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Help Reviewing my Math and Reasoning Here.

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Patrick

Sun Aug 21 2016, 08:52PM

Registered Member #2431 Joined: Tue Oct 13 2009, 09:47PM
Location: Chico, CA. USA
Posts: 5639

Please excuse my barbaric use of jpg's to convey text, but I couldn't export 3 of 44 pages from google docs to a pdf or word form without losing the formatting of the formulas and equations, which was driving me insane.

The basic help Im needing is two fold.
A) is my reasoning for each formula and equation plausable, or have I wandered off real math and physics into mumbo jumbo?
b) Did I actually do the math right? and physics right ? (This is a less formal report to my experimental aircraft association, not a research paper to my professors.)

I dont want to look stupid by suggesting 3+3=1, or apples fall upward.

Page 28
I think "4.08" should be left the way it is for significant figures right?

Page 29

Page 30

I need to revisit the MLA citation, seems like i forgot something there:
Figure X. A Boeing 737, seen with an undesirable bird strike in an undesirable location.
Abbey, Jennifer. "United Airlines Flight Strikes Bird on Descent to Denver." ABC News.
She wrote the article, i wrote the caption. Everything should be left justified, with "Figure X" italicized i think?

I dont know if i got the formulas and equations (as words in sentences) were placed right. so an equation is a statement right? and formulas are relationships ?

Dr. Slack

Mon Aug 22 2016, 06:22AM

Registered Member #72 Joined: Thu Feb 09 2006, 08:29AM
Location: UK St. Albans
Posts: 1659

Several comments, one about a diagram, one about assumptions and physics, and one which is more about style than substance, but it may affect the readability.

If you are going to reason about complex mechanical structures, and then use very simple forumlae to argue about them, I feel it is necessary to have a diagram showing your assumptions.

The use of 'constant acceleration' formulae makes assumptions that are not true for physical vehicles, but it does make the sums more tractable.

In the event that the braking structure is entirely springy and doesn't yield, then the kinetic energy before impact will be stored as potential energy in the spring structure, and the vehicle will execute a quarter-sine SHM cycle as it comes to rest. The braking distance will be a function of the spring constant and the incoming kinetic energy.

In the event that the braking structure yields, and let's idealise it all the way to an ideal crumple zone, say a metal foam, which will tend to yield at a constant or progressive slightly increasing force, that force will be a function of the crumple zone itself, and independent of the incoming speed or its length. For slow impacts the structure will yield a little bit at the crumple force, for the design impact it will yield its length at the same crumple force, and for faster impacts it will yield its length at the crumple force, then the force will increase when it is fully crushed.

In practice, any structure will be a mix of at least these two, and possibly more, so your equations will always be wrong. Anybody reading your paper who can follow the maths will know this about structures, so will need the reassurance of you being explicit about the assumptions you are making. This is where acknowledging the spherical elephant in the light frictionless room is necessary.

it's common to deal with this complexity by doing the sums for pure spring, and pure crumple, as two bounds on the problem. If they predict broadly similar outcomes over a range of impact speeds, then great.

The assumptions that you might put into your paper are 'assuming an impact speed of 2m/s, and a crumple zone designed to fully fail at that speed in 0.05m, and a springy suspension designed to fully compress by 0.05m ...' and mention what breaks at higher speeds, and the differences at lower speeds.

Style. I was taught the formula v2 = 2fh (note that's for constant f, never true as mentioned above) quite early on in mechanics and physics, and it rolls up at least equations 1, 2, and 3 and is easily findable on the net, so I'm not sure you need to spend several lines to derive its equivalent. It's also easier to format in a single line, and easy to invert for f by inspection.

When finding the acceleration due stopping from v in h, you should calculate it m/s2 initially, the general units. Normalise it to g if you want to, in a separate step.

I would have stated that 40m/s2 was about 4g (but then I have been accused of premature approximation in the past). I know that g is stated to three sig figs, but the sum does include multiple WAGs, aka assumptions, aka wild arsed guesses, hence my suggestion of 1 sig fig.

