck'?

23rd May 2004, 19:01
I know it is rather tedious to read due to the old-fashioned language used, but "Handling the big jets" by DP Davies explains it all. ISBN 0 903083 01 9.

Captain Stable
23rd May 2004, 19:14
Critical mach is a aeronautics term that refers to the speed at which some of the airflow on a wing becomes supersonic. When this occurs the distribution of forces on the wing changes suddenly and dramatically, typically leading to a strong nose-down force on the aircraft. This effect led to a number of accidents in the 1930s and 1940s, when aircraft in a dive would hit critical mach and continue to push over into a steeper and steeper dive. This problem is often lumped in with the catch-all phrase compressibility.

Wings generate much of their lift due to the Bernoulli effect; by speeding up the airflow over the top of the wing, the air has less density on top than on the bottom, leading to a net upward force. The relative difference in speed is due largely to the wing's shape, so the difference in speed remains a fairly constant ratio over a wide range of speeds.

But if the air speed on the top of the wing is faster than on the bottom, there will be some speed where the air on top reaches the speed of sound. This is the critical mach. When this happens shock waves form on the upper wing at the point where the flow becomes supersonic, typically behind the midline of the chord. Shock waves generate lift of their own, so the lift of the wing suddenly moves rearward, twisting it down. This effect is known as mach tuck.

23rd May 2004, 19:29
You need to consider the complete airframe and not just the wing.

Mcrit is the lowest Mach number at which the local airflow somewhere over the airframe reaches 1.0M.

Mach buffet is caused by flow separation due to the compressible nature of the airflow and I believe could occur at less than Mcrit on straight wings with relatively high thickness:chord ratios. Remeber that compressibility has a major effect on the aerodynamics of a wing before a shockwave actually forms.

Mach tuck is due to the rearwards movement of the centre of pressure of an airframe (mainly the wing) at high transonic Mach numbers. The severity of this will be affected by the CP shift over the whole span, the wingsweep angle, and the change in downwash angle at the tailplane. It occurs over a speed range and is basically a region in which the aircraft exhibits apparent longitudinal static instability.

A Mach trimmer is a device which varies the pitch trim automatically as a function of Mach number to oppose Mach tuck and thus restore apparent longitudinal static stability.

Therefore, only Mach tuck and Mach trimmers are directly related. Mcrit and Mach buffet are both characteristics due to the compressible nature of the airflow, but the complex 3D nature of an airframe makes any direct relationship difficult to predict.

Panama Jack
23rd May 2004, 20:22
Great answer Lomcevok & Captain Stable. IRRenewal, yes, I've read the book. Now I am trying to take the learning process from rote memorization to correlation. ;)

Do modern transport jets normally cruise in the realm beyond mach crit where the mach trimmer is doing it's thing (yeah, I know what Davis' book talks about there too). Is mach crit a speed you know as a pilot of your type, and how far back is it from Mmo on any type of aircraft.

Thanks again to all for indulging me.

23rd May 2004, 20:38
PJ - since no-one appears to be answering your query, this is my go!

Mcrit is the point at which the drag of an airframe starts to rise significantly due to the formation of shock waves. My own view is that NORMALLY it is extremely inefficient to cruise above Mcrit and therefore not likely. Concorde excepted, of course.

square leg
23rd May 2004, 21:26
Here is another explanation:

There is an increase in the speed of airflow over certain parts of an A/C (i.e. over the top surface of an airfoil). However, the A/C may be travelling at a speed well below the speed of sound, but the airflow relative to certain parts of the A/C may exceed the speed of sound. Therefore, that Free Stream Mach Number at which any Local Mach Number reaches 1, is called the Critical Mach Number.

So, no, jets will be cruising well below Mcrit. But through design changes the Mcrit can be raised to delay shock-induced separation.

At a point about 5-10% beyond Mcrit, a sharp rise in drag is perceptible. You need powerful engines to go beyond Mcrit.

On pax jets TODAY, you will not experience Mcrit or higher under "normal" conditions. Maybe Dassault will build the next supersonic pax jet.

