# Drag Force Ratio

Gold Member

## Homework Statement

Calculate the ratio of the drag force on a jet flying at ##1200 km/h## at an atttude of ##15 km## to the drag force on a prop-driven transport flying at half that speed and altitude.The density of air is ##0.38(\frac {kg} {m^3})## at ##10 km## and ##0.67(\frac {kg} {m^3})## at ##5 km##.Assume that the air-planes have the same effective cross-sectonal area and drag coefficient C

## Homework Equations

##F_D=\frac 1 2CAρv^2##

## The Attempt at a Solution

Here C and A are the same so ## F_D## jet will be ##F_1## and ##F_D## plane will be ##F_2##
##F_1=ρ_1(v_1)^2## and ##F_2=ρ_2(v_2)^2##

The question ask ratio so we dont care about units ( I guess )

##ρ_1## which at 15 km is I found approximately ##0.235 (\frac {kg} {m^3})## ( from Inverse ratio )
##ρ_2## which at 7.5 km is I found ##0.525 (\frac {kg} {m^3})##

So ##\frac {F_1} {F_2}=4 \frac {0.235} {0.525}=1.79##

I dont know where I went wrong

Thank you

mfb
Mentor
I don't see how you would get 3.3.

You have some rounding errors, apart from that I get the same result assuming the atmosphere has an exponential distribution in density. I guess you are supposed to make this assumption.

• Arman777
Gold Member
I don't see how you would get 3.3.

You have some rounding errors, apart from that I get the same result assuming the atmosphere has an exponential distribution in density. I guess you are supposed to make this assumption.
Yeah...I dont know too.This is all writes in the question.

Thanks

haruspex
Homework Helper
Gold Member
2020 Award
You are given the densities at 10km and 5km, but asked about drag at 15km and 7.5km. Smells like a question that has been altered to different data, but not consistently.

Gold Member
You are given the densities at 10km and 5km, but asked about drag at 15km and 7.5km. Smells like a question that has been altered to different data, but not consistently.

I know...So I think I just let it go :)

mfb
Mentor
You are given the densities at 10km and 5km, but asked about drag at 15km and 7.5km. Smells like a question that has been altered to different data, but not consistently.
It wouldn't fit to those values either, but of they might have altered even more values.

Gold Member
It wouldn't fit to those values either, but of they might have altered even more values.

What an interesting question....