## Sunday 7 February 2016

69) “The New York City skyline is clearly visible from Harriman State Park’s Bear Mountain 60 miles away. If Earth were a ball 25,000 miles in circumference, viewing from Bear Mountain’s 1,283 foot summit, the Pythagorean Theorem determining distance to the horizon being 1.23 times the square root of the height in feet, the NYC skyline should be invisible behind 170 feet of curved Earth.”

### You asked for refraction? Or is tall buildings being tall sufficient?

So, here we are again. The distance is 60 miles, the elevation is from Bear Mountain ( 1283 feet). Among the clearly visible buildings is the Empire state building (1250 feet), I think?

It doesn't really matter. The height of Bear Mountain allows for a horizon  at
76 km. However, what we forgot to include is that New York City is at 500 feet elevation itself.

Let's use my intuitive guess from earlier and just add those. That gives us
89.9851 km, which still isn't enough.

So yes, part of the tall buildings will be hidden. That's why it is called a skyline. Because it's the upper part; the bottom of the buildings is cut off. The Empire state building is
381 metres high - the 52 m  drop they discuss still allows you to see it.

A quick calculation using the height from Bear mountain, the 500 feet elevation of new york, and inversing the horizon distance formula, tells me that any building higher than
124.2365 m is visible. That leaves more than a hundred buildings in new york that are visible [Tall buildings in New York].

False claim + phony numbers
I measured the distance from Bear Mountain to Manhattan and it's 40 miles, not 60. The distance to Manhattan Island is between 60 and 65 km. Let's take the 63 km to Empire State Building. You can calculate the distance to the horizon dependent on your height of observation using this more accurate formula:

https://en.wikipedia.org/wiki/Horizon#Geometrical_model

If you don't want to do that, you can just punch in your elevation on this website and get the same result:
http://www.ringbell.co.uk/info/hdist.htm

The result is 70.8 km for 393 m height (Bear Mountain). Even if you don't factor in atmospheric refraction or the height of the buildings and even if you don't factor in the 14m ground elevation at Empire State Building according to this topographical map
http://en-us.topographic-map.com/places/New-York-168850/

.. it's a geometrical fact that you have to be able to see Manhattan from Bear Mountain.

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