Question

A “coast-down” test was performed to estimate the aerodynamic resistance coefficient CD and the rolling resistance coefficient fr of a road vehicle. The test was conducted on a level road with a tail wind of 8 km/h. The vehicle was first run up to a speed of 96 km/h and then the transmission was shifted to neutral. The vehicle decelerated under the action of the aerodynamic resistance, the rolling resistance of the tires, and the internal resistance of the driveline. The vehicle slowed down from 96 km/h to 88.5 km/h in a distance of 160 m, and from 80 km/h to 72.4 km/h in a distance of 162.6 m. The vehicle weighs 15.568 kN and has a frontal area of 2.32 m2 . Assuming that the rolling resistance of the tires is independent of speed and that the internal resistance of the driveline may be neglected, estimate the values of the aerodynamic resistance coefficient CD and the rolling resistance coefficient of the tires fr.

Answer 1

Tailwind velocity=8 km/h= 2.222 m/s

Let the velocity of car be v

The relative velocity between car and wind is

Total resistance force opposing the motion is

f= drag force+rolling resistance

A= frontal area= 2.32 m²

W= weight of vehicle= 15568 N

= air density=1.225 kg/m³

Hence

Since the velocity change is small we assume the average C_d shall correspond to average relative velocity.

For the first case:

Average relative velocity is

The deceleration is

From kinematics

Hence

Or

-----(1)

Similarly for the second set

Hence

----(2)

Substracting (2) from (1)

Substituting in (1)