24th May 2004, 13:40
Airliners routinely cruise above M crit. The development of the supercritical wing allows this with little drag increase, initially. And they do not become longitudinally unstable, if flown below max permissible mach. Mach trim systems allow aircraft to meet stick gradient certification requirements when hand flown. Not required for autopilots, nor FBW aircraft, as far as I know. Pilots do not know when they are at M crit. It depends primarily on AOA, or weight when at 1 G flight if you prefer. Although there could be charts published by Boeing.
Mach buffet occurs above mach crit, say .1 above or so, when flow separation affects the wing enough to cause vibration, and adverse handling characteristics, again, will not happen if the aircraft is kept within altitude, mach, weight and G envelope.

At high enough machs, intial aft movement of C of P means stick gradient not per certification. Even higher, and I’d guess stick gradient could reverse, and contribute to mach tuck. The dangerous mach tuck was caused by downwash on the tail, no longer allowing the elevator to provide it’s downforce. Aircraft then pitches nose down.
The “all flying” horizontal tail may have helped prevent this.

414, did the 707 have a fixed horiz stab and elevator? The L1011 an all flying horiz tail?
If so, this may explain it. Also, the tri star had one of the first super critical wings, IIRC

Capt Stable,
Not sure what you mean by “shock wave generate lift of their own”, but indeed, hi subsonic flight does produce a rear ward shift in C of P

I don’t fly airliners, and of course I could be wrong.
I’ll leave it to Keith Williams or Bookworm to shoot me down.

24th May 2004, 15:49
Oddly enough, the Lockheed TriStar had no descernable untoward effects, in this area.

It did however suffer from fatigue (cracks) above the flightdeck due to local shockwave formation.


24th May 2004, 16:16

Yes, the 707 had a fixed (altho trimable) horizontal stab, with elevator.
The jackscrew that trimmed the stab had one rather undesirable problem...it was underdesigned, and could stall with heavy elevator inputs. This was not a problem in 'normal' flight, but was noticed when a few brave (foolish) crews climbed well above the optimum altitude (for the weight) and found themselves looking at a jet upset recovery.
One or two even chucked an engine off the pylon on the way down.

The L1011 does indeed have an all flying tail, but also has an elevator, that was linked to the stab for extra authority.
It was my normal practice to hand fly the aeroplane to altitude, as the control forces were delightful.
At M.865, no decernable mach trim inputs were noticed.
Having known quite a few of the Lockheed test flight guys later on, they mentioned that the mach trimmers fitted were really not necessary, but the FAA insisted, for certification.
Oddly enough, when the L1011 came onto the UK register, the Mmo was reduced to M.88 from the usual M.90.
Scarfed pitot at work perhaps...


Have flown some of the really older models, and don't remember any structural cracking in the area you mention.
Of course, I didn't look for any either, so you could indeed be correct.

25th May 2004, 02:02
Hey Hawk37

Best you edit your bit about movement of the C of G.

A Typo perhaps.

Sure you mean C of P

Herc Jerk
25th May 2004, 04:27
And another explanation...

My understanding of the original post is:

Mcrit is the %mach for a given wing (determined in 1g level flight, at a given weight) at which shock waves will begin to form on it's upper surface.

Mach Number Buffet is the result... and yes, you will feel it, but it could feel like a pre-stall buffet.

Mach Tuck is a negative stability inherant in the design of some acft that leads to a nose down pitching moment at high mach numbers during the approach to Mcrit (and certainly past it). The way i understand this is that the local flow is NOT yet sonic below Mcrit, but TRANSsonic, which does change the airflow and CofP caracteristics somewhat due to drag increases on the wing's upper surface, and therefore gives us the beginning of the nose down instability. This last bit is not in D.P Davies book but is only my understanding of it which may well be wrong. Pls comment...

Mach Trimmers are installed so that the acft can be certified stable in all flight regimes (and outside of them). This is not "true" stability, but an augmented stability which is why it may not be req on FBW acft (as someone said earlier).

For eg, the 737 mach trimmer is active above M.61. If it fails in the classic then there is a limit of M.74 but the NG is only limited to its Mmo of .82. So... the classic becomes negatively stable above M.74, but the NG (like some acft described earlier) remains stable up to its Mmo, but the mach trimmer is still required for certification (due to needing to be certified over and above normal flight parameters eg Mmo).

