
Could You See the Curvature of the Earth in This Airport? - gabriel34
http://www.wired.com/2014/03/see-curvature-earth-airport/
======
Theodores
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
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
Key is "whole" thing. If curved, a 4 cm ball (say, cue ball?) would not be
visible at all.

------
timdierks
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)

------
snowwrestler
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...](http://www.reddit.com/r/askscience/comments/29jrhq/how_if_at_all_do_architects_of_large_buildings/)

~~~
funnynickname
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.

------
harshpotatoes
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.

~~~
lutorm
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.

------
Someone
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
> 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
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
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.

------
idlewords
"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!

------
frenchman_in_ny
No discussion of beam divergence in his calculations?

------
dredmorbius
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.

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

------
KhalilK
a couple of broken reference links in the article; never forget
"[https://"](https://") when adding a link.

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

~~~
daveloyall
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! :)

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

------
stansmith
"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
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?

~~~
dalke
It's familiar because it's a not uncommon comment. Well, except that most such
comments refer to the Verrazano-Narrows Bridge, which has a longer span than
the Golden Gate. For examples:

\- Guinness Book of World Records (1973) made it with the Verrazano-Narrows
Bridge -
[http://books.google.com/books?ei=93b7U_XoBuT5yQPkqYGIBQ&hl=s...](http://books.google.com/books?ei=93b7U_XoBuT5yQPkqYGIBQ&hl=sv&id=P28RAQAAMAAJ&dq=curvature&focus=searchwithinvolume&q=++curvature)

\- So did Henry Petroski in Engineers of Dreams: Great Bridge Builders and the
Spanning of America:
[http://books.google.com/books?id=1J9qUcgoUvkC&pg=PT460&dq=cu...](http://books.google.com/books?id=1J9qUcgoUvkC&pg=PT460&dq=curvature&hl=en&sa=X&ei=tnT7U-uuK4v9ywPl7YGIBQ&redir_esc=y#v=onepage&q=curvature&f=false)

\- and Popular Science in December 1995
[http://books.google.com/books?id=7n5BWbJWMXMC&pg=PA102&dq=%2...](http://books.google.com/books?id=7n5BWbJWMXMC&pg=PA102&dq=%22bottom+because+of+the+curvature+of+the+Earth%22&hl=en&sa=X&ei=ynj7U6iUE-r4yQPW_YDABQ&redir_esc=y#v=onepage&q=%22bottom%20because%20of%20the%20curvature%20of%20the%20Earth%22&f=false)

It's not unique to the V-N Bridge. Here's a generic version in:

\- a NASA report from 1978, Skylab EREP Investigations Summary, says "For
example, the support towers on each side of a long suspension bridge are
several centimeters further apart at the top than at the bottom because of the
curvature of the Earth"
[http://books.google.com/books?id=MEYgAAAAIAAJ&q=%22bottom+be...](http://books.google.com/books?id=MEYgAAAAIAAJ&q=%22bottom+because+of+the+curvature+of+the+Earth%22&dq=%22bottom+because+of+the+curvature+of+the+Earth%22&hl=en&sa=X&ei=ynj7U6iUE-r4yQPW_YDABQ&redir_esc=y)

and two links for the same observation for the Humber Estuary Bridge in:

\- The Guinness Book of Records (1993) -
[http://books.google.com/books?id=RsNPAAAAYAAJ&q=humber+estua...](http://books.google.com/books?id=RsNPAAAAYAAJ&q=humber+estuary+%22curvature+of+the+earth%22&dq=humber+estuary+%22curvature+of+the+earth%22&hl=en&sa=X&ei=6337U8f3OOf4yQPYvYCYBQ&redir_esc=y)

\- Transport, Volumes 1-2 -
[http://books.google.com/books?ei=sX77U-DMN8bmyQOUr4KgBQ&id=X...](http://books.google.com/books?ei=sX77U-DMN8bmyQOUr4KgBQ&id=XIm2AAAAIAAJ&dq=%22curvature+of+the+earth%22&focus=searchwithinvolume&q=+%22curvature+of+the+earth%22)

That said, for Golden Gate-specific comments, see:

\- Ghost Hunter's Guide to the San Francisco Bay Area (2005) ("The engineering
is so perfect that the towers are actually five inches further apart at the
top than the base to account for the curvature of the Earth.")
[http://books.google.com/books?id=oD52WFx2mykC&pg=PA71&dq=gol...](http://books.google.com/books?id=oD52WFx2mykC&pg=PA71&dq=golden+gate+curvature&hl=en&sa=X&ei=iHT7U_OvCsa_ywOEtYCYBQ&redir_esc=y#v=onepage&q=curvature&f=false)

\- Practical Digital Wireless Signals (2010) ("As an example, for the Golden
Gate Bridge at San Francisco the tops of the towers are further apart than the
tower bases by about 9 cm due to the curvature of the Earth") -
[http://books.google.se/books?id=itG9Zwf7eHAC&pg=PA261&dq=%22...](http://books.google.se/books?id=itG9Zwf7eHAC&pg=PA261&dq=%22golden+gate%22+%22curvature+of+the+earth%22&hl=en&sa=X&ei=O3_7U6SfMITMyAPMuoDQCw&redir_esc=y#v=onepage&q=%22golden%20gate%22%20%22curvature%20of%20the%20earth%22&f=false)
.

Therefore, do you really believe that you are the originator of that fact, and
due special attribution?

~~~
_archon_
What tools are you using to locate these sources?

~~~
dalke
books.google.com , which is also the domain name for all of those links. The
searches were various combinations of "golden gate" "curvature of the earth"
and a few other bridge names.

