# Thread: Mathematical Model of a Catenary

1. ## Mathematical Model of a Catenary

Hi everyone,
I have a Yr 11 maths assignment which investigates the geometry of a suspension bridge (mainly catenarys). I used a piece of 5m rope to create the shape of one and recorded the following measurements:
X Axis (cm)
0
39.1
78.2
117.3
156.4
195.5
234.6
273.7
312.8
351.9
391
430.1
469.2

Y Axis (cm)
90
68.5
51
37.2
27.4
19.7
17.8
19.7
27.4
37.2
51
68.5
90

One of the questions asks to generate a mathematical model using either y=ax^2, y=ax^3, y=a/x or y = the square root of x.The textbook also states
sometimes non-linear relationships can be reduced to linear relationships. For instance, y =m/x + c is a hyperbola. However, if we substiture p for 1/x, the rule becomes linear: y=mp+c. The graph of y versus p will be the straight line with the gradient of m and the y intercept of c. These values (m and c) can then be established from the graph and thus the hyperbolic model can be determined.
What do I use? How can I generate a model? I have tried but none have worked for more than one value .
Daniel

2. Hyperbolas can be rotated so that the orientation is closer.

You will have to keep modelling until you settle on the Hyperbolic Cosine, $\displaystyle cosh(x) = \frac{e^{x}+e^{-x}}{2}$, but that's a different animal than those you have suggested.

3. Originally Posted by daewoo_lowrider
Hi everyone,
I have a Yr 11 maths assignment which investigates the geometry of a suspension bridge (mainly catenarys). I used a piece of 5m rope to create the shape of one and recorded the following measurements:

X Axis (cm)

0

39.1

78.2

117.3

156.4

195.5

234.6

273.7

312.8

351.9

391

430.1

469.2

Y Axis (cm)

90

68.5

51

37.2

27.4

19.7

17.8

19.7

27.4

37.2

51

68.5

90

One of the questions asks to generate a mathematical model using either y=ax^2, y=ax^3, y=a/x or y = the square root of x.The textbook also states
sometimes non-linear relationships can be reduced to linear relationships. For instance, y =m/x + c is a hyperbola. However, if we substiture p for 1/x, the rule becomes linear: y=mp+c. The graph of y versus p will be the straight line with the gradient of m and the y intercept of c. These values (m and c) can then be established from the graph and thus the hyperbolic model can be determined.
What do I use? How can I generate a model? I have tried but none have worked for more than one value .
Daniel
For instance, take $\displaystyle y = ax^3$. Define a new variable $\displaystyle p = x^3$ and calculate all the p values. Then do a linear regression using p as your "x" value and y as your "y" value.

-Dan