A Reims Aviation SA F182Q diesel conversion lost the prop back in 2007. No adverse handling after it´s departure.
Report in English: Link
If you loose a tip/bit of the prop, I can get interesting…… Quote from the crash of C-150 LN-LMP back in 2003 (Norwegian report only)
The instrument panel began to detach from the fasteners and I decided that a forced landing had to be carried soon as possible as I was concerned that other, more important parts of the machine should break.
Propeller bolts have been known to crack through and break. It happened to a friend of mine flying a Lycoming 360 powered amateur built. Four of the six bolts broke (in succession, I expect) until finally he noticed quite a vibration. He landed with the prop, but not by much. I opine that if you loose a metal prop off a type certified aircraft, you will have a C of G change so great that you may go out of limits, and have a challenging aircraft to fly at the corners of it’s operating range.
I would have thought that a prop issue is much more likely to be a blade coming out (or a blade tip coming off) than a whole prop coming off and flying off cleanly.
The prop is screwed on with a good number of massive bolts. It will take a lot to make it come off. The crankshaft flange would have to come off.
And if you lose a blade, the engine is fairly likely to get ripped right out of the aircraft, which will give you a really bad W&B issue 
I recall this happening to somebody with a TB10; fortunately it happened at the runway holding point. In a second or so, the engine was ripped right off its four mountings and ended up lying about 45 degrees off its normal axis. I saw some photos of it. With a bit of luck, if it happened in flight, the cowlings would have prevented the engine falling right off…..
Afterwards, IIRC, the pilot commented that maybe the 6 yearly UK prop overhaul requirement might be a good idea after all. But that does depend on how the plane had been looked after, whether it was hangared, etc. For example any grease leakage around the base of the blade(s) is definitely a very very bad sign.
The AAIB report is here.
If a prop goes on an SEP then I’d guess you will get a big increase in gliding range, although if it’s a CS prop the windscreen will probably be smothered in oil!
Google translate of the bulletin update from the AIBN
Description
During training acrobatics flight with LN-KAP in the training area “airworks Alfa” northeast of Bjørkelangen arose a noise in the plane followed by gentle shaking. The plane was when the woodland, ca. 4700 ft above ground level (AGL). On board the plane was the pilot / instructor and student. The pilot reduced the throttle and implemented horizontal flight. After 4-5 seconds sounded a loud bang, and propeller parts disappeared on each side in the horizontal plane. The commander gave impetus for best glide and heading towards the nearest land only area that was several suburbs north of Bjørkelangen. Mayday message was sent approximately 10 seconds after the propeller disappeared. Communication with air traffic control was maintained while they slid down the agricultural region. The emergency landing was successful, and no one was injured. Rollout of the field was completed approx. four minutes after the propeller disappeared. Beyond the lack of propeller were no other significant injuries.
Last updated: 20.05.2014
Location Northeast of Bjørkelangen
Event Date 05/18/2014
Aircraft Other light motorized aircraft
Operator Lower Raumarike Flyklubb
Reg notice LN-KAP
Flight conditions VMC
County Akershus
Type of Event Serious incident
Type of flight School
Category Aviation Lightweight, aircraft (<5 700kg)
Flykategori Land plane, single-engine
FIR / AOR ENOS (Oslo ATCC)
I know the FI. Kind of funny to see him again in these circumstances. Shaken, not stirred.
For those who have not google translated the article, he says the propeller appeared to split in half so each of the blades went off to either side of the aircraft. They tried to reach ENKJ twenty something nautical miles away but ended up doing a power-off landing in a field.
Presumably this goes on until a stalling angle of attack is required.
The propeller will start windmilling once the aoa goes through zero. This will keep the angular momentum up and stabilise it.
Just a couple of thoughts:
If the aircraft propeller detaches and does move forwards cleanly, then the initial thrust force is several thousand Newtons, but the propeller mass is only a few tens of kilograms, so the initial acceleration is hundreds of metres per second squared.
But as the propeller disc gains forward speed, its angle of attack (and so its thrust) decays.
I think the steady state speed is where thrust equals drag, but now if all forces are of the same order as drag forces, we have a ballistic tumbling stick.
Because the initial acceleration is so huge I imagine this happens in a few tenths of a second.
(Order of magnitude, it should be an exponential decay).
The helicopter rotor case is different, because it moves upwards, not forward.
We start arguing like we did with the propeller, but now the steady state speed is where thrust equals weight plus drag.
So long as weight comfortably exceeds drag, we could have a reasonably aerodynamic rotor.
As the rotor rotation speed decays, more angle of attack is required to match weight, and the ‘steady state’ vertical speed changes accordingly.
Presumably this goes on until a stalling angle of attack is required.
I saw a video of an RC helicopter where the owner hadn’t secured the jesus bolt. When the heli got about 3 inches off the ground the entire main rotor departed the mast and judging by watching the owner’s eyes, it must have climbed at least a couple of hundred feet (you could see his eyes watch it go in a big, curving arc, before he walks off to collect it!) which suggests that it remained reasonably stable for long enough to impart quite a bit of upward momentum.
QuoteWhen it’s inertia/angular momentum is consumed by drag, the remaining part of the aeroplane will catch up on the propeller again and eventually overtake of hit it.
That’s assuming you have multiple engines and the others are still pulling the aircraft forward. But in a single engine the airframe doesn’t have trust anymore, so it will slow down because of its own drag. So it’s a toss-up between the momentum and drag of the propeller vs. the momentum and drag of the airframe.
In any case, I don’t think a prop rotating on its own will be in a stable state. My gut feeling is that it will start to tumble immediately, instead of continuing to rotate and provide a measure of thrust. Especially since the plane of rotation might not be exactly perpendicular to the direction of movement – something that’s called p-factor while the propeller is still attached to the airframe, and is one of the reasons you need right rudder on takeoff. That tumbling will just cause more drag, way more than the relatively stable airflow around the airframe. So my money would be on the propeller moving backwards virtually immediately after detaching.
