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For this homework assignment I wanted to try and see if I could find a correlation between a dragsters rear tire expansion in comparison to its velocity by using either the method of Laplace transform or the Fourier series. To help me with my model I will me using the Army's dragster for some of my data. If you would like to check it out you can find it at [http://www.goarmy.com/army-racing/nhra-top-fuel/dragster.html]. If you want to watch a video of dragster tires click here : http://www.youtube.com/v/V3yj_OGezWc?version=3 |
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*[[Signals and systems|Signals and Systems]] |
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==Fourier Transform Applications== |
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'''Data:''' |
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<b>Unfortunately, the Fourier Transform isn't a Transformer. |
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* Outside tire diameter = 36.5" or up to 40.5" due to tire expansion |
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<br>(This handsome fellow is named Roolbar.)<br> |
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[[Image:transformer_roolbar.jpg]]<br> |
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So, what is a Fourier Transform? </b> |
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<br>Check any of the other pages on this site to find fifty different ways to explain what a Fourier Transform is. If you already know what it is, or you're too lazy to look at the other pages, here's my super trite description: A Fourier Transform is a bunch of sinusoids of different frequencies and time offsets added together create a just about any function you want. A Fourier Transform is the way of representing a function in the frequency domain instead of the time domain. |
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* Inside tire diameter = 16" |
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Instead of describing the Fourier Transform itself once again, the following pages describe how Fourier Transforms are analyzed and utilized in a computer. |
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* Width of tire = 17" |
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* Air pressure in tire = 7 psi |
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== Fourier Transform Applications == |
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===The "Fast" Fourier Transform=== |
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* Volume of Tire = 9.82 ft^3 **(you have to add about 1.5ft^3 to account for possible expansion)** |
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* Fastest quarter mile time = 4.428 sec |
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<b>What is a Fast Fourier Transform? (FFT)</b><br> |
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* Fastest quarter mile speed = 337.58 |
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It's an algorithm that can compute the discrete Fourier transform faster than other algorithms. In digital systems, continuous Fourier Transforms are sampled, turning them into discrete Fourier Transforms which then can be computed and manipulated using Digital Signal Processing. |
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'''Equations:''' |
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An intuitive brute force way of computing a Fourier Transform means rearranging the the summation so that you don't compute the transform in sequential order - you group similar elements together and simplify before combining them. This cuts down the adding and multiplying, thus cutting computation time down by about 100 times. |
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Volume = [(pi)*(R^2)(h)-(pi)*(r)(h)] |
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y = .075/(Vmax-Vmin) **(this is the number of inches that the tire should expand given the current velocity.)** |
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<br><b> Cooley-Turkey Algorithm </b> |
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One of the most popular FFT algorithms is the Cooley-Turkey algorithm. Which I have to figure out before I explain it to you -I will explain on Friday. Have patience. |
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Latest revision as of 20:23, 31 October 2010
For this homework assignment I wanted to try and see if I could find a correlation between a dragsters rear tire expansion in comparison to its velocity by using either the method of Laplace transform or the Fourier series. To help me with my model I will me using the Army's dragster for some of my data. If you would like to check it out you can find it at [1]. If you want to watch a video of dragster tires click here : http://www.youtube.com/v/V3yj_OGezWc?version=3
Data:
- Outside tire diameter = 36.5" or up to 40.5" due to tire expansion
- Inside tire diameter = 16"
- Width of tire = 17"
- Air pressure in tire = 7 psi
- Volume of Tire = 9.82 ft^3 **(you have to add about 1.5ft^3 to account for possible expansion)**
- Fastest quarter mile time = 4.428 sec
- Fastest quarter mile speed = 337.58
Equations: Volume = [(pi)*(R^2)(h)-(pi)*(r)(h)]
y = .075/(Vmax-Vmin) **(this is the number of inches that the tire should expand given the current velocity.)**