I can't imagine (assuming i'm right in the above) any std airliner cruising above Mcrit due to the high drag and loss of efficiency that would result, vis-a-vis the shelving of Boeing's sonic cruiser.


25th May 2004, 08:54
About M crit.

Early 'high speed' but subsonic jet aircraft such as the Meteor and Vampire had Mcrits of about 0.8 and 0.78. They tell me that the Spitfire and Mustang were in that range.

The enormous drag increase and the random movements of the shock waves as those mach numbers were reached created an almost impenetrable boundary principally as a result of the buffet and inadequate elevator power to overcome the resultant nose down pitch as the centre of pressure for the wings jumped around as it moved aft.

For the single seat Vampire Mcrit was reached as airflow over the fuselage reached mach 1.0. In a dive to reach Mcrit it felt as though the aircaft would break up at any moment with the stick kicking around randomly. Take it just a little faster and the nose would start to go down uncontrollably with buffet yet increasing. One rarely had a desire to do it twice.

Subsequent wing and tail designs resulted in lesser effects at M crit and caused the critical to become non critical.

The F86 Sabre and Hunter, much assisted by wing sweep, slipped through Mcrit fairly easily in a steep dive. Some noticeable buffet and unpredictable roll going through followed by smooth flight supersonic as the shock waves became established and consistent.. In some rare light conditions I have been able to see the shock waves dancing around on the wings as the light going through the shock waves became refracted through the changing air densities of the shock wave..

Meanwhile engine powers kept on increasing, substantially with afterburning/reheat together with ever improving wing /fuselage design to result in predictable and relatively smooth shock wave behaviour.

A sonic boom is one of those shock waves going past you at the speed of sound.

The Super Sabre, the F104 and the Lightning were then able to go supersonic almost without the pilot being aware. So over time M crit has become that Mach No at which there is a sharp increase in drag and a need to substantially increase thrust to go faster.

Most of today's aircraft have not been able to efficiently penetrate the drag rise so have to cruise at Mach Nos somewhere between 0.8 to 0.85. Try to go a tab faster and
and your fuel flow will be a big cause for concern.

The Vulcan delta had twinges of buffet as it went above 0.9 IMN and an automatic Mach trimmer in the elevator controls smoothly applied increasing up elevator from 0.86 through to 0.96 which became the limiting Mach No for aircraft operation as there was then not much elevator movement remaining. One got away from me once and it went to Mach 1.04 pitching nose down with the stick hard back. Seriously considered letting it go under inverted to roll out coming up the other side. However with power off the Mach No dropped off with rapidly decreasing altitude and increasing air density and the fully up elevators gradually took effect.

Now there are a few fighter designs that have enough engine power and low enough drag to be able to cruise supersonic without resorting to ineficient afterburning..They have a 'supercruise' capabiliy. The F22 can supercruise at about Mach 1.6 which will alow it to run rings around F15s and the like.

Others such as the Concord and Blackbird managed to have engines and engine intakes which gave increasing thrust as speed increased at about the same rate as the increasing drag. I guess that if a Concord becomes short on fuel the pilot will resort to subsonic flight at about Mach 0.9. Any ex Concord pilots out there?

What next with Scramjets? The Heat Barrier.

25th May 2004, 23:18

The subsonic cruise on Concorde was M0.95 (or M0.93 without the autopilot). The reason for this was that at higher subsonic mach numbers the shockwaves started to dance with enough asymmetry that the fly-by-wire elevons would work so hard that fatigue was a worry. M0.96 to M1.7 was driven through as quickly as possible.

Out of interest - the last thing you wanted when fuel was short was to go subsonic; this immediately lost 25%ish of your range - she was designed to efficiently super-cruise without reheat and that she did - Mach 2 was where she belonged.

26th May 2004, 00:15
Milt, Yes I meant C of P, as in “high subsonic flight (actually transonic would be a better term) will give an aft movement in C of P, not C of G. thanks, and I corrected the post.

