Another C lost with fatality Arizona City, AZ.

[Matt Ward]

43 minutes ago, Hank said:

It's 1 in 6 on every roll. You are not guaranteed to roll each number every six throws. 

1/6 x 6 = 100% chance to roll a 1 in six throws. 

1/6 x 6 = 100% chance to roll a 2 in six throws.

1/6 x 6 = 100% chance to roll a 3 in six throws.

1/6 x 6 = 100% chance to roll a 4 in six throws.

1/6 x 6 = 100% chance to roll a 5 in six throws.

1/6 x 6 = 100% chance to roll a 6 in six throws.

See how silly this is? 

That's not what anyone is saying though.  The question is the odds of throwing a six in any one of your six rolls.  One roll is a 16.7% chance.  But give me six rolls, and there is a 67% chance at least one of those rolls is a six.

[skydvrboy]

49 minutes ago, Hank said:

It's 1 in 6 on every roll. You are not guaranteed to roll each number every six throws. 

So you're saying that if I play Russian Roulette with a six shooter twelve times, I'm not guaranteed to die twice?  The hell you say!  

[jaylw314]

What's all this about?

The chance of rolling at least one of any number on a die in 4 throws is 51.7%, and after 6 throws is 66.5%

[cliffy]

Its all fun and games to toss around numbers but-

 

The real figures are probably on the actuarial tables used by the insurance companies 

They're the ones paying out the money

 

[201er]

2 hours ago, 1980Mooney said:

Over 10 years that will be 7,340 accidents and claims for this group. If spread evenly, that is about 6% of the SEP plane owners that will be effected.

This guy must really skew the stats! 

https://www.record-eagle.com/news/seawind-saga-pilot-who-crashed-in-lake-michigan-had-7-crashes-in-7-days/article_867676c0-e8d7-11eb-be82-db592d516d36.html

[Matt Ward]

17 minutes ago, 201er said:

This guy must really skew the stats! 

https://www.record-eagle.com/news/seawind-saga-pilot-who-crashed-in-lake-michigan-had-7-crashes-in-7-days/article_867676c0-e8d7-11eb-be82-db592d516d36.html

I do wonder how much impact places like Alaska have on this. It seems like their accident could skew this quite a bit. The survey kinda breaks out AK but I don’t know that the Nail data does explicitly. 

[jaylw314]

18 minutes ago, 201er said:

This guy must really skew the stats! 

https://www.record-eagle.com/news/seawind-saga-pilot-who-crashed-in-lake-michigan-had-7-crashes-in-7-days/article_867676c0-e8d7-11eb-be82-db592d516d36.html

Yeah, that one came out on a previous thread here somewhere, but dang it's still mind blowing to think about...

[aviatoreb]

Handy dandy math prof here.

Thats right.  If say rolling a 6 sided die and p=1/6 of rolling a 5.  Then you expect a 5 one sixth of the time

That does not mean that in 6 roles you will have a 100% chance of rolling a 5.  Or in 60 rolls you will have a 1000% chance (whatever that means!)

Here's how to do this.  p=Prob(die falls on 5 on any one roll)=1/6.  1-p=Prob(die falls on annoying but a 5 on any one roll).

(1-p)^n = (1-p)*(1-p)*...*(1-p)=Prob(die falls on anything but a 5 on roll 1)*Prob(die falls on anything but a 5 on roll 2) *.... *Prob(die falls on anything but a 5 on role n).=

(5/6)^n.

q(n)=1-(1-p)^n=Prob(not die falls on anything but a 5 on roll one and roll 2 and roll 3... roll n)=Prob(die falls on a 5 on at least one of those rolls)=1-5/6 ^n

n=1: q(1)=1/6

n=2: q(2)=0.3056 vs 2/3=.333...

n=3: q(3)=0.4213 vs 1/2=.5

n=6: q(6)=0.6651 vs 1

n=60: q(60)=0.999982252988238 vs 10 (there Is not probability 10 - probabilities must be between 0 and 1).

If your chance of death on a flight is 1/100,000 hrs of fly and you fly 1 hour, then in 100 hours thats

1-(1-1/100000)^100=9.995e-04 that's one typical private pilot year.

IN a lifetime of flying say 50 years. 

1-(1-1/100000)^5000=0.0488 = 4.9%. YIKES!  Anyway  that is quite different from 5000* 1/100000= .05.  OK its not that different, but at least you can see there is a difference.  The difference clearly becomes more pronounced in the limit of n->infinity.

