Do I really NEED Tropo to hear the Puerto Rican FM Broadcast Station? Or are we just close enough to do this line-of-site?

 

WIDI 99.5 FM from western Puerto Rico continues to put a full quieting signal into the eastern Dominican Republic.   The station is so regularly strong that this made me wonder if I am really using tropospheric ducting to hear it.  If I was using tropo ducting, I think there should be some variation in signal strength over the course of 24 hours right?  But it is always strong.  Why?  

I checked the distance:  97 miles.   With its antenna at 2800 feet, its visual horizon will be 64.8 miles away.  I am about 98 feet above the ocean.  This means my horizon is 12.22 miles away.  There appears to be a gap, right?  I mean 64.8 + 12.22 = 77.02 miles.   So it looks like there is a gap of about 20 miles.  

But wait!  Mike WN2A reminded me that there is a difference between radio line of sight and visual line of sight.   Radio line of sight = 4/3 of visual line of sight. 

AI explains where the 4/3 factor comes from: 

The radio horizon appears longer than the visual horizon by a factor of about 4/3 due to atmospheric refraction, which bends radio waves slightly downward. To simplify calculations, this effect is modeled by treating radio waves as if they travel in a straight line over a larger, "effective" Earth with a radius 4/3 times the actual radius. This increased effective radius allows radio waves to "see" further over the Earth's curvature, extending the line-of-sight range compared to what is seen by the human eye, which is not affected by atmospheric bending to the same degree. 

So that puts WIDI's radio horizon at 86.4 miles.  My radio horizon is 16.16 miles.   86.4 + 16.16 =  102.56 miles No gap.  We should be able to hear WIDI, even without tropospheric ducting.