Increasing jet aircraft range.

[deefer dog]

Can you experts please advise. The aircraft i fly quotes LRC at M0 .74. When i look at the AFM I note that, as one might expect, the TAS is reduced as weight decreases...so too does the Mach.

I have two questions.

1. If i want to extract as much in terms of range from the aircraft, and assuming still air, would I benefit by flying slower than published? (And by this I mean reducing towards the best L/D speed as indicated in the speed tape) ?

2. When flying into wind, by how much should I increase my IAS or Mach no? Is there a rule of thumb?

3. When flying in tailwind, by how much should I reduce?

In all cases to get max range...not endurance.

Many thanks.

[bfisk]

For Boeing... Set cost index to 0 and fly ECON speed.

[Intruder]

Rule of thumb I've used is increase TAS by 40% of headwind, decrease by 40% of tailwind. Min speed is max endurance. Max speed is where the knee in the fuel flow / TAS curve is (you will likely have to estimate it).

[autoflight]

Years ago I generated data for B727-200 levels for best range for various head/tail winds and weights at M.80. At lower levels I used the recommended IAS. That was a huge job with interesting results and it was mainly used on Sydney - Perth runs. TAS and fuel flow changes related to different levels was the best way to adjust for wind gradients Thirty years ago the traffic was sparse enough to not need more complex calculations for speed changes at a fixed level.
Rules of thumb for wind gradients turned out to be a poor substitute for a lot of better preparation.

[deefer dog]

Thanks for the replies.

Here is my difficulty in understanding. The LRC schedules call for speeds which are always in excess of green dot speed, so are always faster than the speed for best L/D.

Why would this be.....or have I completely missunderstood all previous teaching that max range IS achieved at best L/D speed?

[Old Smokey]

Defer dog,

Maximum range cruise categorically is well above max L/D ratio speed. This speed (with very Minor adjustment) is more representative of Max Endurance / Best angle of climb / Minimum rate and angle of descent during OEI DRIFT-down.

Max range cruise occurs on the conventional drag curve at the point of tangency to the curve drawn from the 0/0 origin. In head and tail wind conditions, the 0/0 origin moves left/right in direct relationship to tailwind/headwind (in that order). Whilst on the subject, don't let any jerk convince you that MRC is at or below Mcrit, it's always above at normal operating levels, but EAS defined below the CAS/Mach changeover level.

[toffeez]

Phew, glad you replied. Posts 6 & 7 were a bit scary for me. Still are.

[HazelNuts39]

See earlier discussion here (http://www.pprune.org/tech-log/430558-max-endurance-max-range.html)

[Linktrained]

For the 707, Boeing published Optimum Altitude data, which showed that as the aircraft's weight decreased with fuel burn-off, the Optimum Altitude increased. This would mean that the Opt. Alt. increased by about 1000 ft./hour. (Of course this would be restricted by other factors in practice.)

[framer]

Here is my difficulty in understanding. The LRC schedules call for speeds which are always in excess of green dot speed, so are always faster than the speed for best L/D.
I think I can help you overcome your difficulty in understanding. Go to your FCOM and look up the definition of "green dot speed", then determine if green dot is relevant to your calculations, or a red herring. I would do it but my aircraft no longer has a green dot so I don't have the books.

[Kefuddle]

have I completely missunderstood all previous teaching that max range IS achieved at best L/D speed?
Indeed, for a jet yes, but your understanding is correct for a prop. As Old Smokey says, for a jet max range is generally faster than l/d speed. I would add that min drag reduces towards l/d with altitude (at max service ceiling they are just about coincident). L/d speed is pretty much the same as clean speed (or flap maneuvering speed with flap). L/d speed is best endurance speed and what you want to fly in a hold.

However, it would seem to me that If really desperate to save fuel, then use l/d speed for descent.

