John Tullamarine
John you presume too much.
At no time have I agreed to the impossible. The impossible is to have zero sideslip under conditions of asymmetric straight balanced flight.
We can't even get close to zero sideslip. Maybe 2/3 degrees for our typical twin. Don't think you will pick it with a yaw string. The SIDE force on the tail is ALL that is stopping us from being that frisby. And at Vmca we are using the total sideforce the tail can muster. There is none left.
Why seek near rudder deflection as in the banked case?
Keeps the flight deck tidier!!! Also we may have run out of rudder trim and that leg is objecting . Real reason is to give us wider options of using over-riding rudder control should we need to use it in a turn or to cope with turbulence or to stay further away from fin stall if this is significant or ---- whatever happens. Penalty may arise from fact that we have had to replace the lift we are using for the sideslip. This and the increased sideslip needed to zero out the rudder we now have adds to total drag.
I really do not know the combination for min drag. It will of course vary with different aircraft and differing directional stabilities.
So someone has come up with the 'rule of thumb' that 5 degrees bank is the best average. But you wouldn't need anywhere near that bank angle for someting like the Concord because the tail's sideforces will vary approximately with the square of the CAS. Slow down to Vmca at low altitude in a Concord with an outer shut down and the others at take off power and you may well benefit from the 5 degrees of bank. My WAG (Wild Arsed Guess) for a Concord's raw Vmca so afflicted would be about 140 Kts in that the engines are fairly close inboard.
I said "Concord's raw Vmca" as I have taken off the 2 seconds do nothing time which allows for the reaction time of the less than average pilot.
Are you there Bellerophon for comments on a Concord's Vmcg and Vmca for a failed outer.?
John - a get together would be a memorable ocassion but I am already considerably outnumbered.