h=Height of aerial above sea level
r=Radius of the earth (3440 Nautical miles)
d=Distance to Horizon
Using Pythagoras d²=(r+h)²-r²
To calculate the Radio Horizon because of refraction we
achieve this by pretending the Earth has a larger radius which we
the equivalent Earth radius Re
which is normally
4/3r in the UK (4587 NM).
There are 6076 feet in a Nautical Mile
The radio horizon between the transmitter and receiver is the
of the horizon of both masts.
Note the size of the ship makes a considerable difference to the
Reception beyond this range is caused by propagation
conditions and will be flukey.
This was checked to see if a ship could actually be below the
The graph shows the angle down to a ship for different receiving
heights. For a ship 1nm from the aerial and the aerial 1000 feet
sea level the angle down would be 10°. From the same aerial
horizon would be under 1°.
To Horizon sin(90-α)=r/(r+h)
To 1 nm tan α=h/d
This significance is high gain collinear aerials increase
gain at the expense
of vertical beam width. The graph shows this could be relevant
high gain aerial close to and much higher than
the ship's aerial ie the ship is "below the radar"
For example the Cushcraft
specification quotes 7dBi gain and a beam width
of 7 degrees. The dipole "donut" becomes a "biscuit" !
For more technical info see the references on my aerial
the Horizon Propagation