But let's not forget the airlines aim for - and achieve - FAR higher safety levels than we do...
Heaven forbid that you seek for,or train to a high level of safety. You don't seek argument, and that's no argument. You have absolutely NO excuse for failing to seek the highest possible level of safety. Moreover, you have every responsibility to do so. That's your job description as PIC, in fact.
But no, I don't maintain I have more cognitive power than experienced airline pilots. Just a much, much wider range of situations to assess, sometimes, and less SOPs. More privileges. More freedom. More risks.
As a private pilot you hold more privilege than the holder of an ATP? Really?
No doubt from your questions and comments you take more risks. That's nothing of which to be proud.
I'm asking about the concept of lifting off slow, and then if the engine fails, pulling the other one and accepting a controlled crash, cos I'm trying to work out whether I could or should operate into my own private strip.
You're asking the wrong question.
The real question should be what length runway you need to depart in order to achieve adequate takeoff speed and distance to enable safely handling the situation if an engine quits. If you're asking if you can handle one quitting while attempting to climb out or takeoff below Vmc, you're asking a stupid question. There really is such a thing as a stupid question. What you're really asking is "If I do something stupid, what are the chances that I'll be fast enough to save myself from my own stupidity?" Which of your instructors taught you to take off below Vmc?
Not that it's not possible to do by any means...but certainly the inexperience offered in the way you ask and your tone suggests that it's not something for you. Of course, you also sound like you intend to do as you please, without regard to what others may have to say.
But let's not forget the airlines aim for - and achieve - FAR higher safety levels than we do, at a certain cost. If we were to aim for the same levels of safety, we would only ever fly out of balanced fields, we'd have a fully trained co-pilot on each flight, we'd have turbine engines with ample excess thrust so a serious climb rate is attainable on one engine, we'd have professional flight despatchers, and we'd have....er....an airline
What makes you think an airline must operate with a balanced field? A balanced field is one in which the accelerate go distance equals the accelerated stop distance, and this is very seldom the case. Rather, a rejection speed is computed which establishes a maximum speed to which the flight can accelerate before recognizing the problem and rejecting the takeoff. If the resulting stopping distance approximates the required takeoff distance, it's merely a coincidence.
You shouldn't be taking off, however, unless you have the ability to recognize the problem, and reject, and stop in the remaining runway, or stopway.
The issue of a first officer is largely one of aircraft certification and the regulations under which the flight is conducted. There's no question that in a highly complex, advanced aircraft, a SIC can be not only necessary, but immensely helpful. However, you make a poor comparison. Your aztec vs. a B747, for example. Consider also the complexity of operations, and the kindof flying you do may not require it. This does NOT mean you are excused from operating at the highest level of safety, and maintaining the highest level of proficiency. You have that full responsibility; operating privately does NOT excuse you from that.
Flight dispatchers are an operational requirement, and not all airlines use dispatchers. Some use flight followers, and not all of them are professionals. You, however, have the same responsibility in full to calculate your performance, know your fuel, your weather, your distances, your climb rates, and your capabilities before you go. Don't try to excuse yourself to a lesser level of safety merely because someone else isn't making the calculations for you. Moreover, regardless of who makes the calculations, the PIC is always responsible for them.
You don't need a turbine engine to act safely. Nor do you need it to assess takeoff performance or plan for it.
You could do that sub-Vmc takeoff in a turbine powered airplane and achieve the same results...if you're below Vmc, it won't matter if it's turbine or piston...pushing the power up will only aggravate your problem, and the fact is that your problems at that point are only compounded. So again, your comment really has no relevance to the conversation here, nor is it an excuse for acting unsafely.
I get the distinct impression that no matter how many people tell you not to go jumping into a higher performance airplane with a little more complexity, and taking it off Vmc, you're going to keep on asking until someone tells you it's okay. Anyone who doesn't is being "argumentative."
I guess I can't really see the difference between flying off a short field in a single, and accepting that if the engine fails in the first 5-10 seconds after airborne you're in deep trouble, and doing the same in a twin.
Therein lies the problem. You're already flying an aztec, you said. You shouldn't have to ask this question.
