In previous and existing hadron storage rings, the horizontal and vertical emittances are normally the same or very close. For the Hadron Storage Ring (HSR) of the Electron-Ion Collider (EIC), the design proton transverse emittance ratio is 10:1. To maintain this large emittance ratio, we need to have an online fine decoupling system to prevent transverse emittance exchange. For this purpose, we carried out fine decoupling experiments in the Relativistic Heavy Ion Collider (RHIC) and reviewed its previous operational data. Analytical prediction and numerical simulation are preformed to estimate how small the global coupling coefficient should be to maintain a 10:1 emittance ratio.