How does the velocity of a turboprop engine relative to the airplane change when a plane is banking?

Question

I saw this YouTube video recently:

And in it, a turboprop engine propeller and gearbox comes out and slashes across the underbelly of the plane, crippling the aircraft. My question is, what aerodynamic force is involved with the turboprop + gearbox being able to fall out specifically during the turn? I can imagine that for whatever reason, when the pilot decided to quickly turn around and head back, that the outermost turboprop must have been moving slower than the plane, and that those forces caused by the turn ultimately tugged the propeller out, and that the turning of the plane brought the propeller under the plane causing the massive damage.

Answer 1

In a coordinated turn, this is purely a geometry question. Let's call the distance from centerline to engine $d$. The plane must bank to allow for centripetal acceleration $a=v^2/r$ with $v$ true airspeed and $r$ turn radius. This places the engines at a lateral distance of $$d^*=\frac{d}{\sqrt{1+\frac{a^2}{g^2}}}$$

from the centerline with $g$ acceleration due to gravity. Finally, the speed of the inner engine is $v_1=v(1-d^*/r)$ and the outer engine $v_2=v(1+d^*/r)$. The speed difference is thus $$\delta=\frac{2vd^*}{r}.$$ If you want you can simplify this to $\delta=\frac{2gvd}{\sqrt{g^2r^2+v^4}}$

You may play around with some real world values, but it's safe to say that no turn will rip off a turboprop engine just from the speed difference - these things are designed to apply many kilonewtons of thrust, also in reverse.

Answer 2

If the turn forces did not dislodge the prop, what did?

After that great crew brought their plane to a stop, the maintenance records for #4 engine may have been first on their minds, after safely deplaning the passengers.

When one considers the props pull the plane along, then what ever bearing that holds that (turbo) prop to its gear case comes into focus. If that bearing fails, the prop will literally pull itself ahead and out of the nacelle.

The rest is seen in the video. Normal turning forces, with passengers comfort in mind, cannot be expected to cause that type of failure.

With the huge propellers that drove that plane, any imbalance in the prop assembly could cause them to "wobble", weakening surrounding structures to the point of failure. This type of accident was all too common in the early age of passenger travel. In the video, one can see an unusual shudder in the co-pilot's control column and the captain making a decision to abort the flight, turn around, and get the plane back on the ground (before all hell literally broke loose).

Stringent quality control and maintenance procedures, along with proper design, are key factors in prevention of this type of accident.