Search IntMath
Close

450+ Math Lessons written by Math Professors and Teachers

5 Million+ Students Helped Each Year

1200+ Articles Written by Math Educators and Enthusiasts

Simplifying and Teaching Math for Over 23 Years

# Catenary Equation [Pending...]

### My question

I understand that a bridges main cable can be modelled using the parent catenary function, y = a cosh(x/a), where cosh(x)=(e^x+e^-x)/2. However, I was confused on how to obtain the parameter 'a'. I've read online that 'a' is a constant to do with horizontal tension? I also understand that 'a', essentially changes the overall wideness of the curve if I'm correct.

### Relevant page

http://euclid.trentu.ca/aejm/V4N1/Chatterjee.V4N1.pdf

### What I've done so far

∫_0^x▒〖√(1+(dy/dt)^2 ) dt=1016.5〗

Secondly, I will consider the equation which describes the height of the towers:

y(x)=206.4

After integrating the first equation and substituting the expression for y from the rationale into the second equations, my two main equations become:

a sinh⁡〖(x/a)=1016.5〗
And
a cosh⁡(x/a)=206.4+a

X

I understand that a bridges main cable can be modelled using the parent catenary function, y = a cosh(x/a), where cosh(x)=(e^x+e^-x)/2. However, I was confused on how to obtain the parameter 'a'. I've read online that 'a' is a constant to do with horizontal tension? I also understand that 'a', essentially changes the overall wideness of the curve if I'm correct.

Can someone please help me to understood how to solve for a?
Relevant page

<a href="http://euclid.trentu.ca/aejm/V4N1/Chatterjee.V4N1.pdf">http://euclid.trentu.ca/aejm/V4N1/Chatterjee.V4N1.pdf</a>

What I've done so far

∫_0^x▒〖√(1+(dy/dt)^2 )  dt=1016.5〗

Secondly, I will consider the equation which describes the height of the towers:

y(x)=206.4

After integrating the first equation and substituting the expression for y from the rationale into the second equations, my two main equations become:

a sinh⁡〖(x/a)=1016.5〗
And
a cosh⁡(x/a)=206.4+a

## Re: Catenary Equation

Nevermind! I ended up being able to solve it

X

Nevermind! I ended up being able to solve it

You need to be logged in to reply.

## Related Applications of Integration questions

• Shell Method [Solved!]
URL:Shell Method | Brilliant Math & Science Wiki Under the section, "When to use the shell...
• Applications of Integrations #11 [Solved!]
I haven't had calculus in many years but I like to work problems every now...
• Finding volume using shells [Solved!]
Exercise 2: The area between the curve y = 1/x, the y-axis and the lines y...
• How to transform the differential equation? [Solved!]
Dear friends, I met a problem. I don't know how to transform the equation (13) into...
• A simple integration [Solved!]
Hi, I am a junior and met a simple problem. How can I solve the...