Effect of altitude on Fuel Burn

[photofly]

From another thread on FTU-isms:

There seems to be a lack of understanding in freshly-minted CPLs (and ahem, some instructors) of what higher altitudes do to your TAS and fuel burns, and how important it is to take advantage of that.

What should I understand about the effect of higher altitudes on my fuel burn figures?

[Beefitarian]

One thing is with increased altitude you lean out the mixture a bit and that should mean less fuel flow.

The first couple things I thought about reading that were. Shhhhh, don't tell them, they can clog up 3000 feet AGL. Next I thought, "Don't you check the upper winds to see what the best level is?" I've noticed a slight head wind at one height and a slight tail wind at another.

The last thing is I'm a bit like the Colonel's dad. I like to be as high as practical. I can glide further, I can have more time for cause checks, I can see more fields as options and it's easier to navigate. (I know use your GPS on the iphone/pad.)

[photofly]

Fuel burn is never the determining factor in a normally aspirated piston-powered aircraft.

Ignoring wind:

At a (sensible) fixed Indicated airspeed your MPG figure gets worse as altitude goes up, but you'll get there faster.

At a (sensible) fixed TAS, MPG gets better as you climb but you don't get there any faster, and you burn extra fuel and time in the climb.

Both of these factors are vastly outweighed by the effect of a headwind or tailwind.

If there's no wind to account for, then with your primary concern as MPG you will be flying at best range speed (at the bottom of the drag curve) as high as you can go - approximately at the absolute ceiling. For a Cessna 182 best range speed, at altitude, is an IAS of around 70 knots. At a service ceiling of 18,000 ft, that's around 100kts TAS. Without taking into account the fuel used in the climb. For most people that's unacceptably slow, and they'd rather fly lower, burn more fuel and get there faster.

[Chuck Ellsworth]

If there's no wind to account for, then with your primary concern as MPG you will be flying at best range speed (at the bottom of the drag curve) as high as you can go - approximately at the absolute ceiling. For a Cessna 182 best range speed, at altitude, is an IAS of around 70 knots. At a service ceiling of 18,000 ft, that's around 100kts TAS.

Forgive me for maybe seeming to be simplistic in my thinking, but would there not be other issues at play here besides just fuel burn.

For instance the cost of and the aggravation of needing supplemental oxygen not to mention the icing problems that that climbing to altitude, flying at that altitude and the descent from that altitude may entail in a Cessna 182?

[Colonel Sanders]

other issues at play here besides just fuel burn

Lots. For example, you can fly very slowly and not use
much fuel, but the trip is going to take longer. Perhaps
much longer. The savings in fuel may be less than the
increased cost in operating the aircraft the extra time.
Those hours on the engine and airframe aren't free.

This is all rocket science, though. In the real world, I'd
be happy if the guy in the left seat just pulled out the
red mixture knob for max airspeed. A small movement
of the mixture can result in a big difference in fuel burn.


I just posted this in the Aerobatics forum, it may be relevant:

What makes x/c MUCH easier in a Pitts (or any other
airplane, really) is a GPS and a fuel totalizer. With a
GPS you can stay perfectly on track, and you know
exactly how long it's going to take you. Combine that
with a fuel totalizer, and you know exactly how much
fuel you're going to have left over when you get there.

Pitts has a tiny fuel tank, so any x/c of reasonable length
is generally always fuel-critical. I'm amazed more people
don't run them out of gas, esp in the Bad Old Days when
we didn't have cheap GPS's, or cheap fuel totalizers.

That said, you can fly x/c in a Pitts. With a ferry tank in
the front seat, I recently flew Cozumel direct Key West,
which was 3 hrs and a bit. 9500 feet most of the way,
TAS around 140 knots. Sitting on a parachute gets painful
after a while, but you get used to it. Needless to say, I
had the GPS and the fuel totalizer humming away!

[Steve Pomroy]

At a (sensible) fixed Indicated airspeed your MPG figure gets worse as altitude goes up, but you'll get there faster.

That depends on what you mean by "sensible". Best range occurs at a fixed AOA, and therefore a fixed CAS. So ignoring the effect of the climb, your best range doesn't change with altitude. If you're operating at a speed off best range (is this "sensible" because best range is too slow?), you will indeed see worse specific range as altitude increases.

At a (sensible) fixed TAS, MPG gets better as you climb but you don't get there any faster, and you burn extra fuel and time in the climb.

This again depends on what you mean by "sensible". For example, starting at best range at sea level and then climbing, you'll see worse specific range at higher altitudes. But if by "sensible" you mean normal-cruise/faster-than-best-range, then you are right.

Both of these factors are vastly outweighed by the effect of a headwind or tailwind.

Definitely.

If there's no wind to account for, then with your primary concern as MPG you will be flying at best range speed (at the bottom of the drag curve) as high as you can go - approximately at the absolute ceiling.

