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How could I minimize the aircraft total takeoff fuel consumption, taking into account all fuel used from start of take-off roll until reaching a safe altitude?

For example, if I fly with flap retracted and the runway is long enough to takeoff, does that mean I could use less energy than flying with flap extended, since I have less drag?

DeltaLima
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VvV
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  • I don't understand this question at all, what does minimizing takeoff energy mean? – GdD Jun 28 '21 at 07:35
  • How about minimizing the total aircraft takeoff power consumption? That is use less energy to accelerate the aircraft and lift it off in air. – VvV Jun 28 '21 at 07:37
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    The lowest takeoff energy is technically negative. This can be seen in some hang glider cliff launches. – Anonymous Physicist Jun 28 '21 at 08:08
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    The question seems pretty clear to me, voted to keep open. – Koyovis Jun 28 '21 at 09:19
  • Yes, it is a good question. Besides flap configuration, is a shallow high speed “cruise climb” more fuel efficient than a best rate of climb? – Mike Sowsun Jun 28 '21 at 11:21
  • A cruise climb certainly will be easier on the engine, with long term benefits there. Flaps up, provided runway length and clearances are OK, is generally more fuel efficient. – Robert DiGiovanni Jun 28 '21 at 13:28
  • You need to edit the title to better match the body of the question. The title says "minimize takeoff energy" which nearly everyone will interpret as minimizing the kinetic energy of the aircraft at the instant of takeoff, but that's not what the question is actually about. Hence, the close votes-- – quiet flyer Jun 28 '21 at 14:01
  • What do you consider a safe altitude? – DeltaLima Jun 28 '21 at 15:24
  • @DeltaLima fair question, but the word "safe" is a red herring here. The most efficient climb to any altitude is the most efficient climb to every altitude. In other words, if there is a way to climb most efficiently to 1000', then when passing through 500' it must have been most efficient there as well. – Kenn Sebesta Jun 28 '21 at 15:29
  • @KennSebesta not at all. You can climb by trading speed for height. Climbing at most economical speed to e.g. 250 ft, followed by a zoom climb to 500 ft and stall speed may get you to 500 ft with the lowest possible total fuel consumption. However, that approach will not get you to 1000 ft in the most efficient way. – DeltaLima Jun 28 '21 at 15:45
  • I think you may be after the most efficient climb strategy. Taking into account the fuel consumed not only during climb to cruise level, but also until a certain distance from the airport is reached. Climbing steep means that the cruise segment is longer and therefor costs more fuel in cruise segment, climbing shallow reduces the length of the cruise segment reduces the fuel burn in that segment. By comparing the total fuel consumption at a fixed distance down route where the cruise altitude has been reached makes climb strategies comparable. – DeltaLima Jun 28 '21 at 15:47
  • @DeltaLima I would consider a zoom climb which results in unsustainable flight as cheating and outside the bounds of the question. There are many ways to game the question: an earlier poster points out that launching off a cliff is a great way to gain relative altitude. I think it's important to be fair in our understanding of what the poster is asking. – Kenn Sebesta Jun 28 '21 at 15:57
  • @KennSebesta the zoom climb I described would not result in unsustainable flight. It would get to the termination altitude in a safe and efficient way, however any further climbing would be not optimal. The whole purpose of my clarification questions is to make sure we understand the boundary and termination conditions the OP is accepting, as there is very little context given to the question. There is nothing unfair about that. – DeltaLima Jun 28 '21 at 16:07
  • A zoom climb, what we glider pilots would call a pilot-induced thermal, is indeed a fuel- and time-optimal termination of any climb so long as we do not concern ourselves with what happens next. In fact, if the plane is not in a full hammerhead at the peak altitude, then we have not yet achieved peak optimality. To get to this second-order termination of the climb must first build on the underlying first-principles optimality. In lay speak, we have first to get within range of the zoom climb; and how to get there is, presumably, the important question being asked. – Kenn Sebesta Jun 28 '21 at 16:30
  • I doubt that it's possible to provide a general answer, since it's going to depend on specific details of the aircraft. And indeed, on the runway surface. For instance, on a grass runway it might be more efficient to use some flap to get the gear out of the grass sooner. – jamesqf Jun 28 '21 at 16:55
  • @jamesqf Then you might wish to explain in your answer how this would affect the condition in the question? – Koyovis Jul 04 '21 at 03:40
  • Voting to keep open for the second time. – Koyovis Jul 04 '21 at 03:41
  • @Koyovis: As long as the wheels are on the ground, the engine has to overcome rolling resistance in addition to strictly aerodynamic factors. Grass runways have higher rolling resistance than nice, smooth asphalt or concrete, particularly if the grass is long and/or wet. – jamesqf Jul 05 '21 at 02:59

5 Answers5

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Assumptions

It's not specified in the question, so I'll assume that it's a gasoline-powered fixed-wing SEL airplane (aircraft is anything which flies, including balloons, rotarywing, etc...) on a standard climbout from a standard (but looooong) runway, etc... I'm also assuming you can't do exotic things like change the engine compression ratio.

I will also assume that efficiency in this context is only energy consumed per unit height. If we want to define efficiency as energy consumed per unit distance traveled, then the problem moves in a different direction and becomes much more complicated.

In my responses below, please understand that these are first-order effects, but second-order effects can lead to modifications. For instance, maximal efficiency might come at a slightly faster/slower airspeed in order to allow for a slightly faster/slower engine RPM.

Also, in general, fuel is not the important consideration for takeoff. Safety is. It's better to burn a few mL more of fuel and keep the airplane from disaster (which would presumably result in wasting a lot more energy).

