Here are a few very good technical references regarding the aerodynamic considerations of turn back performance (these are referenced in Charlie's discussion on the topic in Sport Aviation and also linked on the EAA web site):
Should You Turnback? Discusses the optimal maneuver for a turnback after engine failure during take-off:
http://www.nar-associates.com/technical-flying/impossible/possible.html
The Feasibility of Turn-back from a Low-Altitude During the Takeoff Climb-out Phase. The complete AIAA (American Institute of Aeronautics and Astronutics) paper that discusses a simulator experiment addressing the turnback after engine failure at low altitude (500 feet) during take-off problem:
http://www.nar-associates.com/technical-flying/jett/jett_wide_screen.pdf
The Possible "Impossible" Turn. This paper discusses the optimal maneuver for a turnback after engine failure during take-off. The paper is quite mathematical. However, any pilot can benefit from the discussion of the results and the graphs. Based on an AIAA (American Institute of Aeronautics and Astronutics) Journal of Aircraft paper of the same title (Vol. 32, pp. 392-397, 1995).
http://www.nar-associates.com/technical-flying/impossible/impossible_wide_screen.pdf
Fly safe,
Vac
FlyONSPEED.org
Jerry, Vx occurs at Minimum Power Required alpha (i.e., the prop is producing maximum thrust); Vy starts at L/Dmax alpha, but since power increases with airspeed it actually varies a bit as Bob pointed out earlier in this thread. But using these two angles for initial takeoff works well from a practical stand point if you've got a system that provides accurate cuing.