Factors influencing endurance

[double_barrel]

Looking at the figures for endurance/range in the C172M handbook, I see that it gives figures for various engine rpm values and altitudes, but assumes max gross weight for all. This led me to wonder how much influence weight has on endurance. I guess that there are a bunch of other factors too, obviously mixture setting is one, and I suppose that trim will have a significant influence on drag and thus range? How important are these factors? Is there any way to quantify them?

[Sam Rutherford]

CG is another that will have a huge impact, particularly in a tailwheel aircraft if it's weighted towards the rear...

[oggers]

Looking at the figures for endurance/range in the C172M handbook, I see that it gives figures for various engine rpm values and altitudes, but assumes max gross weight for all. This led me to wonder how much influence weight has on endurance. I guess that there are a bunch of other factors too, obviously mixture setting is one, and I suppose that trim will have a significant influence on drag and thus range? How important are these factors? Is there any way to quantify them?

Theoretical best endurance will occur at the minimum power speed in level flight. If the weight is reduced minimum power will also be reduced and it will occur at a lower speed. If the performance data in the POH doesn't give your endurance speed you would find it by slowing down until you start to have to add power back to maintain level flight, then speed up just enough to get yourself back on the right side of the power curve.

As mentioned trim and cg are factors. A rear cg although less stable is more efficient aerodynamically as the tailplane is providing less downforce.
Altitude: unlike a turbine, the piston is not optimised for cruise efficiency at 36000'. Lower is better. The aerodynamic reason is that for any given IAS your TAS is lower at lower altitude and therefore so is your power because power is TAS x drag.
Mixture would be leaned to 25LOP if permitted, or recommended best economy for your aircraft. 25LOP is theoretical best specific fuel consumption for the Lyconental engines ie it is lowest fuel flow per horsepower produced, but it might not be recommended.
RPM with a VP would be low eg 1800. Volumetric efficiency is higher at low RPM. For a fixed pitch you don't have a choice, the RPM wil be whatever it needs to be to maintain speed.

All the above apply to flying for best endurance as per the thread title. Theoretical Best Range is slightly different, you fly at minimum drag speed (L/D max, also best glide speed) instead of minimum power, and you operate at the altitude where you can just get the requisite power with a wide open throttle (or somewhat below to give you some reserve power for maneuvering). In a headwind your best range speed would occur somewhat above minimum drag speed and vice versa. A rule of thumb is to add or subtract quarter of the headwind component.

[sablatnic]

Drag, span loading, weight, specific fuel consumption.

[eckhard]

Bladder volume?

[Pilot DAR]

The trim is only a factor in that you probably would like to have the aircraft trimmed for hands off flying. Thus the trim setting will provide hands off flying at a further aft C of G, if you choose to fly that way, and can arrange loading that way. This will be a small factor in endurance, probably too small to notice in a 172, but worth a try. The aft C of G reduces drag in any conventional airplane, as the horizontal stabilizer does not have to lift down as much - in any stable, normal flying, the horizontal stabilizer of a GA plane never lifts up. The undercarriage configuration is not a factor in range nor endurance, other than to say that if you have converted a tricycle plane to be a taildragger, then yes, it will have less drag, and more range and endurance.

Otherwise, as said, flying a suitably slow speed (known as the "bottom of the bucket" on a power curve chart), and lean according to the engine operation manual are your best means of achieving best endurance.

Understanding these principles is important for pilot skills and understanding, but for recreational flying in a GA plane there will will likely only be two occasions when you will put this to practice: If an examiner asks you to set up for it, to prove you understand, or you have to hold for improving weather or some other delaying situation. There is a close relationship to realizing that you are low on fuel, and may not make it to any destination, but this would still be flight for best range, rather than endurance, but it demands similar discipline. Once, with 300 miles to go, a steadily increasing headwind, and zero airports between me and the fuel airport, I sure optimized my range and fuel use, and made it - just. Failing to optimize fuel and range, and I would have landed short for sure.

One other factor I employ if I'm planning a long trip, is a wash and wax of the whole plane, that's good for a couple of free knots of cruise speed, and I've never heard of an owner complaining if you offer to was and wax their plane!

[Maoraigh1]

If you want range rather than endurance, the wind is important. Max permissable cruise speed into a headwind may give longest range. Calculate on the forecast wind at that time.

[foxmoth]

A rear cg although less stable is more efficient aerodynamically as the tailplane is providing lift.

not quite, generally the tailplane provides a downward force and by having a rear cg this downforce is reduced.

[oggers]

...you are correct.

[selfin]

Endurance scales, very nearly, by a factor of ( 1 + 3 * [ -1 + sqrt( M / ( M + m )) ] ) where big M is the original takeoff mass and small m is the (signed) mass either added or removed. For an aircraft similar to a C172 this is roughly equivalent to a 15 per cent increase in endurance for each adult passenger removed.

Edit: changed the approximation sqrt(M/(M+m)) to (1+3*[-1 + sqrt(M/(M+m))]. The correct but more complicated factor will be evident from inspecting the Breguet endurance formula.