Rule of thumb I've used is increase TAS by 40% of headwind, decrease by 40% of tailwind. Min speed is max endurance. Max speed is where the knee in the fuel flow / TAS curve is (you will likely have to estimate it).
I had not heard of that one. My guess was that given that a typical drag curve is very flat at around min drag speed for a jet, I assumed that one would want to increase speed into a headwind by much more than one would want to reduce it with a tail?

[bfisk]

A common misunderstanding is that LRC gives you max range. It gives you exactly what is says - long range - but not max range.


-Max endurance speed is whatever you get with the lowest fuel flow. It is not affected by wind. On the Speed/Drag curve, this is the lowest point.

-Max range speed is defined by the lowest fuel flow pr. ground distance covered, thus it is dependent on wind. Assuming no wind, then on the Speed/Drag curve, this is the tangent with the lowest angle.

-Long range cruise speed is slightly higher than max range speed, and is a tradeoff, that gives you a (relatively) big speed increase for a (relatively) small range penalty. On the Speed/Drag curve, this will be a bit further up-and-to-the right from the max range; you will see that although the drag increases, the speed also increases by nearly the same amount.


http://www.theairlinepilots.com/forumarchive/principlesofflight/totaldrag.jpg
(image courtesy of the internet)

[framer]

Thanks for that graph.

I use the Cost Index to give me an approximation of VMR in the 737 but I am aware that it is taking account of the wind while in EcON mode so isn't exactly right.
1/From VMR can I work backwards to get VMD in IAS?
2/ Is VMD purely a function of weight and therefore the same IAS at FL380 or 2000ft for a given weight?

[deefer dog]

Thanks again, Now I think I'm starting to get a clear picture.

So, in essence, what some of you are saying (in a jet) is this:: Best L/D speed for a given weight would give max range, but because the engines may not work as efficiently at this lowish speed, a better mileage per pound of fuel is obtained at a speed somewhat above that of best L/D. Is that it?

What I didn't understand was the post by toffeez. What did you find so scary about my post 6, which, after all, was only another question? Was it that I asked a stupid question?

[HazelNuts39]

Is VMD purely a function of weight and therefore the same IAS at FL380 or 2000ft for a given weight?
No, at FL380 VMD would be higher due to Mach effect on L/D.
Best L/D speed for a given weight would give max range, but because the engines may not work as efficiently at this lowish speed, a better mileage per pound of fuel is obtained at a speed somewhat above that of best L/D. Is that it? No it isn't. Best L/D speed VMD is the speed V for minimum drag D.
VMR is the speed for minimum D/V.
For a parabolic drag polar in still air VMR is equal to VMD times the 4th-power root of 3.
If it assumed that engine efficiency (thrust specific fuel consumption) is constant, then VMD is the speed for max endurance and VMR is the speed for maximum range.

[bfisk]

I use the Cost Index to give me an approximation of VMR in the 737 but I am aware that it is taking account of the wind while in EcON mode so isn't exactly right.

Well, it is actually right, because Vmr (max range) is dependent on wind.

On the 737:
For Vmd (min drag, best endurance), use HOLD page to get holding speed. This is close to Vmd.
For Vmr (max range), set cost index to 0 and fly ECON CRZ.
For Vlrc (long rang cruise), use LRC CRZ. (cost index has no influence).

(For info, LRC is equivalent to ECON speed at cost index around 35-ish. Ie, if you fly at a low cost index, say 15 or 20, going from ECON to LRC will actually decrease your range slightly)

[framer]

Hazelnuts, any idea where I could read up about Mach effect? A google search brings up medical info.
Bfisk, thanks for that.

[deefer dog]

HazelNuts, thanks for informative answers. Could you please explain what 4th power root of 3 means.

An example would help. What is the 4th power root of 3 if the starting number was, say, 10?

Thank you.

[deefer dog]

And a question to bfisk, please.

I read elsewhere the numbers 1.32 and 1.37 as in your diagram. Can i therefore assume that in a jet, VMR is always VMD x 1.32?

