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.
Last edited by Old Smokey; 20th Jul 2004 at 01:27.