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(TFT) altitude
If I make an equilateral triangle ABC, I can form a right triangle ADC by
dividing ABC in half, thus dividing the subtending angle of AB in half.
Tan (ADC) = length of opposite side / length of adjacent side = AD / DC
Clearly, this ratio is getting smaller as C moves further out. In fact, the
limit as C moves away from AB is 0, and the Tangent of an angle is zero when
the angle is zero.
If AB is 1.3m then AD is 0.65m...
Of course this is only half the question, the other part is concerned with
the resolution of the human eye.
With favorable terrain and weather conditions it is certianly reasonable to
assume that a M1A1 (Dimensions: Length: 32.25ft (9.83m) Width:11.98ft
(3.65m)) can be "spotted" at distances over 3000m, subtending an angle of
about 0.06 degrees or just around 1 mil.
On a computer display at the start of "high-res" (640 by 480 pixels) the
field of view would have to be reduced to about 36 degrees to display the
tank as a single pixel.
Double the field of view and you can't see the tank after about 1500m.
...
Things like night vission, eagle sight or orcs in bright sun can be
described as resolution, and stuff like great helms can limit field of
vision, making back stab oppertunities and etc. crop up more frequently.
Note the locus of verteces for a fixed angle subtending a fixed segment is a
circle. If a segment defines a cord of a circle, then any point on the
circle outside the arc formed by that cord subtends that cord (or segment)
at a fixed angle.
Mark your hex centers on transparency film (leave the hexes off), set your
altitude in Google Earth and print.
Bloody feet.
1.3m ~4.25ft.
4.25 * 9 (8 by 10 hexes is a battle map so this is a rough average) =
38.25ft
3000 meters = 9 842.51969 feet
A rough rule of thumb has battle maps subtending about 1 mil @ ~10,000ft.
This suggests that looking straight down from an altitude of about 100 feet
with a field of view of about 180 degrees a Figure should see the best part
of 4 battle maps...
I can drop the altitude in Google Earth below 10 feet.
12 foot tall giant looking at their feet?
< groans at bad pun >
So the question becomes, should I use the same number of hexes to cover the
sphere reguardless of its area?
In other words, are there the same number of infinate points along the
circumfrence of a circle of radius 1 as there are along the circumfrence of
a circle of radius 2?
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