Mach Crit, Mach Number Buffet, Mach Tuck, and Mach Trimmers
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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.
Hawk
" 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.
Hawk
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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.
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.
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Written by someone who knows EXACTLY what they are talking about!
Kind of reminds me of my ATPL teacher, and my Father.
He never ceases to amaze me, and I am EMINENTLY proud of him, although I don't seem to say that much.
Kind of reminds me of my ATPL teacher, and my Father.
He never ceases to amaze me, and I am EMINENTLY proud of him, although I don't seem to say that much.
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fyi
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
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
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"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?
Hawk
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?
Hawk
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Hawk,
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.
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.
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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.
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.
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Victor.
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.
Hawk
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.
Hawk
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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
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
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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.
Hawk
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.
Hawk
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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.
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.
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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,
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,
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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?
Hawk
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?
Hawk
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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?
....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?
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 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
Last edited by slice; 16th Jul 2004 at 08:34.
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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.
A picture is worth a thousand words.
Hope that helps. Ask if you need further clarification.
Last edited by Old Smokey; 19th Jul 2004 at 15:20.
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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.
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.
Last edited by Old Smokey; 20th Jul 2004 at 01:27.