BUT this model has a major flaw.  It assumes statistical independence. Like that is a good model for rolling dice. Maybe mot so good for things like flying.  We like to think that after 100 hours of flying our personal probability goes down.  After 1000 hours it goes down even more.  I don't know.  It could be that for some people it goes up!  That classic ATP accident in a Cessna 150 scud running despite 10,000 hrs of experience?  I don't know.  But I doubt these are statistical independent.

Here is another problem with the model.  That is a bulk population probability.  Which for inspecting a population is good - since if you select a random pilot from the population, I would use that.  But if you are one pilot - I am me, I presume my personal probability (behavior) may be quite different. I could argue convincingly (correctly?) that some of us have personal probabilities that may deviate from that bulk probability by a lot.  Maybe an order of magnitude?  There is an old saying that in some areas that population risk is concentrated, 90% of the risk concentrated on 10% of the people - so goes the saying.  Some pilots are just risky folk and they have such a high personal risk tolerance that their probability of fault may well be 10 times higher than the population - or more!  And hopefully, many of us balance out, are what - hopefully on order of 10 times better than that bulk statistic?  This all comes out to conditional probabilities - next classes lesson.

Hopefully my behaviors and practices I have a personal probability of demise that is one tenth of that bulk probability?

 

[201er]

33 minutes ago, aviatoreb said:

 There is an old saying that in some areas that population risk is concentrated, 90% of the risk concentrated on 10% of the people - so goes the saying.  Some pilots are just risky folk and they have such a high personal risk tolerance that their probability of fault may well be 10 times higher than the population - or more!  And hopefully, many of us balance out, are what - hopefully on order of 10 times better than that bulk statistic?  This all comes out to conditional probabilities - next classes lesson.

Hopefully my behaviors and practices I have a personal probability of demise that is one tenth of that bulk probability?

I dunno. Sounds like a Student Pilot flying solo is less likely to buy the farm than an instrument pilot on board a Mooney.

[aviatoreb]

2 minutes ago, 201er said:

I dunno. Sounds like a Student Pilot flying solo is less likely to buy the farm than an instrument pilot on board a Mooney.

Could be.  And student pilots spend lots of time flying circuits in the pattern.

[Schllc]

6 hours ago, 1980Mooney said:

Your numbers are all off by a factor of 100 since you are showing as percentage.  And it looks like you have a typo in your first assumption - the numbers you have are for 3 hours of flight not 2.  A single hour of flight has a 0.0051% chance of accident.  And a single hour of flight has a 0.0009% chance of being a fatal accident. If you fly 90 hours per year that annual risk of an accident is 0.46% based on overall GA numbers and 0.081% of being a fatal accident.  So that doesn't sound like much but if you fly for 10 years your chance or having an accident is 4.6%.  Your chance of having a fatal accident is 0.81% 

But wait - those numbers have all GA in them - the jets, the turboprops and the much safer fixed landing gear pistons - and it includes the hours flown by professionals.  So the risk we face is greater.

Using 2019 FAA Survey and Nall Reports:

106,065 General Aviation Single Engine Piston aircraft were actively flown for Personal use and another 10,816 Single Engine Piston were actively flown for Business - Self Flown in 2019.  Personal SEP total hours were 5.422 million and Business - Self Flown SEP total hours were 860,921.  That is 116,881 GA SEP aircraft actively flown for 6.283 million hours flown for Personal and Business - Self Flown (only one fourth of the total GA).  I have intentionally left Student Instruction Flight out.   There were 734 Single Engine Piston accidents in this group of which 148 were Fatal accidents.

That is an accident rate of 0.63% based upon population and based upon hours it is 1.05% if you fly 90 hours per year.  The fatality rate is 0.127% per year based on population and 0.212% if you fly 90 hours per year.  So once again over a 10 year period of flying that means your chance of an accident is 6.3% to 10% if you fly 90 hours per year (more than average).  And the chance of a fatal accident over that same 10 years is 1-2%.  

We tend to dismiss the risk of flying.  These risks are high compared to other forms of transportation and probably higher than you want to recognize.

I also found it interesting that the FAA estimates that there are only 32,035 Single Engine Piston GA airplanes with RETRACTABLE GEAR being ACTIVELY flown for a total of 2,666,504 hours.  Mooney may have built 11,000 -12,000 planes but I bet only about 7,000 or less still actively exist (lost to accident, corrosion, hangar queens).  Also see the Nall Report that shows an accident in a Retractable Single Engine Piston plane is twice as likely to be lethal than in a Fixed Gear plane. - 26% vs 13%.  I suppose it is because the Retractable is more likely to be high performance but that is not true compared to Cirrus.

