二次函数$y=\dfrac{2}{3}x^{2}$的图象如图所示，点$A_{0}$位于坐标原点，点$A_{1}$，$A_{2}$，$A_{3}$，…，$A_{2021}$在$y$轴的正半轴上，点$B_{1}$，$B_{2}$，$B_{3}$，…，$B_{2021}$在二次函数$y=\dfrac{2}{3}x^{2}$位于第一象限的图象上，若$\triangle A_{0}B_{1}A_{1}$，$\triangle A_{1}B_{2}A_{2}$，$\triangle A_{2}B_{3}A_{3}$，…，$\triangle A_{2020}B_{2021}A_{2021}$都为等边三角形，则$\triangle A_{2020}B_{2021}A_{2021}$的边长$=$______.