Application of different curve interpolation and fitting methods in water distribution calculation of mobile sprinkler machine

In the calculation of water application in mobile sprinkler machines, various interpolation and fitting methods have been applied to describe the radial water distribution pattern of sprinklers. However, few studies have been carried out related to the accuracy and applicability of these methods. In this study, the radial water distribution curves were obtained by adopting cubic spline interpolation, Lagrange interpolation, least-squares polynomial fitting, and simplified geometric curves, respectively. The mobile spraying water distribution and spray uniformity coefficients were calculated based on these radial water distribution curves. The results indicated that the cubic spline curve and the least-squares polynomial fitting reflected the water distribution characteristics accurately, with the maximum deviation between the calculated values and the measured values being less than 10%. The existence of Runge's phenomenon in the Lagrange interpolation method led to sharp oscillations at both ends of the radial water distribution curve, resulting in large inconsistencies between the calculated value and the measured value of irrigation depth. The curves of the simplified geometric method were too simple to accurately characterise water application. Although the cubic spline interpolation showed high calculation accuracy, the large number of interpolation polynomial coefficients hinder its practical application. The least-squares based polynomial fitting curve showed both sufficient calculation accuracy and simple expression form, while the number of polynomial coefficients is only one more than the degree of polynomial. The recommended degree of polynomial fitting was six in this study.