A variable rate field sprayer utilizes Pulse Width Modulation (PWM) solenoid valves operating at a fixed frequency of $10\text{ Hz}$. At a baseline forward travel speed of $6.0\text{ km/h}$, the duty cycle is set to $40\%$ to deliver the target dosage of $150\text{ L/ha}$. If the tractor accelerates to $9.0\text{ km/h}$, to maintain the exact same application rate of $150\text{ L/ha}$ without altering spray line pressure, the required PWM duty cycle in percentage is ________ (answer in integer).
Answer Key:
60
Step-by-Step Solution & Explanation
Nozzle flow rate $q$ in a PWM system is directly proportional to duty cycle ($DC$):
$Q = \frac{600 \times q}{w \times v} \propto \frac{DC}{v}$
To maintain constant application rate $Q$:
$\frac{DC_1}{v_1} = \frac{DC_2}{v_2}$
$DC_2 = DC_1 \times \frac{v_2}{v_1} = 40\% \times \frac{9.0}{6.0} = 40\% \times 1.5 = 60\%$