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Earth Curvature Calculator

Earth Curvature Calculator analyses how much of a distant object is obscured by the curvature of the Earth and finds the total height of the target that is hidden behind the horizon. Just give the eyesight level distance to the object details and hit the calculate button to avail the distance to the horizon, obscured object part easily.

Choose a Calculation
Distance To Object:
Eye Sight Level:
Distance To Horizon:
Obscured Distance:

Earth Curvature Calculator: Calculating your distance to the horizon, the height of the target hidden behind the horizon of an Earth curvature is a complex process. But by using this handy Curvature of Earth Calculator, you will get the result quickly. Have a look at the simple steps to find the distance to the horizon, how far you see before the Earth curves and formulas. Also, get the definition of earth curvature, steps to solve it for a better understanding of the concept.

How to Find Obscure Object Part, Distance to the Horizon?

Below given are the steps to calculate the distance to the horizon and obscured object part easily.

  • Get the distance to the object, eyesight level details.
  • Add Earth's radius to the eyesight level and square the sum
  • Subtract it from the square of the Earth's radius to check the distance to the horizon.
  • Add squares of the distance to the horizon, distance to the object and Earth's radius
  • Subtract it from the multiplication of double of distance to the horizon, distance to the object.
  • Apply square root to the result
  • Subtract it from the Earth's radius to get the obstructed part.

Earth's Curvature Definition

Let's imagine, you are looking at the sea. You can be able to see endless blue waters, shimmering in the sun. You can make a line that dies the seawater and sky and that line is called the horizon. When you are moving toward's the horizon, then you can see the shape of the target that is hidden behind the horizon because the Earth shape is similar to the sphere.

The surface between you and the target is bulges up a bit. Due to these bulges, it has obstructed your view. The measuring of the bulge is called the earth's curvature and it is represented as the height of the bulge per km or per mile.

Obstructed Height of an Object

To know the exact distance between you and the horizon, you have to know two values i.e your eyesight level, radius of the Earth. The equation is as follows:

a = √[(r + h)² - r²]

Where,

a is the distance to the horizon

h is the eyesight level above mean sea level

r is the Erath's radius, which is 6371 km or 3959 miles

Earth Curvature

To determine the obstructed height of an objet, you have to know the distance to the horizon, distance to the object, and eyesight level. The formula to calculate the object obstructed height is given below:

x = √(a² - 2ad + d² + r²) - r

Where,

d is the distance to the object

x is the obscured object part

Example

Question: If the distance to the object is 28 miles and the eyesight level is 0.0021 miles, find the distance to the horizon and obscured object part?

Solution:

Given that

Distance to the object d = 28 miles

Eyesight level h = 0.0021 miles

Distance to the horizon a = √[(r + h)² - r²]

a = √[(3959 + 0.0021)² - 3959²]

= √(15,673,697.627 - 15,673,681)

= 4.08

Obscured object part is x = √(a² - 2ad + d² + r²) - r

x = √((4.08)² - 2 x 4.08 x 28 + 28² + 3959²) - 3959

= √(16.6464 - 228.48 + 784 + 15,673,681) - 3959

= 0.07228

Therefore, the distance to the horizon is 4.08 miles, obscured object part is 0.07228 mi.

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FAQ's on Earth Curvature Calculator

1. What is the Earth's curvature?

The curvature of Earth is nothing but the measure of the bulge. Bulge is the surface between the ship and the person in the sea. The Earth curvature is expressed as the height of the bulge per kilometre or per mile.


2. What is the formula of curvature of Earth?

The formula of Earth's curvature is a = √[(r + h)² - r²]. Here, a si the distance to the horizon, h is the eyesight level above mean sea level, r is the Earth's radius.


3. How far do you see before Earth curves?

The curvature of Earth is 8 inches per mile. When a target person of 5 feet or so off the ground, the farthest edge that you can see is 3 miles away.


4. How does Earth curvature affect weather?

The Earth curvature affect the weather by the latitude or distance from the equator. The temperature drop at an area is because of the curvature of the earth.


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