# of Aircraft Club Members - Math Formula Wanted

Hello,

I'm looking into different shared ownership arrangements, including
clubs, fractionals and partnerships.

I once spoke to a flying club member who said that the availability of
their club aircraft improved with 30 members and three aircraft
compared with 15 members and only two aircraft.

Is there any kind of mathematical formula that could take into account
the number of aircraft, the number of pilots, and predict what the
average aircraft availability would be? I imagine that fractional
companies must rely on something like this to help them decide how
many shares of an aircraft they can sell, and still keep their
availability promises.

Richard

On 14-Sep-2004, (Rich) wrote:

Is there any kind of mathematical formula that could take into account
the number of aircraft, the number of pilots, and predict what the
average aircraft availability would be?


I'm not really a mathematician, but I am familiar with this type of
analysis. The analysis will be very complex if different airplane types are
involved, but if they are all the same (or are all equally acceptable for
all uses) the analysis isn't too bad. The variables that would then be
pertinent would be:

- Number of pilots involved OR number of airplanes involved (you have to
know one to determine the other, of course).

- Average number of hours of use that each pilot will want on the busiest
day of the week (typically Sat. or Sun. in most clubs), and number of "prime
time" hours in that day. Note that the term "hours of use" refers to the
number of hours the plane is checked out (and thus unavailable to others),
not number of flight hours.

- Average number of hours each airplane will be unavailable (due to
maintenance or other issues) during the busiest day of the week.

- Tolerable likelihood of being unable to book an airplane when desired.
(e.g. it may be tolerable that, if you want to book at a particular time on
the busiest day of the week, you will be disappointed 10% of the time.)

If we assume demand for aircraft hours of use has what is called a "Puissant
distribution" (not perfectly accurate, but probably close enough) then we
can use Erlang-like calculation to find the answer, given values for all the
variables.

Here's an example. Let's say that we have 20 pilots who, on average, want
to check out a plane for 1 hour out of a 16 prime-time hour "busiest day" of
the week. (Of course, some will want more, and many will want none on any
given day. The 1 hour is an average.) It is predicted that each airplane
will be "down" an average of 1 hour during the same period. (This is
derived from a more understandable 1 in 16 probability that a given plane
will be "down" during that whole 16 hour period.) Finally, we decide that
it will be acceptable that there is a 10% probability that a given desire
for use during that period will be unmet. How many planes are required? My
Erlang calculator program suggests that the number is 4.

An Erlang calculator is available on he Web at
http://www.erlang.com/calculator/erlb/ If anybody is interested, I can
suggest a formula for deriving the variables to insert into this calculator
based upon the variables I describe above.

Of course, somebody may have a more appropriate calculator or algorithm for
performing this analysis.

--
-Elliott Drucker

In a previous article, (Rich) said:
I once spoke to a flying club member who said that the availability of
their club aircraft improved with 30 members and three aircraft
compared with 15 members and only two aircraft.

Is there any kind of mathematical formula that could take into account
the number of aircraft, the number of pilots, and predict what the
average aircraft availability would be? I imagine that fractional

Probably not, since flying hours per member varies with the economy.

Back when our club was nearing 15 members per plane, it was getting damn
hard to schedule a plane when you wanted. But the reason we had so many
members was the same reason the members we had were flying more hours than
usual - the economy was booming, and people had more money. Now we're
down to 11 members per plane, and the members we have aren't flying as
much, and it's much easier to get planes. Back then we put on 300-400
hours per year on each plane, this year some of our planes are going to be
lucky to break 150 hours, and one of them got a new engine in June and we
still haven't done 50 hours of break-in.

--
Paul Tomblin http://xcski.com/blogs/pt/
"The means of defense against foreign danger historically have become the
instruments of tyranny at home." - James Madison

Wow! Thanks Elliot, this is exactly the sort of information I was
looking for.

I know I cannot expect to calculate an exact number, but averages and
probabilities will be just fine for the type of analysis I want to do.

Many thanks!

Richard