Altitude, gravity, and air density effects on flight

[brainstorm]

I'm very unfamiliar with energy-use in aviation, but I am wondering about what effect altitude has on parameters such as gravity (i.e. weight of the aircraft) and air-density, which I would think affects friction and combustion as well as lift.

One thought I've had is that higher velocities through lower density air is equivalent to lower velocities through higher density air. It seems like air density could be treated as a rate of particle flow against the aircraft. So, for instance, I would think a jet traveling twice as fast in air half as dense would experience friction and combustion the same as it would at half the speed in 2x dense air. Is that clearly expressed?

Also, I wonder about the effect of decreasing gravity on the performance of the aircraft. It seems like the efficiency gained from higher altitude could be recovered in long distance flights, but is that a poorly conceived hypothesis?

Finally, if high altitude flight was ultimately more efficiency for long distances, I would think the stumbling block would be using jet power to continue to climb through lower density air. However, if rocket propulsion was briefly used just to achieve extra altitude, would gravity allow the aircraft to achieve a speed that would generate sufficient air flow/density to keep the engines going? In other words, could jet engines run at a much higher speed in lower density and lower gravity atmosphere?

 

[russ_watters]

Altitude has little effect on gravity for a plane, but a huge effect on air density and therefore drag and engine performance.

And yes, airplane speed is often measured in terms of (essentially) how many molecules of air are hitting it. That's known as indicated airspeed: http://en.wikipedia.org/wiki/Indicated_airspeed

It works well until you get near supersonic speed.

Jet engines are more efficient than rockets, even at high altitude.

 

[Trexman89]

I've also heard that jet engines allow planes to go faster than their current "top speed." The reason why jet planes don't go any faster is because the friction with the air would melt the nose of the plane.

 

[cjl]

I'm very unfamiliar with energy-use in aviation, but I am wondering about what effect altitude has on parameters such as gravity (i.e. weight of the aircraft) and air-density, which I would think affects friction and combustion as well as lift.

It has almost zero effect on gravity, but the air density effect is enormous. At high altitude, as you guessed, engines make less power, and the aircraft has lower drag. The wings also make less lift.

One thought I've had is that higher velocities through lower density air is equivalent to lower velocities through higher density air. It seems like air density could be treated as a rate of particle flow against the aircraft. So, for instance, I would think a jet traveling twice as fast in air half as dense would experience friction and combustion the same as it would at half the speed in 2x dense air. Is that clearly expressed?

You have the right idea here, although you're slightly off on the relationship. Dynamic pressure is the commonly used metric, and it scales with velocity squared. So, if you go up to an altitude with 1/4 of sea level density, you will need to fly twice as fast to get the same dynamic pressure.

Also, I wonder about the effect of decreasing gravity on the performance of the aircraft. It seems like the efficiency gained from higher altitude could be recovered in long distance flights, but is that a poorly conceived hypothesis?

Decreased gravity is pretty much negligible at the altitudes that aircraft fly. There are actual efficiency benefits though, for a couple of reasons. The reduced drag at high altitude is one of the main benefits, as is the colder temperature (jet engines operate better with extremely cold intake air).

Finally, if high altitude flight was ultimately more efficiency for long distances, I would think the stumbling block would be using jet power to continue to climb through lower density air. However, if rocket propulsion was briefly used just to achieve extra altitude, would gravity allow the aircraft to achieve a speed that would generate sufficient air flow/density to keep the engines going? In other words, could jet engines run at a much higher speed in lower density and lower gravity atmosphere?

The main stumbling block is actually the wings ability to make lift. Above a certain altitude, the aircraft doesn't have the capability to stay in the air, since it can't fly fast enough to keep the wings producing lift.

Specifically, all airliners have what is known as an MMO, which stands for mach maximum operating. This is the highest mach number which they can safely operate at, which is usually around 0.9 for commercial airliners. At high altitudes, the speed of sound doesn't change very much, so this speed is roughly constant regardless of altitude (in reality, mach actually slows down somewhat at altitude because of the cold temperature, but I'll ignore that for now). They also have a minimum indicated airspeed that they can operate at. This is because there's a certain minimum speed below which the wings can't keep it in the air. This speed is based on the indicated airspeed however, which is based on dynamic pressure (which scales proportional to the density). So, for the same true airspeed (speed with which the air is actually flowing over the wing), the indicated airspeed drops off with altitude. So, to stay in the air, the airplane needs to go faster the higher it goes. At some altitude, the maximum operating mach number (which doesn't really change with altitude) will only be a tiny bit faster than the minimum operating airspeed (which increases with altitude). This is what is usually the absolute limit on altitude for a given design.

