Thought experiment (debate with friend)

[Joe seki]

TL;DR

I’m having a continuous discussion with a friend of mine regarding bricks around the earth

Thought experiment.
Let's suppose I lay bricks around the entire Earth going up 50 miles in height. I am assuming this way there's going to be more bricks at the top than at the bottom right?

Well...
What If I was to get a football/soccer pitch (100meters in length and concreted with spirit level) and then attach additional pitches end on end all the way round earth.

Would this mean there will be the same amount of bricks on the top and at the bottom of the wall around the circumference of the earth, on these pitches rather than general Earth

Thanks for reading and any opinions welcomed

 

[Ibix]

If I'm understanding your question right, you are asking if the ~400,000 football pitches form a 400,000 sided polygon and if the circumference of the polygon is greater or less than the Earth's circumference.

It depends on how you use your spirit level. A level will always show the direction perpendicular to vertical, and this does change very slightly over the length of the pitch. So if you use a level at each point then your pitches are slightly curved, just like the surface of the Earth. On the other hand, if you put the level on the pitch's center line and use a laser or ruler to set a straight line, you'll get a straight pitch - one that's slightly higher (i.e. further from the center of the Earth) at the ends than at the middle.

So with the first method of using the level there's no difference between the Earth "naturally" and the pitches. With the second method, the pitches would be slightly shorter than the natural Earth circumference if you scrape away some ground at the middle of the pitches, or slightly longer if you build up the ends.

So: it's either fewer bricks, the same number of bricks, or more bricks. The devil is in the detail!

 

[DaveC426913]

What If I was to get a football/soccer pitch (100meters in length and concreted with spirit level) and then attach additional pitches end on end all the way round earth.

All you're doing here is breaking up the arrangement into pieces too small to notice or measure the discrepancy. That doesn't make the discrepancy go away.

Notice on the second setup, you stop short of the scale in the first set up. The first set up was 50 miles tall. A gap might not be noticeable at a height of six feet, but at 50 miles, it will be multiplied by (5,280x50/6=) 44,000 times.

 

[Baluncore]

You cannot have a level playing field in a global economy, without an assumption of a flat Earth.

 

[DaveC426913]

If I've done my calculations right, a wall the length of a football field (360 feet) and 50 miles tall will have a gap at the top of about 60 feet between it and the next wall. That's about 120 bricks more per football field needed at the top than at the bottom.Earth dia = 7800mi; circumf = 24,504mi

Earth dia + (50x2) = 7900mi; circumf = 24,818mi

That's an extra 314 miles per 360 degrees
0r 0.872 miles per degree

 

[jbriggs444]

If I've done my calculations right, a wall the length of a football field (360 feet) and 50 miles tall will have a gap at the top of about 60 feet between it and the next wall. That's about 120 bricks more per football field needed at the top than at the bottom.Earth dia = 7800mi; circumf = 24,504mi

Earth dia + (50x2) = 7900mi; circumf = 24,818mi

That's an extra 314 miles per 360 degrees
0r 0.872 miles per degree

I get about four and a half feet.

We are talking about a radius at the top that is $\frac{4050}{4000}$ times the radius at the bottom. That is an increase of about 1.25 percent.

Multiply by the length of a football field (360 feet) and you get about 4.5 feet.

Now let's look at that 0.872 miles of increased circumference per degree. I agree with that figure. 4604 feet of circumference per degree. With 1011 football fields per degree, 4604 divided by 1011 gives 4.5 feet per football field.

 

[Joe seki]

Sorry for the late reply, I would like to thank you all for the very informative responses.

My friend has read your replies and insists you are mistaken and had sent me 2 (badly drawn) diagrams proving he is correct lol I will add them below, he said in the first one the bricks go inside the Earth and therefore the number of bricks would be equal then he offered an alternate suggestion which he prefers

 

[DaveC426913]

Sorry for the late reply, I would like to thank you all for the very informative responses.

My friend has read your replies and insists you are mistaken and had sent me 2 (badly drawn) diagrams proving he is correct lol I will add them below, he said in the first one the bricks go inside the Earth and therefore the number of bricks would be equal then he offered an alternate suggestion which he prefers

The attached diagrams have no discernible relation to the scenarios as-written in earlier posts.

Either you and your friend do not have a meeting of the minds, or you are describing the scenarios incorrectly.

We cannot adjudicate your argument without an accurate description of your scenarios - and your diagrams contradict those scenarios.

 

[berkeman]

I still haven't been able to figure out his original problem statement, let alone his latest figures. An accurate drawing would have been a big help in his first post, but I guess that was too much trouble...

 

[berkeman]

After a Mentor discussion of a user report about this thread, this thread is closed.

@Joe seki -- if your friend wants to debate this subject here, he/she needs to create an account and post for themself. They also need to start the new thread with good sketches of the proposed thought experiment, so that we can all be on the same page. We don't allow ill-formed thread starts here. Thank you.