One thing that has been gnawing at me is the stability of the airframe after the engine departs.
Well, they still flew for a little while with wings level, so I don't think it's that big of a deal.
Let's assume that there is no damage to the hydraulics and the slats/flaps remain in their takeoff configuration. Let's also assume that #2 and #3 continue to operate at 100% N1.
Unlikely that all that happened - If it had, we wouldn't be having this conversation.
When the engine departs the airframe, you have a profound shift in lateral CoG, without an inherent shift in axial CoG.
When you say "axial" here, what do you mean?
I think the CG would shift aft and right upon departure of the #1 engine, but unless they were already right at the aft limit I don't know that it would have been particularly significant - Possibly the most significant outcome of that would be Vmc going up slightly with the CG going aft due to the lowered CG-CP arm.
One outcome could be an increase in climbing performance: the aircraft just shed 30k pounds; if the aircraft can maintain a nominal level of climb at max weight and 100% N1 on engine #2 and #3, this would mean that the wings are generating a "constant" lifting force.
It would appear that they weren't getting 100% from both #2 and #3, or again, we'd be having a very different conversation here.
Another outcome could be a shift in the wings deflection, which may erode lifting force because the shape of the wing is now inherently more parabolic, because you don't have 30k pounds hauling it down. This could induce an increased left roll as the wings are not providing a balanced lifting force.
Are you talking about the shape of the wing as viewed from in front or behind? Sure, the tip would probably go up some relative to where it had been without the weight of the engine, but it wouldn't be that big of a change IMO. More lift would be necessary from the right wing as it'd be heavier, but had they been able to climb away from the ground I think they'd have been OK. Not sure what the transport category limits are for minimum controllability, but this doesn't feel like it'd be big enough to take them down on its own.
Of course, this doesn't even account for the change in yaw caused by the imbalance in drag, as now the left side of the airframe has less drag on it.
With the #1 engine out in normal circumstances, there will be *more* left yaw tendency than if the engine departs - We're getting thrust from the right engine in either case, but with the engine departing there is no longer extra drag on the left, so this would actually be beneficial.
V1 is defined as Takeoff Decision Speed. Any decision to reject must be made, and the reject initiated by V1.
I know you already know this
@Larry in TN, but for the benefit of everyone else: They've actually changed wording slightly, and no longer call it "takeoff decision speed" - *At* V1, you can no longer decide to reject; You must have *already taken the first action* for the reject to be successful. As such, I guess the FAA no longer calls it "takeoff decision speed" though as I understand it this is a pretty recent thing so there are still some materials with the older wording. There's more about it here:
https://skybrary.aero/articles/v1
The updated (yet somewhat klunky) definition: "The maximum speed in the takeoff at which the pilot must take the first action (e.g., apply brakes, reduce thrust, deploy speed brakes) to stop the airplane within the accelerate-stop distance. V1 also means the minimum speed in the takeoff, following a failure of the critical engine at VEF, at which the pilot can continue the takeoff and achieve the required height above the takeoff surface within the takeoff distance."
Thought we don't usually see it, there is a V1min and a V1max. V1min is the lowest decision speed at which you can continue the takeoff and V1max is the highest V1 at which you can reject and stop on the available runway. The actual V1 will be somewhere in between. They are the same only when the runway is the minimum length allowable for your takeoff weight.
... or thrust, for a reduced thrust takeoff.