Aviation Mathematics

[747 forever]

Hi everyone,
In a very soon while Im going to take my GCSE options. Im working to become an airline pilot so I have the subjects planned out well. The list goes
Mathematics
Science (physics, chemistry)
Geography
English
French
P.E (compulsory at my school but the leadership awards would look good on my CV)
(possibly Business studies)
And regarding Mathematics Im wanting to know what kind of maths pilots do. Ive done some research but people simplify it to much and say "we leave it to the computers"
Would the kind of math you do consist of
Formulae Speed, Distance & Time
Mass, Area & Volume Trigonometry
I found that off somewhere but I really want the pilots here to tell me what math you use and which one I should take.
Thanks

[MarkerInbound]

Um, let's see.

1. Split bar bill

2. Convert money

3. Convert Z time to local

Ok, about once a year I have to do manual W&B, but I use a calculator. And every once in while the MEL will say "increase fuel burn .4%." Again, I use a calculator. That's about it.

[Intruder]

A bit of algebra to use the numerous rules of thumb (2%/1000', 300'/NM...).
Some trig for crosswind calculations.
A bit of differential calculus to use in arguing density altitude and power/thrust output here.
Some discrete/combinatorial math for logic arguments at the bar...

The heavy math will be in all the ground school courses and tests, where you have to show you can do it by hand, on your own. Once you have a real job, the first one is the most often used.

[parabellum]

Very much as Intruder says. Make sure you have the Sine, Cosine and Tangent rules safely in your head for the navigation exams, if they still do plotting on a chart.

[Dariuszw]

Here you will find aviation formulas used everyday by pilots.
Suggest drop the guy email you want it and he will help you out, Im sure:ok:

Aviation Formulas (http://dariuszwielgat.com/Paypal%20Cart_Formulas.htm)

[Tugnut]

747 forever

Like the previous posts have said the most arduous part is during your training. Once you are there and have a job, make sure you know your 3x table for top of descents and 5x tables for rates of descents. The rest is simples.

Good luck

[747 forever]

thanks for the replies! So basically knowing every basic math is what I should do. What exactly is calculus anyway? I have read the example of thrust ratios etc but what is it? Like method and calculations etc

[Intruder]

Calculus is applied math, used for many things from CALCUlating velocity, acceleration, and distance traveled, to CALCUlating Mach or True Air Speed from Indicated Air Speed, air density, and temperature. Much of Physics, Astronomy, and other "hard" sciences rely on Calculus.

The fundamentals of differential and integral calculus are finding rates of change over decreasing intervals, eventually finding a formula for larger intervals.

[747 forever]

ah yes we are doing some calculus in physics today,
Efficiency=total useful useful energy
Total Energy
We have a test on wednesday so, yeah could think of that as a kind of calculus.

[average-punter]

Calculus is not covered at all at GCSE, you only get introduced to it at a-level. Although it is implicitly covered when you are told in Physics. The gradient of a velocity/time graph is the acceleration and the area under the curve of a velocity/time graph is the displacement.

[747 forever]

Can you give me one example of the type of calculus and when it is used? Just to get a rough idea of what its about

[BOAC]

Forget it - you don't need it for flying!

[Johnny Tightlips]

If you can multiply any number up to 50 by 3 then you will be fine:ok:

[747 forever]

any reason? I can do that but I want a reason to why.

[747 forever]

Also from what I have searched you really honestly don`t need to be that good at maths, the world has miss judged pilots

[proudprivate]

Calculus is basically the study of how functions change over time. Velocity is an example : it is the rate of change of your position over time.

It is a very elaborate subject, and has many applications. The two most important ones are the ability to find extreme values (minimum / maximum) of functions and the ability to estimate how good an approximation really is.

In the general professional pilot community, these are reflected in tables, graphs, and rules of thumb, so that you don't see calculus at work. Indeed, many professional pilots just learn those rules by heart and just look at graphs, or trust their computers / calculators when the result of a formula pops up.

People who are good at calculus (and who understand the applications) have an easier job at remembering formulas or the shapes of curves, because they understand the mechanics behind it. That has helped me in sitting some of the career exams, and it allowed me to write some flight planning software myself. But in all honesty, you would rarely use calculus directly in flight.

the world has misjudged pilots

The general public still reveres the pilot community, seeing pilots as the pinnacle of both intelligence and skill.

