Perceived Distance on a gaming table?
#1
I have a question about gaming scale for everybody. I think I have it figured out, but it is a little complicated so a second opinion on my math would be very helpful. What is Perceived Distance you may ask, and why is it important to me? Simply put how much detail is really needed on that piece of terrain to make it look realistic! To know the answer to that question you need to know what something would actually look like from a distance, were it appears to be the same size as your gaming miniatures are.

Two 18mm (1/100) miniatures placed on a table one meter apart are 100 meters apart in game scale. That part is very easy to calculate since it is a simple matter of converting scales. The problem is when you want to calculate how far away that miniature appears to be to someone standing over that table. This is a range finding formula that tells you how far away a miniature would be from you if it was real size.

In the real world range finding formulas are very straightforward, so I decided to just figure out a way to modify one four use with miniatures. Military grade binoculars have stadia lines that are used to measure the size (angle) of an object from any distance. These are marked in minutes of angle or mils depending on what system of measurement you have. As long as you know the size of the object and the angle then it is possible to calculate the distance to that object.

Obviously a range finding reticle isn’t practical for us, but using a tape measure is so the first step is to get the angle mathematically. The formula for this is (Tangent: tan(θ) = Opposite / Adjacent). Not being terribly good with math I simply use a “Right-angled Triangles Calculator” that I googled. As an example an 18mm tall miniature 2 meters away is .515 degrees. The angle is then converted (so that we can use the formula) to mils by multiplying by 17.45 (number of mils in a degree). This gives a reading of 8.997 mils. We now have a simulated reticle reading that can be used in a standard ranging formula.

Using my handy range finding slide rule I am able to determine that a 6’ tall man that is 9 mils is about 224 yards (205 meters) away.

Four those of you who don’t have a range calculator the formula is.
(Object Size in Inches X 27.78) / Object Size in Mils = Range in Yards
(Object Size in Yards X 1000) / Object Size in Mils = Range in Yards
(Object Size in Meters X 1000) / Object Size in Mils = Range in Meters

So at first I thought the difference between the scale distance and the perceived distance is very close. This surprised me because I was expecting a much larger difference. Then it occurred to me that I was comparing it incorrectly. My eyes are 838 mm above the table, and the 2000 mm of distance is actually the Hypotenuse. The table scale distance is only 181.59 meters. That is a difference of 18.9 meters (to scale) between the scale distance and the perceived distance.

At this point if you have been paying attention you have probably noticed that I have come up with a very elaborate way of getting the same number I would have gotten by just measuring the distance and multiplying it by the scale. I really thought that it would be a bigger difference, so I learned something, and it was very interesting finding it out. The perceived distance (in scale) is the same for us (out of scale) looking at a model as it is for everything that is in scale.
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#2
(03-07-2016, 12:56 PM)Vet Sgt Wrote: I have a question about gaming scale for everybody. I think I have it figured out, but it is a little complicated so a second opinion on my math would be very helpful. What is Perceived Distance you may ask, and why is it important to me? Simply put how much detail is really needed on that piece of terrain to make it look realistic!

<< very long snip >>

At this point if you have been paying attention you have probably noticed that I have come up with a very elaborate way of getting the same number I would have gotten by just measuring the distance and multiplying it by the scale. I really thought that it would be a bigger difference, so I learned something, and it was very interesting finding it out. The perceived distance (in scale) is the same for us (out of scale) looking at a model as it is for everything that is in scale.

The only part of your maths I can check is that, yes indeed: 1:100 is 18mm. (But I have a simple chart for that.)

Also, every three inches is 25 scale feet at that scale. So, you had two objects one meter apart? I calculate that they are 328 scale feet apart. Your eyeball was viewing from 2000mm? Then your scale distance to the objects was twice 328 = (656 ft).

What I am not following is how any of this tells you how much detail to incorporate. Particularly if viewing things through magnification (binoculars were mentioned at one point?)


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