Herc Jerc, we seem to have some different understandings.
1. the buffet from flying above M crit is actually almost non existent at speeds slightly above m crit. Its once the shock get strong enough that it causes flow separation that mach buffet becomes a problem. Hence, Mmo is well above M crit, for most wing designs we see today.
2. Mack tuck would occur, if at all, above M crit. And when local flow just starts to become sonic, this is the definition of the beginning of transonic flight. If DP Davies says otherwise, please quote. I don’t have his book, and if this is wrong I’d like to know.
3. I can certainly imagine an airliner cruising above M crit. With third generation supercritical wings, the drag associated with flight above the M crit does not increase like non supercritical wings. Minimum fuel cost does not drive the choice of cruise speeds, even at $40 a barrel.

Milt, your quote “So over time M crit has become that Mach No at which there is a sharp increase in drag and a need to substantially increase thrust to go faster.”

That mach is known as the drag divergent mach number. M crit has always been where first sonic, or M1.0 flow occurs locally, somewhere. The sharp increase in drag occurs at various speeds above M crit, depending on the aerodyamics. As I said earlier above, supercritical wings were able to delay the increase in drag, allowing higher cruise speeds before this significant drag rise.


30th May 2004, 08:19
dear hawk37,

supercrit wings serve to increase the Mcrit so the aircraft is still flying somewhat below this speed. a typical margin of .2 (no turbulence expected) to .3 (normal) G is maintained by the Mmo with respect to the high speed buffet and cruising speeds are lower than this. typical cruise speeds are well below high speed buffet, except when operating very close to max altitude for the weight.

the need for mach trimmers seems to be more of a certification issue on many modern airliners, though i daresay there could arise (not normal) situations where they could save the day.

31st May 2004, 01:06
Catpinsin, I'm having a little trouble understanding your first sentence, however I will offer this quote from J d Anderson's Introduction to flight

" the airfoils on modern subsonic jet aircraft, such as the DC10 wide body, are relatively thin profiles dedigned to increase the drag-divergence mach number. In fact, NASA has developed a new supercritical airfoil, designed to place the drag divergence mach number extremely close to 1.0 ....the flow over the airfoil is largely supersonic, and the airfoil shape is designed to discourage the formation of shock waves......the cruising speed of such airplanes can be increased by incorporating airfoils with high values of M drag divergence......the next time you have an opportunity to fly in a jet airliner and the sun is directly overhead, look out along the span of the wing. Due to the refraction of light waves through shock wave, you can sometimnes see with the naked eye the transonic shock waves dancing about on the wing."

clearly, airliners with supercritical wings can cruise above M crit, and with (small) shock waves. After all, thats what the "super" in supercritical stands for!

As for your other points, agreed.

Old Smokey
21st Jun 2004, 18:23
Panama Jack,

Hawk37 gave you a good reply, read it well. Hawk's reply could be seen, if you looked askance, as being for the more modern supercritical wings.

Jet aircraft have been routinely flying above Mcrit long before the super critical wing came along.

A large exceedance of Mcrit will yield a host of aerodynamic / control problems, including the onset of 1G 'Mach buffet'. The manufacturer obligingly places Mmo just below the threshold of aerodynamic problems, leaving a portion of the flight envelope between Mcrit and Mmo for normal operations - The problem then becomes one of additional drag due to the shock waves - wave drag.

Wave drag increases very slowly at first, up to about M0.05 above Mcrit, and then rises exponentially. The new drag curves (High speed polars) attributable to wave drag can be superimposed over the total drag curve (Low speed polars) and show some interesting properties.

Maximum Range Cruise (Cost Index zero for all you FMC users) is found by at the point where a straight line originating at 0/0 is tangential to the 'revised' drag curve. Due to the very shallow curve of the High Speed Polars for the first .04 or .05 above Mcrit, this 'Maximum Range Plot' invariable leads to Maximum Range Cruise just above Mcrit.

Consider Long Range Cruise, which by definition offers 99% of the economies of Maximum Range Cruise or 1% additional fuel burn per mile. The line is drawn from 0/0 at a 1% steeper gradient than that for the Maximum Range case, and has a low speed and a high speed intersection with the Total Drag curve. The higher plot (Long range Cruise) is at a point even further beyond Mcrit.

