1. A study of the Brooklyn Bridge
Suspension Bridges
A study of the Brooklyn Bridge

2. Background
This activity would be appropriate for student at the 10th grade level
The activity would proceed as follows:
1. Find out background about the Brooklyn Bridge/Suspension bridges in general
2. Discuss the parabolic shape of the main cable of suspension bridges
3. Use dynamic technology to “eyeball” a parabola that resembles the main cable of the Brooklyn Bridge (TI-nSPIRE)
4. Research the dimensions of the Brooklyn Bridge
5. Determine the equation of the parabola for the main cable of the bridge using TI-nSPIRE
6. Determine the cost of the cable using the equation

3. 1. Facts about suspension bridges
Suspension bridges are able to achieve longer spans than many other types of bridges
They can be cheaper to build than other types of bridges
In the NYC area, there are several suspension bridges, including the Brooklyn Bridge, Manhattan Bridge, Verrazano Bridge, George Washington Bridge, and others.
Source:

4. 2. The main cable of a suspension bridge is in the shape of a parabola.
If a string (or cable) is suspended the shape formed is called a “catenary.”
When the suspended cable is secured to the span of the bridge, it takes on a parabolic shape.
Source:

5. 3. Use the dynamic “grab & move” feature of the TI-nSPIRE
The basic parabola y=x2 does not look like the center cable of a suspension bridge

6. 3. The “grab & move” feature allows us to stretch out the parabola
This graph still does not visually resemble the center cable of a suspension bridge

7. These graphs look more as we expect a suspension bridge to appear.

8. 4. What are the dimensions of the Brooklyn Bridge?
Span between towers: feet
Height of towers: feet
Height of towers above roadway: 117 feet
Therefore, if we consider the lowest point to be the origin of a coordinate axis system, the parabola would intersect the points (-798,117), (0,0) and (798,117). [798=1596/2]
Source:
and

9. 5. We can determine the equation for the parabolic cable
We can fit a curve to the points(-798,117), (0,0) and (798,117)

10. 5. Equation of the parabola
The equation of the parabola according to the quadratic regression is y= x2
This can also be calculated by hand using algebra

11. The graph must be scaled properly
It is impossible to see using the standard scale of the
TI-nSPIRE

12. The zoom feature allows a better view

13. The equation of the parabola can be used to:
Calculate the amount of cable necessary to build the bridge
Calculate the cost of the cable
Build a model of the bridge

14. Difficulties
Students must know proper scaling when dealing with real life situations and large numbers
Although the new TI-nSPIRE has a wide variety of capabilities, it is not user friendly
The “regression” feature would seem mysterious to students; it would be ideal to do an algebraic derivation of this work and compare results to what the calculator found.

15. Extensions
Students could compare the equation of the parabolic cable of the Brooklyn Bridge to the equation of other local suspension bridges
Students could do a historical study of the Brooklyn Bridge

16. Assessment This type of project would require ongoing assessment.
A rubric might include such categories as
Uses a sensible coordinate axis system to represent graphs
Is able to interpret results of the graph and apply to solving problems
Is able to determine whether results make sense in the context of examination of the bridge