What are the odds???

[David Flynt]

I'll take a crack at the question.  Maybe if we put our heads together we
can determine the actual odds.  Let's speculate that one flight out of every
2000 results in a mid-air collision, so long as there is at least one other
plane in the air.  Now, let's enumerate the common type of model airplanes
that can fly off a paved runway.  There are 1) pattern planes, 2) trainers
3) 40 - 120 size sport planes, 4) scale planes, 5) pylon racers.  Most
planes are in the 2) and 3) category, but to keep the numbers simple, let's
say there are an equal distribution of each type.  A further simplification
is that each plane category shares the airspace equally, which will
certainly skew the calculation.  For example, I would argue that it is more
common for two or more pattern planes to be in the air at the same time,
than it would for a pattern plane and a trainer to be in the air at the same
time.

Ok, so now, out of every flight that occurs at your field, lets say that 1
of every two flights has at least two planes in the air.  The result then
is, on any given flight for two trainers to collide, 1/2000 * 1/5 * 1/2 = 1
in 20000.  The results for two pattern planes would be the same.  Now for
two trainers to collide on day one, followed by two pattern planes to
collide on day two, might be a little tricky to calculate.  I don't think
that it is simply 1/20000 * 1/20000.  It should be the same odds of "What is
the probablility of any two randomly chosen people have a birthday one day
before the other".  I think that the answer is 1/365 * average number of
flights per day, say 10.


So I think the odds are rougly 1/20000 * 1/20000 * 1/365 * 10  = 1 chance in
14,600,000,000 flights that occur at your field.  And you can be sure that
your field will never see that many flights.  For comparison, McDonald's has
sold about 7 times as many hamburgers.

My intuition says that my assumptions and math must be way off, because with
odds that low, the scenario you describe would be near impossible to
observe.  Any math wizards out there have a better answer?

A more interesting question to me is, how offten do pattern planes collide
at contests?  I can control mid-airs outside of contests, but we are all
subject to the odds of a mid air if we participate in a contest.  Let's say
there are 10 mid-airs out of all the 8 NSRCA districts each year.    And
lets say there are 7 contests per district on average.  Then that is 56
contests.  Then the odds of having one mid air in a contest is 1 in 56.  Now
if there are 20 pilots average per contest, then your chance of mid-air is
1/(56 * 10) = one chance in 560 contest attendances (I think).

David Flynt


  -----Original Message-----
  From: discussion-request at nsrca.org [mailto:discussion-request at nsrca.org]On
Behalf Of FlyFutabaGuy at aol.com
  Sent: Saturday, August 02, 2003 1:36 PM
  To: discussion at nsrca.org
  Subject: What are the odds???


  Yesterday, during our annual fun day for the ARC (association of retarded
citizens) fun day. I was coming in to land the trainer I was flying the kids
on, and I mid-aired Gordon Anderson, who was also flying a trainer. Luckily
I got mine back, Gordon's was a little lift impaired with 1/2 a wing and
didn't get his out of the flat spin.. This was the first mid-air I have ever
seen... Today, practicing pattern, my dad took his Olympian off, and on the
procedure turn mid-aired with Dennis Cone, another local pattern pilot. Both
planes destroyed.... WHAT ARE THE ODDS??? think we should take a week off to
let the curse wear off??

  -Brett Bowen
  District 8 Advanced
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