Question about Viewing the Curvature of the Earth

View from 90,000 feet over Nevada's Black Rock Desert on JP Aerospace's Away 9 balloon in May 2002. Landmarks include Honey Lake (lower left), Mount Lassen (middle) and Mount Shasta (upper right)

I received this question in e-mail about where you can see the curvature of the Earth. The sender saw my personal web site and thought I might be able to answer. But I have a lot of friends who can help make an even better answer. So I asked them for input too. The question and received answers are posted here.

-- IanKluft - 30 Aug 2006

From: Jim ...
To: Ian Kluft
Subject: can you help?
Date: Tue, 29 Aug 2006 20:46:29 -0400

Ian, I am trying to settle a bet and from some of the pix on your site, it sounds like you might be the guy. Three of my family members think the curvature of the Earth can be seen from: a helicopter in Hawaii, a cell tower of 400 ft. in MI, and a beach in HI. I thought I had heard it was visible only from 50k feet and higher. Who is correct?

Answers

We received several responses. The general theme is that the senders, in their bet among themselves, are either all correct if they're looking for any hint at all that the Earth is round, or all wrong if they're looking for a height at which curvature is visible in the horizon.

60,000 feet is the number that keeps coming up from different sources for the point where the curvature of the Earth is visible.

Answer by Ian Kluft

I think the senders are tripping over different definitions of seeing
the curvature of the Earth.  All of those can give you some sort of
hint of it.  The more altitude, the better.  They could all be right
for various definitions of the question.

If they're defining the problem as any view that gives any evidence that
the Earth is round, even the beach in Hawaii or anywhere you see a
continuous horizon is a hint of sorts.  The more altitude the better.
So a 400' tower in MI would be better than the beach.  A helo over Hawaii
would have ocean in most or all directions, and would be even better.

The best I've seen with my own eyes is from 40,000' in an airliner.
It's still hints of the curvature of the Earth at that altitude.
I've never had a clear enough day to see a sharp curve on the horizon
from that altitude - and I expect it's always that way.  But you can
tell you're getting up there where the curvature should be visible soon
if you could go higher.

If you want to see the curvature of the Earth with the atmospheric glow
like a view from space, my experience with video from high-altitude
balloons is that 60,000' is where the curvature of the Earth clearly
comes into view.  Pictures from a JP Aerospace balloon in May 2002 up to
90K are at
   http://ian.kluft.com/blackrock/jpa200205/
Note at the end of the flight when the balloon landed, it got pictures of
us taking pictures of it when we recovered it.

Answer by Arik Baratz

Arik says his response is "licensed under the Creative Commons Attribution-ShareAlike 2.5 License."

The answer depends on what the meaning of "seen" is. If what you want
to do is to observe that, indeed, the earth is not as flat as the Flat
Earth Society say, you can observe it by using a simpler experiment.

Take two points on the surface of the earth - A and B - with the
surface distance d between them (for example, drive d miles on a
straight road, without ascending or descending). There is a straight
line between those two points going through the earth, and there is a
curved line connecting them on the surface (length d).

About 10 minutes with a pen, a piece of paper and some geometric
kong-fu show that in their middles, the distance between those two
lines is:

h = (1 - cos(d/2Re)) * Re

h is the hight of the "hill" that blocks the direct line view of A and
B, Considering Re is the radius of the earth and the calculation is
made in radians. Putting real approximate  values into this equasion
(Re=4000 miles) and a road 5 miles long gives about 8e-4 miles or just
over 4 feet.

So, find that road, put a stick perpendicular to the ground with a
bright LED every feet, drive away and watch in amazemnt as the 4th one
disappear after about 5 miles.

The only caveat I can think of is that a road that straight is hard to
find. If you want to scale the experiment, use a stronger light source
and drive further apart. You might want to make sure you have the
altitude right by means of a GPS or a barometric altimeter.

This formula has practical uses too: If you want to connect two points
50 miles apart with a WiFi link (line of sight), you need to erect two
towers at least 413 feet high.

Answer by Craig Anderson

There are so many clues to the curvature of the
earth and most people don't notice them.
You can see the curvature of the earth "in action"
from the shore as you watch a ship slowly sink
as it goes over the horizon.  That is the same at
all altitudes, the horizon just moves out as you
go up.

If you were on top of a ship's mast in the middle
of the ocean you would not be able to see the curvature
(even though this would seem to be the best place)
because you look out to the horizon in all directions
in a flat plane.  Only when you get high enough
does your view change from a flat plane in all
directions to more of a cone to the visible horizon.
But where that change
from a plane to a cone noticeably happens is anyone's
guess.

Answer by Randall Clague

None of the above.  The X-plane pilots and SR-71 & U-2 pilots give
around 60,000 as the altitude at which you clearly see the curvature
of the horizon.  There's no sharp delineation, but horizon curvature
is definitely not visible from any point on the surface of the Earth,
or attached to the surface.

More responses accepted

More answers will be accepted if anyone wants to add any substantive content to this.

Pictures of the curvature of the Earth by Concorde passengers

Concorde flew at 60,000 feet while in service from 1976 to 2003. Its passengers have seen the curvature of the Earth with their own eyes. Many photographed it. Some have posted pictures on the web.

• Beating fear of flying - on Concorde - BBC
• Ben's Concorde Trip Report - Part 5 - The Flight
• Eric's Concorde Tribute Page
• Concorde: end of an era > Vital statistics - UK Science Museum

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