What's the max height a 747 plane can fly, under the St.louis arch?

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?

Hello, StuG1944!

Quote:

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: . $y \:=\:693.8597 - 68.7672\cosh( 0.0100333x)$

Wingspan: .195 ft 8 in
Tail height: . 63 ft 5 in

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

Also, i'd like to also figure our other wingspans also.
What would be the way to sovle this?

The wingspan is: . $195\frac{2}{3} \:=\:\frac{587}{3}\text{ ft.}$

Then: . $x \;=\;\frac{587}{6}$

Hence: . $y \;=\;693.8597 - 68.7672\cosh[0.0100333(\frac{587}{6})]$

. . . . . . $y \;=\;589.2161828$

To clear the wingspan of the Boeing, it can fly as high as 589.2 feet.

But this leaves only $630 - 589.2 \:=\:41.8$ feet clearance at the top.
And this does not allow for the height of the tail, $63\frac{5}{6}$ feet.

Therefore, the maximum altitude of the Boeing is:
. . $630 - 63\frac{5}{12} \;=\;566\frac{7}{12}$ feet.

Thanks for the help! Just sent a donation to the forum for it.