Graphic depiction of ratios and relative speed

[sevenperforce]

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?

[whitelancer64]

Unless you have a very specific need to show this visually, the best way is to just describe it. For example, say light travels .9 k in the same time it takes the X-43 to travel one cm.

[sevenperforce]

Unless you have a very specific need to show this visually, the best way is to just describe it. For example, say light travels .9 k in the same time it takes the X-43 to travel one cm.

It's for an illustration in an article, so I kind of need a visual punch.

[MrHollifield]

How about comparison with familiar, related items? For example, if the goal line on a football field is 3 inches wide, the photon would cover 62.73 football fields (including end zones) while the X-43 crossed the goal line. Most US readers would recognize the football field and be able to picture it, even if the fields were not shown at the same scale as the goal line.

[whitelancer64]

I don't think there's any way to compare it directly to scale.

I think what I would do is something this: have a picture of the X-34, then say, In .01 second the X-34 travels its length, 4.74 meters. But in that same time, light travels nearly 3,000 km. Find something close to 3,000 km long, like the length of Japan, and have that as a comparison image.

[J-V]

Unless you have a very specific need to show this visually, the best way is to just describe it. For example, say light travels .9 k in the same time it takes the X-43 to travel one cm.

It's for an illustration in an article, so I kind of need a visual punch.

Just use a stack of paper, like in https://xkcd.com/1162/

[Nomadd]

 I actually did that in a radio class once. I used a marathon with a human runner against a photon, but if you used the X-43 you'd get something like, by the time the photon finished the marathon, the X-43 would have traveled 2cm.

[KristianAndresen]

This is a solved problem in science, you use a logarithmic scale, and instead of worrying about the reader not understanding what "logarithmic" is, you just explain that taking a step to the right means multiplying by a factor rather than adding a fixed amount.



You can add things like alpha radiation speeds to fill out the scale.

In science journalism, there is way too much "football field" visualisation of large and small numbers, and these visualisations are way too often an attempt by the journalist to make the numbers either seem "really big", or not, depending on what makes the story "more impressive" and therefore sellable. A very common way this is done is by choosing the dimension, volume or length, when describing sizes, according to your goals. This trick has often been employed to make dinosaurs seem bigger than they are. A serious journalist trusts the science to sell itself without manipulation, and trusts the audience to not need things dumbed down.