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For a high school engineering project, a friend and I have found ourselves deriving an equation for how to most efficiently configure a system.

We found an equation that, given a few parameters about the system, equates the amount of material added (and thus weight), to the amount of energy this system will gain. Along the way, we needed to find an equation that, given an amount of material, would describe how to most efficiently use the material.

We were thinking we'd write this up in a nice paper, and publish it somewhere. (For resume building, college applications, etc.).

Where/how could we do this (if anywhere), and how long would it take?

I posted this on Physics StackExchange and it was recommended that I post it here as well.

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  • Has an answer on Physics, worth checking if you are about to answer: physics.stackexchange.com/q/498498
    – Solar Mike
    Aug 24, 2019 at 18:29
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    Coming from somebody with very little knowledge of academia and the field of physics: What speaks against publishing it on your website? I would assume your target audience is students who google their problems, not researchers who regularly read papers (Of course, I could be wrong)
    – lucidbrot
    Aug 25, 2019 at 10:48
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    @lucidbrot: why do you assume they have a homepage?
    – user111955
    Aug 25, 2019 at 12:50
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    In all likelyhood, this is already published in some obscure paper in german/russian 60 years ago. Go find a professor, and they will help you decide if there is enough novelty to warrant trying to publish it (Probably not, but go for it).
    – Issel
    Aug 26, 2019 at 0:10

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The big question here is whether what you've done is new to the world - whether it's a genuine new advance that nobody in the world has done before, or whether it's something known to the world that you, and perhaps your teacher, have not seen before. Without meaning any disrespect to you and your friend, the second option here is more likely - but the first is of course possible.

If it's genuinely new, you can look to publish in a scientific journal. If it's not new (but perhaps still unusually advanced for a high school student), you should perhaps look for other types of publication, which could still be good for your resume. The difficult question is how to tell which category your work falls into.

My suggestion is to speak to your high school teacher about this. They have seen a lot of different students' work. If they think that it may be a novel development, then either write, or get your teacher to write, to a professor in a relevant subject at a local university. See if they will look it over and advise you.

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    And another factor making this aggravatingly worse is that it is extremely difficult to, say, electronically search databases of papers specifically for mathematical formulas.
    – The_Sympathizer
    Aug 25, 2019 at 22:19
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Check out the American Journal of Undergraduate Research. You need a faculty mentor. Make contact with your state university.

Do plenty of online searches to see if your work is already published. This will take some time. Use various keywords.

Even if your formula or equation is not new, if the derivation is new, you can still publish. This is especially true if your derivation yields new insights into the result, or if the derivation serves as a model to solve harder problems. So take a look at the derivation to see if it yields any insights to harder problems.

If you have something publishable, don't give up. Be persistent. This may not happen for a while, but keep at it.

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Do you both have any contacts in the engineering field? They may be able to situate your issue and have contacts that might be able to help.

It is a big ask for high school students I know but try to spend the time to do the research if you can? Paywalls to journals are a big problem. What else has been done around your issue and question. What other available equations can be used? What do people do now to sort out this problem? This would give you a clue to who and what sort of people/researchers are tackling the problem and would be interested in your equation if it is indeed unique. Even if it is not unique, the contacts may also become a useful resource for your future.

Physics SE have not addressed your question and I suspect that your equation addresses a pragmatic issue rather than a theoretical problem so maybe the Engineering StackExchange might be a better fit. However, spend the time going through the various tags and branches in the SE rather than just jumping from one StackExchange to another. Write a couple of paragraphs about the current approaches available, quote other relevant questions or sites that explain the issue in better detail and explain how your equation is unique. This skill of "situating" the problem and being to respectful to others trying to solve the same problem while discussing the background in an engaging way is an important and underappreciated part of "doing research".

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I agree with @lucidbrot's comment.

Even if you are not the first to derive the formula, successfully doing it on your own shows you have a fairly good understanding of it. This puts you in a good position to help others understand it or learn of its existence. Write it up, post it online, give a talk, whatever. There are many opportunities created for young people to practice their communication skills or get recognised for impressive work. And you can create your own opportunities.

I'm sure you have read useful online tutorials about technical things; hardly any of them are actually written by the first person to publish that concept!

A journal is not the right avenue unless there is something new and of significant value in your work. But there is nothing stopping you from writing things up on your website, or making some YouTube videos. There are online communities of various sorts (hobbyist communities may be a good bet). Also you should see if there are student awards that may be applicable to what you've done, and look at the criteria.

Do try to find an existing publication about the formula (or a more sophisticated version of your formula.) It's great to give a simple, practical explanation and then say, "by the way, you can check out xyz."

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