Coordinated turn with an inoperative engine on a twin
 

Hello everyone, I am doing my multi-engine ground school. Appreciate if someone can shed some light on the below question that I wasn't able to find an answer from books and websites.
I learnt that to fly zero sideslip in a straight flight, we need about 5 degree bank angle into the good engine, and the inclinometer will show about 1/2 ball deflection for a coordinated straight flight;
How about when we are doing a coordinated turn towards either side? How should the ball look like?
Thank in advance!

Good question; just like flight with both engines running, a coordinated turn is made with the ball in the same place as when not turning. But in this case, the ball is displaced instead of centered.

However, something else: it's not quite right that a 5 degree bank is what you need. It's a common misconception that mixes up 2 things. A bank does two things:

A) Increases controllability. Banking to the right, is essentially the same as putting in right rudder. So with a left engine failure, to prevent left yaw, if you're maxed out on rudder (for example, you're at full power on the running engine and at a slow speed, like around Vmc) and need more right rudder but you don't have it, then right bank will give you some more. If you DO have more rudder available, then using bank instead of rudder doesn't do anything, as far as A goes.

B) Increases performance... but only up to a (small) point! With thrust asymmetry, the bank (and ball off center point) that yields zero-slip (airflow is aligned straight down the fuselage) flight, is not zero bank but rather a small amount. This bank amount is usually not published and there's no direct way to find it out other than flying with a tuft on the windshield. But as a vague generality, it's about 2.5 degrees, and let's just go with that number as an example. Any more than that, and you'll be in a slip but the opposite way compared to zero bank, which is just as bad with respect to drag due to slip.

So where does the 5 degree thing come in? Where performance (B) is maximized at 2.5 degrees (and too much is just as bad as too little), controllability (A) has no limit. The more you bank the more yaw moment (i.e., rudder help) it will give you. You can bank something absurd like 45 degrees, and it will give you a huge amount of yaw moment... and will successfully keep the airplane straight at speeds far lower than the published Vmc. But this huge (helping) yaw moment (A) will come at the cost of an equally huge drag penalty, and will absolutely require a steep descent to maintain flying speed. (Keep in mind that light twins can barely maintain level with an engine out, to begin with, even under normal circumstances.)

Well the 5 degree *limit* (not target) is the maximum that airplane companies are allowed to use in flight test to establish the Vmc. Any more than 5, and they *could have* obtained an even lower Vmc (due to A) which is good for a quick glance at a sales brochure, but comes at a drag/descent penalty that means you'll never be able to main altitude (actually, you know, keep flying!) at that low Vmc. Think of it as a "cheat" that's prevented by limiting the bank, to a number that doesn't kill the performance too much.

Although the article starting on page 9 may not answer the question directly you may be able to use it as a basis for turning situations. N.B differences in direction of turn.

There is a version of the article - EPTS notes, which shows the associated vector diagrams.

https://www.dropbox.com/scl/fi/0q3o3...xjjxbulzn&dl=0

Edit: the vector version

https://www.dropbox.com/scl/fi/hnb1d...dk25g59ct&dl=0
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Super thanks, Vessbot! that cleared many things up!

Thanks PEI_3721! The diagrams are helpful!