Determining the maximum endurance speed
 

Hello!
Just found your forums and I'm very impressed by tons of information you have here!

My question is: How to determine the best endurance speed using an experimental method?

For ex. I can find the maximum range speed by changing the power from cruise setting by 100 RPM and see what drop in speed I'll get. For ex, cruise is 2300 RPM, I set 2200 rpm and get a 5 kts speed drop, then I go to 2100 and so on. At 1900 RPM I get the drop more than 5 kts (approx 10). So I go back to 2000 RPM and lean the mixture. This is the best range speed.

These settings were used on Cessna 172, but I guess it works on all small airplanes

So, how to find the maximum endurance speed the same way?



Thank you very much!

Maxim

It sounds like you're on the right track,

If you plot the power required vs indicated airspeed on a graph, you will see a "bucket" shape, with the power required rising on both sides. On the slow side, as the power required increases (to fly more slowly), you are in the zone referred to as "behind the power curve".

The best endurance speed will be about where a line from the origin of the graph (0,0) intersects the line you have drawn. I did this exactly for my C150 many years ago, and found that 2100 RPM is the best endurance power setting, and 1900 RPM is the minimum power required to mantain level flight.

You will probably find the graphs midway down this Propeller Aircraft Performance and The Bootstrap Approach: Formulas and Graphs page informative.

There is lots of printed information on this subject, and I can recommend so reading if you like. I'm sure that you'll get many other answers from very well informed aviators here as well.

Welcome to PPRuNe, Pilot DAR

I have been doing some digging around this area and have come to the conclusion that while the traditional performance formulae (which can be found all over the internet) work well for a glider, they break down as soon as an engine is present! This is because engine and prop efficiency are not constant over power output.

I think the way to determine the best endurance speed is to set up the engine peak or lean of peak, and bring back the power until the plane just holds the altitude. But not so far as to allow it to fall onto the back of the curve.

Obviously the figure will vary with altitude, temperature, loading.

However, one may have a problem with engine cooling, so may have to run the engine rich, say 100F ROP, to get a cooler combustion.

Best-endurance speed might be handy for an extreme holding situation but is useless for normal flying - largely due to poor engine cooling. For my plane (TB20) the handbook gives a power setting which gives about 100-110kt - way more than Vbg for the airframe which is ~ 95kt.

Why do you believe this is best range speed? You don't seem to have taken fuel consumption into account at all.

To determine these values experimentally, you really need an accurate fuel flow meter, like a Shadin. Fortunately these tend to give a direct readout of both endurance (max endurance is just min fuel flow anyway) and ground miles per gallon. Note that the speed for best ground miles per gallon will vary slightly with wind, so you'll need to find a still air day or at least, for an approximation, turn crosswind.

There is another factor which is overlooked. Wind speed and direction.
Ie flying from A to B with a tailwind try flying a groundspeed.

Reduce power to maintain a planned groundspeed with a tailwaind and increase power as the winds change with direction change to try and maintain the same planned grounspeed.

Pace

The best RANGE speed is simply the power setting which gives you the best MPG displayed on a GPS which is linked to a fuel flowmeter.

Wind will affect the absolute value but you are only looking for a peak in the data.

The power setting will certainly be peak EGT or slightly LOP.

It will depend on weight, loading (and CofG fore/aft), and altitude, and temperature.

I've done extensive tests on this on the TB20.

A lower rpm (2200) is about 10% better than 2400.

Peak EGT is 10% better than 100F ROP and about 20-30% better than flying full rich. Going 25F LOP is only 1% better than peak EGT - within measurement noise really.

Weight seems to make no measurable difference - most likely because there is no way to increase weight without loading the back seats, which moves the CofG aft which reduces the elevator AoA which reduces the elevator drag.... just enough to compensate. I always load any junk in the boot rather than the back seat.

Altitude seems to make no measurable difference - beyond FL100. This suprised me. This has some theoretical support, but I don't understand it. Once wide open throttle (~FL100 say) any additional climb reduces the engine power, which makes the friction and pumping losses greater as a %, but you get a gain due to thinner air. You also get a gain due to reduced exhaust back pressure.

