8 Inches Per Mile Squared Is Wrong

So here s the thing. Where r is the radius of the earth we will use 3959 miles d is our distance and δ which is our unknown quantity the drop height so we can put these into the equation as follows.

Is The 8 Inch Per Mile Curvature Rule Valid For Long Distances

The eight inches per square mile is pretty accurate for a globe if your height is 0.

8 inches per mile squared is wrong. This is fair use. If you draw a large circle and a straight edge extending straight out from the top of the circle you will see that each incremental measuring unit along the straight edge correlates with a longer drop than did the previous unit. The biggest problem is that flat earthers with few exceptions apply the formula to the wrong situation.

From the pythagorean theorem we have the relationship. A b c. How to derive 8 per mile squared and why it s wrong.

If you see. Eight inches per mile squared is wrong. One thing you hear flat earthers say often is that the curvature of the earth is 8 inch per mile squared.

I think everyone on this site will agree that the earth is not parabola shaped. This is only a rough estimate for the first few miles though. But that isn t even the biggest problem with eight inches per miles squared.

But for a globe shaped earth the curve near the vertex of the 8 mi 2 parabola is pretty close to the curvature of the earth so it works well for approximations over small distances. The 8 inches per mile squared is actually correct for up to around 100 miles. For most practical purposes though it suffices for measuring the drop.

Unfortunately if you height isn t zero if you re standing up then that equation rapidly looses all meaning. The 8 inches per miles squared approximation function underestimates the correct value at distances less than 391 1 km or 243 1 mi so at 391 1 km it is the most accurate. Eight inches per mile squared never curves back on itself and becomes progressively less circular as the distance increases.

Both calculators also agree more or less with 8 inches per mile squared thereby validating rowbotham s simplified ball park equation. At 1 mi or 1 609 km its error is about 0 0314 and decreases to 0 at 391 1 km or 243 1 mi. 8 inches per mile squared is only useful up to about 100 miles though after which something more precise is required.

On longer distances the error starts to increase again. In our case we will let c r δ. 8 inches per mile squared describes a parabola.

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