Question

An airplane weighing 5000 lb is flying at standard sea level with a velocity of 200 mi/h. At this velocity the L/D ratio is a maximum. The wing area and aspect ratio are 200 ft2 and 8.5, respectively. The Oswald efficiency factor is 0.93. Calculate the total drag on the airplane.

Answer 1

Answer:

98.15 lb

Explanation:

weight of plane (W) = 5,000 lb

velocity (v) = 200 m/h =200 x 88/60 = 293.3 ft/s

wing area (A) = 200 ft^{2}

aspect ratio (AR) = 8.5

Oswald efficiency factor (E) = 0.93

density of air (ρ) = 1.225 kg/m^{3} = 0.002377 slugs/ft^{3}

Drag = 0.5 x ρ x $v^{2}$ x A x Cd

we need to get the drag coefficient (Cd) before we can solve for the drag

Drag coefficient (Cd) = induced drag coefficient (Cdi) + drag coefficient at zero lift (Cdo)

where

• induced drag coefficient (Cdi) = $\frac{Cl^{2} }{n.E.AR}$ (take note that π is shown as n and ρ is shown as $p$)    

        where lift coefficient (Cl)= $\frac{2W}{pAv^{2} }$=$\frac{2x5000}{0.002377x200x293.3^{2} }$ = 0.245

        therefore

       induced drag coefficient (Cdi) = $\frac{Cl^{2} }{n.E.AR}$ = $\frac{0.245^{2} }{3.14x0.93x8.5}$ = 0.0024

• since the airplane flies at maximum L/D ratio, minimum lift is required and hence induced drag coefficient (Cdi) = drag coefficient at zero lift (Cdo)

• Cd = 0.0024 + 0.0024 = 0.0048

Now that we have the coefficient of drag (Cd) we can substitute it into the formula for drag.        

 Drag = 0.5 x ρ x $v^{2}$ x A x Cd

Drag = 0.5 x 0.002377 x (293.3 x 293.3) x 200 x 0.0048 = 98.15 lb