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Math and Science Report

Cris Belfer
Systems Engineering II
1/10/08

Math and Science Report

Introduction

When making an LED lighting fixture, math and science are a key element of the process, shaping the design aspects as well as functionality and performance. Designing a lighting fixture requires quite specific calculations and measurements. These along with precise scientific information, specifically heat and light properties, tie into the overall success of the fixture. But, none of this would be possible without the fast-growing and advanced technologies that aid in material manufacturing as well as product marketing.

Science

The science aspect of my design revolves around light-emitting diodes. And, one of the biggest factors when dealing with LED’s is their heat. If an LED gets too hot, its efficiency starts failing rapidly which would basically render the LED useless and the fixture a failure. So to compensate for the temperature, it has become common practice to give the heat a place to escape, away from the LED’s. For my design, I integrated the cylinder, in which the two LED strips reside, with ridges on the outside so that the surface area is greatly increased and allows the heat to run off.

Math

Artificial light sources are usually evaluated in terms of a related quantity, the overall luminous efficacy. This is the ratio between the total luminous flux emitted by a device and the total amount of input power (electrical, etc.) it consumes. This is often simply called “luminous efficacy”, which can be confusing as it also has units of lm(lumens)/W(watt). The range of a white LED is 26-70 lm/W with a 3.8%-10.2% efficiency. This compares to a 100 W incandescent (220 V) which has 13 lm/W and a 1.9% efficiency. This all compares to the theoretical maximum of 682.002 lm/W (100% efficiency).

Technology

Many technologies are used in the making of my design. In this case, LED’s are the prominent technology. Very small (figure 2.1) and very efficient, LED’s are widely popular for their longevity and applicability. From remote controls to streetlights, they are used in every capacity available and will have even more use as technology progresses (doubling every eight months).

Conclusion

In conclusion, making an LED lighting fixture requires all three categories (math, science, and technology) to be perfectly in tune. Without the science of how LED’s give off heat would we be able to compensate properly. Or without the math of lm/W could we see what the LED’s overall luminous efficiency is. And without the help of newer and better technologies it can get done faster and safer.

Selection Rejection

During last summer I research on use and how-to’s for producing a lighting fixture. This lighting fixture is meant to fix to a wall, have its own power source, and the ability to point the light source, used to elucidate artwork, trophies, plaques, and other prized possessions.

The first solution is a basic premise that has two joints, one at the head of the fixture and another in the middle, for turning ability. Its head is cylindrical and its shape provides a sleek and uniform appeal. The lens contours with the shape of the head to make a full circle.

Pros - sleek design
- adequate turning
- variability

Cons - complicated design

The second solution is similar to the first design except that the head is flattened at the lens to allow a different lighting angle. Also the joints are at the base of the head and at the connection of the back-plate to the fixture. This also allows for a sleek and uniform appeal to the industrial world.

Pros - Sleek design
- adequate turning

Cons - complicated design

The third solution is the more dissimilar of the other two. Its head is a lamp-like shape and makes for a circular lighting. There are also three joints in this design and it allows for various degrees of movement. This will also have LED lighting as the other two do.

Pros - great degree of turning
- simple design

Cons - unappealing design

Alternative Solutions

Brainstorming

Background Information

From The Eiffel Tower to a desk, lights are everywhere. They are a part of our everyday lives and without those humans would not be nearly as advanced as they are now. They allow us to function at night and therefore we can be active throughout the entire 24 hour day. As for survival, lights can be used for entertainment purposes. A museum at night with no lights is of no use; it needs lights to be successful.

“Light is a form of energy that can be released by an atom. It is made up of many small particle-like packets that have energy and momentum but no mass. These particles, called photons, are the most basic units of light. Photons are released as a result of moving electrons. In an atom, electrons move in orbitals around the nucleus. Electrons in different orbitals have different amounts of energy. Generally speaking, electrons with greater energy move in orbitals farther away from the nucleus.

For an electron to jump from a lower orbital to a higher orbital, something has to boost its energy level. Conversely, an electron releases energy when it drops from a higher orbital to a lower one. This energy is released in the form of a photon. A greater energy drop releases a higher-energy photon, which is characterized by a higher frequency.

As we saw in the last section, free electrons moving across a diode can fall into empty holes from the P-type layer. This involves a drop from the conduction band to a lower orbital, so the electrons release energy in the form of photons. This happens in any diode, but you can only see the photons when the diode is composed of certain material. The atoms in a standard silicon diode, for example, are arranged in such a way that the electron drops a relatively short distance. As a result, the photon's frequency is so low that it is invisible to the human eye -- it is in the infrared portion of the light spectrum…

…Visible light-emitting diodes (VLEDs), such as the ones that light up numbers in a digital clock, are made of materials characterized by a wider gap between the conduction band and the lower orbitals. The size of the gap determines the frequency of the photon -- in other words, it determines the color of the light.” -Tom Harris