Why as high as you can go? Assuming we're talking about piston/prop aircraft here, your best available specific range doesn't change with altitude. You're better off not wasting fuel climbing and flying at best range at the lowest safe/reasonable altitude available.

For a Cessna 182 best range speed, at altitude, is an IAS of around 70 knots. At a service ceiling of 18,000 ft, that's around 100kts TAS. Without taking into account the fuel used in the climb. For most people that's unacceptably slow, and they'd rather fly lower, burn more fuel and get there faster.

This is why we need the Carson speed. It is usually referred to as the least wasteful way of wasting gas:

http://www.eaa1000.av.org/technicl/perf ... rfspds.htm.
http://cafefoundation.org/v2/pdf_tech/M ... Carson.pdf.

With regard to max range and max endurance:

For prop aircraft:
- Specific endurance is better a lower altitudes.
- Specific range doesn't change with altitude, it is fixed.

For jet aircraft:
- Specific endurance doesn't change with altitude, it is fixed.
- Specific range is better at higher altitudes.

The difference is due to the fuel burn. In a piston engine, fuel burn is approximately proportional to power. In a jet engine, fuel burn is approximately proportional to thrust.

If you look at cruise performance charts in flight manuals you may see a variety of trends, depending on what exactly the manufacturer is trying to tell you. For example, if you look at the range profile in some flight manuals, you will see that range increases as altitude is gained. This is because the chart is based on a fixed %-horsepower, so as you climb, you get closer to your best range (i.e. - same power, higher TAS, lower CAS). Some other flight manuals show a curving profile, with range increasing as you climb through the lower altitudes, and then decreasing as you climb above some intermediate altitude. These charts are also based on a fixed %-horsepower in cruise, but also account for fuel and distance in the climb.

Cheers,
Steve
http://www.skywriters.aero
http://www.flightwriter.com

[Colonel Sanders]

In a piston engine, fuel burn is approximately proportional to power

People like to talk endlessly about how many angels
can dance on the head of a pin (about 10th order
consideration) but I find it odd that rarely do practical
subjects get discussed, such as:


With a constant speed prop, there is a wide range
of combinations of manifold pressure and RPM to
produce the same power. For any given engine
and airframe, how do you know what combination
is most efficient for climb, cruise and descent?

[photofly]

is this "sensible" because best range is too slow?
....
if by "sensible" you mean normal-cruise/faster-than-best-range, then you are right.

In both cases, that's exactly what I mean. Best range speed at sea level for a C182 is probably 65 KIAS. That's a silly speed to fly, under normal circumstances.

Why as high as you can go? Assuming we're talking about piston/prop aircraft here, your best available specific range doesn't change with altitude. You're better off not wasting fuel climbing and flying at best range at the lowest safe/reasonable altitude available.

Agreed. Not considering the fuel required to climb (I did say that) higher is better, though, because you get there faster at no extra cost (just to be ultra ultra ultra clear - not counting the fuel to climb.) Faster clearly has some advantage: were we not concerned with speed at all, we'd go by horse or by boat.

The Carson speed thing is interesting; it may be referred to as the least wasteful way of wasting gas, and some people may think it's optimum - but the people who think it's optimum are subscribing to a particular view of "optimum". If your idea of optimum is to get there as quick as possible, it's not optimum. If your idea of optimum is to get there on the least amount of fuel, it's not optimum either. "Optimum" is subjective, and depends on your mission. If your definition of optimum matches Carson's, only then is the Carson speed the optimum speed.

The difference is due to the fuel burn. In a piston engine, fuel burn is approximately proportional to power.

We thrashed that out in great depth in a 12-page thread a couple of months ago. I know that's often quoted, and it's a useful approximation from the point of view of drawing nice graphs, but it's an inaccurate approximation in real life mostly because of the prop efficiency curve. And a thousand times more so for a fixed pitch prop than a constant speed one.

[photofly]

With a constant speed prop, there is a wide range
of combinations of manifold pressure and RPM to
produce the same power. For any given engine
and airframe, how do you know what combination
is most efficient for climb, cruise and descent?

Von Mises goes through the theory; Mike Busch writes about it from a practical point of view here:
http://www.avweb.com/news/airman/184483-1.html

It's also discussed on pages 59 and 60 of the P&W Manual of Engine Operation that you posted a link to, here:
https://dl.dropbox.com/u/16541550/PWRadial.pdf

[Steve Pomroy]

In a piston engine, fuel burn is approximately proportional to power

People like to talk endlessly about how many angels can dance on the head of a pin (about 10th order consideration) but I find it odd that rarely do practical subjects get discussed ...

I'm not sure if I missed some subtle sarcasm here. Surely you're not suggesting that the relationship between power setting and fuel burn has no practical consequence??

