Efficient altitude, reciprocating engines?

[Mark1234]

OK, I could (and probably should) spend a bunch of time with a POH, to figure this out, but can anyone explain in understandable terms how the tradeoff between height, speed, and fuel burn works for light a/c, normally aspirated engines?

e.g. is there a specific alt for best speed and/or economy, high as you can? presumably at some point the lack of aerodynamic efficiency starts to hurt?

Thanks.

[411A]

normally aspirated engines?

e.g. is there a specific alt for best speed and/or economy, high as you can?

Normally...between eight and twelve thousand feet, lower end for speed, higher end for economy.

[Tinstaafl]

A number of factors are involved, along with some background to set the picture.

In level flight the aircraft has a certain weight acting towards the centre of the Earth which must be countered by an equal but opposite force called Lift. Lift is produced by moving an aerofoil through the atmosphere which causes the air to be deflected downwards resulting in an opposite reaction.

The reaction can be divided into two components: Lift, acting opposite to Weight, and Drag, acting opposite to the direction of flight. Nothing is free and Drag is the cost of producing Lift caused directly by the Lift production and also just the act of shoving the airframe through the air.

In order to maintain the forward motion producing Lift then a force (Thrust) acting equal to and opposite to Drag must be provided. Hence the need for some sort of engine shoving air backwards to produce the desired opposite reaction forward. That requires fuel.

As it happens, Drag is at a maximum at low speed, reduces to some minimum as speed increases, then rises again until there is no more Thrust available to make the aircraft go faster. So, there is a speed where Drag is at a minimum for the Lift being produced, thus requiring the least amount of Thrust from the engine, and, for piston power, that is the speed that will result in maximum range ie the equivalent of best miles per gallon in a car.

Of course one would also need to ensure that anything that unnecessarily increase drag are kept in in their lowest drag configuration eg gear up, flap up, minimum weight (more W = more L needed = more Drag = more thrust required = more fuel burnt).

A normally aspirated piston engine is most efficient - thus will be able to produce its maximum power) with minimal obstruction interfering with the airflow through the engine. A throttle reduces the power the engine produces by restricting the airflow through the engine. It really does throttle the engine, no different to someone with their hands around your neck. Also its fuel flow is approximately proportional to the power produced.

A normally aspirated engine produces more power when the air is dense. Less dense air means fewer oxygen molecules to match to the fuel. The atmosphere becomes less dense with increasing altitude so normally aspirated engine experiences a reduction in max power available as the altitude increases. At low altitude it produces more power than is needed to produce the Thrust required to counter Drag produced at the speed flown and must be throttled. That has an adverse effect on efficiency.

To maintain power as altitude is gained the throttle must be progressively opened. At some point the throttle will be fully open and the engine will be at its most efficient.

So, the upshot is that the airframe must be flown at the airspeed that produces the least amount of drag and at an altitude high enough that the throttle must be wide open to produce the power needed to maintain that airspeed.

NB: I've ignored leaning and centre of gravity considerations

[sprocket check]

....and isn't this what we call Full Throttle Height?

and it shouldn't be too hard to find in the manual in the performance tables.

My understanding is - for a given power setting and engine RPM there is an altitude at which the engine will perform at max efficiency on full throttle, ie max volumetric efficiency.

The Lycoming Flyer (http://www.lycoming.com/support/tips-advice/key-reprints/pdfs/Key%20Operations.pdf) is useful for all this.

sc

[waren9]

So, there is a speed where Drag is at a minimum for the Lift being produced, thus requiring the least amount of Thrust from the engine, and, for piston power, that is the speed that will result in maximum range


Dont think so.

Minimum drag is normally associated with minimum power required, and therefore best endurance.

Best range on the other hand, is found at the TAS where a line from the origin of the (Horespower Req'd/TAS) graph meets the Horsepower Req'd curve as a tangent to that curve, and therefore gives the best ratio of TAS versus HP req'd (and therefore miles per fuel burnt)

It is normally faster than best endurance speed.


....and isn't this what we call Full Throttle Height?



correct.

[IO540]

I have been looking into this and I don't think there is a clear cut answer - because engine efficiency is not constant over power, and neither is prop efficiency so even if you had a constant power you would not have a constant thrust.

If the thrust was truly constant, the answer would probably be that the MPG (or range if you like) is independent of altitude - so long as the flight is done at Vbg at all times.

[bookworm]

e.g. is there a specific alt for best speed and/or economy, high as you can? presumably at some point the lack of aerodynamic efficiency starts to hurt?

