## What's the max height a 747 plane can fly, under the St.loui

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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?
StuG1944
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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 $y=\frac{-613}{68121}x^{2}+613$

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.
galactus

### 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.
StuG1944
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Joined: Mon Jul 12, 2010 11:31 am

68121 = 261²
skipjack
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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???
Lisklures
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