Actually it’s slightly more than twice, as you may have a double engine failure in a twin.
It’s slightly less than twice (making some assumptions such as the probability of failure being identical for both engines). To illustrate, let’s imagine we have a batch of horribly unreliable engines, which have a 1-in-10 chance of quitting on takeoff as this keeps the numbers within the realm of mental arithmetic.
For a single engine aircraft, it’s simple: we have a 1-in-10 chance of taking off and having it quit.
But for a twin we don’t have a 2-in-10 chance of taking off and having at least one quit, the probability is slightly lower. We have a 1-(9/10)^2 chance of having at least one engine quit. Calculating, this becomes a 1 – (81/100) chance of having at least one quit on takeoff, which is a 19/100ths chance of having at least one quit (which is a slightly lower probability than 2 in 10. That isn’t to say that “double the chance of failure in a twin” isn’t a fair approximation, of course!)
Similarly if we had a 10 engined aircraft with these 1-in-10 chance of quitting engines, many would assume this means you’re certain to suffer at least one failure on takeoff, after all, 1 in 10 chance and ten engines… but this isn’t so. The probability of at least one stopping on takeoff is only around 63% (and indeed you can prove that for any given 1 in X chance where you have X independent events (and each engine on the plane here is considered an independent event), as X approaches infinity the chance of at least one in whatever event it is happening will be around 63%. To prove this calculate lim x→infinity 1-(1/x)^x. Indeed for any probability smaller than 1 in 5, for a 1 in x chance and attempting x times, the probability will be between 68% and 63%, tending towards 63% as x gets larger.
I think the engine failures are not idependent, and likely have some reasonable amount of positive correlation:
- bad maintenance
- design issue
- maintenance not done
- wrong fuel
- not enough fuel
- bird flock
and so on
I wrote nonsense :-)
DELETED (no longer relevant)
Not so. Following your logic, if you have a 50% chance (1/2) of an engine failing, you would have an engine failure EVERY take-off (1/2 + 1/2 = 1).
The probability of AT LEAST one engine failing really is 1 – (1/2)^2 = 1 – 1/4 = 75% in that case. Basic statistics.
25% – all goes well
50% – a single engine fails
25% – both engines fail
Ok, ok, you were faster replying than me deleting
…it takes the unique community of the forum to introduce Boethius to GA
Agreed, but it has happened on type before – here
The Navahoe is an Avgas type however…. I’d be hard pressed to find a condition when Jet A1 blows up like that.
I’d be hard pressed to find a condition when Jet A1 blows up like that.
There is one single case I am aware of, where an inflight explosion was most probably caused by an air-fuel mixture in an empty tank ignited by sparks from a defective cable: https://en.wikipedia.org/wiki/TWA_Flight_800