Max Endurance Speed / Min Fuel Flow

[TJQ]

Hi Guys

Why is the speed for Minimum Fuel Flow (i.e. Holding Speed or Max Endurance Speed) BEHIND the drag curve...?

You would expect minimum fuel flow to occur with minimum drag but this is in fact NOT the case! The speed for minimum thrust/fuel flow occurs at a slower speed where there is greater drag - which strikes me as unusual.

I've been doing a lot of research on the web and in these forums and although I can find the confirmation that it is indeed true, I can not find a reason explaining why.

Obviously there must be more factors involved than just "thrust required to overcome drag"...

I've had a read of Boeing's "Jet Performance Test Methods" manual (1989 edition) and they don't really give a comprehensive reason in layman's terms as to why you burn less fuel with more drag.

Anyone want to give it a go and make my day...?:ok:

Many thanks if you can help...!


TJQ

[Jane-DoH]

That sounds odd, I thought with ram compression and everything a jet would perform better at higher speed due to ram compression effects though at the speed optimum for that, the wing's L/D ratio would have already started falling off.

Is this a general rule for all aircraft, or a particular aircraft in question?

[Golf-Sierra]

The speed you are referring to is the minimal fuel flow per unit of time.

The drag at this speed will not be optimum (greater than minimum) - and hence the fuel flow per unit of distance covered will not be optimal.

Think of a car analogy - if you want to travel the furthest possible on a tank of fuel you want to be in top gear and at motorway speeds. A single tank will get you say 700km, and at an average speed of 120km/h will last you just short of 6 hours. In congested city traffic (doing 30km/h on average) the same tank may only allow you to do 300km, which nonethelsss equates to 10 hours of driving.

Golf-Sierra

[Rob82]

As Golf-Sierra has said. Minimum fuel flow is exactly that, its the point where the aircraft is flying above the stall speed but as slow as possible with the minumum fuel entering the engines.

Think of at the point of minimum drag. Say the aircraft is burning 1000kg/hr to maintain say 250kts.
Now if everything was linear and drag wasn't involved you could say at 500kg/hr you would be flying at 125kts. Obviously this isn't the case, but with the extra drag at 500kg/hr you would maybe be flying at 100kts. As long as this speed is above the stall speed then your a happy chappy.

Basically the extra drag will cause you to lose some airspeed but you can still get a lower fuel consumption than flying at the minimum drag state.

After all the whole reason for minimum fuel flow, is exactly that. You want to burn as little as possible to stay in the air as long as possible, you are not looking to get anywhere fast, and so are not concerned about the increase in drag.

Its probably clearer in my head that what i've tried to describe but hope it helps.

[Capn Bloggs]

You would expect minimum fuel flow to occur with minimum drag but this is in fact NOT the case! The speed for minimum thrust/fuel flow occurs at a slower speed where there is greater drag - which strikes me as unusual.

I've been doing a lot of research on the web and in these forums and although I can find the confirmation that it is indeed true...
I'd be interested in the sources that claim this.

According to Handling The Big Jets page 64 and Mechanics Of Flight page 186 (although I think I've spotted an error by Mr Kermode - there are 2 Jet Min Drag speeds on the diagram; the 160KIAS one is the correct one according to the text), Max Endurance is at Min drag ie bottom of the drag curve.

[FE Hoppy]

Having spent many many hours patrolling the oceans at max endurance speed I can assure you that Vmd is where it's at.

A good operational practice is to use Vmd +5 as this will negate the constant use of thrust to maintain speed as a reduction in speed will give a reduction in drag and therefore the aircraft will accelerate naturally back to the previous speed without the addition of thrust.

This of course neglects the TSFC which could have an effect of the speed if your engines are running in a poor speed band.

One solution would be to shut one or more down but I wouldn't recommend that in a civvy jet!

[Golf-Sierra]

Capn Bloggs thanks for pointing out my obvious error.

FE Hoppy according to wiki (http://en.wikipedia.org/wiki/V_speeds) Vmd is often equal to Vbr - Best Range speed.

The OP is referring to Vbe - Best Endurance speed.

Are you sure you're not mixing the two?