You're in deep trouble only if you fail to plan accordingly in the single. Your takeoff should be planned such that you already know where you're going to go and what you're going to do. You're going to be landing at a slower pace with far less mass energy, with a much lower stall speed, much lower touchdown speed, and better slow speed landing characteristics in the single; you can glide much more comfortably, farther, longer, and have none of the inherent dangerous characteristics that take place in the twin.
You may have no choice but to retard the good engine when a failure occurs in a light twin. It happens. However, especially in an airplane such as the 340, you should be planning your takeoff such that your weight, takeoff distance, and obstacle clearance area and departure area mean you don't have to. If you plan your takeoff by intentionally departing from such a short strip that you have zero options and your game plan is to put yourself in an emergency situation below the minimum control speed, then you've already decided to live a mistake before you ever start the engine. Starting with the fact that you've already placed yourself in a position where control may not even be possible.
Add to that the fact that aircrat such as the 310 and 340 use tip tanks with additional mass in the tip tanks and once a roll starts you may not be able to stop it.
Double the engine failure risk, of course, but neglible + neglible = close to negligible, doesn't it?
There again is a big part of your problem. You're assuming, guessing. Your condemn the airline operation for it's high level of safety, which is a foolishly mind-blowing concept in it's own rite. However, safety need not be the purview of the airline pilot alone, nor the corporate pilot only...it needs to be yours. The difference between you and the professional pilot is that the professional pilot plans the takeoff with a failure in mind, not hoping that it doesn't. Forget professional...the responsible pilot plans in advance for each contingency, and thus plans for the safe outcome of the takeoff regardless of whether the engine fails or not. You don't need to be flying a transport category airplane to do that.
And to answer your question, negligible doesn't equal negligible. Your engine will either run, or it will not; that's a one out of two chance, and it doesn't get any better the longer you fly...or the more engines you carry. You have that opportunity every single takeoff, and had better be planning for it. Not just assuming it's such a slight risk it probably won't happen. When it does, in the twin you not only lose 80% of your available thrust, but the remaining value is fighting to take control away from you.
Strive to eliminate risk, not embrace it.
I'm guessing that we're talking about a 5 second period between rotation and a reasonable VMC-proof speed.
The problem is that unlike having a failure occur at a speed above Vmc where you have the luxury of losing airspeed all the way to the minimum control speed...when you lose the engine below Vmc, you can't accelerate to Vmc. Adding more power only aggravates the problem. That leaves you in a regime where your ONLY choice is to reduce power on the good engine because you have no more aerodynamic control authority. Often this speed occurs close to the stall speed, which will also be the case if you're attempting to depart from a very short field near minimum control speed...and you can get there in a big hurry as you slow when the first engine goes. You have to recognize and react to the situation (an inexperienced pilot will invariably attempt to push the power up, rather than retard it, and handle the directional control with aerodynamic controls alone), and then correctly apply reduction of power on the good engine.
In the meantime, you're applying opposite rudder to the failed engine, and opposite aileron. You're already slow, at a high angle of attack, and at maximum takeoff power. The lowered aileron on the side of the bad engine increases the local angle of attack, increases adverse yaw, increasing the effects of the failed engine, as well as potentially causing a stall along the section of wing occupied by the aileron. The yaw is made worse, the roll is made worse. As the wing starts down in the 340, additional rotational inertia is imparted to the fuel in the tip tanks, making the turn and the roll even harder to stop. Additionally, as the wing with the good engine still has airflow, local lift is created which isn't available on the side with the bad engine, increasing the roll. Further, as the yaw occurs, the wing with the good engine moves forward increasing lift, while the airflow over the retreating wing decreases lift, further aggravating the roll. Even if you pull the power, you may continue to roll once it's started. How far, how fast, really depends on some of the factors previously cited (including CG, flap position, gear position, weight, density altitude, etc. If you're near the ground at the time, you may not have to roll very far before you catch a wingtip, and you may be lacking the performance to climb much to avoid it. Your time to recover is further reduced.
Rather than find out when it's too late, don't put yourself in that position to begin with. You needn't be an airline pilot to be safe.