Temperature? Not sure which way this works. But if you leave the plane out, with full tanks, in -10C, and top off the tanks before flight, you are carrying 4% more fuel mass (i.e. energy) than if you depart with the fuel tanks heat-soaked to +30C :) But your turbine fuel flowmeter measures volume, not mass...

Got to make sure the plane flies straight i.e. ball in the middle, wings level, ailerons equal (so if solo, run down the LH tank by the appropriate amount). I know of pilots who say that if you have a quartering tailwind you need to use the rudder to fly straight :) :) :) :) :) :)

Interesting, the engine performance curves for my IO-550 (different engine, but the same theory!) show significantly better economy at 25F LOP compared to peak.

One thought: in making those measurements at peak EGT and 25F LOP, IO540, were you using the richest cylinder or the leanest? If you have GAMIjectors (sorry, I can't remember if you have), the spread between the two may only be 0.5 USG/Hr. If you don't, spreads are commonly in the 1.2 to 1.8 USG/Hr, and the 'average cylinder' is actually running quite LOP when set up for peak EGT of the richest.

Islander - Are you sure ?

I don't have a good copy of the performance curves, but looking at a graph of some test stand data on an IO-550, BSFC seems to vary only 2-3% from Peak to 100 LOP with Gamis

I've always remembered/used the following:

Vx = lowest drag = best angle of climb at full power = best endurance at low power = lowest sink at no power
Vy = best L/D ratio = best rate of climb at full power = best range at low power = best glide at no power

This isn't entirely accurate because of prop/engine not being as efficient at low power/low speeds (therefore the "official" Vx and Vy speeds are slightly higher than the numbers you would get if you would only take the airframe into account), and it also does not incorporate wind drift. But as an approximation it works quite well.

Of course, if you plan a maximum endurance flight, or a maximum range flight, the numbers in the POH should be used instead. Or determine the numbers for your specific aircraft using the methods described earlier in this thread.

I've got GAMIs, and yes there may be something in this, but equally I found that going much deeper LOP (say 100F LOP) there is no measurable difference, and the power loss is pretty significant.

I believe the theory more or less supports this, since power can come only from burning fuel, and once you are stochiometric (peak EGT) or just past, the only additional gains can come only from reducing the pumping losses, and if you are already WOT and at low RPM then there is nothing left to play with.

What I didn't make very clear in my post is that all this is with WOT (wide open throttle) which is not feasible at low levels, say 3000ft, because the engine power is too high. I have tried flying with WOT at say 3000ft but leaning deeply LOP, to achieve say 65% power, but the engine sounds pretty unhappy, so I don't bother. At low levels I fly 23", 2400rpm, 11GPH which is marginally LOP, and everything works nicely. Except that I am getting a good 10% less MPG than I would be getting at FL100, WOT, 2200rpm, 9GPH (also marginally LOP).

The problem is that the POH was written in 1780, by Isaac Newton, before modern engine instrumentation revealed what can be done if the engine is set up accurately. So e.g. my TB20 POH says "best economy" at a certain %power and TAS is at 12GPH when in fact it is at c. 11.1GPH - a difference of about 9% and that ups the range from the POH value of c. 1150nm (from memory) to 1300nm which is what I actually get computed by the Shadin/GPS system on a real flight.

I really do not think that in all the years that these engines have been around, say 40 years for the old Lycos, nobody really paid much attention to these details. The instrumentation was not around. Only GPS made really accurate TAS measurement really easy, and more to the point only a flowmeter-GPS coupling delivers a constantly recomputed range / fuel at destination figure, without which you would not be confidently doing long trips, and if not doing long trips then you wouldn't bother optimising things in the first place and you would be flying just like most people do: stop when you need a leak :)

I suspect some of the old pioneers (Lindberg?) did suss this out, and used it as far as they could. Then, certified GA with its certified flight manuals covered in certified rubber stamps, took a step back in time, discarding this knowledge.

10540

Leaning is never a way to true economy. Concentrating solely on engine management rather than trip management is looking at an isolated point rather than the whole picture.

In pure engine management overleaning will reduce the life of the engine and hence make a mockery of the bits of fuel saved.

Correct and conservative leaning for a given power setting is important but greater savings overall are made by trip management.

Trip management for me is selecting the best levels to fly at considering winds TAS etc.

Aircraft vary but the principals are the same. There is a whole lot more to look at than purely engine management.