In addition to this effect, engine power drops off with altitude, and when aircraft are heavily loaded, they will usually hit an engine power limit before they will hit the maximum mach limitation outlined above. A heavier aircraft will have more induced drag, and will require more engine power, so above a certain altitude, they might simply not have the thrust to stay in the air. For a very large jet at near MTOW, this could be as low as 30-35 thousand feet, whereas later in the flight after it's burned off much of the fuel, it might climb up to 38,000 or even higher.

At every stage in the flight, there's an optimum altitude that the airplane needs to fly at to use the minimum amount of fuel. This altitude balances the fact that it can fly faster at higher altitudes with the same amount of drag with the fact that the engine power is dropping off, and the optimum altitude for a given airplane will be higher the lighter the airplane is. This is why if you're ever on a very long (>10 hour) flight, an airplane will usually start out its cruise in the low 30,000 foot range, and it will climb throughout the flight until it finishes several thousand feet higher than it started. That's the pilot adjusting the altitude to always be close to the optimum for the plane's weight as the fuel is burned.

 

[cjl]

I've also heard that jet engines allow planes to go faster than their current "top speed." The reason why jet planes don't go any faster is because the friction with the air would melt the nose of the plane.

That depends on the airplane. For almost all aircraft, this isn't true, but there are a couple for which this is somewhat the case. The SR-71 was easily capable of exceeding its specified maximum mach of 3.2, but there was a chance of both engine and airframe damage if this happened for long. The russian MiG 25 was also capable of ruining its engines through speed.

 

[russ_watters]

There is a story that an SR-71 accidentally got up to about Mach 4 once due instrument malfunction. The pilot realized it when things started failing due to the heat.

 

[mugaliens]

http://maggiesfarm.anotherdotcom.com/archives/7821-Major-Brian-Shul-I-loved-that-jet.html"Maj Brian Schul's account of flying an SR-71 to just about the fastest velocity that's still considered "safe."

What he apparently didn't tell you here is that by the time they checked the fuel out over the Mediterranean, they were well ahead of their fuel curve. Like a ramjet, the faster the SR-71 travels, the more fuel efficient it is per mile travelled.

ETA: http://gizmodo.com/5511236/the-thrill-of-flying-the-sr+71-blackbird" , but with much better formatting and a slew of pictures. :)

 

[brainstorm]

Thanks for this super-thorough answer. It was very readable as well.

You have the right idea here, although you're slightly off on the relationship. Dynamic pressure is the commonly used metric, and it scales with velocity squared. So, if you go up to an altitude with 1/4 of sea level density, you will need to fly twice as fast to get the same dynamic pressure.

I wonder why this is. It seems like the engines and the wings would not know the difference between air densities if the same number of molecules per second were flowing past the plane. I wonder if pressure plays a role, even while the air flow brings the dynamic pressure to a point equivalent to the lower altitude.

The main stumbling block is actually the wings ability to make lift. Above a certain altitude, the aircraft doesn't have the capability to stay in the air, since it can't fly fast enough to keep the wings producing lift.

If the MMO was unlimited, would high enough speed produce adequate lift and pressure to run the engines at any altitude? I wonder why the speed of sound doesn't vary proportionately with air density. It must have something to do with how fast the air particles move, not just how many there are per unit volume.

But would it be the case that if a plane was designed to fly at higher speeds and higher altitude, that it would be more fuel efficient while also flying faster? I would assume this because I wouldn't think maintaining constant velocity would be much of a power-drain with drastically reduced wind resistance/drag.

 

[Dr Lots-o'watts]

I'm very unfamiliar with energy-use in aviation, but I am wondering about what effect altitude has on parameters such as gravity (i.e. weight of the aircraft) and air-density, which I would think affects friction and combustion as well as lift.

The change of gravity is negligible. The actual mass of the aircraft however (and thus its weight) is considerably reduced throughout the flight as its fuel is burnt. This is much more important than any change in gravity due to altitude.