Nall Report Figure View - AOPA

General Aviation and Part 135 Activity Surveys - CY 2019 (faa.gov)

 

My analysis was pretty reductionist, that’s a fair point. 
There is plenty of room for scrutiny and refinement, even in your analysis.  

The risk is for each of us to evaluate with our own criteria, and with either analysis, the risk is low enough for me to cause no concern. 

I’m not scared of dying, I’m scared of not living. 

[jaylw314]

4 minutes ago, Schllc said:

My analysis was pretty reductionist, that’s a fair point. 
There is plenty of room for scrutiny and refinement, even in your analysis.  

The risk is for each of us to evaluate with our own criteria, and with either analysis, the risk is low enough for me to cause no concern. 

I’m not scared of dying, I’m scared of not living. 

That's a romantic attitude, but the people around you may not share your sentiment, though.  Given that most fatal accidents occur near airports and urban areas, it's hard to imagine that your neighbors and the general public are comforted by that position, so that's probably not a great banner to carry.

[Schllc]

what banner would that be? 
I am pretty sure all I said was I find the risk acceptable, as do all pilots.  
Or I would assume they do, otherwise why be pilots in the first place?  

[Ragsf15e]

6 hours ago, Hank said:

So many people mangle statistics and percentages. If the risk is 0.46% per year, it is.not 4.6% over ten years.

Roll a single die. The chance is 1 in 6, or 16.67%, that you will roll a 6. Now roll the same die four times--are your odds now 4 in 6, or 66.67%, that you'll roll a 6? No, your odds are still 1 in 6 . . . .

Same for flying, driving, scuba diving or being a couch potato.

Your odds of having an accident in your 2000th hour are not 2000 * 0.0051% = 10.2%!

But people talk, write.and live as if this is true. Please learn real math before discussing probabilities and statistics!

@aviatoreb can probably shed some light on this, if he can tone it down enough for those of us without PhDs to understand. 

Maybe I misunderstood what you meant… yes your odds on the last roll by itself are still 1/6, but cumulative chances of getting a 6 out of say 5 rolls are higher.

Thus, having lived for 35 years / 5000 hours accident free, my chances of an accident on my next flight are no more than that of a brand new pilot on his next flight (or maybe better if I put my experience to good use).  Just like if you roll no 6s on the first 4 rolls, then you’re back to a 1/6 chance on the last roll.
 

However, if I look 10 years into the future and fly 100 hours/year, I’d have to combine the risk of each flight just like anyone else.

[hais]

6 hours ago, Matt Ward said:

Interesting data but I'm seeing it a little different.  My stats are rusty but I think I remember the key is solving the inverse.

From that Survey, it looks like 7.849m hours personal GA flying.  From Nail, it looks like 730 accidents.  Granted it's two different data sources, but ok.  So the probability of having an accident in the next hour is 0.00009 and not having an accident is 0.99991.  The probability of not having an accident over 90 hours is  0.991664 and having one is  0.008336, or, 0.83%.  Over 900 hours, the probability of having one is more like 8.03%.  That's not because of "times 10", it's the exponential of not having an accident.

So yeah, over a 10 year period of about 90 hours per year, about 92% likely you don't have one and 8% you do.
 

Is it safe then to reason that a pilot flying 5 hours a year is safer than another who flies 200 hours a year? 

[Matt Ward]

47 minutes ago, hais said:

Is it safe then to reason that a pilot flying 5 hours a year is safer than another who flies 200 hours a year? 

Well, no. We are talking statistics which assumes population similarity. You’re talking behavioral economics which would try to quantify individuals’ factors. Like someone said earlier, we’re just playing with maths. The point made was that flying is inherently risky, probably more so than many folks realize. And it’s compounded by exposure like anything else. So you can use that insight to adjust your personal approach as you like and manage your risk profile. But it’s a good sanity check against the “it’ll never happen to me” bias. 

[jaylw314]

3 hours ago, Schllc said:

what banner would that be? 
I am pretty sure all I said was I find the risk acceptable, as do all pilots.  
Or I would assume they do, otherwise why be pilots in the first place?  

I was referring to how we are perceived by the non-flying remainder of society.  When we publicly declare that we find the risks involved acceptable, it tends to produce resentment and retaliation.  The outward position we should take is that we find any risk to be clear and present, we need to make every reasonable effort to reduce that risk, and that we need to make that effort on a never-ending basis.

I realize that's perhaps a distinction that may only affect public perception, but, like it or not, our ability to fly is at the leisure of our neighbors

[aviatoreb]

Anther comment on safety statistics.