Take a ferry in a jet. We are required not only to fly for range but to save the ferry company money.

That will mean firstly flying high, getting up high as quickly as possible as with jet engines the fuel flows drop considerably as the aircraft climbs into the high 30s.

Weight and climb rate to cruise ie how long you are at max power in the climb to get to your desired level.

Can you get to your desired level? step climbs, carrying less fuel on shorter trips etc. They all come into the equation.

Then flying a fuel flow and accepting the N1 that produces. Obviously the more you reduce the more the speed reduces until you get into a negative situation.

Then we bring in the winds. Tailwinds and we can reduce to maintain a groundspeed. Headwinds and its a compromise between higher thrust settings and reasonable fuel flows.

Remember we loose more flying a headwind on recipricol legs than you would gain with the tailwind.

Question is it better to fly lower levels with lower headwinds and higher fuel burns or accept higher headwinds with lower fuel burns?

Descent in a jet it is better to stay high for as long as possible and then to fly fuel flows in the descent.

While I appreciate that jets and pistons are very different animals the principals of fuel management being more important to trip management are clear and while not all the principals are relevant many are.

I know a Seneca five owner who has had to renew his engines early because of overleaning to save a few litres of fuel. There are far bigger savings by concentrating more on trip management especially regarding winds, weight, levels, climbing, descending, power and speed management etc.

Pace

No it won't. Google on John Deakin, avweb.com etc, for some background reading.
Yes but that is a separate issue.

If you have a headwind, you fly somewhat faster than still-air Vbr.
If you have a tailwind, you fly somewhat slower than still-wind Vbr.

Jets and pistons are different; jet performance is much more heavily affected by altitude, and because they need to fly so much higher (to get any meaningful economy) the winds aloft become much more important because you can easily hit a 150kt wind.

In a piston plane, one can optimise cruise altitude for the forecast or actual wind aloft, and I do that too sometimes, but since the context is usually airway/IFR flight, one tends to not have a great deal of vertical leeway. One cannot fly below the MSA, one will find it hard to get an ATC service below the airway MEA (except in an emergency e.g. icing), one doesn't want to fly in IMC (icing, comfort) so VMC on top is the way to go, and one's operating ceiling is probably only a few thousand feet above all this. Then, if nonpressurised, one has oxygen to think about, and since getting a refill is nearly impossible in Europe, and if you get one at an airport "bizjet FBO" it might cost you £100, one isn't likely going to cruise at FL190 with everybody pulling hard on the cannulas, to pick up another say 20kt of tailwind, only to use up all the o2, have to hunt around for a refill, etc.

Anyway, of course you are right but nonpressurised piston pilots tend to not be so sharply driven to do a given vertical profile, whereas in a jet it is vital - I doubt if a 747 would even make it across the Atlantic at 2000ft :)

He needs seriously educating :) He probably also needs to spend some do$h on engine instruments...

Pace,

Applying jet concepts to piston engines is risky. there are a number of quite differnent aspects to the performance of the powerplant.

For example,

high in jets is good for speed, range, specific fuel consumption, etc

High in piston props doesn't really help range but does get you there faster.

The other thing is that if you take the winds aloft forecasts, say FL120 v FL160, the error might be as much as the actual difference, whereas the jet stream is probably forecast pretty well.

Generally, with a tailwind, I will go higher especially if o2 is not an issue. One can quickly see (on the GPS) how the constantly recomputed ETA shapes up, so one can stop climb when there is nothing else to squeeze out.

In a steady frontal weather one can expect more wind higher up, but if flying in a large-scale high pressure zone, the wind could easily be all over the place, varying -20kt to +20kt seemingly randomly, several times during just one flight.

Ok I own up :) I used this to drag the conversation into trip management rather than purely looking at the powerplant.

I realise that jets are as different as chalk and cheese :) 10540 continues to amaze me with his depth of technical knowledge and I always read his contributions with interest.

Engine management is only part of the picture. While the level margins to play with are much smaller in a piston the principals are the same ie if climbing to cruise at FL120 do you fill with fuel and pax to max grosse weight to go 250 nm? Do you accept a much longer full power climb to get there and the much higher fuel burns?

