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Bridge building, earth curvature, and math nerd

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MathTeacher
(@mathteacher)
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I watched an old TV show yesterday about NYC bridges. It said that the towers for the Verrazzano Narrows bridge are 1 5/8 inches further apart at the top than at the bottom because of the curvature of the earth. Furthermore, that was a design criterion.

The towers are 693 feet tall and 4260 feet apart at their bottoms. If the 1 5/8 inches is a design criterion, then it had to be calculated. 

Here's my CAD VVL (very very lite) drawing:

 I used 3959 miles as the radius of the earth because that's what my 1942 spherical trig book uses and got 1.694746 inches as the difference in distance between the top and bottom of the towers. That's a bit more than 1.625, but the answer only has to round to the nearest eighth.

That means that it has to be less than half-way between 1.625 and 1.750. or less than 1.6875, which it isn't

There's probably rounding involved in all of the given lengths, but if there's not, an earth radius of 3976 miles will give a difference of 1.6875 inches.

Forgetting the math nerd stuff, it's instructive to see how curvature affects big construction.

Carry on, and for gosh sakes be more productive than I am.

 
Posted : October 2, 2022 11:03 am
Jitterboogie
(@jitterboogie)
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GIF
 
Posted : October 2, 2022 12:01 pm
Brad Ott reacted
MightyMoe
(@mightymoe)
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It might be possible that they are calculating to the connection points and not the actual top of the tower which would shorten the length slightly. Looking at a picture of the bridge shows that point only a bit lower than the top, maybe it could make the difference. 

 
Posted : October 2, 2022 1:41 pm

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Jitterboogie
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I was just thinking about the 'ten points' it would take to layout those amazing huge spans, wow!

 
Posted : October 2, 2022 2:14 pm
Brad Ott reacted
MightyMoe
(@mightymoe)
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20,906,000 ft was the number used for NAD27 calcs. That matches your 3959 miles,,,,,more or less. 

One of those numbers repeated so many times it sticks in my old memory. 

 
Posted : October 2, 2022 2:14 pm
MathTeacher reacted