PanAm747 From United States of America, joined Feb 2004, 4242 posts, RR: 8 Posted (11 years 3 weeks 1 day 15 hours ago) and read 16229 times:

Hello all!!

As a junior high school algebra & geometry teacher, I am constantly asked "when are we ever going to use this?". A legitimate question, I understand, but having never worked really in other fields, I cannot provide specifics. I would love to use aviation as an example.

I know that pilots and co-pilots must make some very complex calculations before take-off, as well as during flights. Does anyone know of a website where I could find out some of the math that is used? If not, are there any pilots who could post some examples of what must be done?

I would love to be able to show my students that it has a practical purpose in real life (other than just being a teacher!). Thanks in advance!!

Pan Am:The World's Most Experienced Airline - P(oor) S(ailor's) A(irline): San Diego's Hometown Airline-Catch Our Smile!

AAR90 From United States of America, joined Jan 2000, 3525 posts, RR: 45
Reply 1, posted (11 years 3 weeks 1 day 14 hours ago) and read 16152 times:

PanAm747,

I see you are SAN located as am I --CMR/RB area. e-mail me with some more particulars and we should be able to put together a bunch of useful real-world stuff {complete airline flight plans, weight/balance tables, performance charts, load plans, FAR formulas, etc.}. I'm off to recurrent training for a few days so give me a couple more days for a response.

AAR90
CA B737 AA
oslaser@sbcglobal.net

*NO CARRIER* -- A Naval Aviator's worst nightmare!

Flyingbronco05 From United States of America, joined May 2002, 3841 posts, RR: 2
Reply 3, posted (11 years 3 weeks 1 day 11 hours ago) and read 16004 times:

I know that pilots and co-pilots must make some very complex calculations before take-off, as well as during flights.

They are mostly done by cockpit computers like the FMS.

Soaringadi From United States of America, joined Apr 2004, 472 posts, RR: 0
Reply 4, posted (11 years 3 weeks 1 day 6 hours ago) and read 15905 times:

What I think is that the older pilots had to know about Vectors... for their wind correction etc., but now it's done by manual, and digital flight computers....... As for the t/o. dist., t/o. speed, density alt. etc., all is managed by computers nowadays....... so I don't really see any place pilots have to work their brains out while in-flight. Even though they are required to know how to solve those problems obviously.....

Backfire From Germany, joined Oct 2006, 0 posts, RR: 0
Reply 5, posted (11 years 3 weeks 1 day 1 hour ago) and read 15805 times:

I know that pilots and co-pilots must make some very complex calculations before take-off

Not really. BA preferred basic maths qualifications for candidates applying for its cadet entry scheme, and it favoured those applicants with mathematical flair, but it was never - as far as I'm aware - of huge importance.

Computers are far better at handling critical number-crunching - why leave a task so obviously suited to computer technology to a human being?

Vzlet From United States of America, joined Mar 2004, 841 posts, RR: 0
Reply 6, posted (11 years 3 weeks 1 day 1 hour ago) and read 15747 times:

Not to make light of your good intentions, PanAm747, but here's an excerpt from a C-130 pilot's letter to a high schooler enquiring about suitable courses of study:

"Take a lot of math courses. You will need all the advanced math skills you can muster to enable you to calculate per diem rates around the world, when trying to split up the crew's bar tab so that the co-pilot really believes he owes 85% of the whole thing and the nav believing he owes the other 20."

"That's so stupid! If they're so secret, why are they out where everyone can see them?" - my kid

EAL757 From , joined Dec 1969, posts, RR:
Reply 9, posted (11 years 3 weeks 1 day ago) and read 15582 times:

Flyingbronco05:

Perhaps I was too vague in my post...but consider the avionics of the modern day Boeing planes...the cockpit of the 747-400 is real close to the 75 and the 76...and these planes are leaps and bounds easier than flying the old 707 and 727 (and original 747 series). The job has gotten a lot easier and I guarantee you a 744 pilot is making a heck of a lot of money with any carrier. Granted, longevity has earned him his spot flying that plane, but my bet is that a UA 744 f/a is making at least $160,000...probably more. And captains are making much more than that. That's a lot of dough.

Sulman From United States of America, joined Mar 2004, 2037 posts, RR: 31
Reply 12, posted (11 years 3 weeks 22 hours ago) and read 15364 times:

Whilst the FMC/MCDU can do all the donkey work, crews check, check, check their work. Even if you fly ultralights or are studying a PPL, whatever level you study at, this is drilled into you.

Machines are very simple: Shit in = Shit out. One of the problems of automation is that crews exert considerable effort making sure the aircraft flys itself as it is supposed to. Your attitude is spot-on.

It takes a big man to admit they are wrong, and I am not a big man.

N6376m From , joined Dec 1969, posts, RR:
Reply 13, posted (11 years 3 weeks 22 hours ago) and read 15312 times:

I think you are addressing the wrong issue. Whether they're going to use it or not, they need to learn the algebra and trig because it will help them learn a way of thinking that will be crucial.

A couple weeks ago, my daughter's babysitter (a 16 yearold high school junior taking a dual enrollment college algebra class at a local community college) asked me for help on some linear regression problems she needed to understand for an upcoming exam. Given that she's 16 and taking college classes I'd say she's toward the top of her high school class.

When I tried asking her if she understood the concept of linear regression she said, I don't have to, all I need to know is how to do it on the calculator. After about 30 minutes of trying to explain to her that the theory was as important as the answer (and that she'd have a far easier time getting the answer if she understood the theory), she told me that the only help she wanted was in learning to use the calculator. I begrudgingly acquiesced because my wife told me not to piss off our best babysitter.