With a constant speed prop, there is a wide range of combinations of manifold pressure and RPM to produce the same power. For any given engine and airframe, how do you know what combination is most efficient for climb, cruise and descent?

Unfortunately, I haven't found much written on this topic (from an aerodynamics standpoint, that is). Photofly has suggested the Von Mises book. I'm afraid I don't have that one in my collection. From what I can logic through on my own, it seems to me that the best RPM/MP combo would be the one that gives you the most efficient advance ratio on the prop, to maximize the thrust-to-torque (i.e. - the propeller's lift-to-drag) ratio. generally, the manufacturer's data is not adequate to determine this. And to be honest, I'm not sure how much of a difference it would make in practical terms.

From an engine longevity and passenger comfort standpoint, we might prefer a lower RPM (the longevity point being supported by one of Photofly's links), at least in cruise and descent.

"Optimum" is subjective, and depends on your mission. If your definition of optimum matches Carson's, only then is the Carson speed the optimum speed.

This is true of all optimization problems. If you haven't defined your objective, optimization has no validity. In the case of Carson's speed, the objective is to get the most speed per unit of fuel burn. IF this is your objective, then Carson's speed would be your best choice.

The difference is due to the fuel burn. In a piston engine, fuel burn is approximately proportional to power.

We thrashed that out in great depth in a 12-page thread a couple of months ago. I know that's often quoted, and it's a useful approximation from the point of view of drawing nice graphs, but it's an inaccurate approximation in real life mostly because of the prop efficiency curve. And a thousand times more so for a fixed pitch prop than a constant speed one.

Alas, I haven't seen that thread.

Of course prop efficiency is important. But when you set power using RPM or RPM/MP, you are setting brake horsepower. and so it has a direct influence on fuel flow. relating fuel flow to airspeed is less simple thanks to variations in prop efficiency. However, the general trend is still valid. In the normal (non-slow flight) speed range, fuel flow will increase approximately with the cube of the airspeed. The increase will be a little slower if the prop efficiency is increasing (likely over most of your cruise speed range if you have a cruise prop), and a little faster if the prop efficiency is falling (likely over most of your cruise speed range if you have a climb prop).

As far as nice graphs are concerned, I've sometimes wondered why the power curve isn't normalized to the thrust power available. This would eliminate (or at least reduce) the complications caused by varying prop efficiency. It would also make important phenomenon like slow flight more apparent. In real power curves (as opposed to the hypothetical ones we might sketch on a napkin or whiteboard) the slow flight range is miniscule, and the increase in power required before the stall is almost always very slight -- hardly worth mentioning. However, if you corrected for the rapidly dropping prop efficiency, slow flight then becomes more pronounced and representative of what we actually see in the aircraft.

Cheers,
Steve
http://www.skywriters.aero
http://www.flightwriter.com

[Colonel Sanders]

I'm not sure how much of a difference it would make in practical terms

Whole lotta theory here. Not much
practical experience, it might seem.

Ever hear of a guy called Charles Lindbergh?

In WWII (FDR hated his @ss) as a civilian,
he showed P-38 pilots in the Pacific theater
how to significantly increase their combat
radius. Do you know how he achieved that?

Back to modern day ... you can measurably
reduce your fuel burn in cruise by using high
MP and low RPM instead of high RPM and
low MP - producing the same power.

How much? What are the limits? For your
engine?

And what about descent? Should you use
high RPM or low RPM? Is the difference
noticeable? (Hint: it sure is).

Again, lots of theory here. Not much practical
knowledge (or interest) in what is significant
and as such I wonder about the appropriateness
for a flight training forum. I shudder to think what
a low-time pilot takes away from these threads.

[Chuck Ellsworth]

Oh for the good old days when we had BMEP instruments and C.B. 16 power.

[Colonel Sanders]

Uh huh. The message seems to be that if you don't
have a PhD in Engineering, you're just too stupid to
operate an aircraft.

Which is frikken hilarious.

Especially given that the most important factors are
ignored, and 2nd and 3rd order factors are discussed
endlessly. The irony is positively dripping.

I am constantly disappointed by people's inability to
prioritize as to what is important, and what is not
important.

[photofly]

Personally I'm not bothered about best efficiency at a fixed power setting, I'm interested in best efficiency at a given fuel flow (very similar but not quite identical: pop quiz - what are the differences?)

My humble experience in this field tells me that the practitioners win over the theoreticians in this case; slower rpm seems to be better: On a given day I might squeeze
- 120KIAS at 2300rpm and 22" m.p. and maybe
- 125KIAS at 2150rpm and 24" m.p. both at 9gph.

Engine smoothness is an issue too though; mine gets lumpier the slower it runs.

Unfortunately, I haven't found much written on this topic (from an aerodynamics standpoint, that is). Photofly has suggested the Von Mises book. I'm afraid I don't have that one in my collection.

