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ryleyra

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Reply with quote  #1 
I have been holding onto this image for a while. I had put it together in order to post it in my original "What Size is a Sector" thread. However, there have been a lot of posts on the subject of the game scale lately, so I thought it might deserve a totally new thread.

This is a diagram of our solar system. The orbits of the planets are shown in the proper scale with regards to each other, but except for the exception noted, the planets themselves are not to scale. I did not try to render the elliptical orbits of the planets, but instead used the average distance from the sun in all cases.


Solar System.png 
There are five recommended sector sizes (outlined in red) displayed on this map. As you can see, the progression of scales from largest to smallest shows that for all but the last 1km/unit scale, even a planet like the Earth is actually too small to be rendered at its true size. Even the orbit of the Moon can't be made out at anything larger than 30 km/unit.

We could make the scale of Artemis any of these five sector sizes:

6000 km/unit - This sector is 4 AU across, and covers the inner planets and the asteroid belt. This is clearly the scale used by the BSG mod, although it could be a little larger. At this scale, however, Warp 1 is much faster than the speed of light. It should take 8 minutes to get from the Sun to Earth, but instead it would take about 40 seconds. You may assume that time is contracted by a factor of 12, though, for playability.

500 km/unit - I believe this is the scale used by the non-scripted game modes. The sector is 1/3 AU, as stated on the image, or 50 million kilometers. Warp 1 is approximately the speed of light, and the sector is large enough to represent an outpost on the frontier. However, this scale isn't good for representing planets, as they'd have to be scaled up to appear larger than the other game objects.

30 km/unit - At 3 million kilometers, this is a better scale for representing planets or gas giants. As shown in the image, the Earth and Moon could be rendered as two distinct objects, although they'd be very close together. Unfortunately, Warp 1 at this scale is only 1/16th of the speed of light, making it more of an "afterburner" than actual Warp.

5 km/unit - At 500 thousand kilometers, this would include both the Earth and the Moon in its orbit around the Earth. Since you can see the Earth and Moon to scale in the image, you can see how small they would have to be. Jupiter would be about halfway between the Earth and Moon, so it would take up a good quarter of the sector. As above, Warp 1 would only be 1/100th of the speed of light.

1 km/unit - Naturally this would be 100 thousand kilometers. It would include the Earth, but not the Moon, and Warp 1 would be 1/500th the speed of light. I suspect this is the smallest usable size, although 500 m/unit might be fine. At that distance, though, you start dealing with orbital mechanics, which can complicate things. As has been noted, 1 m/unit would be within the radius of the Earth, as would anything less than 130 m/unit.

I have some interested observations about this solar system map as well.

First, it is interesting that it takes light almost exactly 500 seconds, or 8.3 minutes, to reach Earth from the Sun. That means the distance from the Earth to the Sun is a multiple of the speed of light. The speed of light is very close to 300,000 km/sec, and an AU is very close to 150,000,000 km, meaning there is a factor of three that shows up a lot in these astronomical distances.

Thom designed his simulator so that Warp 1 is 600 units/second, and so again, there is a factor of three in the speed of Warp Drive. That's why 5, 3 and 6 keep showing up in the sector sizes.

ryleyra

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Reply with quote  #2 
All right, this is not exactly approaching the issue from the same direction as above, but I was reading an article on this site here: http://www.livescience.com/33895-human-eye.html which states that it is possible for the eye to distinguish a "human scale" object at 3 km. The example given was the headlights of a car, which can be assumed to be about a meter apart.

As above, I can use a picture to more clearly show this:

Untitled1.png

For the example above, x is 3000 m and y is 1 m. I decided to verify this, and found that what we call "20/20 vision" is defined to be the ability to resolve two points of light separated by a visual angle of one minute of arc. The lowest row in an eye chart is designed to be about 5 minutes of arc across for a person standing 20 feet away, thus the "20" in "20/20" (It's 6 meters in Europe) That smallest row is 8.86 millimeters tall, so one arc minute would be 1.772 mm tall.

Converting to the same scale, we could say that at 3000 meters, the eye would be able to distinguish two headlights 0.886 meters apart, which is a bit smaller than the 1 meter given above, but that could be "fudged" to give a round number. Let's note that since our diagram above is an isosceles triangle, the ratio x/y is a constant. The relationship between distance and height is linear.

Using that comparison, if we were to use the length of the Artemis as y, 100 meters, then the distance x would have to be 300,000 m, or 300 km. In Artemis, a ship can be distinguished at 5000 meters, possibly as much as 7500 meters if the visual range to when an object first appears is used.

My conclusion here is that the scale of the Artemis can't be the same as the scale of the sector. Even if we just define it in terms of "units", the Artemis as displayed on the screen is at least 40 times the units being defined for distance.

janx

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Reply with quote  #3 
Good research Ry!

Should screen size also come into play for consideration of "scale" or relative size on screen?

Right now, whether I use a 60" TV at 1920x1080 or a 14" laptop at the same resolution, the game doesn't know this.

As a result, the Artemis at 3km away on the laptop is super-duper tiny.  But on my 60" screen, it's plenty big enough.

As a thought experiment (meaning don't expect Thom to actually change the code), what if the game knew how big my screen was.

And that it made the display mimic the visibility of a virtual window out the ship.  Thus, the 14" display represents a 14" viewport with a narrow field of view.  If the Artemis at 3km would appear to be 1/2 inch wide in real life (made that up), then on screen, I could measure it and get the same 1/2" width.

Likewise, on my 60" TV, it represents a wider field of view, but the artemis would still be 1/2" wide per the same math that perspective would be computed by (as measured with a ruler on my screen).


ryleyra

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Reply with quote  #4 
Quote:
Originally Posted by janx

Should screen size also come into play for consideration of "scale" or relative size on screen?


This gets back to a TV joke.

When they show a movie on the TV, they always print a disclaimer, "This movie was originally made for movie theaters. The image has been adjusted to fit your television." The joke is, "How do they know the dimensions of my TV?" [biggrin]

Of course the answer is the image isn't adjusted to the size of your TV, it's been adjusted to fit the aspect ratio of your TV. Your TV automatically scales the image to fit its dimensions.

At any rate, the size of the image on screen isn't relevant, it is the ratio between the distance the ship is away from you and its length. If your monitor is smaller, then the distance (which is an illusion anyway) is just smaller. How far you sit from the screen will also change how big you perceive the image to be.

What I would expect to be "two arc seconds", as picked up by the eye would be two pixels across the screen. This would probably not be 5000 m away, but the image disappears at 7500 m, and I would expect for most monitors, a ship at that range would be two or three pixels across. Note also you usually see ships face on so it would be 50 m wide, instead of 100 m long.

Quote:

As a thought experiment (meaning don't expect Thom to actually change the code), what if the game knew how big my screen was.

And that it made the display mimic the visibility of a virtual window out the ship.  Thus, the 14" display represents a 14" viewport with a narrow field of view.  If the Artemis at 3km would appear to be 1/2 inch wide in real life (made that up), then on screen, I could measure it and get the same 1/2" width.

Likewise, on my 60" TV, it represents a wider field of view, but the artemis would still be 1/2" wide per the same math that perspective would be computed by (as measured with a ruler on my screen).


This would be interesting, but probably would complicate play. It's probably better to scale the image to the size of your Mainscreen, so a little monitor shows you just as much information as a big screen TV. You really don't care what size the ship is, you just care what position is has with respect to other ships.

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