## 3 Results
The drop velocity, falling height, and kinetic energy relations to the drop diameters are described by polynomial equations of 3 rd, 4 th, and 5 th degrees and R2 values. When planning rainfall simulation experiments, researchers have to choose the drop size, which largely determines the needle to be used, and rainfall intensity, which is the product of the drop size, dripping frequency, and the number of drippers per unit area. The spacing between drippers should provide a uniform rainfall. Several dripper distribution patterns have been applied, such as rectangular [36], triangular [37], and circular [38]. For the accurate placement of drippers when designing a dripping rainfall simulator, a paper scheme with the position of the drippers is typically used. However, if the location of drippers is determined by measuring with a tape, it is possible to achieve a maximum precision of 1 mm (Figure S3). \begin{table}
\begin{tabular}{c c c c c c} \hline
**Gauge Number** & **d** & **d** & **d** & **R2** & **Equation y = a \(\cdot\) x3 + b \(\cdot\) x2 + c \(\cdot\) x + 0** \\ **Number** & **10** & **Max** & **Avr** & **R2** & **Equation y = a \(\cdot\) x3 + b \(\cdot\) x2 + c \(\cdot\) x + 0** \\ \hline / & mm & mm & mm & / & mm \\ \hline
16G & 3.48 & 3.69 & 3.59 & 0.90 & y = \(1.95\times 10^{-9}\times\) x3 \(-3.56\times 10^{-6}\times\) x2 \(+1.68\times 10^{-3}\times\) x + 3.46 \\ \hline
18G & 3.15 & 3.34 & 3.24 & 0.87 & y = \(2.30\times 10^{-9}\times\) x3 \(-3.90\times 10^{-6}\times\) x2 \(+1.68\times 10^{-3}\times\) x + 3.13 \\ \hline
19G & 2.98 & 3.19 & 3.08 & 0.82 & y = \(5.09\times 10^{-9}\times\) x3 \(-6.31\times 10^{-6}\times\) x2 \(+2.16\times 10^{-3}\times\) x + 2.96 \\ \hline
20G & 2.79 & 2.98 & 2.89 & 0.85 & y = \(4.96\times 10^{-9}\times\) x3 \(-5.65\times 10^{-6}\times\) x2 \(+1.96\times 10^{-3}\times\) x + 2.77 \\ \hline
21G & 2.69 & 2.85 & 2.77 & 0.85 & y = \(2.51\times 10^{-9}\times\) x3 \(-3.83\times 10^{-6}\times\) x2 \(+1.49\times 10^{-3}\times\) x + 2.68 \\ \hline
22C & 2.57 & 2.74 & 2.65 & 0.87 & y = \(9.14\times 10^{-9}\times\) x3 \(-8.57\times 10^{-6}\times\) x2 \(+2.24\times 10^{-3}\times\) x + 2.55 \\ \hline
23C & 2.45 & 2.61 & 2.53 & 0.88 & y = \(8.66\times 10^{-9}\times\) x3 \(-8.53\times 10^{-6}\times\) x2 \(+2.31\times 10^{-3}\times\) x + 2.41 \\ \hline
25G & 2.26 & 2.37 & 2.31 & 0.84 & y = \(5.28\times 10^{-9}\times\) x3 \(-6.00\times 10^{-6}\times\) x2 \(+1.65\times 10^{-3}\times\) x + 2.24 \\ \hline
27G & 2.09 & 2.18 & 2.14 & 0.85 & y = \(1.94\times 10^{-8}\times\) x3 \(-1.38\times 10^{-5}\times\) x2 \(+2.32\times 10^{-3}\times\) x + 2.07 \\ \hline
30G & 1.70 & 1.94 & 1.82 & 0.76 & y = \(5.23\times 10^{-8}\times\) x3 \(-3.17\times 10^{-5}\times\) x2 \(+5.50\times 10^{-3}\times\) x + 1.65 \\ \hline
32G & 1.42 & 1.74 & 1.58 & 0.74 & y = \(9.55\times 10^{-8}\times\) x3 \(-5.01\times 10^{-5}\times\) x2 \(+7.88\times 10^{-3}\times\) x + 1.35 \\ \hline \end{tabular}
\end{table} 
Table 2: Hypodermic needle gauge numbers and corresponding drop diameters at 4 10, d Max and d Avr for a 3 rd degree polynomial equation in the form of y = a \(\cdot\) x3 + b \(\cdot\) x2 + c \(\cdot\) x + 0. R2 values describe the relation between the drop size and dripping speed for different needle sizes. Note: “y” represents the drop diameter, while “x” represents the dripping speed. Note: colors indicate the color code from ISO 6009:2016.