Maximum range for NA pistons - down low?

[Lumps]

I have searched other threads and haven't found any discussion: can anyone explain why for a set MP/RPM range decreases with altitude, until reaching I presume full throttle height, then increases again only to regain the same sort of range at quite high altitudes (mid-teens). Normally aspirated only.

The following, if I am lucky, is a chart of a Baron 58 to better describe what I am talking about:



I assume the actual horsepower delivered INCREASES if you hold the same MP/RPM with ascent, along with increasing fuel flow and increasing TAS. In summary, the most efficient altitude to fly negating wind seems to be SL.. I always thought to go maximum range get up nice and high 7-8000ft have a decent TAS on the same fuel burn as a lower TAS down low. This chart proves me wrong.

[Oktas8]

For best range, you should fly at or just above minimum drag speed, which is substantially less than a typical light twin's normal cruising speed.

If you fly at high power at low altitude, your IAS will be aerodynamically inefficient, so range will be reduced. If on the other hand you fly at low power at low altitude, your engine will operate inefficiently. How much is gained by flying at high altitude depends on the type of engine, whether it is turbocharged, and fuel burned inefficiently in the climb. It seems the Baron gains very little range by climbing to 14000'. Above that altitude I would guess the normally aspirated engine produces so little power that it's impossible to reach the most efficient cruise speed.

This graph seems to illustrate that best range is obtained at low power at low altitude (aerodynamics are more significant than throttle setting) and low rpm (reduced engine friction). Flying high will of course give higher TAS and perhaps less travel time, as you suggested.

actual horsepower delivered INCREASES if you hold the same MP/RPM with ascent, along with increasing fuel flow and increasing TAS

Yes, I think so. Since best range would be obtained at a lower power (for aerodynamic reasons), increasing power as you climb is reducing range. Once full throttle altitude is reached, power drops off rapidly with further climb and range increases rapidly.

Everyone learns in flying school that increased altitude results in increased range. The graph illustrates that real-world complications of aerodynamic versus engine efficiency complicate that to the extent that, for a normally aspirated light aircraft, altitude has little effect on range. It's a good question for a flight instructor initial issue test, to test ability to interpret a real world flight manual against a theoretical textbook.

Hope that helps.

[Cough]

(guessing) Same MP on way up, but decreasing pressure on the exhaust side may mean that the waste gasses exit the engine more efficiently, which in turn may mean more charge on the way in... More power, higher burn?

[Oktas8]

I was thinking of reducing temperature as you climb, at constant MP, gives increasing density and therefore increasing air mass in each charge.

[Lumps]

thanks guys, all good points. What I still don't get though is as far as I know - for a given mixture lets say 20°C lop in the B58 the engine, producing say 195 hp it would take the same fuel to produce 195hp at this mixture setting at sea level or at 5,000ft. If no, why not?

And if you are producing 195hp at 5,000ft, does this mean your TAS is higher because of reduced drag, or do propellers lose efficiency proportionally meaning you don't get money for nothing i.e... go faster for the same fuel.

So if the chart plotted horsepower instead of engine settings, then all the lines would slope from the southwest to the northeast - increasing altitude for the same HP increases range. Have I got it!?

Following that thought - if leaned accurately every time then fuel flow becomes your pseudo BMEP gauge, indirectly tells how much horsepower the engine is producing. Or have I gone too far.

[mushroom69]

Although your questioning may be to get at the basic underlying theory, think more in terms of real-world situation. You are never going to fly at sea level, so let's say you want a "low level flight" of between 1000-2000 feet.

25/2500 would give you 975 in range and about 184 knots

25/2100. 1175. 161


Now climb to 10000 feet at the same power settings and you see

25/2500. 1100. 194

25/2100. 1270. 170

So the old axiom is true, that as you climb, you will gain range and speed. Looking at the lowest possible power setting and the lowest altitude (flying in ground effect(!)) you could increase you total range (but at huge huge cost in relative time and comfort. Stuck over the ocean in a 0 wind situation, it might some day pay off to be there.

In the real world, consider a 1000nm trip in your Baron. At highest possible power, 5.1 hours, at a moderate normal cruise 5.4 hours and at low-level 7 hours.

Go to your fuel flow table and compare the fuel burns.

Probably clear why normal cruise is normal...normal meaning most totally efficient. And at these power settings, climbing does indeed give you better range and greater speed RELATIVE to the same power at a lower altitude, except for a very small range at the lowest end of the table, which is not often a good place to be for other reasons in the real world....

IMHO

[Lightning Mate]

Cough has got it right.