The maths on sheet 1 looks OK. I haven't checked the rest, so you'll need to check for typos.

hen918

Mon Aug 22 2016, 04:49PM

Registered Member #11591 Joined: Wed Mar 20 2013, 08:20PM
Location: UK
Posts: 556

Looking at grammar and punctuation, as well as readability:

There are waaaay too many apostrophes, remember they are for ownership and contractions only. Eg: "Henry's laptop" and "let's" (a contraction of "let us")
"gs" should not have an apostrophe.

The first sentence on the second paragraph seems to make out the crash is descending, when actually the object is descending, only crashing when it stops descending :)

The last sentence in the fourth big paragraph on the second page also needs attention.

Sorry for the English lesson if you didn't want it :)

Patrick

Mon Aug 22 2016, 05:47PM

Registered Member #2431 Joined: Tue Oct 13 2009, 09:47PM
Location: Chico, CA. USA
Posts: 5639

Yes I wanted the English lesson too, I'm terrible at writing. I tend to think in notes, cram them into sentences, then cram those into paragraphs. I do that here on the forum a lot too. I always cringe when turning in class work.

Dr. Slack wrote ...

The assumptions that you might put into your paper are 'assuming an impact speed of 2m/s, and a crumple zone designed to fully fail at that speed in 0.05m, and a springy suspension designed to fully compress by 0.05m ...' and mention what breaks at higher speeds, and the differences at lower speeds.

Yes this sounds better. But the "crumple" zone isn't a designed structure, in case others didn't realize that. The damage seems to start at the leading edge, 0.00m and come to rest at -0.05m destroyed, with pieces of wood, carbon and plastic scattered everywhere. So inelastic I think ?

The 2m/s seems to be a terminal velocity for my drones. I should explicitly state this so that it doesn't look like a magic number.

Im not sure how to draw the "springy-ness" nor "crushy-ness" force diagram.

Remember, I wanted some math that explained the common drone crash g-load (of mine and others). So was it 4, 600 or 9000 g's ? instead of a random unfounded guess.

BigBad

Sun Aug 28 2016, 09:46PM

Registered Member #2529 Joined: Thu Dec 10 2009, 02:43AM
Location:
Posts: 600

The basic physics looks about right, but you should multiply by a finagle factor, like 4 or something, to make an allowance for the fact that the structures won't crush smoothly.

Patrick

Mon Aug 29 2016, 07:25PM

Registered Member #2431 Joined: Tue Oct 13 2009, 09:47PM
Location: Chico, CA. USA
Posts: 5639

BigBad wrote ...

.... multiply by a finagle factor, like 4 or something, to make an allowance . .

will do, is 4 a magic number ?

Dr. Slack

Tue Aug 30 2016, 10:34AM

Registered Member #72 Joined: Thu Feb 09 2006, 08:29AM
Location: UK St. Albans
Posts: 1659

Remember, I wanted some math that explained the common drone crash g-load (of mine and others). So was it 4, 600 or 9000 g's ? instead of a random unfounded guess.

Math only puts the detail into physics reasoning, what you have to justify are the assumptions.

Remember, in politics, you follow the money. In physics and engineering, you follow the energy.

If you drop a drone onto concrete, then the deceleration will be dominated by the drone structure. If onto grass, then the width of the drone will recruit a lot of springy stems to help absorb energy. So right away, there's an assumption about the surface to state.

I suspect there is a sort of informal 'safety factor' that has evolved out of the drone being light enough to fly, but strong enough to handle and land, that limits the strength of the structure. While you could build a drone as strong as a tank, nobody would. Averaged over enough users, that probably comes out with a fairly narrow distribution of 'stopping' g-forces from a given velocity. The point is, that distribution is something that you would have to observe, rather than mathematically argue for. If you want to argue for the whole population, having observed only your own, then you might be on shaky ground. Try to sample a range of sizes and brands.

Similarly, there's a mass and size ratio (each raised to some suitable power if necessary) that might be reasonably constant, which would give rise to a constant(ish) terminal velocity. But again, you'd need to observe a range of examples to see whether that's true.

TOT - I went to a music festival recently which had posted amongst the site rules 'No drones anywhere on site'. Perhaps their mostly unregulated heyday is drawing to a close.

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