Golf-Sierra

[Capn Bloggs]

FE Hoppy according to wiki Vmd is often equal to Vbr - Best Range speed.
Caution: for a prop aircraft, Vmd is Best range speed. Perhaps that is what Brandon (Wiki ref) was considering.

Vmd is definitely not Best Range in a jet. See my references above.

[keith williams]

The problem with the statement that


You would expect minimum fuel flow to occur with minimum drag


is that it is based on a number of (often forgotten) simplifying assumptions.

One of these assumitons is that the fuel required to produce each unit of thrust is constant.

Vmd is the speed at which the thrust required is a minimum.

Vmd will also be the speed at which fuel consumption rate is a minimum provided the fuel flow required to produce each unit of thrust is constant at all speeds.

The fuel flow required to produce each unit of thrust is the Thrust Specific Fuel Comsumption (TSFC). Unfortunately TSFC is not constant at all airspeeds.

To find the speed at which fuel flow will be minimum and endurance will be maximum we must take into account both the variation in drag and the variation in TSFC. In many cases this will give us a speed that is slightly higher than Vmd.

[FE Hoppy]

@GS

I'm sure ;-)

[hawk37]

Keith wrote In many cases this will give us a speed that is slightly higher than Vmd.

Keith, isn't it true that for turbojets/fans as speed increases, fuel flow must increase if one wants to maintain a certain thrust. Thus, for an aircraft the speed for minimum fuel flow will be slightly LESS than the speed for minimum drag?

[keith williams]

I do not believe that it is always as simple as that.

If we take the example flown by FE HOPPY

This of course neglects the TSFC which could have an effect of the speed if your engines are running in a poor speed band.


With all engines operating the thrust required at Vmd may be too low to enable the engines to run an an efficiently high RPM. In some types of patrol aircraft the best endurance is achieved by shutting down some of the engines to enable the others to be run at a more efficient RPM.

But if we were obliged to continue to use all of the engines the best compromise would be at a speed greater than Vmd to enable the engines to run at a reasonably efficient RPM, without incurring too much extra drag.

In this case the problem is one of having too much installed thrust at Vmd. But the way that thrust and TSFC vary with airspeed depends on engine type (turbojet, low by-pass turbofan or high by-pass turbofan).

So best edurance could be higher, lower, or at Vmd.

[Lancman]

The only reason that I can see is that by increasing your drag, and therefore requiring more thrust, you might bring a jet engine rpm up into a more efficient operating range. But flying on the wrong side of the drag curve,whilst theoretically more efficient, is a rotten idea in the real world.

[cwatters]

I think there is a short answer to the original question. The units...

Fuel consumption is a measure of power (eg energy per second) where as drag is just a force.

To calculate a "power" from a "force" you have to multiply by velocity.

So in short fuel consumption is proportional to drag x velocity not just drag alone. It's the product that has to be minimised.

[cwatters]

Can also point out that drag is actually proportional to the drag coefficient times velocity squared. So fuel consumption is proportional to velocity cubed.

Means a 10% change in speed is much more important than a 10% change in the drag coefficient.

This was the approach taken with the Gossamer Condor. They opted to minimise flying speed whereas most other attempts at man powered flight had concentrated on minimising drag.

[wondering]

http://www.pprune.org/tech-log/225816-vmax-range-vs-vmax-endurance.html

'Jet Airplane Performance' by LH Systems is your friend ;)

[TJQ]

Thanks for all the replies guys, it's much appreciated.

I've taken on board all that's been put forward and read the other thread, but still can not establish a definitive answer.

The best endurance speed is DEFINITELY slightly behind the drag curve, not at Vmd. I don't know how to post a picture in the thread without a hosting site but the graphs I have are from Mr Boeing himself and are very similar to those posted in the linked thread above.

However, I believe Cwatters may be on to something:

I think there is a short answer to the original question. The units...

Fuel consumption is a measure of power (eg energy per second) where as drag is just a force.

To calculate a "power" from a "force" you have to multiply by velocity.

So in short fuel consumption is proportional to drag x velocity not just drag alone. It's the product that has to be minimised.


This seems the most plausible scenario, for my small brain anyway.

Unfortunatley, none of the technical pilots/TRE's in my current OR my previous company are able to offer an explanation as to why in straight and level, static cruise conditions the min fuel flow occurs with higher drag - only confirming that it IS true.

