As we explained in Chapter 7, the air resistance to the motion of a vehicle is something...

As we explained in Chapter 7, the air resistance to the motion of a vehicle is something important that engineers investigate. As you may also know, the drag force acting on a car is determined experimentally by placing the car in a wind tunnel. The air speed inside the tunnel is changed, and the drag force acting on the car is measured. For a given car, the experimental data is generally represented by a single coefficient that is called the drag coefficient. It is defined by the following relationship:

where

C_d = drag coefficient (unitless)

F_d = measured drag force (N or lb)

ρ = air density (kg /m³ or slugs /ft³)

V = air speed inside the wind tunnel (m/s or ft /s)

A = frontal area of the car (m² or ft²)

The frontal area A represents the frontal projection of the car’s area and could be approximated simply by multiplying 0.85 times the width and the height of a rectangle that outlines the front of a car. This is the area that you see when you view the car from a direction normal to the front grills. The 0.85 factor is used to adjust for rounded corners, open space below the bumper, and so on. To give you some idea, typical drag coefficient values for sports cars are between 0.27 to 0.38, and for sedans are between 0.34 to 0.5.

The power requirement to overcome air resistance is computed by

where

P = power (watts or ft · lb/s)

1 horsepower (hp) = 550 ft · lb/s

and

1 horsepower (hp) = 746 W

The purpose of this exercise is to see how the power requirement changes with the car speed and the air temperature. Determine the power requirement to overcome air resistance for a car that has a listed drag coefficient of 0.4 and width of 74.4 in. and height of 57.4 in. Vary the air speed in the range

of 15 m/s < V < 35 m/s, and change the air density range of 1.11 kg /m³ < ρ <1.29 kg /m³. The given air density range corresponds to 0 to 45°C. You may use the ideal gas law to relate the density of the air to its temperature. Present your findings in both kilowatts and horsepower as shown in the accompanying spreadsheet. Discuss your findings in terms of power consumption as a function of speed and air temperature.