How far is the horizon from the shore?
The formula for distance from the viewpoint to the horizon on any sphere is d = square root of (2Rh) + (h squared) (I wasn’t sure if superscripts would show up) Where R is the radius (of the Earth or any sphere) h is the height of observer d is the distance from observer to horizon (note: both R and h in this equation must be given in the same units) All calculations depend on the water’s surface being completely smooth, no waves! Sounds like a very calm day. Using this a person with his eye level at 5 feet 8 inches above water could see the horizon 2.92 miles away. Metric: 1.73 meters and 4,695.06 meters. If you are standing on a ship 30 feet above the water line, the horizon is 6.71 miles away. Metric: 9.14 meters and 10,794.12 meters. If you are standing on a hill 100 feet above the water, the horizon is 12.25 miles away. Metric: 30.48 meters and 19,707.29 meters. .
