How does the curve calculator work? Not adjusting for refraction

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nethe0 : Your 5 minute video has more education than every flat earth video put together.

Busted Shark : A great example of the elegance of a profound mathematical principle. Nicely presented as well. From my schoolboy days:THE SQUAW OF THE HIPPOPOTAMUS A Cherokee Indian chief had 3 wives all of whom were pregnant. When the first squaw gave birth to a boy, the chief was elated and built them a teepee made of buffalo hide. The second squaw also gave birth to a boy a few days later. The chief was extremely happy and built them a teepee of antelope hide. Soon, the third squaw gave birth, but the chief kept the birth details secret. He built them a teepee of hippopotamus hide (I know there are no hippopotami in North America,but just go with it.) He challenged the people of his tribe to guess the latest birth details, and whomever was right would win a fine prize. Many attempted but failed to guess the details. Finally, a young brave came forth and declared that the third squaw had had twins. "That's correct" said the chief."How did you know?" "Simple, " aid the brave. "The value of the squaw of the hippopotamus is equal to the sons of the squaws of the other two hides." I got detention for that!

AJ Hieb : It astounds me that flerfers still cling to the 8 inches per mile squared surveyor's shortcut. For starters it is _obviously_ not the formula for a circle (rather a parabola) and secondly, it is the formula for drop, not hidden height, so it is doubly wrong. (3x wrong if you include the fact it was just an estimation in the first place) Actually I take it back. It's not surprising at all that flerfers are clinging to something obviously wrong.

DavidB5501 : Great explanation. The 8" x miles-squared formula *can* be used to get an approximation for 'hidden', but it requires a two-step approach. First you need to calculate the distance from the observer to the horizon, using Pythagoras as you show in the video, then use the 8" formula on the distance of the target *beyond* the horizon. For reasonable distances (less than 50 miles, say) this gives a surprisingly good result, because the 'drop' in this case is not very different from the required 'hidden' figure. Taking the figures in the video, the distance of the target beyond the horizon is 74952 metres = 249506 feet = 46.57 miles (all figures approx.) Applying the 8" rule to that gives a 'drop' of 1446 feet = 441 metres, which is very close to the 440 metres for 'hidden' given by the 'proper' method. Of course there is no need to go through this if you have access to a suitable curve calculator!

Carl Edwards : NOT boring at all! When something is EXPLAINED, unlike the flat earther "models" it can be tested and either proven to work, or proven to match reality. Well, it becomes the best model at that point in time. Knowing HOW to calculate things, rather than just throwing stuff into a magic machine and accepting the answers, means that WE can all do the calculations for ourselves and arrive at an answer unaffected by belief. Unless, of course, we choose to NOT believe in mathematics.

Rocket Rhys : I have just realised I've forgotten alot since school 😳

Kevin Isitt : Remember that in the southern hemisphere you have turn the hypotenuse upsidey down. FECU.

CrAsH : Hi CC. This will be really good for nerds like me who like to understand the mechanics. How refreshing after just watching Dels live stream for a laugh....... ravings of a lunatic. Do you think the comments will get spammed by the flearthers denying the math?

mk2gtf : My question is: why is your 80000m distance line a tangent and not the distance on the surface? I was under the assumption that distances on maps are not line of sight based but are adjusted for curvature. Usually flattards use google maps to “measure” distances and google maps surely isn’t line of sight based but uses great circles. So in my eyes those calculations won’t work anyways.

Sir Monacle : This is great. I wasn't sure about dividing into two channels but I think it will work. This reminded me of a condensed version of fiveredpears stuff.

Wolfgang Abraham Poe : My favorite bald guy teaches my favorite subjects on the internet, my favorite media. Life's good.

Bigplans Littledrive : I never even once heard you say ‘angle of attack’ is this real 😆

MCToon : Wait, how did you convert from kilometers to meters? You multiplied by 1,000? WRONG! According to a YouTube video I once watched you DIVIDE by 1,000. Duh!

David Price : It's worth noting as well that flattards have no way of calculating the distance to the horizon on their space biscuit, nor a working explanation of why an horizon forms at all on a flat surface in the first place. (Credit to Cool Hard Logic, testing flattards)

nellie360 : FFS where’s Del when you need him? All this Maffs and the great mind of Garden Shed Institute is busy doing a roll up

David Price : Pythagoras walks into a bar and says "If a right angle triangle has a short side x, a long side y, and an hypotenuse z. Then the sum of z can be calculated by squaring the value of x and the value of...... Urmmmmmm...... ....." The barman says, "Y! The long face". 🙋

Steven Deans : I always enjoyed the parts of your videos where you whipped out the white board best anyway.

Alan Crabb : Enjoyed it, thanks. So it turns out there is one good thing about FE : it reminds us of the importance of getting basics right. A bit like typhoid and hygiene. More please!

KeiraR : Like being back in school only this time I want to be and I'm actually paying attention. I'm too old to go ice skating all day now anyway. :D

SuperReactionman : Thank you for all your efforts!

MARVEL GIRL : Not boring at all. I feel a lot more capable of understanding, and so, explaining, and best of all, ARGUING it now!

Sneky15 : Thank you for the conversion in metric.. the way you are explaining reminded me of my math teacher and its why i loved math in school.

Hoosier Atheist : You're left handed, illuminati confirmed.

Jenn Morgan : This is what makes you so good. A clear, simple teaching style that makes it a breeze and pleasure to learn. I remember my (1968?)9th grade science teacher taking two days of class to teach this and still, few “got it.” Thanks for the refresher.

