Well you might think it’s almost impossible to know, but a rather clever tool called Tweriod will tell you exactly what you want to know.
Sign up using your Twitter account and Tweriod will analyse your followers and their Twitter behaviour, specifically your followers last 200 tweets.
The free analysis covers up to 1,000 followers and, once complete, you’ll then receive a report showing the times when you will have most exposure, down to the day and hour.
I think Tweriod is great, just think how much more effective your tweets will be armed with the knowledge that your followers will be most receptive on a certain day at a certain time.