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Maths Exploration

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Well hi guys, so I'm in the final year of my IB diploma programme and I'l like REALLY struggling with this Maths Exploration.
It's a long post but I beg you to read it. I'm quite demoralized by this exploration.

Yeah so I initially started to think about ideas back in July, and already then I knew I wanted to do something calculus orientated. Some people suggested that I could do "mixing problems" and set up a differential equation to describe the rate of change in a contaminant, or even a lake because a real world example is what I should really go for.

I should use calculus to explore real life problems. So I actually found a document of a person who had set up their own model describing how the rate of contaminant changed over time using Calculus and then he applied this to some lakes in real life which I thought was cool.
So I showed my teacher this document and she said I couldn't do that as I would take somebody else's model and it wouldn't be my authentic work. So I had to switch idea.
Now for the past months together with my struggle in the IB I've gotten many ideas, but I've always been centered around calculus.

The teacher sat down with me and told me what I was interested in and we dug deap until we decided to do something with airplanes.
Airplanes are a huge fascination of mine. I love the engineering, the structure, it's greatness. I even love airports. The strange thing is that I'm super afraid of flying airplanes (partly because I've watched all Mayday episodes).

So initially I thought lets create a model to optimize a flight profile for the least amount of fuel consumed. I then thought I would look at which airplanes to take for different trips. At which altitude you should fly, what speed you should have, when should you start descent etc... to optimize flight profile for least amount of fuel consumed.
This turned out to be really hard as there were many variables involved and I had to give up that idea after to 15+ hours research if not more...

Then I went on by thinking well lets look at airplane descent and try to model the descent of an airplane. I would then look at different airplanes at different airports.
Which speed should the airplane have initially when should it start to descent etc...
I found a model on the internet which did model this but after 8 hours with it I gave up, I thought it was a bit too hard to comprehend.
I thought I could use the model and then compare with real data and probably see that they were not the same and then discuss this.
In theory it was a great idea but once again I couldn't pull through.

So then I took a step back and thought what made me interested in planes, and then I thought about the dimensions, and structure etc...
The wing loading and flexibility of airplanes are super important to me when I choose a trip by airplane. Since an increase in wing loading and flexibility decreases any turbulence felt by me in the fuselage and that is a dealbreaker for me.
I also always sit by the wing as it's statistically the safest place to sit at (but also the noisiest).
In the airplane the three structures which are the most important to me and the ones I worry about the most, are the wings, the engines, and the rudder/stabilizer.
I'm especially scared that the rudder/stabilizer will malfunction or get stuck, as it will often have fatal consequences.

Now I said this to my teacher and she was like: "You should compare the dimensions of different aircrafts, perhaps those big ones with small ones, and surely you can get some calculus there"
That was what she said, now after spending about 25 hours trying to find out what to do I'm getting really demoralized and at the same time the school is giving me a rough time (understandably so but really I have been trying a lot)
I have collected dimensions of four different aircrafts, two long-haul and two short-haul. At least I've tried to find as much data as I can. I especially got a lot for the Airbus A380 but now I'm like what am I supposed to do with the data, which essentially is only dimension data. Where can I use my calculus, and then what....

After spending more than 60 hours on this I'm getting really demoralized and sad really, and I can feel the pressure increasing. What should I do guys really feeling hopeless at the moment. The school is really getting sick of me too.

In this "Maths Exploration" the maths definitely does not have to be complicated as you guys now, and this is a very good example of a maths exploration which scored a perfect 20/20


I really need your help guys :(

I just need my topic and then the writing stage will go much faster

Cheers guys!

P.S. my maths knowledge is equivalent to that of a Maths HL student.

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Hi, I'm from the previous batch so i'm not so sure about the new change in syllabus. First of all, try to think of an aim. Remember, calculus is the study of changes. You have dimensions of aircrafts. Therefore, you can calculate the area and volume of these objects. Even surface area. A possible example could be see the rate of change in the volume as you change the sizes. As volume increases, the exposure of the plane increases as well. This can be bad as it might increase the chances of a lightning strike! Since you're doing Math SL, i think this would be appropriate. You might want to discuss this with your teacher in more detail. Hope this helps. IB can be demoralizing but just don't give up hope!

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Well yes I do have the dimensions but the plane parts have awkward shapes and not typical geometrical shapes. Consider for example the shape of this engine on a commercial aircraft. I have the dimensions but how do I use calculus to determine the volume of the engine? Am I missing something here?

I just don't understand how to use calculus with airplanes :( .

I appreciate you taking the time to help me.

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Well yes I do have the dimensions but the plane parts have awkward shapes and not typical geometrical shapes. Consider for example the shape of this engine on a commercial aircraft. I have the dimensions but how do I use calculus to determine the volume of the engine? Am I missing something here?

I just don't understand how to use calculus with airplanes :( .

I appreciate you taking the time to help me.

Hmm.. I doubt a majority know how to do that as well. haha. Hmmm.. It does look complicated. You can't use calculus to determine volume, use the old area x height. Perhaps you could take an estimation of the volume of the engine by assuming that the first half is rectangular rather than having a weird shape. As I said, perhaps a discussion with your teacher can further aid you in this exploration.

About the calculus.. Does it have to involve calculus? Because I feel a study on geometry would be much easier considering the data you have. Don't get me wrong. The idea of using calculus here in interesting but it might be a bit difficult and will require a bit of creativity.

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Dear shwareb,

I wanted to ask you if you did your math SL IA something on aeroplanes. I am trying to calculate the whole surface area of aeroplanes. please not only him, everyone who wants to help me send me something on my email [email protected] please don't ignore me. I'm facing problems on how to make it more complex. And Shwareb, please if you see this can you send me the websites that you used. I know it has been a long time but I really need help as my IA is due to 24 hours.

Thanks,

Eyoel

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