How can air density be accurately calculated at different altitudes?

[Addez123]

Homework Statement

A plane flies at a height of 15km with velocity of 1200km/h.
Another plane flies at half that speed and altitude.

Air density at 10km is .38
Air density at 5km is .67

Assume they have same cross section area A and drag coefficient C.
Calculate the ratio of the dragforce of the two planes.

Relevant Equations

D = 1/2 * CpA*v^2

Just calculating D1 (15km altitude plane) and D2 (7.5km altitude plane) turns out to;
D1/D2 = 4*p1/p2
p being the air density at each height.

How am I suppose to calculate p? We have had no such formulas, not to mention it depends on temprature etc.
Doing a linear estimation will yield wrong answer.

Correct answer is 3.3

 

[jbriggs444]

How am I suppose to calculate p?

You are given $\rho$.

Air density at 10km is .38
Air density at 5km is .67

 

[Addez123]

I'm given air density for 10 and 5km. I need air density for 15 and 7.5km.

 

[jbriggs444]

I'm given air density for 10 and 5km. I need air density for 15 and 7.5km.

Ahah. That makes more sense.

Suppose that you model the atmospheric density as an exponential function of altitude. If a 5 km delta in height results in a factor of $\frac{0.38}{0.67}$ reduction in density, What ratio would one expect for a 7.5 km delta?

 

[Addez123]

I seriously doubt we're ment to estimate an exponential function. That's more of a math question, this is suppose to be fundamental physics. Appriciate the suggestion tho!

 

[jbriggs444]

I seriously doubt we're ment to estimate an exponential function. That's more of a math question, this is suppose to be fundamental physics. Appriciate the suggestion tho!

You've never been set a problem with radioactive half-lives?

 

[Chestermiller]

Make a graph of log-density vs altitude. Don’t forget to include density 1 at z = 0. It should be virtually a straight line.

 

[jbriggs444]

Make a graph of log-density vs altitude. Don’t forget to include density 1 at z = 0. It should be virtually a straight line.

Interesting. For these figures, it is not even close to a straight line.

 

[Chestermiller]

Interesting. For these figures, it is not even close to a straight line.

You're right. For this data, a liner fit seems to work best. Of course, that's now how the real atmosphere works.