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Mainly because of what pilots learn about density altitude and aircraft performance, any idea that an increase in temperature could improve performance seems counterintuitive. And indeed it is. Here's what got me thinking about it.

In studying for a written test I ran across a question phrased something like this:

An aircraft flying at a constant power setting flies from a colder temperature to a warmer temperature. What happens to true airspeed and true altitude?

The correct answer turned out to be that true airspeed and true altitude both increased. I knew immediately on the altitude because I remembered reading how very cold temperatures can cause dangerous errors in altimeters, but the airspeed didn't make sense.

I still don't understand why the increased temperature lead to an increase in true airspeed. Obviously a reciprocating engine doesn't perform better in warmer air. We don't install "interwarmers." Does it really mean that warmer air can actually improve performance? Or does this need a deeper explanation?

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  • $\begingroup$ Maybe "improves aircraft efficiency", rather than "performance"? $\endgroup$
    – rbp
    Commented Jul 22, 2015 at 15:24
  • $\begingroup$ "I remembered reading how very cold temperatures can cause dangerous errors in altimeters" - Be careful with that; your altimeter, by definition, shows indicated altitude, which is affected by temperature. Your altimeter will read higher than your true altitude in cold air due to the increased density (which is what's dangerous), and thus the indicated reading on the altimeter will decrease as the outside air warms. The question must assume you're also maintaining a constant indicated altitude, in which case as the air warms and your altimeter reading decreases, you'd climb to a higher TA. $\endgroup$
    – KeithS
    Commented Jul 22, 2015 at 15:39
  • $\begingroup$ The Instrument Flying Handbook outlines a scenario where the temperature is -50C and the difference between charted altitudes and corrected altitudes had to be calculated in order to conduct a safe approach. I've never been in that situation but it's good to have it in mind. $\endgroup$
    – ryan1618
    Commented Jul 23, 2015 at 4:21
  • $\begingroup$ I'm open to improving my understanding of both facets of this question in future, but best I can tell the reduced air pressure makes the wing more efficient in terms of ratio of drag to true airspeed. The engine may become more efficient, but may render less total horsepower because of the reduced availability of air. $\endgroup$
    – ryan1618
    Commented Jul 26, 2015 at 18:19

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Drag (and lift) increases with density. Density decreased and so did drag. So at the same power, you can fly faster.

Now I don't know whether reduction of power of a normally aspirated spark-ignition reciprocating engine at constant throttle setting would be higher or lower than the reduction of drag. But the question says power setting.

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  • $\begingroup$ Re "Density decreased and so did drag. So at the same power, you can fly faster."-- how do you know that Drag decreased? I think that this answer "puts the cart before the horse" -- I'd submit that you have to understand how IAS changed before you can make any prediction about how Drag changed. For more, see alternative answer aviation.stackexchange.com/a/95818/34686 $\endgroup$ Commented Nov 7, 2022 at 15:30
  • $\begingroup$ @quietflyer I was (implicitly) comparing the same velocity. But … you are right, I forgot to take into the account the decrease in lift. Because while the same power lets you fly at higher velocity (true airspeed), it will correspond to lower indicated airspeed. And that means performance only improves if you are above the minimum drag speed. $\endgroup$
    – Jan Hudec
    Commented Nov 8, 2022 at 10:04
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Lets be very clear here, aircraft performance is determined by three things; weight, altitude and temperature (WAT). An increase in any one of these three things reduces aircraft performance. Drag is only considered in performance charts in respect to flap settings and other drag devices.

If you have ever calculated the takeoff and climb performance of an aircraft departing from a high elevation airport on a hot day at maximum takeoff weight you will clearly understand this.

The test question you posted is somewhat poorly written as it makes some assumptions. It doesn't mention pressure changing as you fly into the warmer air and so you have to 'assume' that the outside 'static' pressure is constant (despite the fact that, flying into warmer air would typically result in an area of lower pressure).

Re: the airspeed. Lets say you are flying along indicating 100Kts and this was also your true airspeed (this would only be the case at sea level on a standard day). As you fly into the warmer air it would become less dense. The dynamic pressure (ram air measured by the pitot tube) will reduce. Therefore the airspeed needle will drop and show a lower speed. Let's say it drops to indicate 98 Kts... but because the power remained constant you are still doing 100 (which is your true airspeed). The question ignores the fact that engine performance decreases with higher temps., but they said 'power constant'... it's a theoretical scenario.

