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Why do turbofan jets fly faster in cold weather at high altitudes?

I read somewhere that prop planes do it due to cold weather means air is more dense, and the prop therefore produce more power.

But what about jet aircraft at say 36000 feet? I looked at performance chart of a jet fighter, and at ISA-15 it could fly 0.17 mach faster than ISA.

Do not misunderstand I am NOT asking why it flies faster higher up. I am asking why it flies faster at winter than in summer at same (optimal for speed) altitude.

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    $\begingroup$ The question is, do they really fly faster? The speed of sound goes down with lower temperature, and it is cold at 36,000 ft $\endgroup$ – Koyovis Sep 2 '17 at 1:45
  • $\begingroup$ Can you post an image of the chart? I believe if the shape of the max speed curve vs altitude (assuming that is what the chart shows) has the same shape as a curve of constant dynamic pressure, it would indicate the max speed limit is a structural limit. If not, the limit is due to another constraint (probably engine thrust?). These two limits also tend to occur for different altitude ranges. So knowing the shape of the max speed line might be very useful to answer the question. $\endgroup$ – Penguin Sep 3 '17 at 11:49
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They don't. They fly slower.

Most aerodynamic effects depend on dynamic pressure. More precisely, lift is proportional to dynamic pressure and drag has parasitic component, which is proportional to dynamic pressure, and induced component, which is inversely proportional. Therefore there is an optimal dynamic pressure at which the aircraft flies most efficiently, and minimal dynamic pressure needed to maintain flight.

Now dynamic pressure is (half of) air density times velocity squared ($q = ½\varrho v^2$) and due to its significance the “indicated airspeed” shown in cockpit actually corresponds to dynamic pressure expressed as equivalent airspeed. All the desired speeds for various phases of flight are referenced to that.

Since cold air is denser, the same dynamic pressure will occur at lower velocity, and because the pilot will maintain the same indicated airspeed, they will actually fly slower.

One more thing: the maximum speed is one of the few exceptions that is not dependent on the dynamic pressure. There are three effects that may limit maximum speed:

  • Aeroelastic flutter depends on true airspeed (velocity), so the temperature does not, actually, have an effect on it. However because true airspeed is not usually indicated in cockpit, the pilots will use tabulated indicated airspeed values and since these are only tabulated for altitude, they will actually fly slower.

  • Mach tuck i.e. loss of lift, accompanied with undesirable change in trim, due to exceeding critical Mach number. Since speed of sound increases with temperature, critical Mach number corresponds to lower true airspeed (velocity) in colder weather, so they'll fly slower again.

  • Engine power. Engines are able to produce more power in colder weather due to being able to achieve higher mass flow with the higher density air. However, engine power is limiting factor mainly for smaller general aviation aircraft, which have low power engines, or fighters at the other end of the performance spectrum, which are designed to fly supersonic and resist flutter. But transport category aircraft generally hit the other two limits first.


Original answer for the version before the reason they fly at higher altitude was explicitly excluded from the question:

There are two, distinct, effects:

  1. Aircraft fly faster at high altitude due to the lower air density. This is because both lift and drag are proportional to air density. So at higher altitude, the plane both have to fly faster to generate enough lift, and can do it because the drag is lower.

    More precisely, lift is proportional to dynamic pressure and drag has parasitic component, which is proportional to dynamic pressure, and induced component, which is inversely proportional.

    Therefore there is optimal value of dynamic pressure where the drag is lowest. The optimal cruise speed is slightly above this point. Since dynamic pressure is proportional to density and square of speed, the same dynamic pressure corresponds to higher true airspeed at higher altitude.

    Dynamic pressure is usually expressed as equivalent airspeed, which is the speed to which current dynamic pressure would correspond at sea level. The indicated airspeed shown on the instruments is approximation of this value.

  2. Heat engines are more efficient at lower temperatures. This is because efficiency of a heat engine (applies equally to both piston and turbine engines and both internal combustion and external combustion (steam) ones) depends on the ratio of temperature, but the combustion increases the temperature by the same (approximately) difference. So if the starting temperature is lower, the ratio is higher and the engines produce slightly more power for the same fuel flow.

    Additionally, the maximum temperature is often limited by what the materials can withstand, so at higher altitude the engine can be operated at higher power (well, not really; the power is also proportional to the density, but the engine will again run more efficiently).

