A mouldboard plough is operated with 6.0 kN pull. Lateral/longitudinal and vertical/longitudinal soil-force ratios are .30 and .50. Driving-wheel diameter is 1.2 m, rear-axle speed 10 rpm and slip 20%. Find drawbar power in kW, to two decimals.
The official solution interprets 6.0 kN as the resultant soil-force magnitude. Thus longitudinal draft is $F_x=6/\sqrt{1+.30^2+.50^2}=5.18321$ kN. Actual speed is $v=(\pi DN/60)(1-s)=\pi(1.2)(10)(.8)/60=.502655$ m/s. Drawbar power is $F_xv=\mathbf{2.61}$ kW. If “pull” meant longitudinal draft itself, the result would be 3.02 kW; the key requires the resultant-force interpretation stated here.
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