[1] https://www.aopa.org/news-and-media/all-news/2011/february/0...
> Captain Mark Radloff was thus faced with an almost unprecedented situation: having already accelerated well past V1, he suddenly realized that his airplane would not become airborne. At that point he faced a choice — keep trying to force it into the air and risk failing, running off the runway at well beyond takeoff speed, or try to stop, and guarantee a lower-speed overrun?
https://admiralcloudberg.medium.com/lesser-of-two-evils-the-...
Basically you'd be unlikely to get the airplane to stop before the end of the runway because brakes are not designed to handle breaking at such speed (keep in mind that an airplane lands at a slower speed than it takes off thanks to the flaps).
It meets these constraints:
1. Low enough such that if you try to stop from that speed you will stop before the end of the runway
2. High enough such that if you have an engine failure at that speed, you will make it airborne on the other engine before the end of the runway
3. Not higher than rotation speed (you can't decide to abort after pitching the nose up and getting the aircraft airborne)
4. Not lower then minimum control speed (you can't keep directional control in case of an engine failure below minimum control speed, so your only option is to abort)
If there is no speed that meets all conditions, then your runway is too short and you can't go. Reducing weight helps, since you'll accelerate faster, stop easier, and take-off at a lower speed. So that's usually the solution if your runway isn't long enough.
Constraint 1 is why you're committed to takeoff above V1. If you would try to stop above V1 there is no guarantee that you'll stop before the end of the runway. While you are guaranteed to be able to take-off above that speed, even after an engine failure. So you take the problem into the air, run checks, and return.
There aren’t a ton of reasons one might think that but a few come to mind like total engine failure or lack of elevator control or similar.
This was the case with Ameristar Charters 9363, which aborted after V1:
> [T]he jammed elevator could only be detected once aerodynamic forces came into play — something which would only happen once the plane was already speeding down the runway. The NTSB was forced to come to an incredible conclusion: that there was no way for the pilots to have detected the problem until they attempted to rotate for takeoff.
https://admiralcloudberg.medium.com/lesser-of-two-evils-the-...