Question

Calculate the ratio of the drag force on a jet flying ?

Calculate the ratio of the drag force on a jet flying at 753 km/h at an altitude of 8.8 km to the drag force on a prop-driven transport flying at half that speed and altitude. The density of air is 0.45 kg/m3 at 8.8 km and 0.70 kg/m3 at 4.4 km. Assume that the airplanes have the same effective cross-sectional area and drag coefficient C.

Answer 1

Drag force `D` experienced a flying object depends on the density of the air; square of the velocity of the object; viscosity and compressibility of surrounding air; the size and shape of the object, and inclination to the air flow of the object.

One way to deal with complex dependencies is to characterize the dependence by a single variable. For drag, this variable is called the the drag coefficient, and designated `C_d`. This allows us to collect all the effects, simple and complex, into a single equation. The drag equation states that drag `D` is equal to `C_d` times the density `rho` of surrounding air times half of the velocity `V` squared times the reference area `A_r`.

Basic drag equation is written as

`D = C_d * A_r * rhoV^2/2`

`:.` The required ratio is

`D_j/D_p=(Cd * A_r * rhoV^2/2)_j/(Cd * A_r * rhoV^2/2)_p`
where subscript `j` is for jet and `p` for plane.

It is given that that the jet and the airplanes have the same effective cross-sectional area and drag coefficient.
Above equation becomes

`D_j/D_p=( rhoV^2)_j/( rhoV^2)_p`

Inserting given values we get

`D_j/D_p=( 0.45(753)^2)/( 0.70(753/2)^2)`
`D_j/D_p=( 4xx0.45)/( 0.70)=2.57`