As for the relation between engine performance and altitude, here are typical numbers in the case of a propeller-driven aircraft (taken out of a 1978 Model Cessna 172 owner's handbook), running at constant 2200 RPM, 15degC - 2degC per 1000ft (in this case at least, the colder air does not compensate for the lower density):

100 knots @ 2000ft
99 knots @ 4000ft
98 knots @ 6000ft
97 knots @ 8000ft
96 knots @ 10000ft
95 knots @ 12000ft

As for the relation between climb performance (feet per minute) and altitude:

675FPM @ 2000ft
580FPM @ 4000ft
485FPM @ 6000ft
390FPM @ 8000ft
295FPM @ 10000ft
200FPM @ 12000ft

Note that the relations are typical for a specific single engine prop plane and has perhaps nothing to do with a jet engine.

 

[mgb_phys]

If the MMO was unlimited, would high enough speed produce adequate lift and pressure to run the engines at any altitude?

If the speed of sound was unlimited yes, otherwise things get a bit different when you want to go supersonic.

But would it be the case that if a plane was designed to fly at higher speeds and higher altitude, that it would be more fuel efficient while also flying faster? I would assume this because I wouldn't think maintaining constant velocity would be much of a power-drain with drastically reduced wind resistance/drag.

Aerodynamic drag is proportional to the density of air * speed squared
So going faster at the same altitude (ie same air density) uses more energy.

 

[cjl]

Thanks for this super-thorough answer. It was very readable as well.I wonder why this is. It seems like the engines and the wings would not know the difference between air densities if the same number of molecules per second were flowing past the plane. I wonder if pressure plays a role, even while the air flow brings the dynamic pressure to a point equivalent to the lower altitude.

The thing is, when the dynamic pressure is the same, the same number of molecules per second aren't flowing past the plane.

It's because the way the wing flies is by redirecting air. If the airplane is flying twice as fast through 1/4 the density, it is only encountering half as many molecules per second, true. However, each molecule is traveling twice as fast, so when redirected through the same angle, you get twice the change in momentum per molecule that you did at the lower altitude and speed. With half as many molecules, but twice the change in momentum per molecule, you get the same effective aerodynamic force (and both lift and drag scale the same way).

If the MMO was unlimited, would high enough speed produce adequate lift and pressure to run the engines at any altitude? I wonder why the speed of sound doesn't vary proportionately with air density. It must have something to do with how fast the air particles move, not just how many there are per unit volume.

If the speed of sound were infinite (which is effectively what this question is asking), then yes, you could always keep increasing the speed as the density dropped to maintain flight. The engine power doesn't scale the same way that the wings' lift and drag does however - since the engine is only encountering half as many molecules per second at 1/4 the density (assuming the same dynamic pressure), it will only make half the thrust (this is a rough approximation of course, but it's not too bad for a jet). So, as you flew higher and faster, you would need larger engines. Interestingly though, since jet engine fuel flow is pretty close to directly proportional to thrust, the larger engines at higher altitude would only use roughly the same amount of fuel as the smaller engines at lower altitude. This also means that in this ideal approximation, you would always get better fuel efficiency by flying higher and faster, since your drag (and thus your fuel flow rate) would remain constant, but your flight time would decrease.

Now, if the speed of sound were still as it is now (~340m/s), but the plane had no limitation on maximum mach number, then it wouldn't be quite that simple. Airflow does strange things when you start exceeding the speed of sound, and it turns out that you tend to be better off flying just below the speed of sound than flying above it, even if you can go to a higher altitude and lower density.

As for the speed of sound not varying with density, you're correct in your guess. It hasw to do more with the speed of the molecules than how many there are (which is why it scales as the square root of the temperature).

But would it be the case that if a plane was designed to fly at higher speeds and higher altitude, that it would be more fuel efficient while also flying faster? I would assume this because I wouldn't think maintaining constant velocity would be much of a power-drain with drastically reduced wind resistance/drag.

Actually, the drag would remain about the same when flying higher and faster, since the dynamic pressure would be the same. As I said above though, fuel usage for the flight would decrease, since you would reach your destination faster.

 

[mugaliens]

I wonder why this is. It seems like the engines and the wings would not know the difference between air densities if the same number of molecules per second were flowing past the plane.

It has to do with the difference between http://en.wikipedia.org/wiki/Kinetic_energy" .

When you understand the relationship between kinetic energy and momentum, you will then understand what's happening as cjl said with respect to still having to go twice as fast in 1/4 atmosphere to obtain the same airflow effect.