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I am aware of this question, this resource (phak), and this resource that explains the science, but I am looking for a more straightforward answer.

I am student pilot and there's a lot of literature on "if there is more heat and humidity, then I need a longer takeoff and reduced rate of climb" and many variations of this statement (e.g. cold and high elevation, etc). But it's all sort of a bit confusing to me.

In the resource I linked above, it says that high temperatures mean the air is less dense but high humidity can add to the pressure so overall the density pressure is increased I need a longer takeoff. But why wouldn't the higher temperatures and humidity not cancel each other out?

I was wondering if someone could perhaps break it down as follows:

  1. Hot temperatures, high/low humidity, sea level
  2. Hot temperatures, high/low humidity, high elevation
  3. Cold temperatures, high/low humidity, sea level
  4. Cold temperatures, high/low humidity, high elevation

For the 8 above conditions, what is the general effect in aviation for take-off, landing, and rate of climb?

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  • $\begingroup$ You used the phrase "density pressure" in your question. You are talking about "density altitude" in that sentence. Density and pressure are two separate properties of air. $\endgroup$
    – TomMcW
    Jul 7 at 20:36
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If you”re looking for an explanation of the cause of change in TO distance:

  • Air expands when heated, so a warm kilo of air needs more cubic meters than a cold kilo. If it cannot expand like in a closed conrainer, the pressure will increase. If it can expand, there will be fewer air molecules.
  • Water molecules weigh less than air molecules. If some water molecules are replacing air molecules at ambient pressure, a cubic metre of humid air will be lighter that a dry m$^3$ and the reduced density will result in less lift.$^1$
  • The atmosphere thins out at higher altitudes. There are fewer air molecule to support the aircraft weight.

With the above in mind, realising that air density is a defining factor in creating power and lift, it should be easy to cross oit the four listed items in the question :)

Update This answer contains a graph on how humidity and temperature reduce air density.

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$^1$ The effect on density is actually very small, main issue is the reduction in power, most noticable in piston engines. But as a mnemonic it should work.

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High temperature reduces engine power due to lower air density (the engine thinks it's at higher elevation), and high humidity reduces engine power because the humidity slows the burn rate of the charge in the engine's cylinder, which has a power reduction effect similar to retarding spark timing; peak cylinder pressure is reached too late to get the most out of the pressure rise in applying leverage to the crankshaft.

How the order your list will depend on the magnitude of each parameter relative to the others, so there are too many variables.

The bottom line is simple:

Lower, colder, drier = better.

Higher, hotter, humid-er = worse.

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  • $\begingroup$ Maybe this is somewhat counter intuitive to me but if the temperature is higher, why would the plane think it's at a higher elevation. Does temperature typically drop as we go up in elevation? $\endgroup$
    – Jonathan
    Jul 7 at 4:30
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    $\begingroup$ @Jonathan The plane does not care about elevation, it cares about air density, and warmer air is less dense similarly to air at higher altitude. $\endgroup$
    – Jan Hudec
    Jul 7 at 5:22
  • $\begingroup$ @John K Why colder air is better? Doesn't it reduces thermal efficiency of engine? Or because it has higher density than hotter one? $\endgroup$
    – Auberron
    Jul 8 at 10:22
  • $\begingroup$ No the colder the air charge the better. The power is coming from the absolute temperature rise from combustion and you don't get a boost from the initial charge being hotter, but you DO get a boost from the charge being denser. At the extremes, like with turbocharged engines, the air charge, although dense from being compressed, is so hot that it eats into detonation margins and you have to either retard the ignition timing or use an intercooler to lower the air charge temperature. $\endgroup$
    – John K
    Jul 8 at 14:11
  • $\begingroup$ "humid-er" -> "wetter", but, TBH, I like "humid-er". ;) $\endgroup$
    – FreeMan
    Jul 8 at 14:33
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“High” and “low” for each of those factors is relative, and I can’t explain how they combine together without resorting to math. Luckily, it suffices to learn which direction each of those factors (in isolation) will move the Density Altitude.

Density Altitude is a single number that tells you how well your plane will perform (how much power your engine will produce and how much lift your wings will produce) under a particular set of conditions. That, in turn, dictates runway required and climb rate.

Low DA is good. High DA is bad.

You are not expected to remember how to calculate the exact DA; there are apps for that, and some AWOS will even tell you directly. But you’re expected to know what conditions will lead to a high DA, and why that can be so dangerous, so that you recognize when there’s a potential hazard to be mitigated.

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  • $\begingroup$ If higher LDA is bad, how come commercial jets typically fly in such high elevations? I understand that there is less drag, traffic, and turbulent weather at that elevation, giving better fuel efficiency. But are the cons of lower air density offset by the pros of better fuel efficiency? $\endgroup$
    – Jonathan
    Jul 30 at 7:07
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    $\begingroup$ @Jonathan It is mostly a problem for normally aspirated piston engines, which lose power with altitude. Turbine aircraft don’t, which is why they can fly much higher generally; they just need longer runways. But even airliners can have problems at high and hot airports like PHX and LAS. $\endgroup$
    – StephenS
    Jul 30 at 12:27
  • $\begingroup$ Ahh i see. I suspected that but wanted to confirm. Thank you $\endgroup$
    – Jonathan
    Jul 30 at 18:35

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