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July 12th, 2010, 08:31 AM   #1
 
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What's the max height a 747 plane can fly, under the St.loui

I'm trying to figure out how to estimate the max height a Boeing 747 can fly, if it were to fly under/through the St.Louis gateway arch?

The equation for the arch is y = 693.8597 - 68.7672 cosh ( 0.0100333 x )

Wingspan 195 ft 8 in (59.6 m)
Tail height 63 ft 5 in (19.3 m)


And the Arch is 630ft tall and 630ft wide at the base.

Also, i'd like to also figure our other wingspans also. What would be the way to sovle this?
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July 12th, 2010, 12:53 PM   #2
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Re: What's the max height a 747 plane can fly, under the St.loui

The 630' dimension is to the outside. If a jet were hypothetically flown under it, the inside dimensions would have to be considered.

Note that if we center the Arch at the origin and let x=0 in the equation, we get 625.0925 feet. This is the distance to the centroid at the top.

The cross-sections of the Arch are equilateral trangles. At the top it has a 17 foot high apex, and at the base it is 54 feet wide.

An equation for the inside dimensions could be found. Even though the Arch is a caternary, one can find a parabola that will fit very closely to

the caternary equation.

The inside at the base would be 630-2(54)=522 and 630-17=613 at the top.

Center it at the origin and find a parabola equation to fit the inside. Passing through (261,0) with vertex at (0,613).

This gives a parabola of

Since the wing span of the jet is 195.67, we can divide this by 2 and let x=97.83. This gives y=526.87 feet high at that point.

613-526.87=86.13. This allows for the tail height as well. The jet just fits through when it is about 527 feet in the air from the ground.

This is just playing around. I hope it helps. You could even maybe find a caternary to represent the inside dimensions if you wish.
 
July 12th, 2010, 04:19 PM   #3
 
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Re: What's the max height a 747 plane can fly, under the St.loui

How did you get 68121? I keep getting a wrong answer for the lower part.
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July 13th, 2010, 07:31 AM   #4
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68121 = 261
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November 2nd, 2010, 12:44 PM   #5
 
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Re: What's the max height a 747 plane can fly, under the St.

How much space would you have between the wing and the side of the arch at 526.87 feet above ground???
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