Best ball earth skeptic guest yet?

This came into feedback (contact.fakeologist.com). My answer is the curve is a formula gleaned from the distance dropped on any sphere…it’s simple trig.

http://www.boatsafe.com/tools/horizon.htm

Name: Ransomovitch
Email: xxx@gmail.com
Comment: hi guys just listened to ball earth skeptic with jeranism good show but 2 important points.

1 . One of us must take a flight from Santiago to Sydney or Joberg to Perth because right up to parting with cash on Qantas/Emirates booking sites, these NON-stop flights are available – no doubt. If they are available and they do actually fly non-stop then we must indeed seriously redraw the flat earth map or believe these planes are flying over the Arctic. As a logically thinking person (I run my own electronics company and electronics is logic through and through) I put this argument up on Dubay’s IFERS site and I was immediately banned for being a chill with no questions asked of me. Just type in Ransomovitch1960@gmail.com on the IFERS visitors site and see what comes up.
2. On your show just now, as well as Eric Dubay on his site, everybody talks quite freely about the drop per mile over a stated distance over the ocean due to earths curvature BUT NOBODY EXPLAINS OR REFERENCES IN SIMPLE ENGLISH THE MATHS BEHIND YOUR WORKINGS OUT. AAAAARRRRGGGGHHHH! It’s driving me nuts. For instance Eric Dubay nonchalantly says on his Atlantean site:

The formula for calculating the ball-Earth’s supposed curvature is 8 inches to the mile, varying inversely as the square of the distance, so the first mile establishes line of sight, the second mile must then descend 8 inches, the third mile 32 inches, the fourth mile 6 feet, the fifth mile 10 feet 8 inches, and by the sixth mile should already be 16 feet 8 inches below your line of sight.

OK I say. Great! But so what? Who’s maths is that? You guys are all quoting from it. Where is the definitive source for that calculation which is then explained in simple English. You guys all referred to this in various forms in the Jeranism show. But PLEASE PLEASE PLEASE can somebody explain to me in simple English and accurately how that formula is arrived at so I can at least post it up as a universal reference point. This is what is needed because nobody is lucidly citing any valid maths references for making these assumptions. It’s all she said, he said, they said. We can’t talk with round earthers if we can’t demonstrate this killer theorem has validity. The maths needs explaining and referencing properly AND SIMPLY and it’s driving me ABSOLUTELY MAD! So many flat earthers are making wrong claims and calculations on their various sites, bringing FErs a bad name. Does ANYBODY REALLY KNOW? A mathematician who can speak plain English would be a godsend at this point. Thanks everybody, I am a flat earther but guys, we all of us NEED THE MATHS CORRECT ON THIS ONE AND RELIABLY SOURCED.

BTW, I have bought a very powerful telescope with smartphone adapter and I plan to make a simple video of various famous long distance UK landmarks and cross-channel (UK – France) spots and using zoom I will once and for all produce a video that cannot be debunked as being too grainy or not light enough or too much sea swell or spliced footage etc etc. When it’s done, do you want me to send you the link? Keep up the good work. But please, somebody get us the historic cited references and the maths for measuring curvature and distance drop over x miles. And how can one apply the same theory to a billiard ball or a spherical beach ball? I hope you can catch the importance of what I am saying. Thanks again

http://www.internationalskeptics.com/forums/showthread.php?postid=1478280#post1478280
No, it doesn’t. You don’t need to find the angle at all, just draw it as a right triangle. The hypotenuse is r+h, the two shorter sides are r and d. You know h, solve for d using the Pythagorean Theorem. No need to determine the value of any angles.

But practically you could, given that the sine function for small angles is equal to the angle value in radians, and that sin^2 = 1 – cos^2. You’d come up with the same answer.