I fly instead of a number of other motor sports that my friends around here do.  They speed boat, snowmobile, car race, ride motorcycles, chain saws (yeah - lumber jack contests are a thing around here and they are crazy scary dangerous even to watch I cringe!).  I bet if I didn't fly, I would end up throwing myself into one of those.  For me its not flying or do nothing and sit in the hammock.  I have a hammock and I manage to sit in it AND fly.  But flying is one way to have a venue to express my passion for things.  If I had never become a pilot I bet I would be a sailor and I bet I would own a 44' something with sails.  Why don't I do both?  Time and money.  Even if I did both, then I would be splitting my time - every hour not sailing would be an hour sailing.

OK, where am I going with that.  My personality is such that I have a burning passion to do something.  Doing something has an inherent risk.  So if I would quite flying, I bet that p=1.e-5 risk of death per hour of exposure (population risk and who knows what my own risk is actually...hopefully smaller) wouldn't drop to zero - it would likely just transfer to some other risky behavior (snowmobiles?  I used to have one but got bored with it - sailing - yes!).  So that should be considered when deciding how risking flying is.  In other words - is it flying?  Or is it you?

Oh last comment on that - I ride bicycles - that's risky!  Worse than flying.  :-(. But I live in a rural area and stick to roads with big big snow lane shoulders.  Mitigate my risk?  I sure hope so.  Helmet.  check. lots and lots of experience and awareness of whats around me?  check?  Music ear buds? Never.  Should I quite riding my bike?  Ummmm....then my risk of the great American disease sloth increases my risk for heart disease and cancer, and stroke, etc.  Or maybe I would take up sailing?  Oh - I scull too (rowing).  Sometimes people drown in small boats.  Ugh - isn't anything safe.  Turns out the largest risk factor in small boats is drowning while drunk.  Well I never drink and go sculling. Haha...

Actually there is a lesson in that.  To improve your personal statistics.  Become a student of the data.  Learn what get's people in trouble.  Avoid those things or understand them and try and mitigate the risk generally. E.g. I don't fly at night in SE airplanes.  My personal behavior.  So any risk of crashing into terrain at night is essentially zero.  Last time I flew at night was 6 or 7 years ago for my required night cross country toward my commercial cert.  I love flying at night - its so much fun. And convenient!  But I don't do it.  If I had a twin or a turbine I would.  And other things I do.....

[ilovecornfields]

6 hours ago, 1980Mooney said:

90% of the risk is in 10% of the pilots?....So the same 10% of pilots will be having the same 734 accidents each year over the next 10 years?....or it is a different 10% each year?  I bet it is the later.  Because if it is the same 10% group year after year then we could have 2 insurance pools.  All us "10 times better people" could be paying 10 times less...about $300 per year and the "risky 10%" should be paying 10 times more or about $30,000 premium per year.  This sounds like the classic denial of reality - "This won't (can't) happen to me"..."I am 10 times better than the average"..."Other people are just risky but not me"....

That 90/10 rule might not be too far off. One of my colleagues who has been involved in backcountry flying for decades describes it as a “self-cleaning oven.” I think he’s on his third overhaul on his Skywagon (made it past TBO each time) and has never had an issue. Others who share his passion have suffered different fates but it seems that they are constantly being replaced by those fearless flyers “living their best life.” As long as the overwhelming majority of accidents have to do with pilot actions and behavior then the risk pool will be unevenly distributed. I’m pretty good at statistics (although not nearly as good as Prof. @aviatoreb) and I openly discuss this with my family when we fly together. I’ve often scrubbed flights I probably could have made because I didn’t think the risk was acceptable given the reward.

Not to put words in anyones mouth, but I think what @jaylw314 was saying was that we can acknowledge the risk and take thoughtful efforts to mitigate that risk instead of just saying “I’m not scared of dying.” Nothing wrong with not being scared of dying but if you’re one of those people who is willing to tolerate a higher level of risk then you should be honest with yourself and acknowledge your higher likelihood of dying or injuring yourself and others. I’m not passing judgement on those whose risk tolerance differs from mine, but I think you owe it to yourself to be intellectually honest with yourself and your passengers regarding what degree of risk you are taking.

I’m pretty sure those two nurses in the Learjet that recently crashed in SEE had no idea how much risk the pilots were taking on their behalf, without their informed consent. If your goal is to give general aviation negative publicity and bring on more oversight, regulation and airport closures then this is the way to do it. The mayor of El Cajon has already announced an investigation into the dangers of the airport given the two recent fatal accidents (even though the previous accident airplane was actually flying into MYF).