A long shot but I don't suppose anyone has an email address for someone technical at Boeing? I'm pretty sure if I email their customer helpline I won't get an appropriate response!

Thanks again guys, keep the suggestions rolling in! :D:ok:


TJQ.

[Old Smokey]

TJQ,

If the following explanation is too messy, refer back to FE Hoppy's first post - Eminently practical and useful:ok:

Sorry that I can't post a diagram, so try to visualise this -

In Performance Analysis, we refer to the relationship between the Drag Curve and the Thrust available curve. The speed for Maximum Endurance lies at the lowest point on the Drag Curve which is tangential to the Thrust Curve (Imagine slowly 'bumping up' the Thrust Curve until it JUST touches the Drag Curve ..... There you have it, the point of tangency is at the speed for Maximum Endurance. Now, here comes the problem -

For PRACTICAL purposes, we assume the Thrust curve to be a Straight Horizontal line. If we accept this as fact, VMD does indeed become the Maximum Endurance speed. It is a VERY good assumption for overall Jet performance understanding, as the Thrust Curve is NEARLY a straight line, but isn't:rolleyes:

At zero speed, and with a particular engine setting, Static Thrust is produced. As speed (TAS) increases, due to the THRUST EQUATION, thrust declines. As Mach Number increases, ram effect causes thrust recovery, weak at low speeds and very high at high speeds. Thus, our simplified Thrust 'Line' is actually a curve, descending at low speeds, bottoming out at about M0.5, with recovery to Static Thrust at about M0.75. Above this Mach Number, thrust will exceed Static Thrust.

Now, as most holding is done at relatively low altitudes, and therefore low Mach Numbers, the point of Tangency of the Thrust Curve to the Drag curve is typically below VMD, as BOTH polars are descending. That accounts for Best Endurance speed below VMD.

If we were to now increase our holding Altitude to that where Holding speed was approximately M0.5, the point of tangency is spot on VMD, the thrust curve at this point is horizontal, just like our assumed and simplified Thrust Line. At even higher altitudes where the holding speed was above M0.5, the point of tangency is at a point where BOTH polars are increasing, and Best Endurance speed will be ABOVE VMD.

If it's still as clear as mud, refer back to refer back to FE Hoppy's first post, the practical solution:ok:

Regards,

Old Smokey

[keith williams]

Fuel consumption is a measure of power (eg energy per second) where as drag is just a force.

Fuel flow is a measure of the power going into the engines, but it is not a direct measure of the power coming out of them.

Power output / power input = Efficiency.

Unfortunately engine efficiency does not remain constant at all airspeeds, engine speeds and altitudes.

To calculate a "power" from a "force" you have to multiply by velocity.

That is true, but because of the variations in engine efficiency it isn't actually very useful in this discussion.


So in short fuel consumption is proportional to drag x velocity not just drag alone. It's the product that has to be minimised.


Drag x TAS = Power required. The value of this is minimum at Vmp. So the above quote suggests that best endurance speed for all types of aircraft is at Vmp. This is true(ish) for propeller aircraft, but not at all true for jets.

For minimum fuel flow (and hence maximum endurance) in a jet we need to minimise the product of drag x TSFC.

The drag will determine how much thrust we need and the TSFC will determine how much fuel we need to burn to produce each unit of that thrust.

[rajarehan]

"You would expect minimum fuel flow to occur with minimum drag but this is in fact NOT the case! The speed for minimum thrust/fuel flow occurs at a slower speed where there is greater drag - which strikes me as unusual.

I've been doing a lot of research on the web and in these forums and although I can find the confirmation that it is indeed true, I can not find a reason explaining why."

Well dear if i am right .. .The Endurance speed is slightly below the Vmd "BUT THIS IS FOR PISTON ENGINE AIRCRAFT" the reason is that in Jet the thrust line is straight but in propeller the power available is a curved line and that why at the Vmd of propeller the difference between power available and power required(Drag) is not maximum rather it is maximum just behind the Vmd and in case of Jet engines the difference between drag and thrust is maximum at Vmd...

i hope it clarifies the statement which you write.. that statement is TRUE but for piston engine aircraft

[Westnest]

Lower speeds meaning less parasites on the wing but more induced drag. That's why even in a low TSFC scenario with no counterwinds still meaning lower angle of attack. And Keith, for the high bypass turbofan engines, more RPM always doesn't mean more TSFC.