Nevertheless, especially since the introduction of low cost airlines, the market (driving pilots' pay) has a more accurate perception of what a professional pilot brings to the table: that is, a medically fit and responsible human being that has completed a 12-18 month specialized (expensive) training. But they are not engineers, they don't have an MBA and it is not a given that they have good interpersonal or management skills.

[BOAC]

But in all honesty, you would rarely use calculus directly in flight.
- actually never! EG d(theta)/d(t) is called Rate of Turn and is normally '1'.

Look no calculus, differential or integral!

3 times table is sufficient for we Skygods:D

Relax, 747. Basic mental arithmetic- division and multiplication will do fine.

[parabellum]

Just curious, do the JAA/CAA exams still do Nav plotting?

Some Old Horses Can Always Have Their Oats Again and all that sort of stuff, or is it long gone now?

[Dan Winterland]

I scraped a pass in maths at O level in 1977. That is probably more than you need to be a pilot. All the maths you use is common sense. You will be given 'rules of thumb' to work with through your training - none of them are complex.


Interestingly, many people think that people with a good scientific education and skills would make the best pilots. But it's often the other way round. From my experience as a RAF QFI, spatial awareness is most important and it's the artists and not the scientists which tend to have this. When I think back to my previous students, the best ones were not mathmeticians - in fact far from it. Of the three I can think of right now, one had come straigt from school with mediocre geography and history A levels, one had been selling second hand cars and one was a piano player! I did have one good guy who was a marine biologist - which is sort of a science - but he had spent most of his university time diving and surfing. One guy had a physics degree from Oxford. He spent all his time trying to understand the mechanics of what we were doing and the more important stuff just passed him by!

[747 forever]

you see I can honestly say I used to not be good at maths but last year it really picked up quite well, its going so well Im a bit disappointed knowing its not that useful. Im not suggesting Im not going to bother but its a bit disappointing for me.

[FlyingSportsman]

Wouldn't like to burst your GCSE bubble - but just because you are good at the subject now, DO NOT assume it will come just as easy at A-level. I studied IGCSE's, A* in both maths and physics, and am still finding both subjects challenging.

Conquer the basics at GCSE, and you will be fine in the GA spam can, and from what most Boeing/airbus drivers have said its not too challenging in the slightly newer, shinier tin can! I know that maths and physics are 'preferred' but as far, I've come across very little related to aircraft, I suppose the waves section I've studied can be loosely related to the sonic boom, but it doesn't form an overly important part of your future!

Best of luck with your choices.

[spider_man]

Follow the subjects you enjoy and do well at, not the ones some pilot career book say are essential. Get used to the volume of material at A level and this will prepare you well for ATPLs. You only need GCSE level maths working knowledge for commercial studies and pilot selection centre tests (including BA).

Better to get A or B in subjects you enjoy/do well than C or D in maths and science.

[pudoc]

Somethings you learn at A-level Physics are useful for the ATPLs. I've found it useful in M&B and POF. GCSE Math is good as algebra has helped me with calculations in the ATPLs such as manipulating forumlas. But it's all taught again in the ATPL manuals so it doesn't really matter.

Don't get down if your results aren't great either, education isn't for everyone, I have IGCSEs B-C, I left my 6th form about 2 years ago too as I didn't like a-levels. That's not to say I'm dumb, I happen to being getting through the flying studies quite nicely. The reason I was crap in school was because I spent so much time thinking about flying and reading aviation books rather than home work or daydreaming about me being interviewed by an airline in lessons. I'd actually read 5 of the PPL subjects at age 14-15. I started my PPL at nearly age 19 and focusing on aviation was more beneficial to my training than that Math homework I didn't do.

Don't work too hard, good qualifications are good to have but don't kiss your teenage life away either. No point having A* everything but having no social skills whatsoever.

[Artie Fufkin]

I have no physics qualifications and a B at GCSE maths. I am now a B737 captain.

At work, as previously said, you primarily need your 3 times table (for descent planning; very generally speaking you need 3 miles to loose 1,000 ft, e.g. if you are at 20,000 ft you should be 60 miles from touchdown). You also need basic mental arithmetic for things like checking the aircraft load sheet. Can be done by calculator, of course.

You may need a bit of basic trig for your written Navigation exams and an ability to manipulate a formula will help in Theory Of Flight written exams. If you pass your GCSE (C or above) you'll have more than you need.