Econ cruise, where the total cost of airframe time (best at high speed) and fuel cost (best at Maximum Range Cruise) is at a minimum. In byegone times, when lower fuel costs prevailed, higher fuel useage was tolerable against relatively expensive airframe time. In the 'fuel expensive' modern era, Econ cruise usually falls between MRC and LRC.

All 3 of these cases indicate that normal cruise operations, even when aiming for maximum possible range, occurred at speeds above Mcrit. The only exception would be low altitude operations when Mcrit is not reached, but this is not the usual habitat for the jet aircraft.

The discussion above spoke of tolerable levels of drag in the cruise phase. Even small drag increases introduce penaltys in climb performance, and here, flight above Mcrit is avoided, or minimally tolerated. If you don't know thr 'generic' Mcrit for your aircraft, the climbing Mach Number will be a pretty good indicator.

Descent employs much the same tolerance of small amounts of Wave Drag as does cruise. Indeed, the rapid onset of drag for a small mach number increase above normal cruise speed will be most beneficial (and demonstrable in the simulator) when maximum possible rate of descent is desired during an emergency descent.

I hope that this helps to fill any remaining gaps in your understanding.

Romeo Tango Alpha
23rd Jun 2004, 01:30
Written by someone who knows EXACTLY what they are talking about!

Kind of reminds me of my ATPL teacher, and my Father. :ok: He never ceases to amaze me, and I am EMINENTLY proud of him, although I don't seem to say that much.

27th Jun 2004, 17:05

The DC-9 has an indicator to show when the mach trim compensator is compensating. It is only a motor with inputs from the stability augmentator comp. that puts up to a 14 pound back pressure on the FO's yoke (CPT & FO's yokes are linked together).

The DC-9's fuel consumption would increase too much to make it efficient to fly above the critical mach number. Which occurrs on the DC-9 around .8m

28th Jun 2004, 02:40
"The DC-9's fuel consumption would increase too much to make it efficient to fly above the critical mach number. Which occurrs on the DC-9 around .8m"

Victor, I'm not familiar with the 9, but I know mach crit is often close to max range cruise speed. Perhaps .80 thus applies for the 9, I'm not sure. But it sounds high to me.
If by efficient you mean it takes more fuel per nm to cruise above M crit, I can agree. However, airliners often cruise well above M crit, and Max range cruise. Fuel price is not the only consideration. I doubt the 9 would be different.
Do you have any data to back up your statements?

28th Jun 2004, 03:19

by the term max range cruise i'm assuming you also mean long range cruise (lrc). which on the -9 is well below crical mach. our lrc numbers are 2% faster then douglas aka boeings numbers. we have found the burns negligable between boeings lrc and lrc plus 2%. i am very familier with the -9 but not other aircraft. when flight planning fuel burn is one of the bigges considerations as far as route, alt, power settings etc. when the -9 reaches mach buffet there is a definite high frequency buffet that differs from low speed buffet which is a lower frequency. at this point fuel burned per nautical mile begins increasing exponentialy and it becomes very innefficient. the -9 max alt is 350 and with its wing low speed buffet is never and issue at high alt.

Old Smokey
28th Jun 2004, 12:17
May I submit that for the DC9-30 to DC9-50 series of aircraft, Mcrit is M0.73, as indicated in the Airplane Performance Manual.

Drag rise between M0.73 and M0.76 is considered acceptable for normal MRC / LRC / Econ operations, whilst aerodynamic characteristics between M0.73 and M0.80 are considered acceptable without compensation. Between M0.80 and Mmo, Mach Trim Compensation is required, and provided.

The DC9 / MD80 / MD90 / B717 family is very large, and if I have commented upon a derivative outside the scope of the discussion here, I withdraw and take a back seat.

28th Jun 2004, 17:37
1. I'm wondering if you're actually talking about what is called the drag divergence mach number, in which case .80 seems ball park for the dc9 series. Mach crit is below this, as Smokey details.
2. Long range cruise is generally taken as speed for 99% of maximum range. So yes, very close to each other.

