Calculus and Engineering in Farming

by Andrew Gurganus

Submitted : Spring 2019

This project shows the use of calculus in determining the length of power cables needed to connect solar array farms into an existing electrical grid. To start, I needed to find the distance between the power station and the connector for the solar farm. This distance was measured to be 1.2 miles or 6336 feet. However, it is not that easy; that cannot be the total length of the cable due to the way the cable sags between utility poles. The next step is to find how many of these “sags” there would be in that distance of 1.2 miles. After that, there is a need to add on the distance between the closest utility pole and the outlet for the solar farm. Once these values are found, the calculations can begin using calculus, especially the arc length formula. Then Newton is needed to find Tow. There is no given tension and so Tow is the horizontal tension at the cable’s lowest point. This helps find the distance of the cable from pole to pole which leads to the total distance of the cable over 1.2 miles.

Catenary is known as the curve which has an equation helped defined by a hyperbolic cosine function (cosh) along with a scaling factor. The scaling factor for power cables hanging by their own weight is known as the horizontal tension on the cable divided by that weight. Weight is also known as w=mg with m being mass and g being the force of gravity. For this problem, both the tension and weight are unknown and so Newton’s method was used to help find these values along with the arc length equation to find the length of the cable and answer this problem. During the duration of this project, I observed and realized some key points. First, I noticed that calculus is a very broad area of math and that it applies to a very large portion of everyday life, particularly things that have been built. It is very similar to physics in this sense and that amazed me a bit because I did not notice the full importance of calculus and how far it branches out into the real world. This project helped me discover how much engineers are actually involved with real-world applications like this. Additionally, many engineering fields are included to solve this problem such as electrical, mechanical, materials and industrial as well as many other professions. In the workforce, engineers can practically work in any one area but collaborate with other engineers and other professions such as doctors, construction workers, business owners, to solve issues such as this to improve real life for all of us.  This is a very exciting to me because the options and opportunities for an engineer in the workforce are endless.

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