I worked on software for the C-130J military cargo plane. It was before my time, but an earlier model aircraft crashed during a test flight. The crash occurred shortly after take off, and the entire crew was lost.
There is a critical time period during a take off when the aircraft is at maximum risk. If an engine fails before rotation (i.e. before the wheels leave the ground) an alert crew can stand on the brakes and use thrust reversers. The aircraft may get dinged up, but there is a reasonable chance the crew (and passengers) will survive.
If there is an engine failure after rotation but before the aircraft has gained sufficient altitude, unless there's a big, flat field next to the runway a crash is almost inevitable.
When an aircraft turns, it will lose altitude unless the crew compensates by adding power. An aircraft without power and sufficient altitude cannot make the turns necessary to go all the way around to land on the runway they just left.
Your post is substantially correct, with a clarification on rotation speed(Vr) vs takeoff decision speed (V1).
There are three relevant speeds for large aircraft. (I'm going to generalize very slightly to keep this short and readable.)
V1, Vr, V2.
V1 is the takeoff decision speed. An engine failure recognized before reaching V1 is handled by aborting the takeoff. An engine failure recognized after reaching V1 is handled by continuing the takeoff. At the V1 callout, the pilot flying removes their hands from the top of the throttles (as a physical reminder that aborting/rejecting the takeoff(RTO) is not happening for a simple engine failure).
Vr is the rotation speed, where the nose wheel is lifted from the ground.
V2 is the speed at which the airplane will climb safely with one engine INOP.
In most cases, V1 is the lowest speed, meaning there are cases (between V1 and Vr) where an engine out with the nosewheel on the ground results in continued acceleration, then rotation, and flight.
It's a checkride bust to RTO above V1 for a simple engine failure.
Thank you for clarifying my post. I am not a pilot. I am a software engineer (retired). I worked briefly on the C-130J mission computer operating system, then on the maintenance software the ground crews used to maintain the aircraft.
I did not know that there was a situation when a flight crew would continue a take off after an engine failure but before rotation.
There is a critical time period during a take off when the aircraft is at maximum risk. If an engine fails before rotation (i.e. before the wheels leave the ground) an alert crew can stand on the brakes and use thrust reversers. The aircraft may get dinged up, but there is a reasonable chance the crew (and passengers) will survive.
If there is an engine failure after rotation but before the aircraft has gained sufficient altitude, unless there's a big, flat field next to the runway a crash is almost inevitable.
When an aircraft turns, it will lose altitude unless the crew compensates by adding power. An aircraft without power and sufficient altitude cannot make the turns necessary to go all the way around to land on the runway they just left.