How much time do professors have to do research on their own?
I found this small-scale, not randomly-sampled survey from Boise State University:

Warning:


  All charts below are from TAWKS Phase 1 Stats, initial survey of 30
  higher ed faculty from Boise State University. While findings are
  highly suggestive, they do not represent a random sample.


Answer to question:


  Only 17 percent of the workweek was focused on research and 27 percent
  of weekend time.


Graphs: