A few pictures from SF

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Just to throw this thread into a tangent, I'm sitting here in my office in Pocatello, Idaho and at this moment I can clearly see the Sawtooth Mountains which are between 115 and 125 miles away. I bet I could see them 250 miles away if they were that far.

Whoops, looks like a storm is coming in...

So, inquiring minds want to know what kind of camera it was?
 
Replying to my own post, and hoping this isn't an empty room...

How high would the mountains need to be if I could see them 250 miles away?
 
To solve the problem, imagine you are on the peak of the mountain that you want to be able to see from far away. Now imagine a line from your eye that goes all the way to towards the horizon, where it becomes a tangent to Earth's curvature. The distance from your eye to the point of tangency is the visible distance.

For all practical purposes, because Earth's radius is so big (3,960 miles), you can ignore how high above sea level you are and that Earth's radius varies a little (+/- 20 miles).

The tangent is perpendicular the Earth's radius, therefore the Pythagorean theorem allows us to calculate the visible distance (distance between point of tangency and eye). BITOG won't let me type the square root sign, so I use ^(1/2) instead:

(radius + height of mountain) ^2 = radius ^2 + tangent ^2
tangent ^2 = 2 x radius x height + height ^2
tangent = ^(1/2) 2 x radius x ^(1/2) 1+ height ^2 : 2 x radius x height
tangent = ^(1/2) 2 x radius x height (1 + height : 4 x radius
tangent = ^(1/2) 2 x radius x height

The visible distance D (from point of tangency to eye) is the square root of two times Earth's radius times height of the mountain:
D = ^(1/2) 2 x 3,960 x height of mountain in miles

For example, if a particular mountain peak is 10,560 feet (2 miles), then:
D = ^(1/2) 7380 x 2
D = 121
You can see a two miles high peak from about 121 miles away, presuming you are reasonably close to sea level (a few hundred feet don't matter) with a clear view. Due to refraction you can actually see farther, if atmospheric condition allow it.
 
An easier way to do the same calculation is to simply take the square root of the height of the peak ( 102.76 ) and multiply that figure by 1.2, which in this case gets you 123.7 :)

Maybe not quite as accurate, but good enough for all practical purposes.
 
Originally Posted By: hate2work

An easier way to do the same calculation is to simply take the square root of the height of the peak ( 102.76 ) and multiply that figure by 1.2, which in this case gets you 123.7 :)

Maybe not quite as accurate, but good enough for all practical purposes.


Most people won't understand how you found the constant factor 1.2.
wink.gif
 
Originally Posted By: hate2work

An easier way to do the same calculation is to simply take the square root of the height of the peak ( 102.76 ) and multiply that figure by 1.2, which in this case gets you 123.7 :)

Maybe not quite as accurate, but good enough for all practical purposes.


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i'm all for simplicity
 
Originally Posted By: Julian
You guys are lucky to have all that cool stuff over in San Francisco. Mostly just corn and beans here.
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I much rather see beans and corn fields than anything in SF/Oakland.

I would happily trade all the developed area around me for beans and corn.
 
Originally Posted By: milwaukee
I much rather see beans and corn fields than anything in SF/Oakland.

I would happily trade all the developed area around me for beans and corn.


We have the Pacific!
wink.gif
 
Originally Posted By: moribundman
BITOG won't let me type the square root sign,



√ √ √ √ √ √ √ √ √ √ √Height

Copied the sqrt symbol from the windows character map. Do a quote and you can see the key sequence to do it directly.

(Height)[sup]½[/sup] That doesn't work but should

(Height)½ Need to be a moderator to do that one.
 
Last edited:
Originally Posted By: milwaukee
Originally Posted By: Julian
You guys are lucky to have all that cool stuff over in San Francisco. Mostly just corn and beans here.
55.gif
(
frown.gif
56.gif
)


I much rather see beans and corn fields than anything in SF/Oakland.

I would happily trade all the developed area around me for beans and corn.


I wish more people felt that way.
 
Originally Posted By: XS650
Originally Posted By: moribundman
BITOG won't let me type the square root sign,



√ √ √ √ √ √ √ √ √ √ √Height

Copied the sqrt symbol from the windows character map. Do a quote and you can see the key sequence to do it directly.

(Height)[sup]½[/sup] That doesn't work but should

(Height)½ Need to be a moderator to do that one.


I can type the root symbol √, but I have no idea if it shows up for other people. I see it fine on my Mac. Do you see it?

What about these?
∞ ∂ ÷ ± ≦ ≈ ∫
Do they show up for you?
 
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