Increasing jet aircraft range.
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From Boeing Jet Transport Performance Methods, Chapter 33: Cruise - Engine Failure and Driftdown (rev. March 2009)
Failure of One Engine in Cruise
At the point of engine failure, the pilots will set thrust on the remaining engine(s) to the Maximum Continuous Thrust rating. You will remember that MCT is a special thrust rating usable only in case of emergency.
What speed should they maintain during the descent? It makes sense to use a descent speed that will minimize the descent gradient, thus keeping the descent flight path as high as possible.
In the chapter entitled “Climb Angle and Rate of Climb” we talked about the effect of speed on an airplane’s climb gradient. There, you saw that the speed for the best possible gradient is approximately the speed at which the ratio of drag to lift is at its minimum value. For planning the descent performance of an airplane following engine(s) failure, we will base our calculations on the use of the speed for the best gradient, which is referred to in the AFM as the “enroute climb speed”. Don’t let the use of the term “climb” in that name confuse you: the climb referred to can be either a positive gradient or a negative one. In either case, the speed is the same.
At the point of engine failure, the pilots will set thrust on the remaining engine(s) to the Maximum Continuous Thrust rating. You will remember that MCT is a special thrust rating usable only in case of emergency.
What speed should they maintain during the descent? It makes sense to use a descent speed that will minimize the descent gradient, thus keeping the descent flight path as high as possible.
In the chapter entitled “Climb Angle and Rate of Climb” we talked about the effect of speed on an airplane’s climb gradient. There, you saw that the speed for the best possible gradient is approximately the speed at which the ratio of drag to lift is at its minimum value. For planning the descent performance of an airplane following engine(s) failure, we will base our calculations on the use of the speed for the best gradient, which is referred to in the AFM as the “enroute climb speed”. Don’t let the use of the term “climb” in that name confuse you: the climb referred to can be either a positive gradient or a negative one. In either case, the speed is the same.
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Drag Polars
thought there was a bit of confusion on here, so perhaps this will clarify things!
The drag polar has minimum drag at maximum L/D, which also equals maximum CL/CD. For aircraft operating well below Mcrit, max L/D occurs when induced drag and zero-lift drag are equal. The variable with the largest effect on minimum drag speed (Vmd) is weight, which increases the induced drag. Vmd increases as weight increases.
Once compressibility effects become significant, particularly when Mcrit is exceeded and wave drag becomes a factor, the drag polar changes partly because the CL/AOA gradient reduces in the transonic region but also because CD increases rapidly as the Mach number gets much above Mcrit.
Vmd is the best RANGE speed for a propeller aircraft and best ENDURANCE speed for a jet aircraft.
For endurance, you want minimum fuel flow. For range, you want to maximise speed/drag or minimise drag/speed. For a jet this occurs at 1.316 * Vmd.
WF
The drag polar has minimum drag at maximum L/D, which also equals maximum CL/CD. For aircraft operating well below Mcrit, max L/D occurs when induced drag and zero-lift drag are equal. The variable with the largest effect on minimum drag speed (Vmd) is weight, which increases the induced drag. Vmd increases as weight increases.
Once compressibility effects become significant, particularly when Mcrit is exceeded and wave drag becomes a factor, the drag polar changes partly because the CL/AOA gradient reduces in the transonic region but also because CD increases rapidly as the Mach number gets much above Mcrit.
Vmd is the best RANGE speed for a propeller aircraft and best ENDURANCE speed for a jet aircraft.
For endurance, you want minimum fuel flow. For range, you want to maximise speed/drag or minimise drag/speed. For a jet this occurs at 1.316 * Vmd.
WF
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For endurance, you want minimum fuel flow. For range, you want to maximise speed/drag or minimise drag/speed. For a jet this occurs at 1.316 * Vmd.
consider the case of a typical aircraft at FL 370, where max range is .82 for this case. divide by 1.316 gives max endurance of .62
Now does that figure make sense?
Hawk
If we look at how the buffet boundary speeds converge as altitude increases we will see that the usable speed range decreases.
At the aerodynamic ceiling there is only one speed at which we can maintain straight and level flight. It follows that this single speed (Vonly?) is both the best endurance speed and the best range speed.
The quoted 1.32 Vmd (or 1.316 if you prefer) is OK at lower altitudes, but is irrelevant at very high altitudes.
At the aerodynamic ceiling there is only one speed at which we can maintain straight and level flight. It follows that this single speed (Vonly?) is both the best endurance speed and the best range speed.
