Drag Force Ratio: Jet vs Transport at 1200 km/h, 15 km Altitude

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Homework Help Overview

The problem involves calculating the ratio of drag forces on a jet and a prop-driven transport aircraft flying at different speeds and altitudes. The context includes air density variations at specified altitudes and the assumption of equal effective cross-sectional area and drag coefficient for both aircraft.

Discussion Character

  • Assumption checking, Problem interpretation, Exploratory

Approaches and Questions Raised

  • Participants discuss the calculations of drag forces based on given air densities and speeds, questioning the accuracy of the original poster's results and the assumptions made regarding air density distribution.

Discussion Status

There is an ongoing examination of the calculations and assumptions, with some participants noting potential rounding errors and inconsistencies in the provided data. Multiple interpretations of the problem are being explored, particularly concerning the air density values at the specified altitudes.

Contextual Notes

Participants highlight that the problem presents air density values at different altitudes than those required for the calculations, suggesting a possible alteration in the question's data. This raises concerns about the reliability of the inputs used for the drag force calculations.

Arman777
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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 don't 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##

answer is 3.3

I don't know where I went wrong

Thank you
 
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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.
 
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mfb said:
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 don't know too.This is all writes in the question.

Thanks
 
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.
 
haruspex said:
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 :)
 
haruspex said:
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.
 
mfb said:
It wouldn't fit to those values either, but of they might have altered even more values.

What an interesting question...
 

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