Depends on what your other constraints are for "economy". Are you prepared to fly as slowly as necessary to achieve the economy? Do you want to fly at a particular power? A particular IAS? A particular TAS?

For speed, the answer is still "it depends" but is easier to express. Speed at maximum power is generally highest at sea level, but at a particular power TAS is highest at the highest altitude at which the power can be achieved.

[Deltabravowhiskey]

Work it out in "total" cost per operating airborne minute...On the ground the costs are generally much lower and fuel burn is often your only real concern (aside from what you charge back to the customer ie padding the margins). That would translate well to help determine your most efficient altitude. "Total" would have to include, Speed (TAS), Groundspeed (GS), Fuel burn, Cost per unit of fuel, Pilot/crew costs, MX cost per operating hour, A/C cost per hour (Payment or rental rate etc).

Using a website like: www.fltplan.com (http://www.fltplan.com) you can calculate your optimal altitude in respect to time and a specific TAS.

You can build a fairly basic spreadsheet that can shift the TAS required to always allow you to flight plan for an optimum speed/cost based on a planned GS for your next segment, in other words taking head wind and tail wind components into account. You could also call all this a "Cost Index" that is used to adjust your performance of the aircraft.

Of course you would need to take into account the long term effects of operating at higher or lower power output and how it relates to the overall reliability(safety) and cost when it comes to overhaul.

DBW

[411A]

Of course you would need to take into account the long term effects of operating at higher or lower power output and how it relates to the overall reliability(safety) and cost when it comes to overhaul.



This was done many years ago with the big round engines found on 4-engine piston airliners.
Altho all these were supercharged, the same applies to others.
Takeoff, max power....every time. Usually wet (ADI) BHP.
Climb at a designated climb BHP/BMEP....usually about 70% BHP.
Cruise...at 45% BHP.
(Approximate numbers, for discussion)

In this way, fuel consumption (taking into consideration the resultant TAS achieved) was optimal, and overhaul time was extended.

How extended?
The best achieved was UAL, and the DC-6B (P&W R2800CB16 engines), 3300 hours.

[airfoilmod]

How would you correlate big round to horiz. opposed? Light twin or hp single? Mostly flown by rpm, not bhp. There is little to recommend lean and mean in a small a/c, engines are too expensive, fuel not so much.

AF

[maxred]

All be it Beech Bonanza related, but a full chapter in John Eckelbars book, 'Flying The Beech Bonanza' is related to this very topic. A lot of trade offs with multiple factors affect the decision. He reckoned 4000' with the fuel injected IO-470-N was optimum. You also have to consider what it is you desire, economy/speed/weather/IFR-VFR etc.

[airfoilmod]

Had occasion to use the O-470-R commercially, Cessna "freighter" flying fish around Norcal. 13gph was fine with me and I operated 4000-9500.
I never understood the pilot who kept voluminous records in an effort to squeeze out a pint or two less. Trying to compete as a bugsmasher with the parameters of flight of the pro is silly.

AF

[maxred]

Yes, I tend to agree. The savings are not much, a lot of time spent with best lean??:rolleyes: Also wind variations at all levels, both in speed and direction, can leave you wasting more time and energy trying to find 'optimum'. I plan my level, cruise at 65%, and may, if ATC allows, change level if wind etc not playing ball. Seems to work and generally return 11.5gph in the Beech. Works for me.

[airfoilmod]

<100nm, lots of taxi, ATC never cost me a dime, winds were interesting @ TO and LDG. only. Mission driven profile in the extreme. With a lot of twitching fish in the "hold", single pilot, and customers waiting, gph I calculated after flying, not trying to bird dog it aloft.

AF

[sprocket check]

There is little to recommend lean and mean in a small a/c, engines are too expensive, fuel not so much.

The Lycoming guides are really useful for this and should be read by all who operate aircraft engines. There is a section on leaning and recommendation of procedures as well as the reasons to do so. One is extended engine life.

Just looking at the thread subject though, if you take the performance table for the aircraft you are flying, copy it into a spreadsheet and add another column that calculates miles/gallon at given performance setting/altitude then you can clearly see the trade-offs for the various engine settings. Plot the range, endurance, TAS, mpg in a graph and voila. This has to be done for each aircraft type, there is no formula as such.

sc

[bookworm]

There is little to recommend lean and mean in a small a/c, engines are too expensive, fuel not so much.

Yesterday I paid about $11/gal for gas in Germany. At that price, saving 2 gal per hour pays for a new engine in half its TBO.

