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For example, for an observer B with a height of h B =1.70 m standing on the ground, the horizon is D B =4.65 km away. For a tower with a height of h L =100 m, the horizon distance is D L =35.7 km. Thus an observer on a beach can see the top of the tower as long as it is not more than D BL =40.35 km away.
The height of the elevated point plus the Earth radius form its hypotenuse. If both the eyes and the object are raised above the reference plane, there are two right-angled triangles. If both the eyes and the object are raised above the reference plane, there are two right-angled triangles.
The radar horizon with an antenna height of 75 feet (23 m) over the ocean is 10-mile (16 km). However, since the pressure and water vapor content of the atmosphere varies with height, the path used by the radar beam is refracted by the change in density. With a standard atmosphere, electromagnetic waves are generally bent or refracted downward.
Graphs of distances to the true horizon on Earth for a given height h. s is along the surface of Earth, d is the straight line distance, and ~d is the approximate straight line distance assuming h << the radius of Earth, 6371 km. In the SVG image, hover over a graph to highlight it.
Range (r) = approximate height of object (h) × (1000 ÷ aperture in milliradians (a)) r = h(1000/a) → where r and h are identical units, and a is in milliradians. r = h/a → where r and h are identical units, and a is in radians. The above formula functions for any system of linear measure provided r and h are calculated with the same units.
Equation [3] involves the average velocity v + v 0 / 2 . Intuitively, the velocity increases linearly, so the average velocity multiplied by time is the distance traveled while increasing the velocity from v 0 to v, as can be illustrated graphically by plotting velocity against time as a straight line graph. Algebraically, it follows ...
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