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Distance of the Horizon |

Given the Height of Eye, Compute the Distance
to the Horizon

Now, how would you figure out the solution to this problem
- one which could become
of great importance in the real world!!

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**

**Well, let's assume you were the one on the left. Your
'distance to the horizon' was computed to be 3 miles after you plugged your
height above water into the formula on this page [or from other modalities]. You
see a light in the distance, and for reasons not explained on this page, you
know it is that of another boat. Yes, you see this light right 'on' the
horizon, 'touching' the Earth' sphere. Now you want to use your VHF radio
to call him. Will you get him?
OK, this is a trick question, in part, but also has some important points to
consider. First, does the other person have his radio on? Well, we
obviously are hoping he does as our boat is sinking. Then, how far will our
radio transmit?
We'll take that up on another web page, but for purposes of making this question
more difficult, let's say that we cannot depend on the line-of-sight rule, but
instead have to do some figuring. Well, though the above diagram says '5
miles', we wouldn't know that, unless we were speaking to the other guy already
and was told that information. Thus, how can we figure that out? Some common
sense comes into play here, and some guesstimating. And, having this web
site on your boat to help you do some figuring may come in handy. We need
to know how tall that boat (light) is, but we don't. So, we'll guess. Obviously
we can figure out that it can be either shorter boat [in height] that is
closer to us, or a taller boat. But how tall. Well, unless it's an ocean liner
[in Jamaica bay??], we can guess that the tallest thing we may see is 38 feet.
(where did I come up with that? Last boat I was on needed that height to clear
the bridges. Pick another number to be even more realistic, and safe). So, believe
it or not if you plug '38' into the above formula, you get only about 8+ miles.
No, you probably don't want to swim it, but, if we ADD THE 8 MILES TO THE 3 THAT
WE KNOW FOR US, we get 11. And we should know whether or not our VHF radio can
handle that.**

**That was easy. In reality, we most often would be working
with 'one side' of the above diagram. If we don't see it coming over the other
side of the Earth [horizon], then we can assume it is WITHIN the 3 miles.
Probably less.**

**Here is a very practical and good homework assignment. When
we look at charts (and we all should have one aboard, a real one, not just an electronic
image on a GPS. They fail, you know.) you will note that they will indicate the
height above water/land of certain structures. Perhaps a water tank that
is near the shoreline. You can use this knowledge to figure out how far you are
from there. Send me your answers.**