Mixture (with important caveat at the end)

The mixture is the biggest control on efficiency. In order to achieve maximal efficiency, you need to run as lean as possible. Preferably lean-of-peak, if this can be done. We're talking 20% savings or more here.

Caveat

If you're not taking off at high altitudes, e.g. in the mountains, don't ever try this if you value your airplane engine's life, and as a consequence your own. The engine needs the enhanced cooling from the rich fuel/air mixture. Only at high density altitudes can/should the engine be run at full power at extremely lean settings.

Throttle

The throttle should be fully open, which will provide the least restrictions to the engine breathing.

RPM

If you have a constant-speed prop, then it should ultimately be run as slowly as possible. This gives maximal time for the burning fuel energy to be extracted, as well as minimizing the number of engine cycles and friction.

The RPM should be advanced at such a speed as to provide peak propeller efficiency for the advance ratio.

Fuel

Use the lowest octane gas you can, as this has more energy content than higher octane. Please note that lower octane increases the propensity of the engine to knock/detonate.

Airspeed

Fly the plane at Vy, which is best climb airspeed. This is the airframe's most efficient operating point.

Flaps

In general, don't use them for optimal efficiency. They increase drag more than the increase lift. That's why we like them on landing because we can come in at a steeper angle of attack.

An argument could be made for rapidly "pumping" the flaps in order to pop the plane off the ground, thus eliminating rolling resistance at an earlier point in the takeoff roll. This technique was employed to great effect at a recent STOL competition.

Kenn Sebesta
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  • Sounds like you're trading a bit of fuel savings for higher maintenance costs and potential flight safety. IANAP, but it would make me think long and hard about these practices. – FreeMan Jul 02 '21 at 15:06
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    IAP, and I couldn't agree more. Several of these techniques would be things I would only employ in a well-instrumented plane in tightly controlled circumstances. If your goal was to set a world record, though, then safety and costs sometimes take a back seat to optimality. In a samilar vein, Kneivel jumping a motorcycle across the Grand Canyon was the "optimal" way across. – Kenn Sebesta Jul 02 '21 at 17:19
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I think you’re asking about how to get to a safe height with minimum expenditure of fuel. As you suggest, the aircraft will generally be more efficient in flight with the flaps retracted, and certainly before liftoff there will be significantly less drag than with full flap. The downsides are that the takeoff run will be longer, and the takeoff speed will necessarily be higher. If what you mean to ask includes reaching normal flight conditions, flaps up, cruising height and nominal airspeed, then a flapless takeoff is very likely to use less fuel. On the other hand, if you consider 10ft to be a safe height and you have an aircraft with small wings and huge flaps then the opposite may be the case.

Frog
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You can do two things:

  1. Use the lowest flap setting you can use.
  2. Reduce power to climb power as soon as you are at your departure climb speed. When you learn to fly, it's full throttle until you are at least at 1000 ft, but on more complex airplanes it's normal practice to reduce to climb power right after achieving climb speed. When I was flying floats, I would come back to 24 square right after clearing the water, although this was mostly to reduce noise from supersonic blade tips, to keep neighbour complaints down.

I used to go a little farther than that when I was flying regularly from an uncontrolled airport with an 11000 ft runway. I would take off using climb power (24" MP), more or less using "flex thrust" like a jet. I would use 2000 ft of the 11000 ft runway instead of 1000 ft. I probably save a thimblefull of fuel or so, who knows.

John K
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  • Could you go into a little more detail? Your approach seems to directly contradict my approach, but perhaps I'm misunderstanding. For instance, if you throttle back, then you are constricting the intake airflow and induction losses are a major source of inefficiency in engines. – Kenn Sebesta Jun 28 '21 at 21:43
  • Yes but when you reduce to climb power you can start leaning, plus the carb or injection system may have a high power fuel schedule or circuit because fuel is providing a lot of the cooling at TO power. It's also to go easy on the engine. Temps and pressures are maxed out, and it's always better to reduce them. It's the main reason for flex thrust in jets; to extend engine life. That old saw about engines liking being run hard is nonsense. No mechanical system last longer when run hard than when run not so hard, as long as it gets regular exercise I cruise my own airplane at 45-50% power. – John K Jun 28 '21 at 22:41
  • Got it. I think the difference is my answer gives "absolute best", with the caveat that you shouldn't expect your engine to live long-- perhaps not even to target altitude-- if you treated it this way. I think your answer is "practical best", which I tend to follow IRL, cruising a 7ECA at 40-50% power. – Kenn Sebesta Jun 28 '21 at 23:20
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Configure airports and planes in such a way that take-off catapults, similar to those used on carriers, can be used to accelerate them up to take-off speeds while using less onboard fuel than would otherwise be used.

Note that the greater distance available with such a ground based "catapult" means that the device can act over both a greater distance and longer period of time, which would reduce the strain on the equipment and passengers.

The complexity of this system would be cost prohibitive to set up and maintain, but if you only care about reducing the fuel usage during takeoff, this would do so.

Caveat: I've been reading a lot of worldbuilding posts recently, and this post was likely highly influenced by that.

Michael Richardson
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    Better still, build your airport on a steep slope at cruising altitude (I’ve seen a few examples in the French Alps, it’s a real thing). Land upslope and launch downslope. – Frog Jun 28 '21 at 21:33
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Use lighter than air aircraft (aerostat) filled with helium or hydrogen. They have other shortcomings but should not use much energy just for lifting up.

h22
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