[airfoilmod]

2gph will fry your engine in 10% of its TBO

[Tinstaafl]

Waren9,

You're confusing power with thrust curves in a *piston*. In a piston engine fuel flow is approx. proportional to power unlike a jet where FF is approx. proportional to thrust so endurance matches the lowest drag point & range the drag tangent

For a piston engine aircraft max. endurance occurs at minimum *power* required. Best range occurs at the tangent to the power curve, which also correlates to Min. Drag, best L/D ratio and best range glide speed/Vg

[waren9]

Fair enough mate.:ouch:

You are quite right.

For those still confused I refer you also to "Mechanics of Flight" by AC Kermode (10th Edition) and the graphs on pages 180,183 and 232.

[Mark1234]

Great response, thanks, caused a number of pennies to drop.

To elaborate some, I'm starting to make some longer trips (rather than the $100 hamburger runs), and aiming to plan better alts. Now, I'm paying for the plane by the hour, wet.. so my main aim is to fly faster - but on the other hand, I'm also a bit load limited, so burning a bit more efficiently helps - both to have more margin from what I'm carrying, and to potentially carry a bit less.

Would I be right in thinking that the drag side relates to IAS, rather than TAS - so hypothetically flying high where the IAS is significantly lower for a given TAS moves us into the more advantageous part of the drag curve - at the tradeoff that the engine/prop efficiency reduces?

Cheers,
Mark.

[Tinstaafl]

If you're paying for it wet then you've already paid for the fuel in the hourly rate. In which case you're best served by going like the clappers to get there & back as quickly as you can.

Fly at the Full Throttle Height (ahem....altitude) for max continuous power in nil wind. If wind then work out the difference in TAS gained or lost by climbing or descending vs. the beneficial effect of more tailwind or less headwind.

If paying for it dry ie you buy all the fuel, then you need to compare the fuel consumption at different power settings vs the flight time to see how fuel consumption costs changes wrt to the cost for the aircraft using the same speeds.

[bookworm]

If you're paying for it wet then you've already paid for the fuel in the hourly rate. In which case you're best served by going like the clappers to get there & back as quickly as you can.

Ah yes. Cost index 9999.

Economy cruise power < Performance cruise power < Maximum cruise power < Maximum rental power

:)

[airfoilmod]

Irresponsible, and why FBO's always rent wet. If renters paid for fuel, with a lower overall rate for the a/c, some dolts would fly with pistons pinging, enjoying their extended time in the air. Pilots are responsible in the great majority, but taking a chance on the odd nitwit isn't worth it, believe me.

AF

[IO540]

2gph will fry your engine in 10% of its TBO

What??? You ought to get current with modern engine management.

Irresponsible, and why FBO's always rent wet. If renters paid for fuel, with a lower overall rate for the a/c, some dolts would fly with pistons pinging, enjoying their extended time in the air. Pilots are responsible in the great majority, but taking a chance on the odd nitwit isn't worth it, believe me.

IMHO, a far bigger reason for wet rental is (a) lack of training on the Red Lever in the UK PPL syllabus, and (b) that most rental stuff is clapped out wreckage without accurate (or any) fuel flow instrumentation so there would be no way to invoice for the fuel separately.

[Mark1234]

Coming back to this - the thread was started with malice aforethought; I did the trip I had in mind this weekend - 8500 out, 9500 back. Fairly high OAT generally - 43C on ground / +20 cruise out, and 30/15 back.

Both ways the chart showed me to be above full throttle height, so I naievely expected to push the black lever fully forward and lean for max rpm.

Interestingly I had to keep the throttle some way back to keep the revs under the red line (cruise was at about 2650rpm, PA28-161). What did I miss?

POH showed 75% at full throttle/2700rpm. Was very thermic so didn't risk running at 2700 due to lack of wobble room...

[waren9]

9500' in a -161 at +20deg? My, you have done very well.

Same prop as the book? Same fuel? Similar weight (wont make much difference)?

Out of interest, what IAS did you manage?

[Mark1234]

Sheer bl00dy minded determination :} - 40+OAT at 2000, felt a lot more inside. If I hadn't had 3 pax plus a whole weekend and accomodation booked at the other end I'd have stayed inside with the house with the aircon on.. Damn silly weather to go flying. I'd have sold body parts for oxygen and the horses to get above it all...

IAS was around 95kts, TAS nearer 110 (according to the twiddlable sub-scale, not particularly accurate). Acceleration from climb was painful to say the least - just slightly less painful than the climb.

As far as I know standard prop - graph was from the aircraft's own POH, but it was a rental. Weight - MTOW less whatever we burned in the climb - probably around 30ltrs. Running on regular 100LL avgas..