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Aviation Mathematics

Wed Feb 02, 2005 12:57 pm

I am currently doing a mathematical project for my IB Math course. The basis of the project is "How Airline Fleet Diversity(how many types of aircraft operated) effects the airline's safety record." Does anyone know what type of mathematical methods I could use for this? Could anyone give me the equations used for determining airline statistics, usage, etc. Thanks!
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RE: Aviation Mathematics

Wed Feb 02, 2005 1:21 pm

I;m not sure what IB Math is but this sounds primarily like a statistics project. You'll probably want to start by getting the raw data (# of types, # of accidents, total number of aircraft, etc). It would probably be best to limit the scope by focusing on just USA airlines or the world's 20 largest airlines or something like that. Also, you should convert # of accidents into #of accidents per hours flown or something like that. That way, the numbers will be more fair. Smaller airlines will have a smaller number of accidents but probably a similar number of accidents per hour flown.

After you get all the fun data, you'll need to run some statistical analysis on it. Excel should do just fine for the level of work you're doing. You'll want to plot a graph in Excel (I think they call it an x-y plot or something like that) If there is a correlation between # of fleet types and # of accidents, there data will fall in a nice line with little scatter. There is an option in Excel where you can get the equation of the line of best fit.

If you need any other help, feel free to send me an e-mail via my profile. I have a college degree in math and am more than willing to help.
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RE: Aviation Mathematics

Wed Feb 02, 2005 1:33 pm

Airlines inevitably produce excess capacity (good for a graph?)

You can use the Hypothetical S-Curve for demand and revenue

I once had a book on Airline Business Formulas, I cant seem to find it, but it is simply like a 500 page black and white book with no pictures, and just CALCULUS formulas and equations on how to run an airline and also create statistics. I am sure they have it in a college Library

Airline economics or something, but its dead-boring and makes you wonder if its about hub and spoke sytems or Quantum Physics

IB would be International Baccalaurate?
There Are Those Who Believe That There May Yet Be Other Airlines Who Even Now Fight To Survive Beyond The Heavens
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RE: Aviation Mathematics

Wed Feb 02, 2005 11:11 pm

Are you doing this for your Extended Essay? I rememeber my days back in IB, I got the diploma and all, but I think it contributed to my drinking habits in my HS days  Big grin Good luck on your paper and all.
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RE: Aviation Mathematics

Thu Feb 03, 2005 1:41 am

ANOVA will be a lot more impressive than a plotted line, and less likely to err. I've seen people shoot themselves in the foot severely by plotting straight lines more than once... even out in the real world. Incidentally, Excel will do ANOVA for you as well.

Determining if you have a significant correlation between the number of types and the accident frequency should be a cakewalk.

Finding the data will probably not be.

First off, the accidents are too few and far between to provide a good data set. Look into adding incidents... but you will be hard pressed to get any significant number of airlines to release their incident information.

Then there's the problem of confounds, which you have to adress. They are significant. Airlines with many types are likely to differ from one-type airlines in other, but systematical, ways.

Don't despair though. Even if you cannot find anything statistically significant, fo the above reasons, writing up a good report on just why it couldn't be done should give you the same credit... with more opportunity to show some brilliance.

Best of luck,
I thought I was doing good trying to avoid those airport hotels... and look at me now.
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RE: Aviation Mathematics

Thu Feb 03, 2005 2:16 am

You could model it like component reliabilities as in system reliability. The hard thing is determining if the reliability rates of the fleet types are in series or in parallel. Then it is either R = r1 x r2 x rn for series or R = 1- ((1-r1)x (1-r2) x (1-rn)) for parallel.

Air transport is just a glorified bus operation. -Michael O'Leary, Ryanair's chief executive
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RE: Aviation Mathematics

Thu Feb 03, 2005 4:17 am

A better route would probably be to compare the accident frequency of the types between airlines/types of airlines to try to see if there is a trend somewhere. Still a long shot, but a better long shot IMO.
I thought I was doing good trying to avoid those airport hotels... and look at me now.
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RE: Aviation Mathematics

Thu Feb 03, 2005 5:19 am

If, as FredT suggests, you want to add incidents (and I think it relevant) then I might have a suggestion for you. (My information is old, but should still be true.)

All work done on airplanes generates a Mechanical Reliability Report (MRR) The FAA publishes a summary of these reports, available by type. e.g. B-737 or A-320

The summaries come out often. (daily?)(weekly?)(monthly?) and should be either free or a modest fee. Might, by now, be available online.

Check that out.
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