What STEM project can I do to fascinate an examination board?

[greg_rack]

Hi guys,

I'm currently attending my last year of high school in Italy and recently got admitted to Imperial College London, for the aeronautical engineering course.
Part of the uni conditional offer consists in getting a 100/100 score at the final high-school assessment(diploma), which in spite of the pandemic, hasn't been canceled, but only modified.

This year, we are given two months to work on a project for which we have few to no directions(apart from the fact that it must cover physics maths and secondly science topics), that will be presented on the day of the exam and will cover a major part of the maths-physics final evaluation.

Getting a 100/100 score will be tough and having a solid, interesting, well-thought and unique project is the right starting point to build upon.

My general thought for it was choosing an interesting physics topic among those covered in the curriculum, and creating some apparatus to display an eye-catching and meaningful related phenomenon.
Then, providing a detailed mathematical description for it, giving a nice demonstration of the calculus skills acquired(maybe with a hint of differential equations, even if not covered by the standard curriculum) over the course.
Finally, finding some real-life applications covering other subjects such as biology or chemistry would be great.

The problem is I have no idea of what could be a valid project or topic to expand and properly connect to other fields, and that's the reason I would like to hear your opinions, ask whether you have suggestions or even small ideas of something interesting which would catch the professor's attention and let me stand out among the others(that's what a 100/100 basically means).
What would you do, if you were me?
I don't mean to copy, of course, I'm aware that the decision must be mine, but suggestions and inspiration would be much appreciated, and thanks in advance for any of those :) ,

Greg.

 

[mcastillo356]

Hi, Greg, nobody answers you, but I think it's a great question. What about non contaminating aeroplanes?. Let's take your question as a brainstorming.
Greetings!

 

[Office_Shredder]

What kind of topics are in the curriculum? Does it include electromagnetism or is it a mechanics course?

 

[etotheipi]

I know you said you didn't have too many details, but do you know at least how long it needs to be and whether it's purely theoretical or if it's advised that you include a practical component? Also, since it's for the diploma I guess it doesn't have to be related to aerospace, although that might be what you're more comfortable with.

In any case, my two cents would be to go for something very focused. Like, just to throw out an example, you could try and investigate the trajectory of a tennis ball when immersed in a fluid (the air), or when launched with a non-zero angular velocity, etc. You could also try something orbital-mechanics related; I don't know, working out the most fuel-efficient trajectory for transferring a satellite into orbit around another chosen planet, or something. These would all be fairly differential-equation heavy!

 

[greg_rack]

Hi, Greg, nobody answers you, but I think it's a great question. What about non contaminating aeroplanes?. Let's take your question as a brainstorming.
Greetings!

Appreciate it! :)
That is surely a really interesting idea, but I think the project should be focused on something less "engineering" and a little bit more theoretical. Something more towards an insight.
Maybe non-contaminating planes could be a subsection of the project, like in the "possible applications of this phenomenon" part, relating to other sciences.

 

[greg_rack]

What kind of topics are in the curriculum? Does it include electromagnetism or is it a mechanics course?

The curriculum covers pretty much all of classical physics, from geometrical optics up to a few words of quantum mechanics(some topics, such as DC/AC circuits, haven't of course been covered in-depth, for the lack of mathematical knowledge). Electromagnetism took a major part of the program along with mechanics, thermodynamics and gravitation

 

[greg_rack]

I know you said you didn't have too many details, but do you know at least how long it needs to be and whether it's purely theoretical or if it's advised that you include a practical component?

I have no clue on the length, but probably it should be regulated for a 20 to 30 mins exposition; it should be mainly theoretical, but adding a practical component is encouraged.

Also, since it's for the diploma I guess it doesn't have to be related to aerospace

That's exact

In any case, my two cents would be to go for something very focused. Like, just to throw out an example, you could try and investigate the trajectory of a tennis ball when immersed in a fluid (the air), or when launched with a non-zero angular velocity, etc. You could also try something orbital-mechanics related; I don't know, working out the most fuel-efficient trajectory for transferring a satellite into orbit around another planet. These would all be fairly differential-equation heavy.

That sounds reeeally cool, definitely something I'd have fun preparing and working on!
Strictly with the high-school knowledge, I highly doubt one(me neither, to a certain extent) could have similarly "sophisticated" ideas for this project, so in case I would definitely be starting a step ahead.
Which maths is involved in the description of such phenomena?
The curriculum covers up to definite integrals and doesn't go much further, so adding differential equations to the discussion was just a thought of mine to make a better impression(like "hey, I've even studied a little bit of that on my own"), but certainly not something to have the maths part focused or based on.

