6 ms·

Could You See the Curvature of the Earth in This Airport?

71 points by gabriel34 12y ago

xSky 12y ago
This is very Five-Thrity-Eight-ish, I love it!
- pavel_lishin 12y ago
  It reminded me of some of Rob Cockerham's experiments as well.
- daveloyall 12y ago
  It reminded me of Randall Munroe's "What If?" work. I'd love to see him critique the author's and our comments. With stick figures! :)
frenchman_in_ny 12y ago
No discussion of beam divergence in his calculations?
snowwrestler 12y ago
Relevant question from Reddit's AskScience section (which is heavily moderated and thus very high-quality): > How (if at all) do architects of large buildings deal with the Earth's curvature? http://www.reddit.com/r/askscience/comments/29jrhq/how_if_at_all_do_architects_of_large_buildings/ http://www.reddit.com/r/askscience/comments/29jrhq/how_if_at...
- funnynickname 12y ago
  It seems to me that unless they went out of their way to make it 'straight' local craftsmen are going to use a level any time they set something like a floor or wall, and therefore the building will follow the curvature of the earth. Above they speak of linear accelerators and how they have to make sure to keep things straight, rather than level. I doubt they'd go to that effort for an airplane terminal.
Theodores 12y ago
Getting on for a century ago this 'problem' was solved: http://en.wikipedia.org/wiki/Bedford_Level_experiment http://en.wikipedia.org/wiki/Bedford_Level_experiment TL;DR - use a theodolite with measurement poles at each end and in the middle. No iphones, laser pens or bowling balls needed. Sometimes it comes down to having the right tools for the job.
- damon_c 12y ago
  Ha, that's awesome. I was going to suggest something similar... just put the bowling ball at one end and if you can see the whole thing at floor level at the other end, it's straight, else it's curved.
  - ctdonath 12y ago
    Key is "whole" thing. If curved, a 4 cm ball (say, cue ball?) would not be visible at all.
Someone 12y ago
One could also use the bowling ball to answer the level vs straight question. Ignoring such nuisances as friction, on a straight floor, a ball let loose would roll towards the center of the hall, and oscillate around it. In practice, it may be possible to somewhat reliably measure a difference in deceleration rolling the ball towards an end of the hall vs towards its center. And of course, if one also has a scale, the weight of the ball can be used to see whether the floor is level.
- jsweojtj 12y ago
  > And of course, if one also has a scale, the weight of the ball can be used to see whether the floor is level. Can you elaborate on this? Why would the weight be different if non-level? Unless you're meaning that the center-of-mass of the ball would be ~2 centimeters further from the center-of-mass of the Earth and 1/r^2 means a decrease?
  - ctdonath 12y ago
    The article depicts the difference between "level" (consistent radius from Earth's center) vs "straight" (line tangent to surface). A bowling ball rolled on a very long straight hall would (assuming nearly negligible resistance etc) actually accelerate toward the center, then slow down, reverse, and oscillate until it stopped in the middle (the lowest gravitational position) because relative to the curvature of the Earth a straight line is higher at the ends than at the center. A bowling ball rolled on a very long level hall would keep going (until resistance or confused staff stopped it) because there would be no gravitational change.
    - dredmorbius 12y ago
      Where the ball centered on would depend on how the hall was constructed. The low point could be anywhere, though it would likely be somewhere between the two endpoints. It would only be at the center of the hall if that's where the floor were tangent with the Earth's circumference.
  - Someone 12y ago
stansmith 12y ago
"The top of the Golden Gate Bridge is almost two inches wider at the top than the base because of the curvature of the Earth" http://datagenetics.com/blog/june32012/index.html http://datagenetics.com/blog/june32012/index.html
- lutusp 12y ago
  This is a fact "borrowed" from my Web site without attribution. Here's the original: http://arachnoid.com/carnival/index.html#Vertical http://arachnoid.com/carnival/index.html#Vertical In the linked article, we also find this graphic used to make another point -- horizon distance: http://datagenetics.com/blog/june32012/globe.png http://datagenetics.com/blog/june32012/globe.png Here's the original, from my Web site: http://arachnoid.com/carnival/resources/horizon_distance.png http://arachnoid.com/carnival/resources/horizon_distance.png Look familiar?
  - sp332 12y ago
    It looks like this blog made their own version instead of copying yours. Since you can't own the fact, and they're not using your picture, they didn't take anything copyrighted or trademarked by you. Maybe you could argue that the stick-figure diagram is copyrightable, but it seems like a stretch.