Re: the altimeter. Because the warm air is less dense, the static air pressure around the aircraft will decrease. The altimeter simply shows the difference between static pressure and a fixed pressure in the bellows (which can be adjusted by the setting in the Kollsman window). Because the static pressure is now lower the altimeter will indicate higher than your true altitude. You would compensate by setting the correct local altimeter setting.

Flying into the warmer air did not increase your performance! In our example above you were doing 100Kts TAS in the cooler air and you are still doing 100Kts TAS in the warmer air, it's just that the airspeed is indicating differently.

In fact, to hold the power constant in the warmer air you would need to increase fuel flow to the engine, which is actually reducing your overall aircraft performance!

Airspeed indicators show 'indicated' airspeed because this is critical for aircraft maneuvering (like rotation, approach, stall etc.). Some altimeters have TAS dials around the edge, you set the temp. and P. Alt. in cruise they have a sub scale that will show your true airspeed. Advanced flight decks (glass) have electronic TAS displays.

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A higher temperature means the molecules are moving faster. Assuming a constant atmospheric pressure, that would translate to less number of air molecules in the same amount of space.

Now, drag is caused by the airframe hitting the air molecules. There is less drag, but the power setting stays the same - i.e. the force of forward thrust is constant, but the force of drag is smaller. Airspeed increases.

Of course, with most engines, if the throttle setting stays constant, engine power is less in warm air. So the question assumes that the loss of power is compensated by an advancing the throttle.

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  • $\begingroup$ How do you know there is less drag? A-o-A is not constrained to be constant; in fact it cannot stay constant, unless IAS also stays exactly constant, which is not a "given" in this problem. For more, see alternative answer aviation.stackexchange.com/a/95818/34686 . $\endgroup$ Commented Nov 7, 2022 at 15:53
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True airspeed is equivalent airspeed corrected for non-standard pressure and temperature.

With a increase in temperature, TAS has no choice but to increase. Notice that IAS did not increase. It has nothing to do with engine performance.

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  • $\begingroup$ @Federico How does this not answer the question? The OP wanted to know why TAS increases and I answered it. It is more simple than the other answers indicate. $\endgroup$
    – wbeard52
    Commented Jul 23, 2015 at 17:43
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    $\begingroup$ my bad, sorry. You addressed the engine performance, but the question is about the overall aircraft one, that includes lift and drag. So, yes, you are right that this answer the question, but only partially. $\endgroup$
    – Federico
    Commented Jul 23, 2015 at 17:49
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Fundamentals:

  • The question is evidently comparing the TAS and True Altitude obtained in warmer air vs in colder air, at a given power setting and a given indicated altitude. So we are taking a "snapshot" of the airplane in steady-state flight (constant airspeed and altitude) in colder air, and another such "snapshot" in warmer air, and comparing the True Altitude and the True Airspeed. The Indicated (not True) Altitude, as well as the power setting, is evidently presumed to be the same in both snapshots.

  • Weight is the same in both snapshots, and therefore Lift is also the same.

  • We can't automatically say "Drag will be less whenever the air is thinner". If Lift is constant, then Drag is determined by the L/D ratio which is a function of Angle-of-Attack. If we are cruising on the "front side of the thrust-required curve", somewhat faster than the IAS for max L/D-- as would normally be the case-- then any decrease in IAS will be associated with an increase in AoA and a reduction in Drag, and any increase in IAS will be associated with a decrease in AoA and an increase in Drag. So in the context of the parameters of this question, Drag needs to be viewed as a function of IAS, not the other way around. We can't simply say that "Thinner air leads to less Drag which leads to more airspeed." So this question isn't really about changes in Drag.

  • For the same IAS, it always requires more power to fly at a higher TAS than at a lower TAS, even through Drag is the same in either case. Therefore if the power output is fixed and the air becomes thinner, leading to an increase in the TAS associated with any given IAS, the IAS must decrease. (Note that this means that the A-o-A must increase. So, assuming that we are cruising on the front side of the thrust-required curve, we do see an decrease in Drag-- just as we would if we decreased power to slow down, while increasing the A-o-A, with no change in the characteristics of the airmass.)

