It is about 1590km by train. If you want a cheap way, you could take train from Beijing to Changsha, but it will take at least about 14 hours by fast train. You can find the exact time through the timetable of Beijing Trains(https://www.travelchinaguide.com/china-trains/beijing-schedule.htm) . If you want to save time, the best way is to take flight from Beijing to Changsha, but it may be a little expensive. You may search Beijing Flight Tickets(https://www.travelchinaguide.com/china-flights/cheap-beijing-flights.htm) for the accurate price.