Beacon over/below horizon

[Jan Hollan <jhollan@amper....muni.cz>]

> > > If a beacon is mounted higher than 267 feet above lake level, it can be
> > > seen directly at 20 miles.

> If the developers have their way and place it back at its original spot on
> the top of the mast, it will be at 555 feet above ground and visible
> directly to someone on the ground 31.7 miles away. 

The visibility reaches mostly just a bit farther, due to refraction. I
remember a nautical formula valid for ``standard refraction'' and some
mean Earth curvature: the horizon on a calm sea is some 2.08 * sqrt(h/1m)
nautical miles far from a point at height h above the sea. There is little
change in refraction influence when the flat surface is less then 500 m
above sea level; refraction makes the horizon usually to be some 8 per
cent more distant.

Using statute mile and foot the formula translates to 
 2.08 * (1852/1609.344) miles * sqrt(h/1ft) * sqrt(0.3408), i.e. 
                   1.40 miles * sqrt(h/1ft)

> If the viewer is well off
> the ground, as pilots often are, it will be visible for a much further
> distance, subject to attenuation by the atmosphere of course.

For a person swimming in the lake, the visibility of the beacon would
reach to 33.0 miles (1.4*sqrt(555)), eyes 5 feet above the lake would add
another three miles (+1.4*sqrt(5)). So the direct visibility is some 36
miles, on flat terrain. A pilot flying at a height of 3000 feet could spot
the beacon from 110 miles. 

Of course, a temperature inversion over a very cold lake could make the
refraction a lot stronger, making the visibilities another ten(s) per cent
larger. However, sunrise or sunset are more adequate tools for studying
such effects (see, e.g.,
 http://www.geocities.com/CapeCanaveral/Runway/4096/polar.html ), 
no obtrusive beacon is needed... 

Ahoy,  (a most popular Czech greeting)
Jenik  (an occasional sailor from a country with no sea)

PS. 
 we are now trying to include light pollution prevention into the 
``Clean Air Act'' now being dealt with in the Czech Parliament. It fits
nicely among other pollution sources, just the emissions are to be
measured in lumens instead of kilograms. The proposed changes (in Czech) 
are inside
 http://amper.ped.muni.cz/light/zakon_oo