It’s fun playing with numbers. Read somewhere that a piston aero engine only has 3500 h MTBF, while a turbine has typically 350k, which looks somewhat reasonable. When using those numbers the graph looks like this (log-log to be able to show turbine):
The graph does not show the probability of a pilot experiencing a full engine failure. What it show is the probability of any single airplane experiencing full engine failure due to constant rate random events (based on MTBF), and set of airplanes started off brand new. Those airplanes who has experienced full engine failure is not returned to service. This gives the special density functions for both single engine and twin. The MTBF of a twin is still only 1.5 times that of a single, but due to redundancy, a twin starts off with a combined rate of literally zero which increases after a certain point, while a single engine starts with the original rate (which remains constant).
The main uncertainty or error is the assumption of the constant rate random failure.
the MTBF of a dual redundant system is simply 3/2 * 1/failure rate
LeSving just curious, what would the rate be with triple & quad redundant systems?
Also it’d be interesting to modify the twin failure scenario a bit:
- The probability of a single engine failure on a twin & one good engine still operating for another 1 hr & the odometer “reset” on the failed engine after a complete teardown. (after a presumably successful single-engine emergency landing)
“but recently I flew back with my family on a trip at night and I started hearing the engine run a little rough (or sound different). It was pitch black below and we were in IMC”
That’s one of the reasons why I’m flying a twin. I’ve been in a single over heavily congested LA & had a rough engine a couple of times. Also tried the same over the Santa Barbara mountains a night. Just a fairly unsettling feeling. Single vs twin is really about getting a comfort feeling in cruise. (whether warranted by numbers or not 
)
LeSving just curious, what would the rate be with triple & quad redundant systems?
I don’t know exactly. It is straight forward I guess, but it involves integrating ugly functions and I have enough gray hairs
The probability of a single engine failure on a twin & one good engine still operating for another 1 hr & the odometer “reset” on the failed engine after a complete teardown. (after a presumably successful single-engine emergency landing)
Good point. But it won’t actually change anything. The underlying failure rate here is completely random in time and constant regardless of age. The failure rate is simply 1/MTBF. The only thing that changes the probability is the fact that complete failure equals a total write off. The aircraft is considered destroyed. This is really only intuitive for the single case.
With a MTBF of 3500 h, the rate becomes 286 failures per million hours. This is also difficult to visualize, so lets say the rate is 0.1 (MTBF = 10h) and we start with 10 engines. After 1 hour we can (statistically) expect 0.1*10 = 1 engines to have failed. We are then left with 9 engines. The next hour 0.1*9 engines will fail and so on. At some point in the future (statistically in 21 h) you are left with one engine with a failure rate of 0.1 (MTBF = 10h). Now, since the failure rate is random and constant, this engine has the exact same possibility of failure as a brand new one entering service at that point. It’s just that statistically the failures are spread out among all engines, hence the probability density function. Replacing all 9 destroyed engines, and the whole thing simply start from scratch again. It’s exactly like Russian roulette. Each squeeze of the trigger is a random 5/6 chance of surviving regardless of how many times you have done it up front. Still, the probability of surviving 1000 squeezes is extremely small, so the overall probability you will survive the thousand’s time is infinitesimal because of this. It is a highly unlikely event to start with, yet the probability is still 5/6 if you manage to get there. For one single person it seems impossible, but if you start out with a million persons, the probability of one of those surviving is much higher (a million times).
For each individual, the only thing that means anything is the MTBF. The MTBF in a twin is only 1.5 times that of a single, even though the probabilities for the “population” is very much reduced, at least initially. This is very counter intuitive, but good for the airline companies and their statistics. A single turbine has a much higher MTBF than a twin piston, but not necessarily less probability of failure initially (first 40-50 hours) when looking at the whole populations of SET and piston twins.
I don’t think one can reasonably speak of a MTBF regarding a complex machine like an aeroplane – the term can IMHO only be applied to components. Further, and still IMHO, the term can only apply to complete failures. An engine that delivers only 70% of its rated power after one magneto gave up hasn’t failed.