Everyday at work I see the results of someone taking a risk and having it end poorly. My wife used to make fun of me because anything fun you can think of I can think of a way it can (and has) ended horribly. Doesn’t mean I don’t take any risks but it does mean I try to be deliberate about the ones I take and make efforts to mitigate those risks and honestly communicate them to those taking the risks with me.

 

 

 

 

 

 

Edited January 7, 2022 by ilovecornfields

[aviatoreb]

One more thought - I could hope to say that my risk of pre-mature death may actually be lower because I fly and participate in the flying culture of go-no-go decisions.  Since I have been flying I have been actively applying that to other activities where in years past, tough guy, I would just suck it up and go.  E.g. driving into icy snow storms, ice rain, blizzards.  Don't judge - but it used to be I would just go.  Now I feel clever for cancelling or delaying a driving trip if weather, fatigue, or whatever merits it.  Same with boating and cycling.  So hopefully those result in lowered risk over all that despite that I fly, my total risk is somewhat lowered thanks to participating in flying.

[Marauder]

One more thought - I could hope to say that my risk of pre-mature death may actually be lower because I fly and participate in the flying culture of go-no-go decisions.  Since I have been flying I have been actively applying that to other activities where in years past, tough guy, I would just suck it up and go.  E.g. driving into icy snow storms, ice rain, blizzards.  Don't judge - but it used to be I would just go.  Now I feel clever for cancelling or delaying a driving trip if weather, fatigue, or whatever merits it.  Same with boating and cycling.  So hopefully those result in lowered risk over all that despite that I fly, my total risk is somewhat lowered thanks to participating in flying.

Now cycling is something I have found to be more dangerous than flying! My wife ended up with an open compound fracture when a driver going in the opposite direction made a left turn into her on an 8 foot wide bike lane!

I’ve been clipped twice by cars and I can’t tell you the number of near misses I had either by the driver’s intent or distracted driving. It has gotten so bad that I find myself on Delaware’s bike trails more than the road.

Ironically, there is a link to aviation. I have just as many strobes on my bike as my plane and I have the cycling equivalent of ADS-B in the form of a Garmin Varia bike radar.


Sent from my iPhone using Tapatalk Pro

[David Lloyd]

When Richard Collins at Flying Magazine wrote almost yearly about things that killed people in airplanes.  Some were mentioned above.  Another common factor was a combination of darkness, mountains and weather.  Airplane doesn't care if it is dark. Airplane doesn't care what is below. Aside from thunderstorms or ice, it really doesn't care what the weather is like.  Handling each is up to the pilot-in-command.  Treat each flight professionally and you will get professional results.  Have a plan, follow the plan.  Have a plan B. And at least have a plan C thought out.  Lack of planning will give poor results.

 

[Matt Ward]

13 minutes ago, Marauder said:

Ironically, there is a link to aviation. I have just as many strobes on my bike as my plane and I have the cycling equivalent of ADS-B in the form of a Garmin Varia bike radar.

Varia + Zwift!  I just did Ironman and probably 70% of my riding was indoors for the very reasons mentioned. 

[Yetti]

14 minutes ago, Marauder said:

Now cycling is something I have found to be more dangerous than flying! My wife ended up with an open compound fracture when a driver going in the opposite direction made a left turn into her on an 8 foot wide bike lane!

I’ve been clipped twice by cars and I can’t tell you the number of near misses I had either by the driver’s intent or distracted driving. It has gotten so bad that I find myself on Delaware’s bike trails more than the road.

Ironically, there is a link to aviation. I have just as many strobes on my bike as my plane and I have the cycling equivalent of ADS-B in the form of a Garmin Varia bike radar.


Sent from my iPhone using Tapatalk Pro

Back during primary I found that more people die on bicycles than GA Aircraft per year.   I have been hit 3 times on a bike and broke my sacrum last time a guy turned in front of me and I rolled off the hood onto the ground.

[aviatoreb]

19 minutes ago, Marauder said:

Now cycling is something I have found to be more dangerous than flying! 

Sadly - I agree.  Anecdotally, and also from having researched the actuarial statistics, its somewhat worse.

Not as bad as hand gliding. (Which I don't do).

In cycling too - a good bit can be done to help mitigate the risks. As you have found with trails.  Here I choose certain roads with massive shoulders out in the country.

Knock on wood everyone.  

(Knocking on wood has been proven scientifically to lower risks of most activities except for competitive lumber jack trials involving speed chain saw drills).