Reduced exhaust back pressure as altitude increases.

Reciprocating piston engines are most efficient when operated at full throttle, because this results in minimum restrictions in the inlet system.

[aerobat77]

ahoi !

this range vs altitude graph takes into account that you first have to climb into your given altitude which means initially lower speed and higher flow ( not leaned ) on the climb.

this downside seems not to be equalized or superiored when you climb just to 5000feet for your cruise here, only later on -at least due to this graph !

[Brian Abraham]

Now climb to 10000 feet at the same power settings and you see

25/2500. 1100. 194

25/2100. 1270. 170

You'll only be able to get 25" up to 5,000. Above that altitude MAP decreases at 1"/1,000. At 10,000 the best you can expect is 20". Anything above 5,000 will be WOT. All spelled out on the OPs graph.



The effect of altitude on the range of a propeller powered aircraft may be appreciated by inspection of the attached graph. An increase in altitude has the effect of moving the graph up and to the right. If a given configuration of aircraft is operated at constant gross weight and the lift coefficient for (L/D)max, a change in altitude will produce the following relationships:

V2/V1= SQRT(O1/O2)
Pr2/Pr1= SQRT(O1/O2)

where
condition (1) applies to some known condition of velocity and power required for (L/D)max at some original, basic altitude condition (2) applies to some new values of velocity and power required for (L/D)max at some different altitude

and
V= velocity, knots (TAS, of course)
Pr=power required, h.p.
O=altitude density ratio (sigma)

Thus, if flight is conducted at 22,000 ft. (O=0.498), the airplane will have:
a 42 percent higher velocity
a 42 percent higher power required

than when operating at sea level. Of course, the greater velocity is a higher TAS since the airplane at a given weight and lift coefficient will require the same EAS independent of altitude. Also, the drag of the airplane at altitude is the same as the drag at sea level but the higher TAS causes a proportionately greater power required. Note that the same straight line from the origin tangent to the sea level power curve also is tangent to the altitude power curve.

The effect of altitude on specihc range can be appreciated from the previous relationships. lf a change in altitude causes identical changes in velocity and power required, the proportion of velocity to power required would be unchanged. This fact implies that the specific range of the propeller powered airplane would be unaffected by altitude. In the actual case, this is true to the extent that powerplant specific fuel consumption and propeller efficiency are the principal factors which could cause a variation of specific range with altitude. If compressibility effects are negligible, any variation of specific range with altitude is strictly a function of engine-propeller performance.

The aircraft equipped with the reciprocating engine will experience very little, if any, variation of specific range with altitude at low altitudes. There is negligible variation of brake specific fuel consumption for values of BHP below the maximum cruise power rating of the powerplant which is the auto-lean or manual lean range of engine operation. Thus, an increase in altitude will produce a decrease in specific range only when the increased power requirement exceeds the maximum cruise power rating of the powerplants. One advantage of supercharging is that the cruise power may be maintained at high altitude and the airplane may achieve the range at high altitude with the corresponding increase in TAS. The principal differences in the high altitude cruise and low altitude cruise are the true airspeeds and climb fuel requirements.

(Courtesy of Aerodynamics for Naval Aviators)

[Oktas8]

The textbook is correct, at constant EAS

The thing that I find is often not grasped is this: all the above is of course correct for best range cruise, or indeed for cruise at any constant EAS as Brian has said. However, the way light twins are usually operated is very much not constant EAS and very much faster than best range.

If you're flying at a high cruise power, the range/altitude graphs change markedly with altitude which can be confusing for someone trained using AFNA as a standard text. Not that AFNA is wrong, just insufficient by itself for a full appreciation. It's important to be able to appreciate why flight manual graphs look so different.

Cheers,
O8

[Lumps]

Thanks BA. So no free lunches!

The Baron range chart looks odd because it lists power settings, not actual power produced - the decreasing then increasing range with altitude a product of the power produced rising then falling.

Does anyone have a chart that has power or fuel flow plotted against range and altitude? Thanks Brian A for the theoretical chart but it takes a chart with numbers and speeds etc on it for this noggin to comprehend properly. (or would such a chart just have a series of vertical lines representing power?)

And while we are at it, can it be explained in layman's why an aircraft indicating 120 knots at 10000ft requires more power than 120KIAS at SL? What is the extra power going to? Losses due velocity induced drag rather than drag related to dynamic pressures? It was probabnly all explained in the naval aviators thingy but not simply enough it seems

[Brian Abraham]

Lumps, if you want to send me a PM with your private email address I'll send some info that should put you in the picture as to how all the various variables affect range. Far too long to post here.