Pilots will tell me that I cannot believe my own eyes, and that planes overhead are much higher than they appear from the ground. I have found that difficult to swallow, so I have fallen back on what I know to be true – trigonometry.

If I observe a plane pass over a point on the ground that is the length of a football field away, or 300 feet, and the angle of elevation from eye level to the plane is 30°, the tangent of which is equivalent to the plane’s altitude above ground level divided by the distance along the ground from the observer to the point directly below the plane, then I can deduce that the plane’s altitude is less than 180 feet AGL, including accounting for the 5.5 feet from the ground to my eyes.

The 300 feet is probably an overestimation, but let’s err on the side of caution. Also, let’s say my angle is off, and it was really 35°.  That’s still only 215 feet AGL. Even if it were 45°, which it was not, that would be just over 300 feet AGL.

These estimations were made on an approach that was announced as instrumental. The GPS-A approach has an MDA (minimum descent altitude) of 387 feet AGL – which is based on the 193 feet above sea level at Tracy Municipal Airport (TCY) in California. If the point of observation is 25 feet higher than the airport, this still does not account for the discrepancy.

Those in the aviation community may not buy the logic, but I’m sure Euclid and Pythagoras would agree.


Tracy, Calif.

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