Gets awfully complicated doesn't it? I remember way back a deputation of 15 disgruntled first officers demanded an audience with the chief pilot, who was a gruff aggressive character handy with his fists. The complaint was that in the simulator each check captain they had flown with had a difference in abort technique - ie who was up who, and who was paying the rent. The first officers were sick and tired of getting hacked around and written down for non-standard procedures. They assembled outside the chief pilot's office accompanied by one of the senior check pilots.
The check pilot timidly knocked on the door, and a loud voice bellowed "Come in". They all trailed in and stood in silence until the chief pilot looked up and said "What the f---k's this all about?"
Clearing his throat with a polite cough, the check captain said that the first officers were cheesed off because none of the check captains seemed standard in the engine failure after V1 actions and that they wanted a ruling from you, sir.
Jeez - said the chief pilot - is that all! It's easy. The PNF calls failure - the PF sez state the type of failure - the PNF sez fire No 1 - and puts his hand on the throttle - the PF sez confirmed - the PNF sez .. The chief pilot stopped in mid-sentence, and said what the @#%$+# wrong with you mate, - to the check captain who had put his hand up.
At this point, the check captain again coughed nervously, and apologising profusely, interrupted the chief pilots burst, saying "Sorry about this, boss, and I hate to correct you - but that's not we're teaching in the simulator.
Seems the first officers had a valid point, when even the chief pilot had got it wrong.
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Interesting also is that although many airlines have a formal "Taking over - handing over policy" when changing handling control, some ignore this policy when it comes to the point where the captain takes over from the co-pilot in order to initiate an abort. That has led to real confusion. Perhaps it should be "I have control - rejecting" Or a similar phase, rather than simply assuming an unspoken change of control responsibility
In addition, I would hazard a guess that any captain that has complete blind trust in the first officer to decide and initiate a high speed abort (the captain becomes just an interested party) would be in for a massive litigation shock if this resulted in an accident. As much as it would be nice to give the first officer his head in the instantaneous V1 abort situation, the legal fact is the captain wears the full blame if the abort was less than successful.