Density altitude

[Btl60]

Hello all,

I'm stuck on the reasoning of density at high altitudes. At high altitudes aircraft performance is decreased due too less density. What's contradictory is that the higher altitude the colder the air causing the air to be more dense. Can someone clear this situation up for me?

I'm currently studying aircraft performance and how high altitude, high temperature and high humidity decrease aircraft performance.

 

[Jim Logajan]

Wrong, but thank you for playing.

The OP used the important qualifier "my understanding". And asked for understanding from the original post. So the snideness was absolutely not called for. There is no point in posting belittling provocations unless your intent is to turn short threads into longer ones. They certainly don't show how clever you are but something else....

Any difference in gravity at altitude is negligible.

It helps to show this mathematically. For example, the radius of the earth is about 4000 miles. Gravitation force Fg at a distance R is Fg = K/(R*R), (where K is a constant for this scenario) so going from 4000 to, say, 4002 mile from the center, the force 2 miles above the surface is still 99.9% of the ground value. On the other hand, the air pressure drops from 14.7 psia to 10.1 psia.

 

[Jim Logajan]

Ah, but density regulates the speed of sound, right? Sound is faster in water than air (4x) and faster in iron still (15x).

Temperature and molecular weight affect speed of sound:

Vs = (γ.R.T/μ)[sup]1/2[/sup]

where:

Vs = Speed of sound (m/s)
T = temperature of the gas (K)
R = Gas constant (8314 J/(K.kmol))
γ = heat capacity ratio of the medium (5/3 for a monatomic gas like helium; about 1.4 for the atmosphere.)
μ = molecular weight of the medium (kg/kmol) (about 28.97 for the atmosphere)

Another way to look at is that speed of sound is some number which is very roughly 1/2 the average speed of the molecules in the medium. You can no doubt find a longer and more precise discussion of the speed of sound by using a web search engine than asking on this forum.