Hello, the fastest is by metro and it takes only above 20 minutes. In the Changsha railway station, the convenient exit or entrance is No. 3, when you get out of arrival exit, turn left and go straight, on your right hand is the metro. In the Changsha South Railway station, the convenient exit or entrance is No.1. So I suggest the time gap should be 1 hour longer in order to catch the next train. Hope it will help you.