Thanks

[HazelNuts39]

Could you please explain what 4th power root of 3 means.
If you have a calculator that produces the square root of the number entered, enter 3, take the square root and you get 1.732 ... . Take the square root of that result and you get the fourth-power root of 3 which is 1,316... .

[HazelNuts39]

any idea where I could read up about Mach effect? Sorry, I can't help you there. Mach effects are due to the compressibility of air. They become important when the local velocity in the airflow around the airplane approaches the speed of sound. I was looking at the aerodynamic data of a wide-body transport.

[woodja51]

So is that where 1.32 comes from as Vimd x1.32 = Vlrc?

I also learnt optimum altitude was best the best product of l/d x Mach for the 707 ... Which sort of lines up with the previous info.
On another fuel matter, when you plug a hold( racetrack) into an FMS it bugs up a few knots over green dot... Now this makes sense as the idea is to fly slightly faster to allow the speed to decay in the turns due to the drag increase and speed up on the straights staying above Vimd... But the idea used to be to leave the thrust constant , avoiding accelerating the engine thus using more fuel...
In modern jets FMS says ' set hold speed' and obviously the autothrust/ throttle then powers up and down as needed to hold constant target speed... Is this correct or counterintuitive to the whole reason hold speed is slightly increased in the first place?? Or am I missing something ... Should I technically be disconnecting A/T if I really wanted max endurance? No one has ever been able to,answer this question.. But some of the folks here seem pretty aero- knowledgable? WJA

[Natstrackalpha]

I would have thought you can get around the hold no problem and that taking autothrust out of . . auto - using manual thrust would stop the excursions of thrust - providing you have enough thrust to get round the corners, in your race track pattern, based on holding at altitude. `Some` ask for a certain speed in the hold like 230 kts.

Also, needless to say, if you "fix" your thrust at a constant setting during your max/long range cruise - you will go faster and faster, or (higher and higher)

Also, needless to mention, the level where you are getting max tailwind is more favourable than into the teeth of a jet(stream) say.

Also, don`t forget the hurricane thing - when flying the outer edges or the affected air of the tropical revolving storm its best to go around with the wind covering more ground and yet a lot faster ground speed.

What I didn't understand was the post by toffeez. What did you find so scary about my post 6, which, after all, was only another question? Was it that I asked a stupid question?

Nothing wrong with your post - you said nothing stupid, toffeez meant that he had to get the graphs out and work for a minute.

Love your thread Deefer.

[HazelNuts39]

Should I technically be disconnecting A/T if I really wanted max endurance? No one has ever been able to,answer this question.. I would think the idea is to keep the airplane on the stable part of the drag curve to avoid the engine constantly spooling up and down. Disconnecting A/T doesn't help because you would have to work the engines even harder.

[Miles Magister]

Deefer Dog,

Despite the theory above all being sound the technique for each aircraft will vary slightly in practice.

Based on many years of experience and in flight trials you will need to record some figures for your own aircraft in flight and come up with a plan. As a guide I have used the following as starting point:

Best range in a jet is often achieved at about 1000' above the max height for weight shown in the AFM. But be careful as you are into the 1.3G margin to the buffet in 3 directions. This point will give you approx 30 AOB to the buffet in a turn.

For head or tail winds I use one third of the wind value, I would expect the 40% mentioned above is equally valid.

To decide whether to to go up or down to loose a headwind component I use a required gain of 7 to 9 kts in G/S for every 1000'. i.e. In a strong headwind if you gain 9kts of G/S by descenting 1000' you will probably be in profit.

But what you need to do is use your FMS to display the specific range i.e. the number of miles you are achieving per unit of fuel. When this is at the greatest then you will be at the best range speed. This speed will decrease with weight. The technique to work this out is to set the parameters on a long leg where wind and temp are constant then set a power for a speed and let it become stable, record the figures and then set a different speed and record the figures. Over the period of a few flights you will get a feel for your aircraft.

If you wish to discuss then please feel free to PM me.

