
Algebra PreAlgebra and Basic Algebra Math Forum 
 LinkBack  Thread Tools  Display Modes 
July 12th, 2010, 08:31 AM  #1 
Newbie Joined: Jul 2010 Posts: 2 Thanks: 0  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? 
July 12th, 2010, 12:53 PM  #2 
Guest Joined: Posts: n/a Thanks:  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 crosssections 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 6302(54)=522 and 63017=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. 613526.87=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 
Newbie Joined: Jul 2010 Posts: 2 Thanks: 0  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.

July 13th, 2010, 07:31 AM  #4 
Global Moderator Joined: Dec 2006 Posts: 16,397 Thanks: 1177 
68121 = 261² 
November 2nd, 2010, 12:44 PM  #5 
Newbie Joined: Nov 2010 Posts: 1 Thanks: 0  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???


Tags 
747, fly, height, max, plane, stloui 
Search tags for this page 
Click on a term to search for related topics.

Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Height of trapezoid  Telu  Algebra  15  June 27th, 2013 01:36 AM 
Triangle plane surface 2m base and 3 height  rsoy  Physics  4  April 23rd, 2012 08:27 AM 
Upper halfplane to lower halfplane  lime  Complex Analysis  2  July 2nd, 2011 09:51 PM 
Transformation of an arbitrary plane in 3D to the z=0 plane  rashed_karim  Linear Algebra  1  June 26th, 2008 12:02 PM 
Height of Helicopter  symmetry  Algebra  3  July 26th, 2007 01:01 PM 