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What if pilot PIC had lowered the nose, flew wings level and maintained flying speed AND did nothing else, what would the outcome be?
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Someone should have addressed your question by now... The answer is
maybe
I have ZERO experience in a C130 or any Large multi engine but here are some of the circumstances that could make even that scenario problematic.
First this crew seemed to never grasp the seriousness of their situation or if they did made every possible wrong decision. I will make a guess but it is unlikely the extra time would have changed their decisions.
Any 4 engine has two different VMC speeds. VMC is the minimum controllable airspeed, with one or even two engines out. At VMC the aircraft can be controlled to fly straight ahead or within 20° with 150 lbs of rudder (max) input and a max bank angle of 5° 'away' from the dead engine(s). Doesn't mean climb it is only a controllable condition. At this point the dead engine(s) need to be cleaned up (feathered) and any other requirements like partial flaps, gear up, cowl flaps closed, etc. met. If this speed and conditions are not met, the aircraft will start an uncontrolled roll into the dead engine side. Many will think you can just add aileron against it but all you are doing is increasing the stall speed. If you are below VMC, the only solution is to trade altitude for for speed and you will have to reduce power on the good engines or you will not recover.
In smaller twins and not really in this particular accident, improper action can also slow you into the magic Region of Reverse Command. That is the speed where drag is so great you don't have enough power to accelerate. Again lowering he nose is the only solution there. The 'reverse' part comes from the fact that if you have power and increase it, the aircraft will actually slow more if you try to maintain altitude. Likewise reducing power and reducing angle of attack will increase speed.
When all this is taking place low to the ground it is very hard to push forward and see the ground rushing up! And in this case it would have been an overwhelming sight!
With their light loading and even with their high drag, it seems to me that if they went to level attitude, zero side slip, and 5° bank, it would have accelerated. Would that have changed the outcome in this case?
Maybe
I hope that give you some idea of the complexity of the conditions that defy simple solutions.