Thursday, January 13, 2011

Math Myths

Bruce Landsberg wrote about Math Myths in this month's AOPA Pilot. Here is the letter to the editor I sent about the column.

Since I am both a CFI and a mathematics professor, I was intrigued by Bruce Landsberg’s “Math Myths” column in January’s AOPA Pilot.

The FAA’s Aviation Instructor’s Handbook (FAA-H-8083-9A) details four levels of learning: rote, understanding, application, and correlation. Landsberg emphasizes the rote part of learning, which is unusual in a safety-oriented column. Safety comes from application, which comes from understanding.

To see the value in understanding, consider the role of formulas, which express a lot of information in compact form. In Landsberg’s example of the increase in landing distance from increased speed, he presents a rote rule, but that application comes from under- standing the equation for lift. Correlation occurs when one uses the same equation to understand minimum control speed (Vmc) in a multiengine aircraft.

Many former myths about aviation were dispelled by mathematics. For example, pilots who did not understand the difference between true air speed and indicated air speed thought that they flew faster at lower altitudes. It took the mathematical model of the International Standard Atmosphere, as outlined in the beginning of Aerodynamics for Naval Aviators, to set us straight.

The real danger lies in not understanding that mathematical problems like computing takeoff distance, endurance, and landing distance must be solved before flying. No amount of mathematical skill can compensate for inadequate preflight planning. Flying well demands that we use our whole intellect, not just part.

The mathematics of flying is still not fully understood, especially in the area of atmospheric phenomena like icing and microclimates. We have to rely on “conceptual understanding” to handle these phenomena safely. But the line between conceptual understanding and superstition is very thin. Tackling these problems does not mean that every pilot needs to study more mathematics, but understanding and applying their solutions means that many pilots should.

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