Distance to the Horizon

[Carl]

On a prefectly clear day I am setting in my boat looking out over the water of Lake Michigan. How far is the horizon and how is it figured. Any information would be appreciated.

[EyeBoy]

Carl;
Back in the old Navy days, and if I remember correctly; if one is standing upright with their feet at the water surface, the distance to the horizon is approx 15 miles. Of course, that would be with a calm falt surface. No 10 foot waves. Maby REW or someone would have more precise data.
ON-PLANE!!!TOM

[tim(WI)]

That would depend on your elevation above sea level. You can find the formula in THE AMERICAN PRACTICAL NAVIGATOR bowditch(1995) under navigational calculations/ D=1.17 SYMBOL FOR PIE hf. hf being height of eye of observer above sea level in feet.

Or you can take the easy way and look in USCG Light List for the Great lakes on page xxxii it has a GEOGRAPHIC RANGE TABLE.

[JeffC]

I always thought it was 7 miles the direction your looking in.

[GullGuide]

It also depends on atmospheric conditions such as humidity, dust in the air, etc, etc. Visibility is never a constant thing and judging how far away the horizon is would of course be affected by visibility.
>"////=<

[RANGER]

LAST EDITED ON Jun-13-01 AT 09:29AM (CST)[p]2.3 miles standing on the beach at the waters edge on a 6 ft tall person. It's a fact! I didn't believe it either.

Variables occur when you start adding in a boat, standing/sitting in a boat, etc. BUT 2.3 miles is the figure at 6 ft off the water.


RANGER


"KEEP YOUR LINES WET, YOUR POWDER DRY and THE BEER COLD!"

[Carl]

That sounds right. Could you give me the equation. Thanks

[RANGER]

Carl,

I don't have it with me. It is at home. Maybe there is someone who does have it handy, if not I'll try to post tomorrow with the formula. Really surprised me though, I always thought it was 5 - 7 miles - NOT!


RANGER


"KEEP YOUR LINES WET, YOUR POWDER DRY and THE BEER COLD!"

[Firetiger(MN)]

LAST EDITED ON Jun-13-01 AT 02:10PM (CST)[p]2.996 mi. = (1.496 x height)^0.5

This equation is used to calculate the distance of FM radio propagation, i.e. Line of Sight (LOS).

Same as below.

[EAGLE EYES]

Distance to the horizon(sea horizon) in miles, equals 1.224 x the square root of the height. example: 6ft. person standing at sea level would be able to see 1.224 x 2.449 = 2.99 miles.

[Hawgeye]

But that formula is considering seeing something at sea level. If you are looking at something that is above sea level, that would change the formula. I would think because the earth is somewhat round, (not technically) you would be able to add your height above sea level plus the objects height that you are looking at, take the square root of that and get your distance. In other words, if you are 6 feet tall and you want to see something 6 feet tall, that would be 12'. The square root of that is about 3.465 X 1.224 = 4.24 miles.

Also, if you are looking for an exact value, you have to use the height of your eyes not the top of your head for those who are jugheads like me out there! :)

[EyeBoy]

LAST EDITED ON Jun-13-01 AT 05:33PM (CST)[p]I knew it! With the high caliber of individuals that frequent this forum I knew that we would get the (A) answer. LOL, boy was I way off the mark. Brain fade due to advanced age. I had no idea that it was that short of a distance. Maby what I remembered was from the deck of a CVA. Great posts.
ON-PLANE!!!TOM

[Firetiger(MN)]

The original question asked the distance to the horizon. Adding a 6' or whatever size object out on the horizon completely changes the logic. Also it was stated that he was on the water looking over the water at the horizon which means sea-level/altitude is not a factor.

The equation given is used in determining the LOS of FM radio towers and is the same as if it were a person standing there instead of a tower.

[Carl]

Thanks for the information. I also found a sight that has the information.

http://www.boatsafe.com/nauticalknowhow/distance.htm

[Hawgeye]

Firetiger,

I didn't mean to sound contradicting. It was meant somewhat as humor. My point being that if you were trying to see a boat or a hill or a tree or a person, you might be able to see farther than the 3 miles listed......thanks for the information.

[Scott Richardson]

Interesting question and thanks for the answers, especially the web site above. It has a clear explanation that encompasses the impact of the height of an object in the distance, i.e. a lighthouse, has on the result. I too always had thought it was something like 11 miles to the horizon...some bit if incorrect information I picked up somewhere. Thanks!

[Banker]

The boatsafe.com website is a great resource and I often use it to look up answers to my general boating questions. However... not to nitpick this topic to death, but the "Distance to the Horizon" formula produces a result that is measured in NAUTICAL miles. To convert nautical miles to statute miles, multiply the result by 1.15.

[EB]

I always wondered as a kid why I needed to pay more attention to math. If only somebody could have explained that it had something to do with boating/fishing I would have had a completely different attitude. When my little boy gets to school age I'll try to make sure he understands that some of the stuff they are trying to teach might not seem relevant now, but when he gets older maybe he can help his dad calculate information when we are out in the boat. Tight Lines-Eric