Subtopic: Functional requirements, principles of working, construction and operation of manual, animal, tractor and renewable energy operated equipment for tillage, sowing, planting, fertilizer application, inter-cultivation, spraying, mowing, chaff cutting, harvesting and threshing
Question Statement:
A tractor drawn rotary mower has a swath width 1.2 m when operated at a forward speed of 5 km·h⁻¹. The specific power loss due to air, stubble and gear train friction per m of swath width is 1.5 kW and the specific cutting energy is 2 kJ·m⁻². The total weight of tractor with mower is 25 kN and the resistance to propel the tractor with mower is 6 % of its total weight. Assuming transmission efficiency between engine to drawbar as 75 % and engine to PTO as 87 %, the total engine power required to carry out mowing, in kW, is __________. (Rounded off to 2 decimal places)
Official Answer Key:
8.60 to 8.80
Step-by-Step Solution & Explanation
Two independent power paths must be added: the PTO path (which drives the cutting mechanism) and the drawbar path (which propels the machine).
Step 1 — forward speed:
v = 5 km·h⁻¹ = 1.3889 m·s⁻¹
PATH 1 — PTO (cutting) power
Area covered per second = swath × speed = 1.2 × 1.3889 = 1.6667 m²·s⁻¹
Cutting power = specific cutting energy × area rate = 2 × 1.6667 = 3.333 kW
Power loss (air, stubble, gear train) = 1.5 kW·m⁻¹ × 1.2 m = 1.8 kW
Total power at the PTO = 3.333 + 1.8 = 5.133 kW
Engine power for this path = 5.133/0.87 = 5.90 kW
PATH 2 — Drawbar (propulsion) power
Rolling/propelling resistance = 6% of 25 kN = 1.5 kN
Drawbar power = 1.5 × 1.3889 = 2.083 kW
Engine power for this path = 2.083/0.75 = 2.78 kW
Step 2 — total engine power:
P = 5.90 + 2.78 = 8.68 kW
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