  • So we know that the IAS must be lower in the warmer air than in the colder air, and the A-o-A must be higher in the warmer air than the colder air.

  • At first glance, it's far from obvious that the TAS will in fact always be higher in the warmer air than in the colder air, for a given power output from the engine. Consider this-- for a given power output of the engine, and with angle-of-attack free to vary as needed, would it be fair to say that an airplane always experiences a higher TAS in level flight at a higher altitude than at a lower altitude? It appears that the answer is in fact "yes". Granted, if power is constant, then at some very high altitude, the airplane will only be able to maintain altitude at the one particular IAS where the power-required is at a minimum-- but the reason for this apparent "shortage" of power is simply the fact that any given IAS is associated with a higher TAS, and therefore requires more power, at high altitude than at low altitude. So yes, if power is constant, it appears that an airplane does in fact always experience a higher TAS in level flight at a higher altitude than at a lower altitude, and similarly, will also always experience a higher TAS in level flight at a given Indicated altitude in warmer air than in colder air.

  • Of course, in the real world, as an aircraft climbs above some certain altitude, the power output of the engine cannot remain constant!

Now as to your specific question--

I still don't understand why the increased temperature lead to an increase in true airspeed. Obviously a reciprocating engine doesn't perform better in warmer air. We don't install "interwarmers." Does it really mean that warmer air can actually improve performance?

Only in the context of the aircraft's TAS performance for a given power output of the engine. Not in the context of the aircraft's TAS performance at the maximum possible power output of the engine at any given altitude, or the TAS performance at any given rpm or throttle lever position.

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"Obviously a reciprocating engine doesn't perform better in warmer air."

Why not? Horse Power increases with inlet temperature. Have a look at your engine handbook and look for something like "Sea Level and Altitude Performance". There should be a chart or table that makes that clear. I'm looking at the chart in my Lycoming engine manual for my Mooney, and the chart clearly shows an increase of horse power with inlet temperature.

"We don't install 'interwarmers.'"

No, we don't, but your reasoning is wrong. The premise of the question is that the air temperature changes by itself. By the way, the air pressure increase in a turbocharged/supercharged engine has an increase in air temperature as one component (although the smaller one) to provide for higher engine power. We close the cowl flaps in cruise flight to keep the engine warm, so we get higher engine output when an increase in altitude provides for cooler air to begin with!

"Does it really mean that warmer air can actually improve performance?"

yes, but not much. Air density changes (from altitude change) are much more pronounced.

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    $\begingroup$ When you say "inlet" are you referring to the temperature of the air entering the intake or the turbine inlet? If you mean turbine inlet that's a measure of the temperature of exhaust gas exiting the cylinder, not intake air, so I don't see how it's directly related. $\endgroup$
    – ryan1618
    Commented Jul 23, 2015 at 4:18
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    $\begingroup$ you are referring to reciprocating engines in your post. There are no turbines in reciprocating engines. But then you also talk about cylinders ... there are no cylinders in a turbine engine ... sorry, I don't see how you're making sense here. $\endgroup$ Commented Jul 23, 2015 at 12:54
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    $\begingroup$ Turbocharged reciprocating engines use a turbine inline with the exhaust. When you refer to "inlet temperature" it sounds like you might be referring to TIT or turbine inlet temperature. My point was was the temperature of the air inducted and I think you were referring to the temperature of the exhaust as it exits the cylinder. $\endgroup$
    – ryan1618
    Commented Jul 23, 2015 at 14:23
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    $\begingroup$ Nope. I'm not referring to turbocharged engines, and I'm not referring to exhaust. Inlet is never exhaust. Have a look at your engine handbook. My Lycoming engine manual has a chart for Sea Level and Altitude Performance and lets you compute horse power with inlet temperature as one of the inputs. Don't get hung up on the word "inlet". For most practical considerations, the inlet temp is ambient temp. That's what is the premise of your question: the plane flies into an area of higher temp. That would be ambient temp. You can pretty much assume that's the same temp that your engine sucks in. $\endgroup$ Commented Jul 23, 2015 at 14:28
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    $\begingroup$ I also found the chart you're referring to. Figure 3-22. 11hc.44rf.com/manuals/engine-prop/lycoming/… $\endgroup$
    – ryan1618
    Commented Jul 23, 2015 at 19:25

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