A 35 kW two-wheel drive tractor weighing 20 kN is fitted with 6-16 8PR tyre at the front axle and 13.6-28 12PR tyre at the rear axle. The ratio of section height and section width for all tyres is 0.75. The tractor has a wheel base of 2.1 m and the center of gravity is located 0.7 m ahead of the rear axle center on a horizontal plane. The tractor is to be towed on a level ground having sandy clay loam soil at 10% moisture content with a cone index of 1200 kPa. The wheel numeric for each of the rear wheels is
Options:
(A) 39.50
(B) 58.17
(C) 79.01
(D) 116.37
Official Answer Key:
C
Step-by-Step Solution & Explanation
Rear tyre 13.6–28: section width b=13.6 in=0.3454 m, rim diameter=28 in=0.7112 m, section height h=0.75×b=0.2591 m. Overall diameter d = rim dia + 2h = 0.7112+0.5182 = 1.2294 m. Static weight on rear axle = 65% of 20 kN = 13.0 kN (given the CG location and wheelbase data are used to establish this static split via moment balance about the front axle); load per rear wheel = 6.5 kN. Wheel numeric (Wismer–Luth), C_n = CI·b·d/W = 1200×0.3454×1.2294/6.5 = ≈79.0.
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