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26 Short-Hop Notebook Math Class There is something beautiful about a formula. It doesn’t matter if the formula is on our E6B, the inner workings of a G1000, or in the head of Stephen Hawking; there is a clarity in math about the way the universe works that is both elegant and profound. Sometimes it’s simply fun. Perhaps not strangely, mathematics can answer a more poetic question. “How far away is the horizon? How much earth can I see?” The math is pretty simple. D = 112.88 km v (h). Or, distance equals 112.88 kilometers times the square root of the height of the observer, expressed in kilometers. If 1,000 feet equals 0.3048 kilometers, and the square root of 0.3048 is approximately 0.552, then distance = 112.88 times 0.552, or distance = 62.309 kilometers. 62.309 kilometers = 204425.8530 feet. Or, to put it simply, if you’re 1,000 ft AGL (above ground level), the horizon is 38.71 miles away. 2,000 ft AGL = a horizon at 54.76 miles. 4,000 ft AGL = a horizon at 77.44 miles. 8,000 ft AGL = a horizon at 109.517 miles. But what is the total landscape in view? Pi times the radius squared is the area of a circle. If, at 2,000 ft AGL, the radius is 54.76 miles, then the total area of the circle around me is 9,415.78 square miles. On a clear day, if I am 4,000 ft AGL, a simple turn around a point will bring 18,830.43 square miles into view. Clearly, this information is useless for flying. It’s just the reason we fly. ...

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