[Natstrackalpha]

Well, here`s my five acres:

Max Endurance is the maximum time you can get in the air. It is not for going anywhere - it is just to keep you airborne.

For example - if you want to hold, for a time or for a long time, you want the fuel to last for as long as possible so you burn just enough to stay airborne. Thats all that is required. It is effecient for minimum fuel over the longest (time) endurance.

Max Range of course, is completely different. Here you actually want to go a distance, at speed, as far as possible. Therefore you fly at the optimum speed where the aircraft flies at its most effecient speed to give you the maximum distance (range) given the weight and altitiude and temperature and least possible drag for the fuel required.

[Natstrackalpha]

That sounds odd, I thought with ram compression and everything a jet would perform better at higher speed due to ram compression effects though at the speed optimum for that, the wing's L/D ratio would have already started falling off.


Jane baby, where have you been, I dream about you constantly.

Well, yeh, (see my note) this is indeed true of cruising for range - but like I said you just want to keep the aircraft airborne - this does not mean max thrust at max angle at the back of the drag curve, that would be silly and you would use loads of fuel, very quickly and cause a lot of noise and overheating and a whole load of stuff not good for engines.

Nor, is the aircraft hanging by the thread of its teeth by the same token.

It is not a fast speed but fast enough to warrant good effeciency from the engines, albeit the entire profile is only effecient for letting the engines run and cool but nothing else, except to keep you effecintly airborne by burning the least amount of fuel over time, hence keeping you airborne over a longer time.

Invariably, but not always, you would probably be holding at the end of your trip. Therefore, you would be lighter than at the start of the trip, so this will work in your favour too. It is not effecient in distance . . . but it is effecient in burning the least amount of fuel possible, over time. Therefore maximising your time in the air. Just swan around slowly, around the hold at the max endurance speed, which is quite slow, until they have bulldozed the dead elephant off the landing runway.

[keith williams]

And Keith, for the high bypass turbofan engines, more RPM always doesn't mean
more TSFC.


You are quite correct, but I do not believe that I have ever said that increasing RPM alsays increases TSFC. If I did it was an error on my part.

At idle RPM most of the energy from the fuel is being used just to keep the engine running. Very little thrust is produced, so the TSFC is very high.

As RPM increases the fuel flow is increasing, but a greater proportion of the energy in the fuel is being used to produce thrust. So the TSFC gradually decreases as RPM increase. But this benefit continues only up to a certain RPM.

At very high RPM internal inefficiencies increase, thereby reducing the proportion of the fuel energy that is used to produce thrust.

The overall effect is that over the RPM range from idle to max RPM the TSFC starts high, gradually decreases until the optimum RPM is reached , then TSFC gradually increases again as RPM continues to increase above the optimum value.

But all of this is only part of the story, because other factors such as airspeed, air temperature and altitude all affect SFC. As I said in an earlier post, basic texts make a number of simplfying assumptions. In most cases these simplifying assumptions are not explicitly stated in the texts. So we should not be at all surprised when we find that real-life aircraft do not comply with the (over simplfied) conventional wisdom.

[HazelNuts39]

To illustrate Keith's #24:

http://i.imgur.com/I08Dybw.gif?1


Posted earlier - from Boeing 'Jet Transport Performance Methods':

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

[Westnest]

Whenever appraoching the subsonic speeds (>0.8 mach), at a great flight level(might be FL360 or more) you will face great amounts of parasite drags which is going to increase your Vmd, but still not SFC at horrible levels. But when at lower, for eg inital approach, there is going to be more TSFC because of drag both caused by intense air and less lift of slower speeds. In this instance, greater N1 might be required, which is going to cause also more fuel flow. But this is a aircraft specific subject. Of course, in a DG-1000 glider, we need no thrust either. All on lift and wing design.

[Natstrackalpha]

Would the optimum using those excellent graphs be: Mach 0.50
graph 1, and, M0.71 in graph number 2 . . ?

[HazelNuts39]

Natstrackalpha,

Supposing you are referring to my post -

RE graph 1: The Boeing source does not provide data below M=0.5. The lowest TSFC will probably be static (M=0).

RE graph 2: Yes