[proudprivate]

Originally Posted by pp
But in all honesty, you would rarely use calculus directly in flight.
- actually never! EG d(theta)/d(t) is called Rate of Turn and is normally '1'.

Look no calculus, differential or integral!

You get the impression that logic is another discipline you don't need when flying an aircraft. My claim was : "Calculus is rarely used in flight"
BOAC's answer to that : "Never !" And then he proceeds with giving an "example" of where calculus is not used. :D

Let me re-iterate : It is not necessary to be good at calculus to become good at flying an aircraft. However, that does not exclude that you could use it in flight.

The first example that springs to my mind is applying the rule that, for small angles, and when the angle is expressed in radials (i.e. parts of 180/pi = 57°), than sin(x) = x (approximately).

So if you move 3 dots (6°) flying perpendicular to a VOR in 1 minute, you know that it takes you about 10 minutes to fly to that VOR.

Do you need calculus to know that ? No, you could learn by heart that sin(x) is approximately x when expressing angles in radials. But if you are moderately familiar with calculus, you would know that of the first 3 terms in the Taylor expansion of sin(x), only x is a non-zero term, so that sin(x)=x makes sense as an approximation when x is a small number.

Is this essential to fly an airliner ? No, because all but the most decrepit aircraft have good positioning systems and flight computers to do most calculations for you.

But the training schedule always runs behind. And so they ask you theoretical questions on exams about dead reconing and moving NDB bearings and all that sh1t where calculus, although not a requirement, can help your understanding of a particular problem.

On the other side of the spectrum an airline pilot friend of mine who got her ppl at 16 (and had to be driven to the airport by her parents because she didn't have a driver's license), started 1st year Maths at university, supposedly because it was a "good preparation" for ATP Flight School. It wasn't to be. She told me she had failed every single exam and it was all a bunch of gibberish to her. But motivated as she was, she made her ATPL with flying colours and is now still flying happily every after.

All this to prove the point that you do not need to be good at maths. But it helps if you can manipulate formulas and understanding how things work makes it a lot easier to assimilate.

Best of luck

[Artie Fufkin]

Whilst the practical application of maths at work has been demonstrated to be somewhat limited, it is only fair to point out that recruitment teams go wild for it.

If you want to get on to an airline mentored MPL course, then Maths and/or physics A Level may be a requirement.

[Still Searching]

Yeah, on the subject of A-level Maths, a few things:

Firstly, it's a huge step up from GCSE. I got an A at GCSE without putting in too much effort in or out of classes, and it's fair to say that I'm struggling at AS level. Same goes for Physics, actually.

Like the previous poster said, if you want to do it at AS level then take the M1 module rather than S1 (which is statistics) because it's far more relevant to flying and also more fun in my opinion. It'll go well with physics too. Of course, it's harder than stats for most people but it's worth it if you want to be a pilot, I guess.

Oh, and you won't touch calculus at GCSE at all - you'll first see it if and when you do AS Maths.

[stilton]

'The general public still reveres the pilot community, seeing pilots as the pinnacle of both intelligence and skill'



That may be the case in Belgium Pp but on this side of the Atlantic nothing could be further from the truth.



Maths in flying these days, your 3 times table and being able to add will do you
just fine.

[Seabreeze]

Maths can give you a better appreciation of physical processes. If you are good at it, then study it, and learn from it; in the long term it will benefit your understanding of issues such as aerodynamics and meteorology. Knowing the parallels between linear and rotational inertia can help you appreciate the effects of control surfaces and thrust on the response to input changes, but it is true you don't need to calculate F=m*a or T=I*alpha in your head while doing a maneuver.

On the other hand the number of pilots who don't triple check TO data such as weight and temp when entering into the FMS suggests they don't really appreciate the consequences of Newtons laws.

I despair at the rush by some pilots to create the impression that they don't need to be able to do anything much..... this attitude just plays into the hands of management types who believe they can manipulate the pilot community. If you act like a dumbs**t then you can be sure that you will be treated as such.

IMHO, professionalism requires a lifetime learning of all aspects of your profession.

Seabreeze

[Pugilistic Animus]

There's only six operations that can be done with math, addition, subtraction multiplication and division,...and really...exponents are fast multiplication and radicals are fast division...no math gets more difficult than that...that's the limit...even with calculus

:)