# Equations for Parabolic Refelctors

• megamax42
In summary, a student at Humboldt State University is working on a final project for their Computational Methods 3 course, where they must solve an engineering problem using numerical methods. They have chosen to optimize a CSP farm by comparing the height, diameter, and number of dishes used. They plan to use equations for light intensity and focal length, with the idea of using the focal distance as the radius in the light intensity equation. However, they are uncertain if this approach is correct and are seeking guidance. They have since found an error and have decided to use polynomial interpolation to minimize costs and find more reasonable values for the diameter and depth of the reflector.
megamax42
Hello everyone, new to this forum, hoping you can give me a hand with finding formulas.

Background
I'm at Humboldt State University Studying Environmental Resources Engineering, currently taking the course Computational Methods 3. For our final project we need to solve an engineering problem using one or more numerical methods learned in class.

Topic Selection
For my final project I have chosen to optimize a CSP (concentrating solar power) farm. As seen below:

Approach
My approach to optimizing the farm is comparing the height of the 'collector' to the diameter of the dish and depth, as well as how many dishes are used.

An equation I was hoping to use was the beam intensity for light:

I = P/4$\pi$r2

Variables explained:
I = light intensity
P = power
r = radius (or more accurately: distance)

I was also hoping to use the equation for the focal length of a parabolic reflector:

f = (D2)/16C

Variables explained:
D = dish diameter
f = focal distance
C = dish depthAnd my idea was to use f (focal distance) from the focal length equation as the r (radius, or distance) in the light intensity equation. Then optimize D (dish diameter) and C (dish depth) to obtain a maximum I (light intensity).

Problem

I'm not sure if I'm on the right track with this approach. I can't help but feel like I'm missing a very important factor in this system of equations, I'm just not sure what it is.

Any help would be greatly appreciated. I am not looking for someone to give me the answers, just a push in the right direction.

Thanks!

Last edited:
I found the error with my approach. The equations will lead to odd dimensions for the reflector, so I've decided to perform a polynomial interpolation on available prices for reflectors based off of the diameter, which is a variable found in the focal length equation. I can then minimize costs at the same time, hopefully leading to more reasonable values of D (dish diameter) and C (dish depth).

## 1. What is the equation for a parabolic reflector?

The equation for a parabolic reflector is y = x^2 / (4f), where y is the height of the reflector at a distance x from the vertex and f is the focal length.

## 2. How is the focal length of a parabolic reflector calculated?

The focal length of a parabolic reflector can be calculated by dividing the diameter of the reflector by four.

## 3. What is the significance of the focal point in a parabolic reflector?

The focal point in a parabolic reflector is where all the reflected rays converge. This allows for maximum concentration of light or sound waves at a single point.

## 4. Can the equation for a parabolic reflector be used for other shapes?

No, the equation for a parabolic reflector is specific to a parabolic shape. Other shapes, such as spherical or elliptical, have different equations for their reflectors.

## 5. How can the equation for a parabolic reflector be applied in real life?

The equation for a parabolic reflector can be used for designing and constructing various devices, such as satellite dishes, telescopes, and parabolic microphones. It is also used in fields such as optics, acoustics, and engineering.

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