Re: (TFT) Hex and Earth LOS ranges

["Craig W. Barber" <craigwbar@comcast.net>]

Useful tidbit for RPGs:

According to my old "SURVERYING" textbook (Moffitt/Bouchard. Harper and Row,
NY):

On *EARTH* (or an equivalant body, which CIDRI is not but lots of places
are):

c = 0.667 K * K, where c is the Earth's curvature in feet and K is the
distance in miles.  Reversing it, we take curvature as altitude or height,
dividing and taking the square root instead do determine line of sight, based
on curvature only, for a body of radius 3959 miles or equivalent local radius.

(Reversing the equation for you:    visible range in miles =  SQRT ( height in
feet / 0.667 ) )

So for an altitude of 66 feet (say, standing on the roof parapets of a 5 story
castle) vis range would be 10 miles.

+++

Refraction, as Moffitt & Bouchard remind us, messes us up thereafter.
Usually, r light bends towards the Earth's surface... but even that's not
always true!

c+r = 0.574 K * K

reversing it:

visible range in miles = SQRT ( height in feet / 0.574 )   <--- USE THIS ONE
UNDER EARTH NORMAL CONDITIONS

Remember the square root.

+++

Finally, remember all the caveats available to the GM:

1.    "Earth?  What is this Earth you speak of?"  If Cidri is a ringworld,
then visibility is actually infinite.  (Think about cosmonauts looking down
from LEO: it's easy to see through a rapidly thinning layer of air only a few
miles thick.  Ditto for Louis Wu looking up at the Arch.)  This one is my
fav.
If Cidri is a monster sphere, then the equations need adjustment.  (Have fun.)
If it's flat (why not?  makes a lot more structural, dynamic and gravitational
sense than most options) then visibility is theoretically "infinite" but
functionally sharply limited by atmospheric scatter: 1 mile of SURFACE air
with normal dust in it is "clear", 10 miles is misty, 100 miles of normal
surface air is a wall.  (NOT equivalent to the cosmonauts view.)
2.    Not all places on Earth are perfectly spherical, in fact, even the
oceanic surfaces have wide altitude variations due to gravitational
anomalies.
3.    "My my my, it sure is hot today...  Hey!  The lost city is right over
there!  Can't be more than a mile away from us!  We won't have to go very far
into the Desert of Sure Death!"
4.    "It's just slightly misty.  Visible range is EXACTLY 250 megahexes.  Now
roll 3 vs. IQ, damnit."
5.    "Sorry, General Pickett, didn't I mention that swale?"
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