  - ctdonath 12y ago
    No it doesn't. Not at all, except insofar as that basic sketch is depicted in a zillion trigonometry textbooks and has been for well longer than you've been alive. The basic idea is pretty obvious. People have been computing "astounding facts" attributable to the Earth's curvature for thousands of years. Golden Gate Bridge is a pretty obvious choice for computing the tangible spread of two apparently parallel towers: WTC towers were too close for a dramatic spread, and other than GGB there isn't any other pair of towers so universally known (at least to an American audience) which are identical and far enough apart for a spreading of inches. If I think about it long enough, I'll probably recall seeing the same computation & example in trigonometry class decades ago. Just because you thought of it doesn't mean you're first - by a long shot. Oh, and your sketch is wrong. The two lines labeled "R" aren't the same length.
harshpotatoes 12y ago
I don't like his method of measuring the curvature distance. I think it will be very difficult to align a local to the local tangent of the earth's surface. Over a distance of 700m, the earth's surface deviates by about 4cm. This means we would have to align our laser to within 50 microradians in order to accurately measure the deviation of the earth's surface. Further more, his two beam system is setup using two lasers spaced about 4m apart requires even greater accuracy. Let's imagine system 1 is aligned to the local tangent at one end of the terminal (x = 0m), system 2 is aligned to the local tangent 4 m away at x = 4m, and heights of the two beams are measured at the opposite end of the terminal (x = 700 m). The height difference between these two beams will be about 1 micron. If we assume that the beams are large enough that there is no spread in beam size, then each beam is about 3 cm in diameter. This means we need to measure the beam height to better 0.003% accuracy relative to the beam size. I think this will be a very difficult measurement. I think there is a way you could very accurately measure the relative angle between two beams in a larger interferometer and two lasers, but I'll have to think about how it would look... Regardless, it's always fun to think about this small corrections to our expectations. To be honest, I was a little surprised to think about it, 4cm of deviation over 700m is actually a bit larger than I expected.
- bmelton 12y ago
  Your approach mirrors what mine would have been. If the curvature of the earth can be measured over 725 meters, then to me, it's inconsequential whether or not that is detectable within this man-made construct. That isn't to impugn the question, or the method, but that I'm less interested in whether the architects adjusted each each to be 4cm higher than they would need to be or not. Even if the airport were built over the course of 5 meters, in which the curvature would be (effectively) undetectable, the airport itself, being man-made, may exhibit irregularities caused by human error, shifting ground, variable bedrock, etc. Regardless, the article was fantastically fun to read, as was your post.
- lutorm 12y ago
  You don't need to align anything: Point a single laser down the hallway and measure the height of the beam above the floor at the ends and at the midpoint. If the hallway is straight, these will fit a line; if the hallway is level, they will not. You can surely measure the heights to an accuracy much better than 4cm, and that's all that matters.
KhalilK 12y ago
a couple of broken reference links in the article; never forget "https://" https://" when adding a link.
sarciszewski 12y ago
Privacy Badger, RequestPolicy, and AdBlock Edge all puked on this Wired page. None of the calculations would load. :(
burnte 12y ago
I live in ATL and now I very much want to go to the airport at 3am and test this.
timdierks 12y ago
Offer the building's super the barometer, if in exchange he'll tell you how tall the building is. [1] Did the author of the article not bother to investigate the actual answer? [1] https://en.wikipedia.org/wiki/Barometer_question https://en.wikipedia.org/wiki/Barometer_question
idlewords 12y ago
"First get a long East-West terminal and see if we can roll a ball all the way to the end of the hallway. There shouldn’t be any Coriolis deflection in that case" The author is confused. That statement would only be true on the Equator. In the northern hemisphere, the ball will always deflect to the right. If I put a pencil on a globe, I can intuitively understand why, sometimes for up to five minutes!
dredmorbius 12y ago
This is really crying out for a follow-up with actual measurements. It would be wonderful if the Atlanta airport authority could arrange for that. A couple of lasers, a couple of levels, 3-4 rulers, and coordinating measurements would do it.

71 points by gabriel34 12y ago

xSky 12y ago

This is very Five-Thrity-Eight-ish, I love it!

pavel_lishin 12y ago
It reminded me of some of Rob Cockerham's experiments as well.
daveloyall 12y ago
It reminded me of Randall Munroe's "What If?" work. I'd love to see him critique the author's and our comments. With stick figures! :)

frenchman_in_ny 12y ago

No discussion of beam divergence in his calculations?

snowwrestler 12y ago

Relevant question from Reddit's AskScience section (which is heavily moderated and thus very high-quality): > How (if at all) do architects of large buildings deal with the Earth's curvature? http://www.reddit.com/r/askscience/comments/29jrhq/how_if_at_all_do_architects_of_large_buildings/ http://www.reddit.com/r/askscience/comments/29jrhq/how_if_at...

funnynickname 12y ago
It seems to me that unless they went out of their way to make it 'straight' local craftsmen are going to use a level any time they set something like a floor or wall, and therefore the building will follow the curvature of the earth. Above they speak of linear accelerators and how they have to make sure to keep things straight, rather than level. I doubt they'd go to that effort for an airplane terminal.

Theodores 12y ago

Getting on for a century ago this 'problem' was solved: http://en.wikipedia.org/wiki/Bedford_Level_experiment http://en.wikipedia.org/wiki/Bedford_Level_experiment TL;DR - use a theodolite with measurement poles at each end and in the middle. No iphones, laser pens or bowling balls needed. Sometimes it comes down to having the right tools for the job.

damon_c 12y ago
Ha, that's awesome. I was going to suggest something similar... just put the bowling ball at one end and if you can see the whole thing at floor level at the other end, it's straight, else it's curved.
- ctdonath 12y ago
  Key is "whole" thing. If curved, a 4 cm ball (say, cue ball?) would not be visible at all.

Someone 12y ago

One could also use the bowling ball to answer the level vs straight question. Ignoring such nuisances as friction, on a straight floor, a ball let loose would roll towards the center of the hall, and oscillate around it. In practice, it may be possible to somewhat reliably measure a difference in deceleration rolling the ball towards an end of the hall vs towards its center. And of course, if one also has a scale, the weight of the ball can be used to see whether the floor is level.

jsweojtj 12y ago
> And of course, if one also has a scale, the weight of the ball can be used to see whether the floor is level. Can you elaborate on this? Why would the weight be different if non-level? Unless you're meaning that the center-of-mass of the ball would be ~2 centimeters further from the center-of-mass of the Earth and 1/r^2 means a decrease?
- ctdonath 12y ago
  The article depicts the difference between "level" (consistent radius from Earth's center) vs "straight" (line tangent to surface). A bowling ball rolled on a very long straight hall would (assuming nearly negligible resistance etc) actually accelerate toward the center, then slow down, reverse, and oscillate until it stopped in the middle (the lowest gravitational position) because relative to the curvature of the Earth a straight line is higher at the ends than at the center. A bowling ball rolled on a very long level hall would keep going (until resistance or confused staff stopped it) because there would be no gravitational change.
  - dredmorbius 12y ago
    Where the ball centered on would depend on how the hall was constructed. The low point could be anywhere, though it would likely be somewhere between the two endpoints. It would only be at the center of the hall if that's where the floor were tangent with the Earth's circumference.
- Someone 12y ago

stansmith 12y ago

"The top of the Golden Gate Bridge is almost two inches wider at the top than the base because of the curvature of the Earth" http://datagenetics.com/blog/june32012/index.html http://datagenetics.com/blog/june32012/index.html

