# Graphic depiction of ratios and relative speed

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So I was trying to come up with a way to graphically represent the scale involved concerning the speed of light. I wanted to make a comparison between that speed (~300,000,000 m/s) and the fastest airbreathing craft in existence (the X-43 at roughly 3300 m/s). It's a pretty large gulf.

The simplest approach, I decided, would be to depict the distance traversed by a photon next to the distance traversed by the X-43 in some arbitrary period of time. Trouble is, the ratio is 90,333:1. That's a hard distance to depict in a simple graphic; I don't know of anybody with a screen large enough to display a 90,333 pixel line.

However, what about a spiral? If I could create a spiral with an arc length of 90,333 cm, then I could display it next to a 1-cm line. That would be a pretty striking way of depicting the difference. If an arc length of 90,333 cm was impossible, I could make a perceived arc length of 90,333 cm...for example, by depicting a spiral with 500 turns and an outer diameter of 180 cm (as if the diameter is constant but the spiral is receding back into the screen).

No idea how I could possibly find a way to render that, though. Any ideas? Or any other ideas of how to depict a scale difference of 90,333:1?

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21 minutes ago, Darnok said:

Yeah, I love that illustration, but it doesn't fit so well in a single graphic.

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This is the problem that's been bothering me for a few years. I always wanted to make a scale model of the solar system, but I can choose to depict either scale distances between planets and the Sun, or their relative sizes. Not both in the same model. Either the orbits would bee too big, or planets too small.

I also had the idea of representing the speed of light as a series of LEDs that would progressively light up with the scale speed of light, depicting it traveling from Sun to Earth, but then who wants to sit in front of some LEDs waiting for more than 8 minutes for something to happen.

The difference between the sped of light and X-43 is so huge that all I imagine possible for depiction would be a statement that the light from the Moon to Earth travels for less than 1,5 s, while it would take X-43 almost day and a half.

Second and a half versus day and a half.

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Just now, Shpaget said:

This is the problem that's been bothering me for a few years. I always wanted to make a scale model of the solar system, but I can choose to depict either scale distances between planets and the Sun, or their relative sizes. Not both in the same model. Either the orbits would bee too big, or planets too small.

You can always have a nice little label that says "orbits to scale; planets displayed on a scale 10,000 times greater".

I'm thinking of doing a receding spiral...something like this:

Where perspective makes the spiral look like it is receding into the distance.

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Yeah, that's how it's gonna end up if I ever decide to go through with it.

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If you can imagine the X33 and a photon rasterizing your 1920x1080 monitor, the photon would complete an entire screen refresh while the X33 was about 1% done with just the first line.

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9 minutes ago, Mr Shifty said:

If you can imagine the X33 and a photon rasterizing your 1920x1080 monitor, the photon would complete an entire screen refresh while the X33 was about 1% done with just the first line.

Yeah, I'm gonna have to figure a way to cheat using perspective.