Distance to the Horizon

The distance to the horizon is determined by the following formula:

    Distance in nmiles = 1.17 * (h) ^ 0.5

Where:
    h is the height of the observer's eye in feet
    Nautical Mile (nmile) = 1.852 km = 6,076 feet = 1.151 statute miles

For easier calculations, you can assume that a nmile is equal to 2,000 yards (it's close enough).

If you'll work with simultaneous equations, you can calculate (speculate) how far you can see an object above the horizon.

For instance, assume that your eyes are 100 feet above the surface of the sea. That means that you can see:

1.17 * (100) ^ 0.5 = 11.70 nmiles to the horizon.

Assume that an observer on top of an object is 64 feet high. So, he could see:

1.17 * (64) ^ 0.5 = 9.36 nmiles to the horizon.

So, assuming perfect visibility, etc., etc., you could see each other 11.70 + 9.36 = 21.06 nmiles.

That's the simple answer. However, there's a problem with the fact that light rays bend (refract) as they pass through water vapor. And, of course, there's more water vapor the closer you are to the sea surface. So, getting a range on a target that is over the horizon is pretty much hit or miss (pun intended). That's one of the reasons optical systems lose their accuracy the farther away they are from a target.

For radar ranging, this refracting works in a favorable way in that the radar waves will actually travel about a third farther than will lightwaves.  So, to determine the effective radar range, use the above formula and multiply the result by 1.33.  The other advantage that radar has here is that a target too small to be spotted by an optical system - such as a pole mast or whip antenna - may still be enough to send back a reflection large enough to be detected by the radar system.

Tony D.

Speaking as an old Gunfire Control Tech., the simple answer is that 'Line Of Sight', or LOS is simply the direct line between your weapon and the targets 'Present Position', as opposed to the 'Line Of Fire', or LOF, which is the bearing and elevation you aim the weapon at to deliver fire onto the target at his 'Future Position'.  The difference between LOS and LOF is referred to as the 'Lead Angle' and there are MANY factors involved in determining the LA.  You might also be interested to know that the LOS can vary greatly between the weapon and the controller which is directing it. That's why proper battery alignment is CRITICAL to effective fire control.  Part of the procedure for battery alignment, involves mounting telescopes in the gun barrels and on the gun director, and then correcting the gun system to aim both scopes at the same star in the night sky; called 'shooting the stars.'  It only takes about 2 months of concentrated studies to understand it all, and after leaving the service, you don't have much need for all the stuff you learned.  That why you end up giving people long-winded answers to short questions, like I just did.  Old sailors NEVER run out of sea stories!!!!

Bye,
Gunner Morris
(Lloyd D. Morris)
.

Back to the Naval Technical Board