Winds are much lower low level but can still be high. I can remember flying UK to Alicante in a Seneca at FL120. I held a GS of 100 kts with a headwind of 70 kts all the way to northern Spain having to make an extra landing at La Rochelle for fuel. Maybe I would have been better going all the way with the 30 kts headwind at 3000 feet?

Descent how do you descend in a piston twin? a managed descent can make a big difference to fuel burn etc.

So as stated its not all about leaning for the last litre. The principals of jets although very different beasts to pistons can be carried over. Trip planning and execution can make a much bigger difference than purely playing with individual cylinder readouts on engine mangement units you can buy.

Flying both jets and piston twins I find I can use a lot of the techniques for trip management in the lower flying, different powerplant twins.

10540 dont believe that :)

Pace

Sorry, Pace, but that demonstrates a real lack of understanding ... and is the sort of dribble that's been put about by the instructing community for years. Overleaned from what? Certainly not overleaned from EGT!

Islander

Its not my plane so have not got a clue what his leaning techniques were.

I am only reporting what he advised me that his maintenance unit gave for the early rebuilds. Damage due to overleaning.

Pace

If the jetstream is not well forecast then somebody could make a bundle by buying and re-selling pireps :)

It's not as if there was a lack of traffic up there :)

Surely the airlines must have this to a fine art by now??

Well, from eye-balling the graphs I thought I was sure that's what Continental's curves say. But now I've marked, measured and done the maths, turns out you're right. :uhoh:

I'm looking at their Operation Manual for IO-550A, B, C dated October 1983 (Form No X30565) ... regrettably, Continental have chosen not to include this useful data in later editions of the manual!

The BSFC graph at 2300RPM/20.5"Hg shows 0.4165 lbs of fuel per BHP-Hr at peak EGT versus a best of 0.4085 at 35F LOP and 0.4095 at 25F LOP. That's approx 2% improvement at 35F LOP and 1.5% at 25F LOP.

Nope, that merely demonstrates the mechanic has a similar lack of understanding.

Overheating, quite likely ... but not overleaning, whatever that means (again,overlean from what?). If so, it could quite possibly be the result of being neither lean enough nor rich enough. (But there again it could also be a host of other things operational or mechanical).

10540

Often the upperwinds including the Jetstreams dont turn out as expected

Pace

I observe that the original question was asked in the context of endurance, not range. As I recall, endurance is not at all affected by winds. Range is. Endurance is simply what is the greatest length of time the aircraft can remain airborne, going somewhere is not a part of that, so winds are not either.

Though leaning and fuel flow will factor into the endurance time, it is the airspeed which must be determined first, as it is a greater factor. You can lean at any airspeed, and leaning will increase your endurance, but not as much as the wrong airspeed will reduce it!

I'm sure that the protracted discussion about winds and leaning is important, and informative, but is it relevent to the original question?

But then, on the other hand, I've certainly been guilty of thread drift too!

Pilot DAR

Fair comment about winds.

But since maximum endurance is obtained at the lowest fuel flow to sustain level flight, I'm truly at a loss to understand how you could argue that a discussion about mixture management to achieve lowest BSFC amounts to thread drift. :confused:

I thought it had been answered - but a quick flick through shows - No we have answered many other questions but not the one asked !

I think the answer is

1 - An airspeed very close to Vx (max excess power so we have the maximum possible reduction in power available - however Vx is determined at full power and the thrust vs IAS curve may be slightly different at lower power settings)

2 - Best possible efficiency of the engine/propeller
a - Leaned to 25 degrees or so LOP (Best BSFC)
b - Turning the prop as slow as allowable (Reduced pumping losses and I believe slightly improved propeller efficiency)

3 - MP set to the minimum value consistent with level flight

You will have a helluva job flying around at anywhere near Vx without the engine getting too hot, due to poor airflow.

Pilot Dar

Hence I tried to kick the subject into something more practical as unless you are flying for some record or doing police surveillance work its pretty pointless :)

Pace

I don't agree. I tend to trim towards my maximum endurance speed when I'm up for a local bimble with no real goal in mind - it means I can get the cheapest flying for my hour between work and sunset when I'm not trying to go anywhere. Equally maximum range is useful for going somewhere cheaply/without refuelling. Obviously you don't go all the way if it results in the engine overheating or other damage, but if you don't know the figures how do even go part of the way there?

