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If you are searching for how to figure the curvature of the earth in an easy way, I created a spreadsheet just for you. I wanted to put in a mileage number and come out with the distance of inches, feet, and miles so I created this spread sheet to do that.
There are 2 formulas. The first formula uses the theorem of Pythagoras. The second one is a quick and dirty formula used by Jeranism and I wanted to compare them to see how accurate the quick and dirty is. It is pretty close but the higher the miles, the more inaccurate it becomes.
That is what you will see in the spread sheet. I used the full formula on the calculators that I created below the spreadsheet.
7/23/2015 Excel Spreadsheet Updated
1. Added line of site formula
2. Fixed the curvature mileage formula that showed mileage far greater than the feet
3. Updated sq numbers to ^2.
Get the spreadsheet here. Earth's curvature.
10/6/2015 Horizon Web Calculator
1. I added the ability to use Ft/Mi or Mt/Km to the horizon calculator
2. I added the formulas for the horizon and ft hidden used.
3. I fixed the error with the horizon in ft showing the wrong number. Miles was correct.
4. I added Meters hidden.
10/7/2015 Horizon Web & Earth Curve Calculator
1. I finished the ability to use Ft/Mi or Mt/Km for both calculators
2. I added images for both calculators to show what is being measured
3. I added the formula used to the Earth Curve Calculator
4. I added the centimeter, meter, and kilometer results to the Earth Curve Calculator
The video below is a look into the difference between the Horizon, Line of Site, and figuring Earths curvature. It also explains how to use each calculator.
This image shows the observer's height and their horizon. It also shows the object that is in the distance with the height of that object that is hidden by the curve. The top part of this object can be seen.
Use the calculator below to determine the curve of an observer/camera using their altitude to the eye of the person/camera. If you are going to enter the distance to the object, don't go above 10,000 ft for the height of the observer.
r = earth's radius
^2 = squared
Horizon Miles: Sqrt of ((r + height / 5280) ^2) - r^2
Feet Hidden: (r - r * cosine( (horizon distance - distance) * .00058042)) * 1000
[ ] Feet
[ ] Miles
[ ] Feet or below are hidden
[ ] Meters
[ ] Kilometers
[ ] Meters or below are hidden
Use this picture below as a reference for the earth's curve calculator that is below the picture. Keep in mind that the earth's curve is 360 degrees. You should see the same curve all the way around at that distance.
r = earth's radius
^2 = squared
Curve in inches: Sqrt of ((r^2 + miles^2) - r) * 12 * 5280
[ ] Inches of Curve
[ ] Feet of Curve
[ ] Miles of Curve
[ ] Centimeters of Curve
[ ] Meters of Curve
[ ] Kilometers of Curve
[ ] Line of site to object 2 in Feet.
[ ] Line of site to object 2 in Miles.
Make sure the 1st, largest degree is 90 degrees.
Formula for distance on Globe. mi/tan'paralax.
mi/69.169 (degree of change on sphere) = visual degree difference
Add smaller degree to the visual degree difference
Subtract 180 - 90 - the new number above = p (paralax).
[ ] Total feet in distance.
[ ] Total miles in distance.
[ ] If Globe, Total miles in distance.
[ ] Paralax
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