 

[etotheipi]

Which maths is involved in the description of such phenomena?

Orbital mechanics is a fairly large subject, and not one that I claim to know a lot about either . First you'd need to learn a bit about central force fields, and in particular inverse square fields and the types of orbits that those permit [conic sections!]. Then you can derive things like the vis-viva equation, which tells you how the speed of a body in a given orbit varies with distance from the central body, and finally look at some common transfer orbits, like the Hohmann transfer orbit or the bi-elliptic transfer orbit, and start to calculate how efficient each transfer is. [rocket scientists like to talk in terms of "delta v's", i.e. by how much a certain burn changes your speed]. A good start for research would be any undergrad classical mechanics textbook, if you can get your hands on one.

As for the tennis ball, you could first consider the case where it's modeled as a point-mass, subject to its weight in addition to certain drag forces, e.g. quadratic resistance. You could start by, e.g., trying to derive what launch angle gives you maximum range in the presence of different types of drag. The case where the tennis ball is considered to be a rigid body is, I suspect, rather more complicated. A starting point could be to consider the Magnus effect.

But these are just a few examples to get the ball rolling

 

[Klystron]

Electronics sounds interesting, perhaps an electromagnet combined with a ferrous pendulum to begin.

Suspend the pendulum vertically in a frame via a non-conducting string. Swing the pendulum. Observe and measure the arc of the swing, establish the period and introduce the relevant equations.

Build or buy an electromagnetic perhaps with a soft iron cylindrical core. Describe how it works with basic equations. Mount the electromagnet on the side of the frame where the core can attract the pendulum. How does the electromagnetic field affect the pendulum?

Just a point of departure with potential.

 

[bhobba]

I am a theoretical guy, but I think doing a write up on Morin's excellent book on Classical Mechanics could be a good one:
https://www.amazon.com/dp/0521876222/?tag=pfamazon01-20

It is really first year uni, and for an honors course at that, but Morin believes it can be used by high school students who have done calculus. His exact words are - they will find it a hoot.

Thanks
Bill

 

[greg_rack]

I am a theoretical guy, but I think doing a write up on Morin's excellent book on Classical Mechanics could be a good one:
https://www.amazon.com/dp/0521876222/?tag=pfamazon01-20

It is really first year uni, and for an honors course at that, but Morin believes it can be used by high school students who have done calculus. His exact words are - they will find it a hoot.

Thanks
Bill

That really intrigues me, but unfortunately there are no options online for me to get it at less than €90...

Are there any internationally-accessible books from which I could draw a valid inspiration?

 

[greg_rack]

But these are just a few examples to get the ball rolling

They seem to be extremely valid and interesting, I'm definitely going to expand and take those into account!

 

[greg_rack]

Orbital mechanics is a fairly large subject, and not one that I claim to know a lot about either .

Have you got some suggestions of textbooks or material to study such topics, to do a write-up on those?

 

[bhobba]

Are there any internationally-accessible books from which I could draw a valid inspiration?

Yes - but unfortuneately not at the HS level. An even better book is Landau - Mechanics:
https://www.amazon.com/dp/B00BCRB50E/?tag=pfamazon01-20

But since you have to buy (I was hoping your parents could help) it too is expensive, and since it does require multivariable calculus it is unsuitable at the HS level. So does Morin - but he carefully explains what you need to know as you go along.

Here is something free you could try on the Lorentz Transformations that may be an interesting project - but again I do not know your mathematical background:
http://www2.physics.umd.edu/~yakovenk/teaching/Lorentz.pdf

Thanks
Bill

 

[hutchphd]

In any case, my two cents would be to go for something very focused.

When beginning students in a writing class are told to write a short story or essay about a subject of their choice, they invariably choose a general topic like "The Civil War" or "good citizenship". Of course the good essays are about some very specific observation and its ramifications or the life of one soldier in one battle. Most important it needs to be something really of interest to you.
The same is true for science. Choose some small aspect of what you see around you and then dissect it using the tools of math and physics. Even the smallest phenomenon when relentlessly pursued will test your analytical mettle. Einstein worried about traveling alongside light. But it should be interesting to you.