Regards

MM

[framer]

Can anyone shed some light on some speeds that I noted from the FMS on a flight I did this morning.
The holding speed ( at FL390) was 220kts. The s/e drift down speed was 231kts, and the Vref 40 speed +100 was 236kts.
From what I have read in the 737 manual I would have thought that the VMD could be obtained from the s/e drift down page or approximated from Vref 40 by adding 100kts.
Bfisk stated that VMD could be obtained from the hold page but I wonder if this is true for our update 10.8 FMC because it seems too slow to me.From experience I imagine that 220kts would have been on the back of the curve and quite "speed unstable".
Any ideas about how those speeds are derived and if any of them are VMD would be appreciated.

[hawk37]

Framer,

If single engine drift down speed is for minimum rate of descent, then it should be at V minimum drag (max endurance speed). If single engine drift down speed is for max range, then it will be greater than minimum drag, ie to maximize the ratio of TAS/fuel flow. All this assumes thrust is proportional to fuel flow, which is fairly true.

[HazelNuts39]

framer,

While I don't know how and why Boeing scheduled those speeds, I would expect the s.e. driftdown speed to be the same as the s.e. climb speed, optimized for best s.e. gradient of climb/descent, without regard to fuel consumption, i.e. close to VMD. Why the holding speed is lower I don't know, but it could be due to the different engine configuration, i.e. both engines operating for level flight vs. one engine out, remaining engine at max. continuous thrust (e.g. different trim drag, different specific fuel consumption).

P.S. I was hoping to find some answers in Boeing's Jet Transport Performance Methods, but unfortunately there is nothing on holding and driftdown speeds, and chapters "Performance and FMCS" and "Speed Stability" are still "to be supplied". Perhaps you should ask Boeing?

P.S.2
Oops, holding is discussed in the "Cruise" chapter. There it says:
In the holding pattern, however, while the emphasis is still on fuel efficiency in this case we want to minimize the rate of fuel flow. Minimizing the fuel flow rate means minimizing the amount of fuel consumed while holding.
“All right,” you say, “we’ll just calculate the fuel flow at the speed for minimum drag. Minimum drag means minimum fuel flow, right?”
Sorry, no. It’s a little more complicated than that. Actually, the minimum flow will occur at a speed slightly slower than the speed for minimum drag. Let’s see why that’s true.The explanation that follows is that the engine TSFC (Thrust-Specific Fuel Consumption) increases with airspeed.

[framer]

That's great information Hazelnuts, thanks.
It explains why Boeing suggest to fly Vref 40 +100 in the hold even though this is invariably faster than the speed on the hold page. Flying slower than VMD at FL390 is a bad idea in the -800. I'm going flying again tonight so I'll jot down the speeds again then to see if the 1.32 factor works.
Cheers.

[bfisk]

A couple of things to note here: the 1,32 and 1,37 constants may be completely arbitary. The speed/drag curve I posted was something I found on a google search in order to illustrate the principles. It may or not be measurable or to scale.

Secondly, I said the hold speed on the FMC will be close to Vmd, not that is Vmd pr definition.According to the FCTM: " Holding speeds in the FMC provide an optimum holding speed based upon fuel burn and speed capability; but are never lower than flaps up maneuver speed".

[framer]

Thanks Bfisk,
I understand what you're saying. I am finding this interesting from a practical point of view for day to day flying and appreciate the info that is coming out from you guys. At this stage I am thinking that VMR is simple, just select CI 0.
VMD is looking more and more like s/e drift down speed and the speed from the hold page is slightly lower than VMD and not a speed I want to use in day to day operations when in the flight levels.
Cheers.

[deefer dog]

Thank you all. Making sense now, and just got an offer from a test pilot who promised to fly with me on a trip to show me how they better book figures. Will let you know in three weeks when we need to do it, and hopefully how its achieved.

