January 1, 2011
By Bruce Landsberg
There is a myth among many in aviation and education that advanced math is essential to fly with any degree of safety and skill. Unfortunately, my father did not pass along his genetic gift for advanced mathematics, but that was little detriment to my becoming a pilot. With the basics of addition, subtraction, multiplication, and division, safe flight operation is well within the grasp of math illiterates.
The late Bill Kershner was a math whiz, test pilot, and engineer. Having to communicate with designers and engineers, which is a language unto itself, he needed to be fluent in calculus and trigonometry. In his flight instruction books, Bill often explained an aeronautical concept in normal, lucid English and then filled a page with math hieroglyphics. I usually got the concept right off and looked for the practical application to flying airplanes. My interaction with engineers remains largely social, so heavy math is irrelevant.
One of the greatest aviation books eschews math. Stick and Rudder, by Wolfgang Langewiesche, discusses the art of flying, and you will find nary a formula for coexisting with gravity in its nearly 400 pages. I used the Langewiesche approach with my flight students, and the Air Safety Institute employed them in the award-winning course Practical Aerodynamics. Another excellent book by John Hoyt, As The Pro Flies, focuses on concept, not math. The whole idea is to keep pilots alive.
My most impenetrable treatise was Aerodynamics for Naval Aviators. Prof. Harrison Hurt from the University of Southern California can’t go more than a page without using Greek alphabet notation, simultaneous equations, and square roots to warm the heart of any engineer. But, it’s brain-confounding for many of us. Critical concepts, for example, on how landing distance performance greatly increases with only minor increases in speed are well explained. A 10-percent increase in landing speed results in a 21-percent increase in landing distance. All pilots should understand that, which makes the ensuing computational bludgeoning unnecessary.
Professor emeritus G.V. Ramathan, of math, statistics, and computer science at the University of Illinois in Chicago, recently noted in an editorial, “Unlike literature, history, politics, and music, math has little relevance to everyday life. That courses such as ‘Qualitative Reasoning’ improve critical thinking is an unsubstantiated myth. All the mathematics that one needs in real life can be learned in early years without much fuss.” Some math professors will have a different take.
Pilots do need basic math for practical estimates and to read charts and graphs—all within the capability of liberal arts majors. When should we begin descent from cruise flight? In a piston-engine aircraft where cooling is a consideration, use five miles per thousand feet. To descend 7,000 feet to the airport, start down about 35 miles out. In turbine aircraft, where cooling is irrelevant, three miles per thousand feet works well. Multiplication.
Taking the Naval Aviators’ percentage, if the landing distance based on the POH (the best the manufacturer’s test pilot can do on a good day with a new aircraft) is 2,000 feet over the 50-foot obstacle and you’re having a bad day by being a bit fast, 2,400 feet is the approximation. From an operational perspective, the Air Safety Institute recommends adding 50 percent to the POH number, so that works out to 3,000 feet. It provides some margin for runway slope, some clearance over a taller obstacle, and less-than-perfect technique.
Climb gradient per nautical mile is required for many instrument departures. That number isn’t in the POH but can easily be translated into feet per minute. The standard gradient is 200 feet per nautical mile. If the ground speed is 120 knots, that’s two nautical miles per minute. Two hundred times two means 400 fpm is needed to comply with the gradient. But there’s a chart to use for conversion if you need it. Tailwind? Be a bit more conservative. Headwind? Fat city!
Remember the elementary school problems of time, speed, and distance? When a train leaves Chicago doing 60 miles an hour and another leaves Nashville doing 30 miles an hour, will they pass somewhere in Kentucky, Indiana, or Colorado—and so what? But for pilots it’s important to know that with 24 gallons of fuel on board and a fuel burn of eight gallons an hour, about three hours after takeoff a collision with the Nashville-bound train is a distinct possibility! Division or multiplication. There are still about two fuel mismanagement accidents weekly, so the basic math bone isn’t working for some pilots—or maybe it has nothing to do with math at all.
Pilots should understand subtraction. The economics of buying an aircraft often require numerous subtraction lines in the checkbook or credit card statement, so perhaps a partner is a good idea—and there’s division again. Like taking a spouse, it’s not the acquisition but the upkeep that becomes expensive.
Basic math used in conjunction with conceptual understanding will keep one alive much longer than computational algebra on why Bernoulli just isn’t working today. As we rebuild the pilot population there’s no need to throw up a high math barrier to aspiring pilots. The guys and gals who build aircraft and airports and design IFR approaches will do the heavy math so the rest of us don’t have to.
Bruce Landsberg was named president of the AOPA Foundation in 2010.
Air Safety Institute,
Pilot Training and Certification
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