Wikipedia:Reference desk/Archives/Mathematics/2019 August 6

= August 6 =

Figuring out uf there's line-of-sight between two towers
I have two towers, with given heights H1 and H2. The distance between them D is also known. I can easily solve this, but under the assumption the terrain height between them is a known constant. Off course, this is not the real solution. I have, through map, the terrain height for any point between them, but that doesn't help me. I can run a brute force numerical solution, but - is there a non numerical solution? אילן שמעוני (talk) 12:39, 6 August 2019 (UTC)


 * The standard school method is to plot a cross-section of the hills, with scaled distance on the x axis and height on the y axis (exaggerating the scale). It is then very easy to see if line-of-sight is possible.  If the towers are hundreds of kilometres apart (or maybe even tens if you want super-accuracy), then the x axis should be replaced by a scaled great circle (arc length is horizontal distance and radius is scaled Earth radius divided by your exaggeration of height scale).  The accuracy of the result depends, of course, on the accuracy of plotting, so this might not be the type of solution you are seeking.  It will show the critical points at which more accurate trigonometrical calculation would be appropriate.  Dbfirs  13:15, 6 August 2019 (UTC)


 * The classic equation used when setting up radio towers is: 1.2 * sqrt(h) = los distance in miles to the horizon, when h is height in feet. So you plot it out and draw the los from tower a and tower b and if the los lines touch then they can see each other (assuming no physical obstructions).


 * Unless the terrain map follows a mathematical formula, I don't see what else you can do. You have to imagine travelling along the line between the tops of the two towers, then see if it intersects the terrain anywhere. 173.228.123.207 (talk) 04:37, 7 August 2019 (UTC)