Polar,
Completely understand your explanation. The part that gets me is the acceptance of an "unbalanced" field. By "reducing" V1 based solely on the fact that you don't have the runway available and you don't want to leave "money" behind boggles the mind.
Granted, as MikeD and I were talking about, most of the info I work with is a Vmcg (Minimum Control Ground) problem with the four engine aircraft. However, I assume that even in the large two engine aircraft of the day, losing one of the motors during the takeoff still would still cause a Vmcg issue depending on just how big your rudder is.
For us, our balanced field length would be based on Vcef (Critical Engine Failure). On a nice day with some hefty crosswinds, we also need to consider Vmcg (Minimum Control Ground). Both of these are considered when we come up with our Critical Field Length (CFL); distance required to accelerate on four engines, lose a motor, and either continue or abort the takeoff. Once these is calculated, we pretty much forget about any "extra" runway ahead of us. If we have a 12,000 ft runway, but our CFL (Critical Field Length) is 7,000 ft, we're "never" going to use the extra 5,000 ft.
What I'm getting from all the "civil" explanations, and yours as well, is that V1 is only based on accelerate-stop speeds, what we would call Vrefusal. We as well, cannot have a V1 above Vrefusal, makes stopping sporty like you've said. But, if we don't reduce weight, now at our "V1," we may not have reached Vmcg or Vcef.
For us,
Normally, Vmcg < Vcef = V1 < Vrefusal and Vr (Balanced Field)
Heavy Crosswinds, Vcef < Vmcg = V1 < Vrefusal and Vr (Unbalanced, as it'll take less room to takeoff than it does to stop)
When do run into the Vcef < Vmcg area, we will reduce the thrust of our outboard engines to regain a balanced field length. However, we can only reduce our motors so much before the inboard engines become more critical and Vcef becomes driven by them. If we reduce them to the limit, we will remain on an "unbalanced" field.
Now, you can make the argument that you can use that extra 5,000 ft for stopping if need be. And that's where we fall into with the OP. If we have a failure AFTER V1 that makes the aircraft INCAPABLE of flight, we'll abort. The extra 5,000 will come in handy and, heck, we weren't going to fly anyways.
But, in all the examples ya'll have given, you base V1 essentially ONLY on the fact about possibly being able to stop in the runway available. While this is GREAT for stopping, it opens up the possibility that you'll be attempting to fly an aircraft, past V1, that is NOT safe to fly. If you lose a motor past your "reduced to carry all the money" V1, are you sure you'll be at or past Vmcg? If you don't have the rudder available, you just don't have it. This is where my sticking point is.
Sorry for the lengthy post, just feel like I'm missing part of the conversation somewhere.
