# What is the relationship between power and fuel efficiency?

We were having a discussion in our ground school that power will make the plane ascend or descend and that you use the stick for speed, forward for higher speed and back for slower speed. So does that mean as you fly higher, that means you increase power and ascend, and then fly from point A to point B, you will burn more fuel compared to if you went from point A to point B at reduced power, hence lower altitude?

• It depends on a lot of factors, but in a word, no. Note that airlines go for fuel efficiency, and they fly almost as high as they are able. – raptortech97 Jan 28 '15 at 5:56
• possible duplicate of Airplane longitudinal control: pitch or power? – Federico Jan 28 '15 at 8:10
• @Federico: that's certainly related, but does not seem to be duplicate as the main question here is efficiency. – Jan Hudec Jan 28 '15 at 9:36
• @JanHudec you're right, I got confused by the introduction of the question (correctly addressed in Steve's answer) – Federico Jan 28 '15 at 12:19
• raptortech97, that is exactly my point, but I am just unable to find a satisfactory explanation for the apparent ambiguity in my mind. – yankeemike Jan 28 '15 at 16:03

It's not this does that and nothing else. It is always a combination.

In climb you need to provide more energy to the aircraft because you are increasing it's potential energy. This can be taken from the energy which would have been spent to overcome drag in horizontal flight by flying slower. Less energy is needed to sustain the now lower flight speed, so some is left for climbing.

When you pull on the stick, you trim the aircraft for a lower flight speed (at least if you fly a naturally stable configuration), so some of the excess energy needs to be spent in other ways. The aircraft climbs.

If you advance the throttle, the trimmed speed will stay the same, but now more energy is available to be spent. It will be spent on climbing, because speed is already set by your elevator angle.

In a non-supercharged (normally aspirated) piston engine, the decreasing air density with increasing altitude will provide less air with every filling of the pistons. You need to lean the engine to keep the fuel-to-air ratio constant, so the engine will consume less fuel at the same engine speed, but also provide less power and thrust. Since air is also thinner for all other parts of the airplane, your true air speed will increase, your drag will decrease at the same true air speed and you can fly faster. But since your normally aspirated engine will provide less power, you need to advance the throttle in order to keep your attitude, speed, and climb rate. At some point, you will reach maximum power, and as you climb further, climb speed will decline until you reach the maximum flight altitude your airplane is capable of.

Flying higher will increase the efficiency of the engine due to lower air temperature, but this effect is small for piston-powered aircraft. Once you switch to supercharged aircraft, turboprops, and jets, however, their much higher maximum flight altitude will make flying higher markedly more efficient.

Flight speed, however, does make a substantial difference, especially for piston-powered aircraft. Their optimum cruise lift coefficient is $c_L = \sqrt{c_{D0}\cdot\pi\cdot\Lambda}$ and is rather high. Flying low means that you will fly a lot faster than what this optimum demands, and the higher you fly, the closer you will be to this optimum, simply because your engine will not allow a higher speed. That is why flying higher helps to fly more efficiently.

• bonus points for trim = (hands-off) speed. also, I don't know if this is a UK/US thing, but "unaspirated" is a linguistic term. In the US, weuse "normally aspirated". – rbp Jan 28 '15 at 13:52
• @rbp In the UK, I think naturally aspirated is the common term. – Holloway Jan 28 '15 at 16:28
• That's strange, I'm in the US and I've always used "naturally aspirated". – Steve V. Jan 29 '15 at 1:01

Unfortunately, the cause and effect in this question is really muddled up. Peter Kampf's excellent answer should explain most of what you need, but it might be that you find his answer difficult to understand because you're still operating under the idea that the stick only manages speed and the throttle only manages altitude.

If this is the case, please consider this analogy: imagine that there are three buckets of energy available to any aircraft: chemical, potential, and kinetic. (note for the pedantic: yes, chemical energy is potential energy. Go away.)

• Chemical energy is stored as fuel (dead dinosaurs). It is released by the engine and can be converted into either altitude or airspeed or both.

• Potential energy is altitude below you - the energy which is stored in the aircraft as altitude. It can be converted into airspeed, but not back into dead dinosaurs.

• Kinetic energy is airspeed - the momentum of the aircraft. It can be converted into altitude, but not back into dead dinosaurs.

As long as the engines are operating, the chemical energy "bucket" is always pouring energy into the other two buckets. The throttle determines how much energy is poured out per second. The yoke (stick) determines the distribution of that energy - whether the kinetic bucket is pouring energy into the potential bucket, or vice versa, or neither.

What this means is that if you want to ascend, it's not enough to say that you simply have to pull back on the stick, or that you simply need to increase throttle. Merely increasing throttle with the nose pointed at the ground does not help you ascend. Merely pulling back on the stick with the airplane already at the critical angle of attack does not help you ascend. To ascend, you need to "fill the altitude bucket", which (as Peter says) is always a combination of pitch and power.

As to your actual question regarding fuel efficiency, since it's based on false assumptions I will only say that it depends on the circumstances of the flight, but it is certainly not correct to say that increased fuel consumption is always the result of the greater throttle setting necessary to achieve a higher altitude.

• You could pre-empt the pedantic by saying "gravitational potential energy" – AakashM Jan 28 '15 at 14:02
• After reading this my mind is fixated with the idea that there are dead dinosaurs stored inside my wings... – kevin Jan 28 '15 at 15:54

I'll add one thing about engine efficiency.

Aircraft engines are either more, or at least not less, efficient at higher power setting.

1. In spark-ignited (gasoline) engines the throttle adds resistance to the intake when closed, so they are most efficient with throttle fully open and slightly lean mixture so that all fuel is burnt. Modern directly-injected engines often support "ultra lean burn" when throttle is left open and power is regulated by injecting less fuel, i.e. very lean mixture, but most aircraft engines are older designs that don't work well with too lean mixture, so they are less efficient with less throttle.

2. Turbine engines are also more efficient at higher power. I am not sure about the reason, but probably because the high-pressure stage takes relatively less energy for driving the compressor leaving more power for the low pressure stage driving the propeller (at idle the power to propeller is minimal, but the core still spins quite fast; often around 60% rpm compared to full power).

3. Only diesel engines where power is controlled by amount of injected fuel only (corresponds to mixture in spark-ignited engines) are not less efficient at lower power settings, but at the cruise power they will not be any less efficient either.

And now combine with the fact, that your drag is about the same at the same indicated speed independent of altitude, but at higher altitude the same indicated speed corresponds to higher true (and therefore ground) speed.

• ...at least it does under the assumption that winds aloft don't vary with altitude. In practice they do, and so choosing the most efficient cruising altitude also involves looking at winds aloft. – Doug McClean Feb 16 '15 at 22:10