The quoted 1.32 Vmd (or 1.316 if you prefer) is OK at lower altitudes, but is irrelevant at very high altitudes.
Last edited by keith williams; 11th Jun 2013 at 13:02.
At the aerodynamic ceiling there is only one speed at which we can maintain straight and level flight. It follows that this single speed (Vonly?) is both the best endurance speed and the best range speed.
' aerodynamic ceiling' ?
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Hawk,
totally agree. Mach 0.62 is not likely to be feasible at high flight levels because your EAS would then almost cetainly be below your stall EAS.
My understanding is that as an aircraft climbs, the stall EAS (for a given weight) remains constant but the limiting Mach Number (expressed in EAS terms) reduces. Therefore if you climb high enough there is an EAS which is simultaneously the limiting Mach Number and the stall speed for a given height/weight combination i.e. the Vonly as posted previously (I like that by the way, Vonly is a good term!)
It appears, therefore, that Vmd ceases to be an option above a certain height (for subsonic aircraft at least) because it would be below the stall speed, and Vmr may ultimately be unobtainable due to the limiting Mach Number and wave drag. I guess that in that case, for max range you need to fly just below Mcrit to avoid wave drag, and for endurance you just fly as slow as you can with a safe margin above the stall.
Anyone care to comment?
WF
totally agree. Mach 0.62 is not likely to be feasible at high flight levels because your EAS would then almost cetainly be below your stall EAS.
My understanding is that as an aircraft climbs, the stall EAS (for a given weight) remains constant but the limiting Mach Number (expressed in EAS terms) reduces. Therefore if you climb high enough there is an EAS which is simultaneously the limiting Mach Number and the stall speed for a given height/weight combination i.e. the Vonly as posted previously (I like that by the way, Vonly is a good term!)
It appears, therefore, that Vmd ceases to be an option above a certain height (for subsonic aircraft at least) because it would be below the stall speed, and Vmr may ultimately be unobtainable due to the limiting Mach Number and wave drag. I guess that in that case, for max range you need to fly just below Mcrit to avoid wave drag, and for endurance you just fly as slow as you can with a safe margin above the stall.
Anyone care to comment?
WF
That sounds good in theory, but who is flying around an airliner at their ' aerodynamic ceiling' ?
1. Not all aircraft are airliners and some ( U2, SR71 and some military) may well operate close to their absolute ceiling.
2. Even at the 1.3 g ceiling the usable speed range between the buffet boundaries is unlikely to extend from Vmd to 1.32Vmd.
It appears, therefore, that Vmd ceases to be an option above a certain height (for subsonic aircraft at least) because it would be below the stall speed, and Vmr may ultimately be unobtainable due to the limiting Mach Number and wave drag. I guess that in that case, for max range you need to fly just below Mcrit to avoid wave drag, and for endurance you just fly as slow as you can with a safe margin above the stall.
As altitude increases, compressibility causes the TAS value of Vs to increase while the TAS value of Mcdr decreases. This causes the buffet boundaries to converge towards a single speed at the absolute ceiling.
Fair enough Kieth. Point taken. I guess I was approaching the thread from a practical airline point of view.
The reality for the aircraft I fly ( 737-800) is that max endurance is a lower speed than Vmd which is lower than Max range up to the aircrafts service ceiling.
Practically what this means is that pilots of the 737-800 need to be very aware of their altitude if thinking about slowing to max endurance for holding or an ATC slow down because it is going to put them on the back of the curve and they will be speed unstable. This may be fine if they have thought about the conditions and how they will manoeuvre etc, but in some circumstances it is not a good idea as the aircraft will be thrust limited and may not be able to claw back any deviations.
Cheers.
Ps, I'm always ready to be corrected and learn something so would be appreciative of any corrections to the above statement.
The reality for the aircraft I fly ( 737-800) is that max endurance is a lower speed than Vmd which is lower than Max range up to the aircrafts service ceiling.
Practically what this means is that pilots of the 737-800 need to be very aware of their altitude if thinking about slowing to max endurance for holding or an ATC slow down because it is going to put them on the back of the curve and they will be speed unstable. This may be fine if they have thought about the conditions and how they will manoeuvre etc, but in some circumstances it is not a good idea as the aircraft will be thrust limited and may not be able to claw back any deviations.
Cheers.
Ps, I'm always ready to be corrected and learn something so would be appreciative of any corrections to the above statement.
Last edited by framer; 12th Jun 2013 at 23:30.