lutusp 12y ago
This is a fact "borrowed" from my Web site without attribution. Here's the original: http://arachnoid.com/carnival/index.html#Vertical http://arachnoid.com/carnival/index.html#Vertical In the linked article, we also find this graphic used to make another point -- horizon distance: http://datagenetics.com/blog/june32012/globe.png http://datagenetics.com/blog/june32012/globe.png Here's the original, from my Web site: http://arachnoid.com/carnival/resources/horizon_distance.png http://arachnoid.com/carnival/resources/horizon_distance.png Look familiar?
- sp332 12y ago
  It looks like this blog made their own version instead of copying yours. Since you can't own the fact, and they're not using your picture, they didn't take anything copyrighted or trademarked by you. Maybe you could argue that the stick-figure diagram is copyrightable, but it seems like a stretch.
- ctdonath 12y ago
  No it doesn't. Not at all, except insofar as that basic sketch is depicted in a zillion trigonometry textbooks and has been for well longer than you've been alive. The basic idea is pretty obvious. People have been computing "astounding facts" attributable to the Earth's curvature for thousands of years. Golden Gate Bridge is a pretty obvious choice for computing the tangible spread of two apparently parallel towers: WTC towers were too close for a dramatic spread, and other than GGB there isn't any other pair of towers so universally known (at least to an American audience) which are identical and far enough apart for a spreading of inches. If I think about it long enough, I'll probably recall seeing the same computation & example in trigonometry class decades ago. Just because you thought of it doesn't mean you're first - by a long shot. Oh, and your sketch is wrong. The two lines labeled "R" aren't the same length.

harshpotatoes 12y ago

I don't like his method of measuring the curvature distance. I think it will be very difficult to align a local to the local tangent of the earth's surface. Over a distance of 700m, the earth's surface deviates by about 4cm. This means we would have to align our laser to within 50 microradians in order to accurately measure the deviation of the earth's surface. Further more, his two beam system is setup using two lasers spaced about 4m apart requires even greater accuracy. Let's imagine system 1 is aligned to the local tangent at one end of the terminal (x = 0m), system 2 is aligned to the local tangent 4 m away at x = 4m, and heights of the two beams are measured at the opposite end of the terminal (x = 700 m). The height difference between these two beams will be about 1 micron. If we assume that the beams are large enough that there is no spread in beam size, then each beam is about 3 cm in diameter. This means we need to measure the beam height to better 0.003% accuracy relative to the beam size. I think this will be a very difficult measurement. I think there is a way you could very accurately measure the relative angle between two beams in a larger interferometer and two lasers, but I'll have to think about how it would look... Regardless, it's always fun to think about this small corrections to our expectations. To be honest, I was a little surprised to think about it, 4cm of deviation over 700m is actually a bit larger than I expected.

bmelton 12y ago
Your approach mirrors what mine would have been. If the curvature of the earth can be measured over 725 meters, then to me, it's inconsequential whether or not that is detectable within this man-made construct. That isn't to impugn the question, or the method, but that I'm less interested in whether the architects adjusted each each to be 4cm higher than they would need to be or not. Even if the airport were built over the course of 5 meters, in which the curvature would be (effectively) undetectable, the airport itself, being man-made, may exhibit irregularities caused by human error, shifting ground, variable bedrock, etc. Regardless, the article was fantastically fun to read, as was your post.
lutorm 12y ago
You don't need to align anything: Point a single laser down the hallway and measure the height of the beam above the floor at the ends and at the midpoint. If the hallway is straight, these will fit a line; if the hallway is level, they will not. You can surely measure the heights to an accuracy much better than 4cm, and that's all that matters.

KhalilK 12y ago

a couple of broken reference links in the article; never forget "https://" https://" when adding a link.

sarciszewski 12y ago

Privacy Badger, RequestPolicy, and AdBlock Edge all puked on this Wired page. None of the calculations would load. :(

burnte 12y ago

I live in ATL and now I very much want to go to the airport at 3am and test this.

timdierks 12y ago

Offer the building's super the barometer, if in exchange he'll tell you how tall the building is. [1] Did the author of the article not bother to investigate the actual answer? [1] https://en.wikipedia.org/wiki/Barometer_question https://en.wikipedia.org/wiki/Barometer_question

idlewords 12y ago

"First get a long East-West terminal and see if we can roll a ball all the way to the end of the hallway. There shouldn’t be any Coriolis deflection in that case" The author is confused. That statement would only be true on the Equator. In the northern hemisphere, the ball will always deflect to the right. If I put a pencil on a globe, I can intuitively understand why, sometimes for up to five minutes!

dredmorbius 12y ago

This is really crying out for a follow-up with actual measurements. It would be wonderful if the Atlanta airport authority could arrange for that. A couple of lasers, a couple of levels, 3-4 rulers, and coordinating measurements would do it.