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

• Jul 12th 2010, 08:25 AM
StuG1944
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?
• Jul 12th 2010, 09:46 AM
Soroban
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: .$\displaystyle y \:=\:693.8597 - 68.7672\cosh( 0.0100333x)$

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: .$\displaystyle 195\frac{2}{3} \:=\:\frac{587}{3}\text{ ft.}$

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

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

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

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

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

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

• Jul 12th 2010, 12:51 PM
StuG1944
Thanks for the help! Just sent a donation to the forum for it.