According to the ASABE standard draft model for a mouldboard plough in silty clay loam soil, the unit draft $D$ (in $\text{N/cm}^2$) as a function of forward speed $S$ (in $\text{km/h}$) is given by:
$D = 6.5 + 0.045 S^2$
A 3-bottom mouldboard plough with $35\text{ cm}$ width of cut per bottom operates at a depth of $18\text{ cm}$ at a speed of $6.0\text{ km/h}$. The total draft force required to pull the plough in $\text{kN}$ is ________ (round off to 2 decimal places).
Answer Key:
15.35
Step-by-Step Solution & Explanation
1. Total furrow cross-sectional area:
$A = n \times w \times d = 3 \times 35\text{ cm} \times 18\text{ cm} = 1890\text{ cm}^2$
2. Unit draft at $S = 6.0\text{ km/h}$:
$D = 6.5 + 0.045 \times (6.0)^2 = 6.5 + 0.045 \times 36 = 6.5 + 1.62 = 8.12\text{ N/cm}^2$
3. Total draft force:
$F = A \times D = 1890\text{ cm}^2 \times 8.12\text{ N/cm}^2 = 15,346.8\text{ N} \approx 15.35\text{ kN}$