« [Warning: Boring Theory] Quantum-Level Voltage | HomePage | Honor (A Framework for Relationship) »
14 August 2006
[Warning: Boring Theory] Sinusoidal Motion and Power
Somebody probably already thought of this. Either that, or its wrong. But I’m too lazy to look it up. Besides, I’d probably have to open an academic journal, which would break my fast on doing that. Kind of like fasting lima beans or dentistry. Ironically, I’m not to lazy to write the theory down, which will take a lot more time than just trying to look it up. Weird, huh? (I mostly only amuse myself. I’m fine with that, though.)
Data points:
1) AC power is better for the transmission of electricity over long distances than DC power, especially at high voltages. Plus you can throw in more phases, which can kick up the total voltage even more. (I use very precise words. Like rockin’.)
2) It feels like (another precise word) there is a dimension hidden in angular motion, as compared to linear motion. Angular velocity looks a lot more like linear acceleration than linear velocity, in terms of what units are squared and all. This makes sense, sort of, because in angular velocity, you have to change two dimensions (x and y) to stay on the circle, but linear velocity has to only change one dimension to stay on the line.
So… look at a sine wave. I’d draw a picture, but (again) I’m too lazy. Here’s the thing. Waves propagate perpendicular to their axis of change. The wave is going up and down in the y axis, so it propagates (over time) in the x axis. I’ll skip all the Fourier crap here. But here’s the crazier thing. Every sine wave, by definition (SOHCAHTOA and all that nonsense) has a complimentary cosine wave. Which is cool and all, but check this out: put the sine wave and the cosine wave on the same time axis, and put their motion perpendicular to each other. You get a corkscrew, propagating down time. And the perpendicular motion to propagation thing continues: along the corkscrew, the tangent line coming off the motion at the leading point of the wave is always within a plane perpendicular to the time axis of propagation. Which is a cool shape, but not that interesting until we consider this in the context of power.
Here’s the (relatively) cool part. So voltage is potential difference. But instead of scary, magic electricity, lets use an analogy to spring force, which holds energy through potential difference too. So DC power exists in one dimension only. Imagine trying to pull a spring apart, only applying linear acceleration to it. The thing is, the spring wants to snap back to its old (zero voltage) equilibrium state. It wants to go totally against the direction that you are trying to pull. So this is going to fight you in transmission, especially at high voltages. The spring doesn’t have any other direction to go, so it wants to go back to zero. And it you were pulling on that spring, you could imagine getting tired pretty quick.
But AC Power is different. Since its got that ‘hidden’ dimension (every sin has a cos,) the spring has somewhere to go that’s not directly against the power placed on it. Imagine instead of just pulling a spring apart, we put a weight on the end of the spring. The distance the spring is pulled apart is the energy in the spring, but we could swing that weight around (in a corkscrew pattern) a lot longer than we could just pull it apart. This is because we gave the spring a direction to go that wasn’t directly against our pulling. In fact, the spring always wants to move tangent to the direction of our pulling (the displacement) ’cause the wave wants to propagate perpendicular to the axis of displacement. So by giving the spring somewhere to go, we don’t have to fight as hard to keep the spring apart. So this is why AC power is better at high voltages and long distances. Maybe.
11:39 Posted in Boring Theories (Sciences) | Permalink | Comments (0) | Trackbacks (0) | Email this
Trackbacks
The URL to Trackback this post is: http://odb130.blogspirit.com/trackback/947253