There is a huge difference between the instruments you need to maintain control or recover from a deviation (a second AI is best for that), and the instruments you need when you have lost control in a spectacular fashion (where the AI may have toppled and a classic turn indicator is best)
I suspect most pilots are better off having instrumentation and training that prevents them from getting into an inverted spin, which includes recovery from the earlier stages of an upset, than having instrumentation and training that helps them recover from an inverted spin.
Hence the sensible backup for an electronic display where you could lose everything when the screen goes blank is an attitude indicator + airspeed, and an altimeter.
Not on a twin with an engine issue
Aircraft are stable in yaw and most powered aircraft need little or no rudder input in a normal turn, so if I stop a turn with ailerons, the aircraft should be essentially wings level with the ball more or less in the middle.
If you straighten with aileron only, what happens to the ball?
AdamFrisch wrote:
For this reason, I’ve been told, it does not work the same way as the T&B and you can’t recover from an upset on it. I’m sure someone more technical than me can explain exactly why.That depends on what you mean by “an upset”. The problem with a TC is that if you’re in an inverted spin, the aircraft will yaw and roll in different directions and since the TC indication is a blend of roll and yaw rate, it won’t tell you anything useful.
But, as Timothy already said, choosing your instrumentation so that you can recover from inadvertent spins on instruments seems pointless to me. Without aerobatics training, you’re unlikely (because of disorientation and the unusual elevator input required) to be able to recover from an inverted spin in visual conditions.
AdamFrisch wrote:
You can do that if you have a working Attitude Indicator as backup to give you bank angle information. Because a T&B/TC is rate-of-turn instrument rather than bank angle instrument and it will not tell you on its own if your wings are level, except for in the correct order that Stark devised. If you stop the turn with aileron, then the ball will be susceptible to acceleration/centrifugal forces and you won’t be able to use that as a wing leveling device.I don’t understand that. If you stop the turn with the ailerons, there will be no acceleration/centrifugal forces.
Now you had me have to look up the word recursive, Timothy. 
Ted, Turn Coordinator blends in some roll data by tilting the gyro, so that it’s a mix of roll data and rate-of-turn. For this reason, I’ve been told, it does not work the same way as the T&B and you can’t recover from an upset on it. I’m sure someone more technical than me can explain exactly why.
AdamFrisch wrote:
swap it for a T&B
What is wrong with a turn co-ordinator if it is correctly damped? The technique as described should work with a Turn co-ordinator, in addition to turn rate it is able to detect a roll rate, the autopilot can do it. (when its working…)
That’s an interesting document, I am not sure I agree with the authors (dated) view on thunderstorms. I was once given the advice for partial panel, of gear down, slow down and use the rudder in preference to the ailerons to avoid a spiral dive. I think the key to to stay calm, and don’t over control. I had a single AI failure once in and out of IMC, but with minimal turbulence. I would rather have two AIs and two sources.
I guess that if I really felt I needed another line of defence, I’d get another AI rather than a rate instrument.
And that argument is recursive.
But in that scenario Adam you can cross check the standby AI against the Altimeter, VSI and compass. It is a serious situation but assuming the second AI is independent I am not sure I would feel the need to have a third backup.