Shivanshu Prasad : Also the distance we get on let's say google maps would be on the surface of the earth, in the shape of a arc. Wouldn't we have to convert it to the distance of that straight line for larger distances.

Red Pill Philosophy : Do these calculations have to account for perspective to be accurate? The bulge of obstruction is beneath your eye level, not exactly at eye level, so over greater and greater distances you'll be able to see more and more of what's behind the bulge.

Mark Russell : So that answers one question I had Distance to horizon is 5048m from viewpoint. But rest of my questions still stand Nice vid btw

Planarwalk : Can the next video be about converting kilometers to meters. I saw you did that in this video and it confused me.

batmanfanforever08 : I found that interesting and obvious as to why flat earthers are wrong.

Old Seadog : That curve calculator sends FEs round the bend.......

Kevin Craig : My momma always said "Boring is as boring does". This proves (somehow, I'm not quite sure what to look at to prove this statement), your Baldy Catz channel is not boring. Yet. Of course, you haven't done the much needed video "How to count to 1,000,000" yet. That one actually appears to be basically necessary for most flat earthers.

gareth milton : Paper..... Paper..... Very posh school this is. Where's the whiteboard or the blackboard ! Good job yer no a teacher, laddie ? Aye, see when I went tae school..... well if I'd went tae school that is.... 🤡

The Snark : Best left handed handwriting EVER.

Robert Lafleur : Clear and simple.

cearnicus : Don't forget to also do a section on where the horizon should be on a flat earth and compare that to what we actually see :) Even when the math is done correctly and we see more than we should according to pure geometry, there's still a part of the object that's hidden. That should simply never happen on a flat earth. At worst, the conclusion would be that the earth is larger than we're being told, not that it's flat.

Thinking Man : It would be nice to think that at least a few potential flat earths might watch some of these, and see the error of their ways, but that may just be wishful thinking. Oh by the way, liked and subbed.

Tony Jackman : Not boring at all, thanks, good stuff.

Starhawk Flying Bright : How I wish you were my teacher

jibstank 87 : I was going to ask "if the 8" per m^2 is that inaccurate then why is it used at all?" Then I found the answer in the comment section.

robert fernandez : Great start to the channel. Have you ever thought about a career in teaching? Lol

Timothy Benedict : This wasn't that boring, as I am waking up. Nah, it's fine. This is the first of a long run for Baldy Catz and I am glad to be here.

BrainlessSteelNL : Interesting stuff. By the way.. can we download the stuff you used in the debate somewhere? Tnx.

FECU! : Sorry, you lost me at 1:36 - you divided it, right? FECU!

gareth milton : Told you I'd love it. Got ma wee brain ticking over slowly so thank you. Is this in response to FlatOut starting FECU ? Great start to Baldy Catz though 👍

iantinnion : Great video..... I wonder how long before a flattard says you are talking crap and your maths is wrong purely because,you are a lefty haha You would have lost the flattard when you said ' rearrange ' to get 5048..... they will think you have used some kind of witch craft

TakeInS2 : Wasn't this supposed to be boring?

Matty Rose : This wasn't boring. Can I get a refund please?

paulsterx : I always like to know the theory behind this stuff, that was beautifully explained sir. Thanks!

ffggddss : That "8 in per mi²" formula will work in this case, if applied correctly, WHICH FE'ers NEVER DO! It's basically good for ground distances that are a small enough fraction of Earth's radius. Keeping in mind that it *is* an approximation, albeit a good one in that regime. What has to be done here, is to apply it separately to each of the two arcs in your diagram. Note that 8 in/mi² is just ≈ 1/R, where R = Earth's radius. (The reason this works, stems from calculus, which is probably beyond the scope of these videos; and is certainly beyond the scope of FE-ology.) And so, you can express it in cm/km², either by units conversion, or by direct computation: 1/R = 1/6371 km = 1 cm/6371 km·cm = 1 cm/6.371 km·1000cm = 100 cm/6.371 km·100,000cm = (100/6.371) cm/km² ≈ 15.696 cm/km² Secondly, the 1/R ≈ 8 in/mi² ≈ 15.7 cm/km² is a rate-of-a-rate; i.e., a 2nd derivative. So being like an acceleration, the correct way to apply it is: s = arc length h = height = ½(1/R)s² = s²/2R This is analogous to the formula for distance fallen under gravity, of an object released from rest: z = ½gt² We're given the total sight distance, D = 80 km = 80,000 m ≈ s₁ + s₂ (which are the two arc lengths) So the first step is to apply it to your height (h₁ = 2 m = 200 cm): s₁ = 1st arc length h₁ = s₁²/2R = ½(15.7 cm/km²)s₁² = (7.85 cm/km²)s₁² 7.85(s₁/km)² = h₁/cm = 200 s₁/km = √(200/7.85) = 5.048 s₁ = 5.048 km = 5048 m The second step is to apply it to the second arc, where now we know the remaining distance, D – s₁ : s₂ = 2nd arc length = D – s₁ = 80,000 m – 5048 m = 74,952 m = 74.952 km h₂ = s₂²/2R = (7.85 cm/km²)s₂² = 44,089 cm ≈ 441 m Almost exactly what you got. Basically, Pythagoras says s = √[(R+h)² – R²] = √(2hR + h²) and the method I show neglects the "h²" term, because it is tiny compared to the other; that is, h << 2R; the heights involved are much less than Earth's diameter. And neglecting that term yields s² = 2hR; h = s²/2R, as I say above. Note that your method is exact, apart from small corrections for refraction and oblateness. This method is "good enough" for most cases. Fred

TheKitsuneCavalier : Yup! Boring enough to make me go "woo hoo! ( in my head, at least)" at the end! ^!^