I showed her how to enter the problem. I ran through two examples with her and then had her try one. As soon as she hit enter I was sure she had the wrong answer (why? Because the data set was upward sloping and the coefficient on the mx + b equation was negative). When I told her that the answer was wrong before looking it up in the appendix, she couldn't understand how I could be certain.

After a few more tries she finally figured out the calculator and was getting all the problems right.

Two days later I found out that she failed her exam because the professor had written the problems in a slight different fact set than what was shown in the text. She told me she was clueless about what to do because she couldn't figure out how to get the data into the calculator.

Though I doubt many of us deal with linear regression problems on a regular basis (I certainly don't), I know that those of us who learned the theory would be able to do it if we had to.

Ben From Switzerland, joined Aug 1999, 1391 posts, RR: 49
Reply 14, posted (11 years 3 weeks 22 hours ago) and read 15296 times:

While the day-to-day maths in the cockpit may be less common these days, to actually get there you have to pass the ATPL exams (or equivalent in the USA). There is a very large amount of maths in those.

Just show your students a mechanical flight computer/circular slide rule and get them to do some calcualtions on it. That might help them get the idea that it's not all done with computers (at least not in the training stages).

Getting proficient with the flight computer massively increased my mental arithmetic skills and gave me a really good understanding of the actual mathematics involved, not just mindlessly plugging numbers into a calculator.

Jhooper From United States of America, joined Dec 2001, 6206 posts, RR: 11
Reply 15, posted (11 years 3 weeks 8 hours ago) and read 15057 times:

Understanding how vectors work really have helped me compute Wind Correction Angles, ground speed, and other navigation-related tasks.

Also, weight and balance problems are based on what your students will probably see in their Physical Science or Physics classes. You know, the problems where a balance beam is placed upon a fulcrum and the weights are balanced out. The basic formula for weight and balance problems is WEIGHT X ARM = MOMENT. Then once you have your total moments of all loads, you can divide this total by the total weight and come up with the Center of Gravity. The C.G. is critical to ensure proper weight distribution.

Last year 1,944 New Yorkers saw something and said something.

Flymia From United States of America, joined Jun 2001, 7401 posts, RR: 6
Reply 16, posted (11 years 2 weeks 6 days 21 hours ago) and read 14952 times:

Well yea in first years of flying and to pass the test I guess you need to know a lot of math. But in modern cockpits the pilots need to know math but it not like they are doing calculations them self the FMC will do that. But there is not much math have in a C152 but once you get to instrument and twin flying is really when the math kicks in I would expect. This is why I have to make sure I have math done. Not to be a commercial pilot but to do all the things before that.
EAL757: Not many pilots are making 160,000. First it is F/O and no F/O will make $160,000 a captain might on a 747. But please Pilots are under paided just like paramedic they are en charged of many lives all day long. And if you don't think it is a hard job then you try making and ILS landing with a 15knt crosswind and .3 visibility. Really just landing a 747 alone in perfect weather is hard enough. Only a 20 year captain on a 747 would maybe make $160,000.

"It was just four of us on the flight deck, trying to do our job" (Captain Al Haynes)

Osteogenesis From Germany, joined May 2003, 647 posts, RR: 2
Reply 17, posted (11 years 2 weeks 6 days 21 hours ago) and read 14893 times:

I always asked my teachers the same things. And they always gave me the wrong answers. The good thing was that later I started to love mathematics because of there beauty and logic. That is why I ended up studding mathematics.

Now I work as a software developer and many people ask me if my math studies have helped me. Although I rarely use any higher math, I know it has helped me to understand and to solve complex problems easier.

Maybe you can tell your students that pilots have a very big responsibility and that they sometimes have to make accurate decisions very fast and with very little information. People who are able to understand math will also understand other complex problems easier.

Maybe you can also tell them that the guys who design the planes and their components have to understand mathematical concepts in order to be able to come up with new and innovative ideas.

Let the computers do the calculations; they do it faster and much more accurate. But in our very technical world those who have a good understanding of math will have an advantage over those who do not.

Av8trxx From United States of America, joined Nov 2001, 657 posts, RR: 6
Reply 18, posted (11 years 2 weeks 6 days 13 hours ago) and read 14778 times:

"I know that pilots and co-pilots must make some very complex calculations before take-off, as well as during flights."

Not really. It's just basic math. For those that still use pen & paper, the weight & balance is simple addition & subtraction. Many carriers now use computer tablets or operations figures these numbers for you. At the most complicated, only simple algebra is used to figure time/distance, fuel burn or descent problems in your head. The most common might be when you are given a descent with a navaid/fix crossing restriction at a certain altitude, so you need to know how many feet per minute to descend to make the restriction. X many feet to lose, at X airpseed, in x number of miles type thing. Plus, as many have pointed out, it's the norm for the FMS to do the simplest calculations these days. I took calculus and advanced math at ERAU and have never used them in the cockpit.

There is a great book on this subject called "Mental Math for Pilots" by Ronald McElroy. It has lots tips & trick to figure the most common mental math problems encountered in the airline environment. You can check it out at-

A330 From Belgium, joined May 1999, 649 posts, RR: 7
Reply 19, posted (11 years 2 weeks 5 days 20 hours ago) and read 14628 times:

Paid too much??
I invite any person saying such utter nonsence to spend one day with me in the simulator or on a random bad weather trip.
We are generally paid way too less for the amount of responsibility, ability and risk (not only life but more loss of licence) we have.