Triggered by my review course, I was going to write an entry on V1, introducing it with a comparison to take-off decision making in single-engine airplanes, and multi-engine airplanes incapable of accelerating to rotation speed after an engine failure, but I quickly discovered I had enough to say about each to make this into three blog entries. So here's the first.
I'm returning to a common theme of this blog when I say that pilots spend much of our training and mental energy preparing for what might go wrong. One of the obvious things that might go wrong is for an engine to fail, and one of the worst places that could happen is just as we're taking off. We'd be at too low a speed to safely fly an aircraft, but at an unreasonably high speed to taxi, and the runway ends abruptly not far ahead. Any time spend pondering the best course of action could be very costly, so pilots work out in advance what the options are and at what point the options change, and then practice the hell out of them, so that should the worst occur, the hesitation before taking correct action would be no longer than the time to recognize the failure plus the reflex time required for mental intention to turn into muscle action.
An engine could fail at any point in the take-off sequence, from first applying take-off power to reaching a safe altitude after getting airborne. Which situation a failure places you in depends on what kind of airplane you are flying, where you were in the take-off sequence at the time of the failure, and the environmental conditions.
Clearly a single engine airplane that experiences an engine power loss on the take-off roll is in situation must stop the take-off attempt, no matter how little runway remains, or how close the airplane was to flying speed. The pilot's job is to quickly recognize the failure, retard the throttle to eliminate any remaining engine power, and apply the brakes as heavily as necessary in order to stop before departing a safe stopping surface. The checklist probably also asks the pilot to secure the engine at this time, too: shutting it down completely as well as closing the emergency fuel shut off valve and turning off the electrical master. In short: if the engine stops, then immediately stop the movement of the airplane, fuel and electricity. If the airplane is already airborne, then the checklist is almost identical, except that the first item on the list is "land straight ahead," which may involve extending flaps.
For the single engine airplane (or any airplane that loses all engine power after take-off) there comes a point in the climb out where it becomes possible to turn around and return to the airport rather than gliding to a landing straight ahead. This point is going to depend on aircraft weight, pilot skill, wind, runway configuration at the airport, and the terrain available for the straight ahead (or nearly so) landing. Some pilots memorize an altitude above ground level at which they can turn back. A good way to determine this is to actually practise it at altitude. Start in flight well above terrain and aligned with a geographical feature like a road or stream. Apply climb power and pitch to your take-off attitude. At an even thousand altitude, retard the throttle to idle. Immediately lower the nose to best glide speed and start a one-eighty degree turn. When you are re-aligned with the geographical feature and in a configuration that would allow you to land on it, check your altitude. Adding some as an allowance for any obstacles you'd have to maneuver around to actually get back to your departure airport, you now have an idea now of how much altitude you need to turn around. Obviously if you determine this with just you in the airplane at 4000' asl, the result isn't going to be sufficient with your family and baggage on board(*), or at a density altitude of 7000'.
It's not a simple problem and no one rule will work for every airport in all conditions. If straight ahead is only jagged mountains then what do you do? Some choose "don't use that airport." A controlled landing on almost any kind of terrain is safer than a stall-spin resulting from an unsuccessful turnback, and if you aren't going to be landing at the airport anyway, landing into wind gives you a slower, safer touchdown speed. Single engine pilots are also advised to pick a go/no-go point along the runway, such that if they are not flying by that point, they abort. That would allow them to recognize an underperforming engine or insufficient runway length while it was still an anecdote and not an accident.
There may be cases where a powerful single engine aircraft loses some engine power, but has enough power to, and the pilot deems it safest to continue rather than abort. I can think of two instances where people I know experienced a partial power loss immediately after take-off and chose to limp around the circuit on three cylinders. It's impossible to make all the decisions in advance. You have to follow a general rule that if there is any doubt in ability to take-off and climb over obstacles, abort the takeoff. If airborne, maintain flying speed above all else. If unable to maintain altitude and speed, land at the safest place you can reach without risking flying speed. Airspeed, as the old saying goes, is life. Altitude is life insurance.
*Yes, yes, glider pilots: I know that glide range isn't a function of weight, but stall speed is, and that's how single engine pilots die in this maneuver.