A tractor-operated rotary tiller (rotavator) operates at a rotor speed of $N = 210\text{ rpm}$ in the direction of tractor travel. The tractor moves forward at $v_f = 2.7\text{ km/h}$. If there are $z = 3$ L-shaped blades mounted in each rotor flange plane, the tilling pitch (bite length $L_b$) cut by consecutive blades in $\text{cm}$ is ________ (round off to 1 decimal place).
Answer Key:
7.1
Step-by-Step Solution & Explanation
1. Forward speed in $\text{m/s}$:
$v_f = 2.7 \times \frac{5}{18} = 0.75\text{ m/s}$
2. Rotor rotational speed:
$n = \frac{210}{60} = 3.5\text{ rev/s}$
3. Number of blade cuts per second per flange:
$f = z \times n = 3 \times 3.5 = 10.5\text{ cuts/s}$
4. Tilling pitch (bite length $L_b$):
$L_b = \frac{v_f}{f} = \frac{0.75\text{ m/s}}{10.5\text{ s}^{-1}} = 0.07143\text{ m} \approx 7.14\text{ cm} \approx 7.1\text{ cm}$