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  • $\begingroup$ There is more to it: Low temperature means there are more Mols of oxygen around to react with the fuel and, most important, there is a bigger temperature margin until the max T4 is reached, so more fuel can be burned. This is the main reason for the higher thrust. It does not mean, however, that the aircraft is more economical to operate - only that more thrust can be had if desired. $\endgroup$ – Peter Kämpf Sep 3 '17 at 17:15
  • $\begingroup$ @PeterKämpf, Mols are proportional to density, no? And since I used density as a reference throughout (because equivalent airspeed also depends on density), there is no additional effect. $\endgroup$ – Jan Hudec Sep 4 '17 at 17:21
  • $\begingroup$ @PeterKämpf, also, if the margin until max T4 is higher, and is taken advantage of, the thermodynamic efficiency—and therefore specific power—does increase. $\endgroup$ – Jan Hudec Sep 4 '17 at 17:37
  • $\begingroup$ Not anywhere near that complicated. Newton's third law: Conservation of momentum. Cold air weighs more than hot air. If you are sucking in more air (by mass) the engine is expelling more mass out the back. More mass means higher momentum equates to higher thrust. $\endgroup$ – Charles Bretana Feb 10 '18 at 13:57
  • $\begingroup$ @CharlesBretana, I was about to explain how that says exactly nothing about efficiency, but then it made me actually re-read the question and replace the whole answer. $\endgroup$ – Jan Hudec Feb 13 '18 at 22:04
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Engines are limited by maximum temperatures/pressures. Above a certain limit either you exceed short term or long term safety margins. When the incoming air is colder, you should be able to increase your fuel flow slightly because the extra fuel mass still keeps combustion temps within margins, because they start with colder air/fuel. Also by having colder air coming in, the same fuel flow produces more thrust/power because of higher thermodynamic efficiency. https://en.wikipedia.org/wiki/Thermal_efficiency Look at brayton cycle for turbines.

Piston engines are typically installed so max throttle keeps a reasonable safety margin even on a hot day, so you can't give it a little extra fuel in a cold day for takeoff, you only get the benefit of thermodynamic efficiency (and a little leaner combustion because denser air is coming in for the same max fuel flow). But turbines are to be operated by professionals or controlled by FADEC (full authority digital engine control). Meaning if there's no FADEC the pilot must limit the throttle manually to a target temperature limit. For instance I flew quite a few times on Cessna 208 Caravans (non FADEC turboprop) on the right seat, just as a private pilot rated passenger. Takeoff throttle had to be hand limited at a given max temperature. As the aircraft climbed, throttle was periodically added to compensate for altitude (honestly I don't think it really was because of altitude but something to do with OAT, otherwise the throttle would have to be reduced with altitude instead). This method naturally leads to a higher fuel flow under the same altitude the colder OAT (outside air temperature) is. On bigger aircraft FADEC takes care of that, you just command the required detent for takeoff (TOGA), MCT/climb (max continuous thrust). The point being that FADEC will command higher thrust for take off using TOGA on a colder day than on a hotter day, to comply with temperature margins, same for other flight regimes. But... Cruising speed at the same altitude for a jet is highly dependent on if the engine still has excess thrust left or not ! If you are below the altitude where cruise will be throttle limited, do you really get faster cruise on a colder day, or is it only high enough where the engine is running at MCT and the colder air produces more thrust naturally ? PS: I'm not an expert on the subject. I have not received turbine training. But I am a private pilot with IFR and have college level physics which allows me to understand all concepts involved. Maybe I shouldn't be posting an answer here at all. Let me know.

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It is simple physics. The law of conservation of Momentum (Newton's third law I believe) says that for each action there is an equal and opposite reaction. The total momentum (Mass times velocity) must remain constant. So if you throw a cast iron anvil out the back of the ship, the ship will move forward faster than if you throw a feather out the back at the same velocity.

Cold air weighs more than hot air. A jet engine operating at high density altitude (when air is very warm) is sucking in significantly less air by mass than a jet engine operating at a lower density altitude (colder) at the same pressure altitude. Higher mass of air sucked in means more mass is being shot out the back. So the Thrust is higher.

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  • $\begingroup$ Nope, Thermodynamics is what you need to look at. Far, far more complex than you think. In fact the denser air argument is a net negative because the drag effect of thicker air on the airframe will be more significant than having more mass to push on the engine. $\endgroup$ – Marcelo Pacheco Feb 15 '18 at 7:27

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