1st Jul 2004, 18:23
Old Smokey,

Read your earlier post and was quite amazed that the normal crize regime of Big Jets is MCRIT or more !!! On the B 738, the other night at FL 390 for some weight which I dont recall, the FMC Cost Index Zero speed ( Max Range ) was .763 and the LRC was .784. Do you mean to imply that the MCRIT for the flight was even less than .763 whereas Normal Econ Crz. for CI 40 was .790 ?????? Please clarify ..........

Thanks :ok:

2nd Jul 2004, 04:07
Sorry, I'm not up to speed on nomenclature. Can someone fill me in on what a B738 is?
I heard 737's were restricted to FL 370 and below, perhaps not true.
If it's a relatively new aircraft, remember that these later generation supercritical wings have very little drag increase as the local flow just becomes supersonic. That's the reason the wing profile was chosen.
And certainly, the normal cruise regime with supercritial wings is above Mach crit. As I said earlier, that's what the super (ie supersonic) term means in the supercritical wing.
Interesting that approximately M.02 is the difference between max range cruise and 99 % range cruise.

2nd Jul 2004, 05:43
A B738 is nothing but B 737-800. Thats how they write in the ATC Flight Plan. And the ceiling is FL 410 for the NGs. ( Classics on Steroids! ;) )

Cheers :ok:

Old Smokey
2nd Jul 2004, 06:06
capt.topgun / hawk37,

Maximum Range Cruise (MRC), Long Range Cruise (LRC, 99% Max Range), and Econ Cruise (Best Time/Fuel cost compromise) all occur above Mcrit, irrespective of the wing, be it older generation or the modern super-critical wing.

Aerodynamacists have always engineered the wing to delay the onset of Mcrit to the highest possible speed, but the advantage of the "modern supercritical wing" is that the initial drag rise after Mcrit is very much slower than older wings, thus enabling more of the speed envelope above Mcrit to be economically useable.

I have only flown the B737-300, not the later generation B737-800 topgun, and M0.763 for MRC and M0.784 for LRC does seem a bit high, I would have thought that M0.74 was about right for a B737, but the later series 737s may have a smarter wing.

Certainly, higher level operations (your post referred to F/L 390), would requir a higher Mach No. for MRC/LRC as the increased high speed polars for higher Mach No. are tolerable in view of decreased low speed polars for the lower EAS/IAS at high levels, and total drag is the sum of the high speed and the low speed polars.

Don't forget that if you're getting these speeds from your FMC, it has calculated the speeds after considering wind (either actual winds or pilot entered winds). As Headwind increases, the required Mach No. increases - If you look at the Total Drag Curve plotted against Ground Speed on one axis and Fuel Flow on the other, a lower Ground Speed (higher Headwind) places the drag curve closer to the 0/0 origin, and the tangent drawn from 0/0 to the curve touches it at a higher speed, even further above Mcrit than before. The reverse is true for Tailwind. As an example of this you may note an FMC LRC speed of, say, M0.78 when flying into a 100 knot Headwind, do a 180 degree turn into the 100 knot Tailwind and see the FMC LRC speed fall to M0.74.

A difference of 0.02 between MRC and LRC seems about right. I returned my DC9 / B737 manuals a long time ago, but memory tells me that such a difference was about right, and normal. On my current aircraft (B777), at typical weights and close to optimum levels, MRC of 0.82 and LRC of 0.84 seem pretty normal.

In times of old when fuel was much cheaper, Econ Cruise was typically above LRC, and crews had little idea of Max Range Cruise speed, indeed many manuals simply did not have such information (most still don't). With current fuel prices, Econ typically falls somewhere between MRC and LRC, and creeping downwards as fuel prices rise. It's only a matter of time before operations at Max Range Cruise are the norm, but be assured, this will still be above Mcrit.

3rd Jul 2004, 13:17
Thanks Smokey.

That did clear some Smoke ;) . Do you know of a link where I can view these graphs that you are referring to in the post. Will just help to visualize whats happening a little better.

Thanks, :ok:

Old Smokey
6th Jul 2004, 15:34

Happy to provide the graphs you refer to, I'm on a long flight just now and will post them on my return home.



