Subtopic: Calculation of performance parameters – field capacity, efficiency, performance index, application rate and losses
Question Statement:
A tractor-mounted boom sprayer carries a horizontal row of 12 identical flat-fan nozzles (spray angle 110°). To achieve uniform coverage, the required lateral overlap between adjacent nozzle footprints at the target plane is 30% of a single nozzle footprint. Boom height is 0.60 m above the target plane.
The tractor is set to travel at a theoretical forward speed of 8 km·h⁻¹. Wheel slip is 8% and the field efficiency is 75%. All other losses are neglected. The total time (in minutes) required to spray a 25 ha field is ________. (Rounded off to the nearest integer)
Official Answer Key:
170 to 190
Step-by-Step Solution & Explanation
Step 1 — single-nozzle footprint width at the target plane. A flat-fan nozzle of included spray angle θ at height h covers:
w = 2h · tan(θ/2) = 2 × 0.60 × tan(55°) = 1.2 × 1.42815 = 1.714 m
Step 2 — effective nozzle spacing with 30% overlap. Adjacent footprints share 30% of a footprint, so the new ground added by each nozzle is 70% of w:
s = 0.70 × 1.714 = 1.200 m
Step 3 — effective boom (working) width:
W = 12 × 1.200 = 14.40 m
Step 4 — actual forward speed (slip reduces the actual speed below theoretical):
S = 8 × (1 − 0.08) = 7.36 km·h⁻¹
Step 5 — effective field capacity:
EFC = (W × S × η_f)/10 = (14.40 × 7.36 × 0.75)/10 = 7.95 ha·h⁻¹
Step 6 — total time:
t = 25/7.95 = 3.146 h = 3.146 × 60 = ≈ 189 minutes
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