I'm sure there are also situations you could find yourself in where it's useful to know how to acheive maximum endurance. All I can think of at the moment are stuck above solid IMC (without IR/instruments) which is expected to clear, and lost at night - neither particularly likely, or situations I intend to put myself in, but that doesn't mean I don't want to know the figures just in case.

Hollo echos my thoughts.

On a nice evening, I take the door off (to be at one with the world) and tour around at a speed more a kin to endurance than range or race. I have had a (fortunately few) occasions, where staying up and orbiting was preferrable to landing right away. Waiting for the clearing of an obstructed runway, and float plane landing area come to mind. On some occasions, where I have a very large tailwind at high altitude, flight at endurance speed is the most efficient, as it becomes about the same speed as flight for best range.

I also participate in public service searches, where flight for endurance is the most appropriate. I have had to interrupt my search to go for fuel, and that's a little embarrassing!

A few additional comments:

Some engine installations are better than others in cooling, but I would expect all engine installations to cool adequately indefinately, during flight at endurance speed. This characteristic would be covered during the climb cooling test at the time of certification for the aircraft. The climb speed would be best rate, which would be very close to the speed for endurance, and the climb at full power and leaned (if appropriate). Presuming design compliance has been shown in this phase of flight, flying at the same speed in level flight with the power pulled well back should have no difficulty cooling.

Turning the prop slowly has merit, but not "over square" unless the engine/propeller design specifically approves this type of operation. Over square operation will rapidly intrduce the risk of detonation, increasing with increased power. Further, it will increase propeller blade strain. We don't think of that very often, but I have been reminded by observations and resulting limitations on a test propeller imposed by the propeller manufacturer, for an aircraft we are flight testing right now (engine change STC). The engine involved (a well know brand in the 200 HP range) is limited with other propellers, so as to have "avoid operation" speed ranges. It looks like this engine/propeller into airframe installation in this case may be similarly limited. Time and testing will tell. We are presently considering the climb cooling performance of this installation.

The mixture setting of an engine will have nearly nothing to do with the speed at which the plane will fly. As the original question was asked about speed, as opposed to fuel flow, I suggest that mixture settings would not be an element of the answer. Mixture is a distinct subject, which will forever be the basis for many discussions. Fiddle with mixture as you will. In a carburetted engine (any older 172) you will never achieve the ideal mixture into all cylinders. There will probably be a power setting at which you come close, but this is not published, varies considerably engine to engine, and can only be determined with careful experimentation with a scanner. For my 150, the preferred RPM for equal EGT for the four cylinders is 2450, If I run more or less power, I'll be leaning only to the leanest cylinder (which changes), and thus wasting gas. Thus, If I fly at the speed for best endurance, two of the cylinders are running un-necessarily rich, and wasting gas. I'm just betting that the amount conserved by the overall reduced power, is better than the amount wasted by the uneven fuel flow. Truth is, I really don't care that much! Fuel injected are a vast improvement over this situation, though still not perfect. Fuel injected dilikes Mogas, and my engine and I like Mogas! In the past, we have converted injected engines to carburettors so we can run Mogas, but I thread drift......

Pilot DAR

Is that necessarily the case if you're actually droning along level at Vx with the engine doing relatively little work? (vs the more normal case of Vx plus engine at flat chat...)

It is important to know the limitations applicable, however, 'not over square' is not that useful a concept. Think takeoff in fixed pitch aircraft (a MP - if you had the gauge- of 29in and 2550 rpm) and almost all operations in turbocharged aircraft.

I have never understood why it is ok to run oversquare at full power for the whole climb (maximum power, maximum heat, low cooling airflow). but if in cruise flight you choose 25 in and 2100 rpm this is a problem.

You are of course correct the mixture has nothing to do with speed, However, the mixture setting you choose will have a considerable impact on the amount of time you can stay in the air (or the cost /hr), which is the whole point of flying at this speed.

Hollo

I dont disagree with why you may want max endurance so am not trying to discredit it. Normally pilots will need to stay up because they have had stronger headwinds than planned to get to their destination. Maximum endurance will not help you there.

Someone stuck above cloud in a pure VFR aircraft would be ill advised to sit there waiting for the clouds to hopefully disappear.

