..."I used to demonstrate in the A320 sim the following to people who were not familiar to airbus fbw aircraft.
T/off, cut one engine at V1+5, rotate to full backstick and let go of the controls (and I mean everything, no rudder, no stick , no power, no autopilot). What happens is the full back stick causes the aircraft to go into the low speed regime (alph protection), alpha floor activates, the aircraft applies TOGA to the live engine, establishes into a 5 degree bank and speed remains at bottom of Vls. The aircraft maintains this attitude and speed/power settings and establishes into a 5 degree climbing turn into the dead engine, until it can climb no more. Quite impressive when you see it first time. It will then sit there turning until it either runs out of fuel or the good engine fails.".....
To me, this is very, very cool.