Tumbleweeds move by rolling across the ground, driven by the drag force they experience when exposed to a breeze. Such a concept has been proposed for developing planetary exploration vehicles to be used perhaps, on Mars [27]. We are interested in calculating the drag force required to just get the tumbleweed to move. There is no sliding friction involved, but due to deformation of the tumbleweed as it contact the ground, the normal force acting on the tumbleweed is displaced a bit relative to the center of mass axis as shown in Figure P13.11. The coefficient of static friction, \(\mu_{s}\), is 0.15 .

a. Perform a moment analysis about the center point and estimate the drag force, \(F_{D}\), required to offset the normal force, \(F_{N}\), and just get the tumbleweed rolling.

b. What wind speed would be needed?

c. The Martian atmosphere is mostly \(\mathrm{CO}_{2}\) with a density of about \(0.016 \mathrm{~kg} / \mathrm{m}^{3}\), an average wind speed of about \(3 \mathrm{~m} / \mathrm{s}\) and a kinematic viscosity of about \(8 \times 10^{-4} \mathrm{~m}^{2} / \mathrm{s}\). If we assume a roving sensor that weights about \(3 \mathrm{~kg}\), a drag coefficient that is nearly 1.0 , and a normal force displacement of \(0.1 r_{o}\), how large would such a tumbleweed have to be to move about?

Transcribed Image Text:

FIGURE P13.11 F F N mg X