DOI: 10.54287/gujsa.1979438 ISSN: 2147-9542

Quadratic Relationship Between Tool Angle of Lift and Draught in an Inclined Narrow Model Chisel Blade: A Soil Bin Parametric Study and Empirical Model Development

Murtala Iyanda, Abdulgafar Usman, Timothy Denen Akpenpuun
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Tool geometry is an underused lever for trimming tillage energy, yet the lift angle that minimizes draught for inclined narrow tools in tropical loamy sand has rarely been quantified. This study established the relationship between the tool angle of lift (β) and draught for an inclined narrow model chisel blade and located the angle of least draught. An instrumented laboratory soil bin was used with a loamy-sand soil (cohesion 16.67 kPa; internal-friction angle 26.6°; soil–metal friction angle 29.8°) at 10–12% moisture, testing five lift angles (20, 30, 40, 50, 60°) within a five-level full factorial in a randomised complete block design, with the tool reaction resolved by three orthogonal load cells. Mean draught traced a shallow U-shape, falling from 125.47 N at 20° to a minimum of 114.63 N at 40° before rising to 119.32 N at 60°; fitting a quadratic to the marginal means placed the turning point at β = 42°. The lift-angle effect was highly significant (F = 555.089, p < 0.001), and its interaction with depth was the most significant two-way interaction in the experiment (F = 97.271). A free-body analysis of the cutting forces accounts for the existence of an interior optimum, while classical frictional formulae locate the idealized optimum well below 42° (16.8–31.7° for the measured φ and δ), indicating that the inclined, cohesive–frictional system shifts the practical optimum to a higher angle. The four-factor model (= 0.998) is recommended for prediction. Setting β = 42° in place of a conventional 20° lowered mean draught by about 8.6%, a worthwhile saving for energy-constrained West African smallholdings.

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