Hello Sean:
Several posts up, you wrote
Normally, depending on atmospheric conditions, the safe altitude in a C-172 is around 500-600 feet. At 500-600 feet I am able to turn the airplane around and land on the opposite runway after a simulated engine failure.
I'm wondering if this premise - the idea of turning a single engine aircraft around to go back to the runway following an engine failure immediately after takeoff - is a bit of a red herring in this discussion, which originally started off as a question about whether it was best to use Vy or Vx after takeoff in a single engine aircraft.
I've already posted my thoughts about the choice of speed (I favour Vy), however, I'm a bit concerned about your perseverance with the 'turn back to the runway' manouver.
I have not flown singles for a long time, for that reason, I'm not up to date on what present 'best industry practice' suggests if you have an engine failure prior to reaching circuit altitude. I think, though, that you would have much better odds of carrying out an uneventful landing following an engine failure at low altitude if you elected to land the aircraft straight ahead or within perhaps 45° of the runway heading.
This is because the 180° turn required to get back to the reciprocal heading is going to use up quite a bit of your potential energy (the altitude beneath you), and when you roll out from the turn, on the reciprocal of the departure runway heading, you may not have enough altitude left to get you to the threshold - and if that is the case, your options, and your time remaining to choose an option will be very limited.
If, instead, you elect to land more or less straight ahead or ±45° from the runway heading, you will have a great deal more time to properly configure the aircraft, establish your desired glide (and, later, touchdown) speed, and fine-tune your choice of touchdown point as you descend. Obviously, you won't be landing on the runway, but I think you will have a much better chance of walking away from the aircraft without injury.
It's a question of priorities - is your greatest priority to avoid injury to the pilot and passengers, or is your greatest priority to avoid minor damage to the aircraft that might arise from an off-airport landing?
Obviously, my proposal won't make sense if you are taking off over water - something that is not unusual in Norway - but otherwise, I think that the 'land straight ahead' option is the safer choice, especially for a pilot with relatively limited experience on type.
Michael