... and to fly that way for quite some time with high confidence of success.
If you think about it: this aircraft was flying to Hawaii; after crossing the west coast, it would be flying almost 2,500 miles over the ocean to get there.
If you lost the engine halfway there (instead of soon after takeoff), you'd either have to turn around and fly back toward California or continue onwards; which is almost a three hour flight.
The concept is called ETOPS for Extended Twin Operations; and the Boeing 777 was the first twin-engine aircraft rated to do this (fly up to three hours for the nearest available airport).
V1: Speed at which the take off attempt should no longer be aborted
Vr: Speed at which the plane should be pitched up (rotated)
V2: Speed at which the plane can safely climb with one engine
If an engine fails after V1 the runway is supposed to have sufficient length that you can hit Vr, rotate, and be 35 feet off the ground and traveling at V2 before you run out of tarmac even with a single engine.
It's kind of poorly worded. Hitting V1 means you are committed to taking off, single engine failure or not - but you HAVE to reach V2 to safely climb on one engine.
This should happen within moments of hitting Vr, but being single-engine after V1 means you went from hitting Vr halfway down the runway to potentially doing so at the ass-end of your minimum runway length. This means you have basically no room for any pilot error or other failures, and why engine failure on take-off is routinely rehearsed.
Not sure where the original disagreement came from. I never said an aircraft should be able to take off at V1. Perhaps you took the "fly" literally which is fine but that was certainly not the intention.
I don't have any specialist knowledge here, but that seems to make sense. If you're under V1 then you can still abort takeoff. Having that be the minimum for single-engine takeoff essentially sets up the rule that if you lose an engine while you can safely abort, then you must.