[deefer dog]

Just to add to the mix, here is an explanation I found:


Professional Pilot - Range Jet (http://selair.selkirk.bc.ca/training/aerodynamics/range_jet.htm)

Too complicated for me though, but some of it rings bells after reading posts from all who have been kind enough to respond (without being "scared" at my lack of knowledge).

[Teldorserious]

Well that's what I do too...when it's late at night running into headwinds and bad weather, all the FBOs are closing down, I don't look at my FMS or pull out the flight manual for long range fuel, I start calculating TAS X 1.32 divided by PI, the Earth's ecliptic squared, subtract the cups of coffee left in the pot behind me, divided by a calculated ounces of bagged cubed, multiplied by the amount of bug splats on my windshield.

:rolleyes:

[HazelNuts39]

From the "Professional Pilot" site:
Thrust Specific Fuel Consumption (TSFC)

Thrust Specific Fuel Consumption (TSFC) is defined as the ratio of fuel flow to thrust produced by the engine:

(...)

For JET engines TSFC is very close to being constant over a wide range of airspeeds. In other words the same amount of fuel flow produces the same amount of thrust at any speed from zero to close to the speed of sound.

We must emphasize the above point: TSFC is very close to being constant for a JET engine. This is a critical point. It means that to determine the fuel flow we simply use the formula: FF = TSFC x Ta. Given that TSFC is a constant this is a very useful and powerful equation. Let's emphasize it again:
From Boeing Jet Transport Performance Methods:

http://i.imgur.com/TC2ufng.png

(...)

http://i.imgur.com/AjPct7Q.png?1

[Linktrained]

HN39

Please thank Boeing for the last paragraph, that " TSFC rises..."

This helps to explain why I had so much fuel left in the Port fuel tank of my Rapide after flying around Blackpool for more than a couple of hours, in the dark ( and ignorance ) in 1951 !

(See the thread " Fuel Economy a Pilot's Reward" #51 9th May )

It worked on twin engined biplanes of the 1930s, too.

LT

[framer]

Went for another fly today and jotted down some speeds.
At 69.2T and FL 370 we we had a s/e drift down speed of 242 and a hold speed of 229. We were indicating 246kts at ci 10.
229 would have been about 10kts above the amber bar (which gives 40degrees bank to the stick shaker).
My assessment of that is that VMD was 13kts above the speed on the hold page which is the minimum fuel burn speed and not a speed I would have wanted to slow to.
Thoughts?

[HazelNuts39]

Not much to add. Your observation is not too different from the JTPM example showing holding speed at FL350 of M.72/242 kCAS for VMD of M.75/253 kCAS.

[framer]

Cool, I think I'm done here. Thank you very much to the OP and everyone else who contributed solid info and links/ examples etc. I have learnt/ confirmed a lot.
Cheers

[hawk37]

My assessment of that is that VMD was 13kts above the speed on the hold page which is the minimum fuel burn speed and not a speed I would have wanted to slow to.
Thoughts?

Framer, before you make that conclusion, can you first be sure that single engine drift down speed, 242 kts, is indeed for least ANGLE of descent. Because if it is instead for best RANGE speed single engine, then your assessment may be incorrect.

[HazelNuts39]

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.

[WeekendFlyer]

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

[hawk37]

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.

thanks WF. I would like to point out that this "fourth route of 3" factor of approximately 1.316 only applies to operations where compressibility is not a factor (generally not true for high altitude ops), and where an engines TSFC is flat with respect to speed (generally close for high altitude ops).

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

[keith williams]

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.

[framer]

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.
That sounds good in theory, but who is flying around an airliner at their
' aerodynamic ceiling' ?

[WeekendFlyer]

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

[keith williams]

That sounds good in theory, but who is flying around an airliner at their ' aerodynamic ceiling' ?

Don't dismiss the matter too lightly because:

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.

Aircraft routinely cruise at speeds (slightly) above Mcrit. The problem occurs when Mcdr (Critical drag rise mach number) is exceeded.

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.

[framer]

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.