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Very Wrong Math

charlespetzold.com

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Re: Very Wrong Math

#41

Post by munch117 »

tempestn wrote: post #29
munch117 wrote: post #23

Earlier quoted context omitted.

Ah, but would they actually be parallel on a flat earth? Say the earth is disc-shaped. Then the center of gravity is only directly beneath you if you're standing at the exact center. You get ever-so-slightly not parallel lines, just like on a round earth. The fun part of a disc-shaped earth comes as you move towards the sides, and gravity, still pointing towards the center, makes you stand at an increasingly acute an…

Depends what causes things to stick to the flat Earth. IIRC flat earthers have various explanations for gravity, including the disc continuously accelerating upward; in that case you'd experience the same force everywhere on it.

If this mysterious disc-accelerating force also accelerated the people and things on the surface, we'd all be weightless.

I guess it must be a pushing force from below.

So, who's doing the pushing? I'm thinking a big turtle.

Re: Very Wrong Math

#42

Post by kergonath »

seanhunter wrote: post #11
kurthr wrote: post #4

Earlier quoted context omitted.

The only issue I see with this is that as a classic physics trope, we've approximated the earth as a sphere. If, instead we approximate it as a fractal... then the distance is infinite, or at least highly dependent on the thickness of the rope! The error in the original is assuming that the radius is proportional to the height above the earth (Earthradius=0?).

We actually model the earth as a very large spherical cow . This is approximately the same for most purposes but ends up being more convenient. P.S. Not a physicist, but my child is studying maths and physics at Uni at present, so I have it on good authority that this is still going on. They told me in their first week one of their classes had a worked example where the lecturer used the phrase "Assume the penguin's…

> I have it on good authority that this is still going on

Do you mean making simplifying assumptions to make a problem tractable? Of course it’s still going on. It has to be, otherwise you just cannot do anything.

> Assume the penguin's beak is a cone

It is impossible to consider the true shape of a penguin’s beak for several reasons:

- you’d need to go all the way down to the electron clouds of the atoms of the beak, at which point the very concept of shape is shaky

- every penguin has a different beak so even if you describe perfectly one of them, it does not necessarily make your calculation more realistic in general.

There is a spectrum of approximations one can make, but a cone is a sensible shape at a first order. It’s also simple enough that students can actually do it without years of experience and very advanced tools.

What do you think they should do instead?

Re: Very Wrong Math

#43

Post by f1shy »

bruce511 wrote: post #19

Even if the math of the arc length was correct (and you don't need to be a math professor to figure out it isn't) there's another logic misstep. Implied in the caption is that the speed is the same at all heights (given that an increase in distance is implied as an increase in time.) This is again obvious nonsense - speed is a function of thrust versus drag, and it's safe to say that both of those are affected by air…

You are literally going way and beyond what the target audience of that post (the original with bad math) was for.

Re: Very Wrong Math

#44

Post by n4r9 »

Don't know if anyone mentioned this yet, but presumably the flight path does not follow a normal vector to gain height, but generally something more diagonal in the direction of travel.

Re: Very Wrong Math

#45

Post by kergonath »

prmph wrote: post #37

One question I've always had with this: How does the rotation of the earth affect an airplane's flight time, if any? And how does this change with altitude?

It does not really, at least not directly. What matters is relative velocity compared to the starting and final locations, and relative to the air around the aircraft. It just happens that there are very powerful atmospheric currents that go west to east (those are due to the earth’s rotation, among others phenomena).

So, when flying towards the east, catching these currents can significantly reduce flying time. When flying towards the west, we want to avoid them by flying below or elsewhere.

Re: Very Wrong Math

#46

Post by f1shy »

prmph wrote: post #37

One question I've always had with this: How does the rotation of the earth affect an airplane's flight time, if any? And how does this change with altitude?

Simple answer: Zero. Because the planes move inside the atmosphere, which moves with the earth.

A more nuisance would be that earth rotating generate all sorts of things in the atmosphere, including winds and Coriolis effect on the winds, and you can account for that considering the winds. Btw a flight from Chile to France and back, will have a leg significantly shorter (up to 2 hs in a 13hs flight) and which leg it is, depends on the time of the year.

Re: Very Wrong Math

#47

Post by f1shy »

tempestn wrote: post #29
munch117 wrote: post #23

Earlier quoted context omitted.

Ah, but would they actually be parallel on a flat earth? Say the earth is disc-shaped. Then the center of gravity is only directly beneath you if you're standing at the exact center. You get ever-so-slightly not parallel lines, just like on a round earth. The fun part of a disc-shaped earth comes as you move towards the sides, and gravity, still pointing towards the center, makes you stand at an increasingly acute an…

Depends what causes things to stick to the flat Earth. IIRC flat earthers have various explanations for gravity, including the disc continuously accelerating upward; in that case you'd experience the same force everywhere on it.

We can give them points for creativity.

Re: Very Wrong Math

#48

Post by kergonath »

kubb wrote: post #9

Curious, does the air being thinner affect flight time?

Yes, because friction depends on the air density. You can think of this as the molecules in the air colliding with a moving object and pushing it backwards, thus slowing it. If there are fewer molecules, there is less friction and the object can move faster with the same thrust.

Thrust itself decreases because there are also fewer molecules to push against, so it can get quite complicated if you want to account for everything. But overall it is easier to fly faster higher up in the atmosphere. Also, atmospheric currents are important.

There is a useful discussion here: https://aviation.stackexchange.com/questions/57209/how-does-...

Re: Very Wrong Math

#49

Post by seanhunter »

kergonath wrote: post #42
seanhunter wrote: post #11

Earlier quoted context omitted.

We actually model the earth as a very large spherical cow . This is approximately the same for most purposes but ends up being more convenient. P.S. Not a physicist, but my child is studying maths and physics at Uni at present, so I have it on good authority that this is still going on. They told me in their first week one of their classes had a worked example where the lecturer used the phrase "Assume the penguin's…

> I have it on good authority that this is still going on Do you mean making simplifying assumptions to make a problem tractable? Of course it’s still going on. It has to be , otherwise you just cannot do anything. > Assume the penguin's beak is a cone It is impossible to consider the true shape of a penguin’s beak for several reasons: - you’d need to go all the way down to the electron clouds of the atoms of the bea…

Bet you’re fun at parties as they say.

I totally understand why simplifying assumptions are helpful in modelling and definitely don’t need you to explain that. It also is a bit ridiculous if you think literally about it which makes it something that is fun to laugh about as here.

Re: Very Wrong Math

#50

Post by pessimizer »

Does "Remember the high you go the further it'll have to travel" really need to be debunked? Did the "design and construction firm" spell "drill" with one "l"?
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