15th Jul 2004, 12:32
Old Smokey
When you say M crit is below max range cruise of .82 for the 777, is this for typical high weights? If so, then at TOD when light, max range cruise has decreased but M crit will have increased since the airfoil is at a lower Cl. Similar to pushing forward to .75 G, lower Cl gives higher M crit.
Is there a M crit range of speeds for the 777 based on weight?

16th Jul 2004, 02:16
For one of PJ's original questions: do modern jet transports regularly cruise at speeds above Mach Crit
....could not see a specific reply.
I ask as i am sure i have seen a shockwave when flying on a trans-atlantic flight and it cast a shadow on the wing, this must mean that airliners do fly in the transonic range?

16th Jul 2004, 06:22
BOAC - Is there possibly some confusion in terms here ?

Old Smokey aticulates but the two terms I know are

Mcdr (critical drag rise) - where drag (due shock wave formation) starts to rise at a much higher rate relative to mach number increase ie the total drag curve shoots up.

Mcrit - mach at which 1st local SS airflow occurs

Old Smokey
17th Jul 2004, 01:34
Couldn't have put it better myself slice, thanks. One day away from home on loooong trip, and will attach some drag curves with a new post.

A picture is worth a thousand words.




Hope that helps. Ask if you need further clarification.

Old Smokey
19th Jul 2004, 16:10
Capt.Topgun, Hawk37 and PMs,

Attached as an addendum to my last post are 3 drag plots for a fairly high flying aircraft, about 5 to 8000 feet above 'other' commercial Jets, but the principals are EXACTLY the same.

Tha plots are for Equivelant Air Speed (EAS), i.e. CAS corrected for compressability so that one drag curve may be used for the same weight at any altitude instead of a series of graphs which would be required for TAS.

They are TRUE plots, not freehand sketches.

The first diagram illustrates basic principals of Maximum Range Cruise (MRC), i.e. the lowest gradient drawn from 0/0 against Thrust and EAS (or TAS). As Thrust is directly related to Fuel Flow, the lowest possible tangential gradient represents the best ratio of distance to fuel, i.e. Maximum Range. Long Range Cruise (LRC) suffers a 1% range penalty as a trade-off for speed, and would be drawn at a 1% higher gradient from 0/0 (In the diagram it is shown 4% higher for clarity).

For this example, MRC occurs for this weight at 250 EAS, and encounters Mcrit for the type of M 0.73 at 32237 feet (CAS = 262, TAS = 426 in ISA).

For THIS aircraft type, at this weight, MRC below 32237 feet would be 250 EAS at all altitudes, above 32237 feet Mach No. would be the governing factor. LRC, as a higher speed would push this 'changeover' level lower than 32237 feet.

Above 32237 feet, Mcrit (M0.73) is reached, and the High Speed Drag Polar is added to the 'basic' Low Speed Drag Polar to produce a new Total drag curve for each Pressure Height 'breaking away' at a fairly shallow angle initially, but increasing in intensity.

As the 2nd and 3rd diagrams show, the point of tangency in all cases is ABOVE Mcrit, increasing in divergance from M0.73 as Pressure Height increases, being most marked in this case at 45000 feet. Topgun, this would account for your fairly high LRC Mach No. at F/L 390 in a B737.

In Headwinds, the point of origin of the tangent is to the right of Zero, 'consuming' some of the aircraft speed, resulting in even higher Mach numbers for MRC / LRC. The opposite for Tailwind.

To respond to one question fielded, MRC for the B777-200 is approximately M 0.82, so long as the aircraft is at or close to Optimum Level. As diagrams 2 and 3 would illustrate, at levels lower than optimum, a lower Mach Number would be scheduled. (And who wants to fly much above Optimum).

To respond to another question fielded, Mcrit does indeed vary according to weight, i.e. in response to varying Angle of Attack. Higher weights require increased angle of attack, thus greater acceleration off air over the wing and an earlier encounter with Mcrit. If Long Range Cruise tables are examined, this explains why in many cases MRC / LRC Mach No. actually increases slightly as weight burns off, until later slowly reducing with weight in the 'conventional' manner.

This was done a bit hastily, I hope that I responded appropriately to this discussion.