He's interesting but not much help: he doesn't consider crankshaft losses or engine efficiency, only prop efficiency.

And to be honest, I'm not sure how much of a difference it would make in practical terms.

From an operating point of view I'm still with Mike Busch: as slow as you can go and still keep the engine tolerably smooth.

For climbs I ramp the RPM up (not necessarily to the limit) and for descents I just close the throttle halfway on my cruise settings; the fuel flow is so low that I'm not too bothered about efficiency. Is there something better I should be doing?

[Colonel Sanders]

for descents I just close the throttle halfway on my cruise settings; the fuel flow is so low that I'm not too bothered about efficiency

Fuel burn isn't the issue during the descent - drag is.
Because of this (again) you want minimum RPM. The
drag of a windmilling constant-speed prop is horrendous.

If you want lots of drag to keep the speed down in bad
turbulence, keep the prop RPM up, like most people do
all the time. If you want minimum drag in the descent,
get the RPM down.

120KIAS at 2300rpm and 22" m.p. and maybe
125KIAS at 2150rpm and 24" m.p. both at 9gph.

Using the rule of thumb that a knot of increased airspeed
will cost around a thousand dollars in STC'd modifications,
you just saved yourself $5,000 by using a better power
setting.

Go oversquare! The question is - for your engine (and
perhaps prop) what is allowed?

I am constantly disappointed that people don't know
this very basic stuff - e.g. for the Lycoming it is very
simple - when it gives such good returns.

slower rpm seems to be better

There's a really simple lesson for the low-time pilots
to take away.


More basic topics that are dealt with amazingly
badly:

1) how do you reduce power after takeoff?

2) how do you level off an airplane in cruise
after a climb?

Again, you would be amazed how badly people do
such simple tasks. This is what people need to
learn to do - in a Flight Training forum.


Another question - always performed improperly:

3) what do you do with the prop control after an
engine failure?

Hint: what do you do with a prop control in a
twin after an engine failure? Why?

I'm still with Mike Busch

A really smart guy. In addition to an undergrad in
math, he's a pilot, owns a twin, and is an A&P/IA
that runs a shop. His combination of theoretical
and practical knowledge is unusual, and leads him
to some really contrary conclusions, such that less
maintenance is better, and TBO is irrelevant.

[photofly]

1) how do you reduce power after takeoff?

I don't; but I don't have any takeoff power time limits.

3) what do you do with the prop control after an
engine failure?

Throttle wide open and prop full slow. Throttle open to minimize power lost against sucking air through the throttle plate, and prop slow because a windmilling prop wastes more energy the faster it turns.

After shutting the fuel off, that is.

Is that right?

[Colonel Sanders]

Throttle wide open and prop full slow.
After shutting the fuel off, that is.
Is that right?

Yes. I merely wish that I could someday be
privileged to observe someone actually do it.

I've never seen someone actually pull the
prop control back after an engine failure
in a single.

[Shiny Side Up]

such that less
maintenance is better, and TBO is irrelevant.

You read those article too I take it? As an aside they were very interesting and I'd tend to agree with his asessments.

[Colonel Sanders]

Mike Busch is a very smart, and very experienced A&P/IA.

[+RA]

So in layman's terms, a constant speed prop is sort of like a manual transmission; the setting that gives the lowest rpm is the most fuel efficient? Just curious as I've only been a passenger on a constant speed prop, never PIC.

[Chuck Ellsworth]

One of the last big radials I flew definitely was needed oversquare for take off, 56 inches of M.P and 2800 RPM.

[Colonel Sanders]

the setting that gives the lowest rpm is the most fuel efficient?

Yes!! Yes!! Yes!!

Someone actually learned something useful here!

[Beefitarian]

the setting that gives the lowest rpm is the most fuel efficient?

Yes!! Yes!! Yes!!

Someone actually learned something useful here!

At the risk of writing something painfull to read...

Does it depend a slight bit on properly leaning the mixture at the same time?

A hundred RPM higher properly leaned might require less fuel than the lowest possible RPM setting at full rich. No?

[Colonel Sanders]

Mixture setting is incredibly important - see other rants.

Set the RPM as low as you can, then
set MP, then
lean for max airspeed.

That's a really good place to start.

If you have multi-probe CHT and EGT you can instead
spend hours messing with LOP.

[Colonel Sanders]

You will probably think I am on crack, but ...

With careful choice of altitude, manifold pressure,
RPM and mixture leaning, you can probably save
(e.g.) 2 gph. That depends on how big your engine
is, of course.

Let's say your engine runs to a TBO of 2,000 hrs
before you overhaul it. That would be 4,000
gallons that you didn't burn. At $6/gallon that's
$24,000 that you saved over the life of the engine -
enough to pay for a frikken overhaul!

Food for thought for a friday evening, as you test
your body's tolerance for C2H5OH.