If my flying involved going nowhere and staying up for as long as possible for as little money as possible I would probably buy a motorglider and only use the engine when I needed to.

Practically saving fuel and thus increasing range has more to do with trip management than engine fuel burn management that was all I was trying to say and that involves so many other vital factors other than how you lean the engine.

Pace

mm_flynn, to use the question you posed me - are you sure?

For that to be true, there would need to be no significant variation in power across the attainable mixture range ... which just isn't the case, especially for those engines capable of operating significantly LOP.

Ahah - I left out an important phrase it should be 'Mixture has nothing to do with best endurance speed.

The reason I (and probably you and IO) keep banging on about it, is that mixture is hugely important in getting the most HP out of a KG of fuel. In this context I need to beg to differ with Pace - in piston aircraft mixture can move specific fuel consumption 30% or more. This is by far the most significant factor unless winds are exceptionally strong (when as in the case posted by Pace he would have been much better off down low - with regard to range), or you are going to really drone along for hours near Vbr (which is very slow)

mm flynn

Could not agree more. Part of the problem is IMO full use of the mixture control is rarely tought during ab initio training (or often even in advanced training):( The mixture control on most training aircraft spends 99% of its time set at either full rich or ICO. And frankly at early stages of training this is a "good enough practice" which allows the instructor to concentrate on teaching more fundamental flying skills/knowledge. However by the time a pilot has obtained his/her PPL it is time to develop a more sophisticated understanding of engine management which includes not only use of the mixture control but also

-engine warm up procedures
-proper runups
-managing CHT's (the No 1 requirement for long engine life IMO)
-selection of cruise power settings
-understanding what the engine guages are really telling you
-recording usefull engine behavior notes for maintainance trouble shooting

Unfortunately there is no "one perfect way" to operate an airplane piston engine, but there sure is a lot of opinions :8 All POH's provide some guidance but most are pretty useless when it comes to the finer points of engine operation. However there is a wealth of good info on the web starting with the engine makers sites. This forum and Avweb also have a lot of good info. Talking to engineers is also very valuable as most have had to deal with the results of poor pilot practices. A bit of research will give pilots lots to think about and allow folks to move from a "cookbook" approach to a real understanding of what is going on under the cowling.:ok:

Hi there,

this is an interesting conversation for a change, but I note that the original question has gone completely unanswered:

(my emphasis)

Ok, so we all know that best endurance speed is Vmd (minimum drag) and this has already been pointed out.

So now the question can be rephrased as: "How does one find Vmd, experimentally, for a particular airframe?" I believe that question had been answered some time ago over at Tech Log or Flight Testing. Those are undoubtedly the best places to ask.

Lastly, I note that the question only asked about the value for best endurance speed so, for all its practical interest, by and large the power settings (mixture and prop pitch) are not relevant as far as this question goes. Best endurance will always be obtained at the same EAS. The amount of endurance you will get out of the aircraft will of course vary significantly depending on the power settings being used but that is not a consideration here, do we agree?

I thought I answered it in post #4. Without an accurate readout of fuel flow, it's very hard to do. With an accurate readout of fuel flow, it's a fairly easy experiment, isn't it?

No, it's not. Best endurance comes at minimum power required, which will typically be less than minimum drag by quite a margin. At Vmd, there will be less drag, but more power required and therefore more fuel burned staying up.

bookworm,

Doh, of course you are right, as usual :O Sorry, I meant Vmp (minimum power) everywhere in my previous.

Yes you did, it was so far at the beginning of the thread that I completely missed. I agree that it's a simple experiment with appropriate equipment--I was again thinking about finding Vmd.

Right, now better go and get some more coffee. Apologies for the misinformation :ugh:

Is this of value?
13.4 Aircraft Endurance

I looked into this (not the above link; Internet hadn't been invented) many years ago when I was considering an affordable means of keeping flying; such as build your own aeroplane. I’d been recently inspired by the, then, new BD5. There was a much simpler formula that related the coefficient of lift/coefficient of drag ratios at different speeds for a particular wing section but I’m damned if I know which box (of many) I placed the papers in. Cl squared over Cd cubed Max rings a bell. I never got as far as worrying about power and fuel burn curves.

That's a more interesting and challenging experiment, even with a GPS-linked Shadin!