As long as the terminology is not clearly defined, we are discussing in the clouds. But a phrase like
The MTBF in a twin is only 1.5 times that of a single
is (for me) void of sense or meaning, because it can only apply to the MTBF of the aeroplane – which is not defined.
Basically, I think the MTBF must be much nearer to 50k hrs than 1k or 2k hrs.
I read in a BEA report that the FAA estimates the number of engines that stopped producing power in flight for what ever reason (basic failures) to be 10 in 100.000 flight hours. For the Centurion Diesels, it is about 5 in 100.000 flight hours.
The Centurions are actually just a little bit over 3 per 100k flight hours – which is better than the ETOPS 120 certification for commercial air transport twins.
This despite running at 90% power all the time while not “being designed for it”.
… that the FAA estimates …
I wonder on what basis they estimate those numbers. I am pretty sure that my three engine failures were not reported to anyone who actually counted them for the statistics. And these were on CofA aircraft. For me, this whole statistics is meaningless because it has no proven basis. And my personal experience and what I can observe around me tells a completely different story. 10 in 100.000 flight hours? No way.
is (for me) void of sense or meaning, because it can only apply to the MTBF of the aeroplane – which is not defined.
Quite the opposite. This is the only thing that is 100% true here (for random occurrence failures). There is no need for the MTBF to be defined by a value for an airplane or an engine. As long as an engine has random occurrence failures (could be anything and everything), a dual redundant system using these engines will only increase the MTBF with a factor of 1.5 . Or said in other words, the mean time between random occurrence failures that will stop both engines in a dual redundant system is only 1.5 times as long as for a single engine. With a properly maintained engine, all failures are more or less random events. If the MTBF already is too short with respect to some measure, a dual redundant system won’t help all that much unless also the MTBF is increased. This is without taking into account the extra failure modes added due to the redundancy. If there is a clever way to increase MTBF, like installing a turbine, then this is a much better solution than twin pistons. Also a BRS would be better (in theory at least) than a twin, because a BRS would theoretically remove the probability that an engine failure, or any other in flight occurrence, causes a fatal accident. Looking at the probability function, it seems like the really huge positive effect of redundancy does not occur until the MTBF the single component is at least an order of magnitude larger than the expected life of the component, which is true for turbines. A twin piston is still a nice and economical way of increasing power though, without having to design a new engine.
I read in a BEA report that the FAA estimates the number of engines that stopped producing power in flight for what ever reason (basic failures) to be 10 in 100.000 flight hours. For the Centurion Diesels, it is about 5 in 100.000 flight hours.
I don’t think we will ever get a correct number. I have no idea what it is, 1k, 30k ? They both seem reasonable to me. I’m just amused by this redundancy stuff.
I’m just amused by this redundancy stuff.
That depends on how you interpret “redundancy”. In terms of system redundancy (the failure of one component (= powerplant) will not fail the whole system) putting a second engine in makes perfect sense. Of course you can expect to get – statistically – twice as many engine failures on a twin than you will get on a single. But they won’t harm you as much. When the (Super) Constellation was still in use, it was nicknamed “the best three engined airliner” by some operators (like Lufthansa) because there were few Atlantic crossings that ended with all four engines running. I am only aware of a single engine related crash of a Super Constellation (Flying Tiger Line flight 923) when three of the four engines failed and it had to ditch. But only the first failure was a genuine engine failure, the other two were caused by the flight engineer performing wrong actions whilst securing the first engine.
I wonder about the title of the thread and the discussion with regard to risks of engine failures and that stuff. Actually I do read the thread title primarily being related to the word ‘AVGAS’ rather than ‘Twin’. So the question is not about Twins in general, it’s about AVGAS Twins. In that respect I too assume that AVGAS turns out to be more and more problematic. Thus, for Twins, costs are too high to run two AVGAS engines when a modern Cirrus SEP offers mostly the same speed and other stuff at lower costs.
The situation could change with the increasing Diesel market. Personally speaking I truly prefer my Twin because of the relaxed emotional situation when flying it in IMC, over the Alps, open water etc. – but this is only affordable with Diesel engines. So my answer to the initial question: yes, the AVGAS Twins are dead.
