An airplane tows a banner that is b = 0.8 m tall and ℓ = 25.0 m long at a speed of 150 km/hr. (a) If the drag coefficient based on the area bℓ is CD = 0.06 m estimate the power required to tow the banner. (b) Estimate the drag force on the banner with that on a rigid flat plate of the same size.

a. Power requirement, P = 30.63 W

b. Force, F = 15.68N

Explanation:

Given.

Velocity = v = 150km/hr

v = 150km/hr / 3600hr/1000km (m/s)

v = 150 / 3.6 m/s

v = 41.67m/s

Density = d = 1.225kg/m³ (at standard temperature pressure)

a. Power required to tow the banner.

Power required to tow the banner is given as FV.

Where F = the drag force and V, = velocity

The drag force is calculated as:

F = ½dACa

Where d = bℓ = 0.06

A = Area of banner (length = 25m, height = 0.8m)

A = 25 * 0.8

A = 20m²

Cd = Coefficient of drag = density = 1.225

So, F = ½ * 0.06 * 20 * 1.225

F = 0.735N

Power = FV = 0.735 * 41.67

Power = 30.62745W

Power = 30.63W - - Approximated

b. Force required to tow the banner on a rigid surface

The drag force is calculated as:

F = ½dACa

Where d = bℓ = 0.06

A = Area of banner (length = 25m, height = 0.8m)

A = 25 * 0.8

A = 20m²

Cd = Coefficient of drag = density = 1.28

So, F = ½ * 1.28 * 20 * 1.225

F = 15.68N