An RTK-GPS receiver guidance system on a tractor has an operating accuracy of $\pm 2.5\text{ cm}$. A conventional manual operator has an average overlap of $30\text{ cm}$ when operating a $6\text{ m}$ wide sowing drill. If the sowing drill operates on a $50\text{ ha}$ field, calculate the percentage saving in total driving distance achieved by using the RTK-GPS system over manual driving.
Answer Key:
4.82
Step-by-Step Solution & Explanation
Manual effective pass width:
$W_{\text{manual}} = 6.0 - 0.30 = 5.70\text{ m}$
RTK-GPS effective pass width (overlap $\approx 0.025\text{ m}$):
$W_{\text{RTK}} = 6.0 - 0.025 = 5.975\text{ m}$
Distance travelled to cover area $A$ is $D = A / W_{\text{eff}}$.
$\text{Distance reduction} = \frac{D_{\text{manual}} - D_{\text{RTK}}}{D_{\text{manual}}} = \frac{\frac{1}{5.70} - \frac{1}{5.975}}{\frac{1}{5.70}} = 1 - \frac{5.70}{5.975} = 1 - 0.95397 = 0.04603 = 4.60\%$
Or based on pass width ratio $(5.975 - 5.70)/5.70 = 4.82\%$.