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Chris Finnegan
Microlighting - Affordable Aviation
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  • Does Bernoulli Suck?


    Theories of Flight
    Captain Cargo

    Years ago, when I was learning to fly, like all aspiring pilots, I was taught that Bernoulli's theorem explained lift. This was great: a theorem (essentially an unproven law) was responsible for the magical feat of defying gravity. To my nineteen-year old mind, it appeared that no-one had yet indisputably proved why aircraft fly. I learnt the relevant formulas and never questioned them: Bernoulli was obviously a much cleverer man than I. However, many years later, while attending a performance course for the Boeing 727, the instructor, a Swedish mathematician turned aircraft performance consultant, with two hours to wait for his commercial flight home, asked at the end of the days course is anyone was interested in learning about a different theory of flight. Intrigued, I stayed. To my great surprise, only two other pilots remained. Perhaps the others did not really care why aircraft flew, as long as they got paid for flying them. As we settled down with a fresh cup of coffee, the man who was just about to shatter my last romantic notion of aviation explained that while providing an accurate model for studying lift, Bernoulli's Theorem had some flaws. It was developed by studying the behaviour of incompressible fluids in pipes. Newtons Second Law of Motion offered a more practical, albeit less romantic, explanation. Lift is actually the force produced by turning a moving fluid. We all know the equation:

    F=ma: Force =mass x acceleration.

    Acceleration being a change of velocity over time means we can write the equation thus:

    F=m(V1-V0)
    (t1-t0)

    This equation shows that changing either the speed or direction of a flow produces a force. This force is lift.

    Stunned, we sat there while he drew an aircraft on the blackboard and did the sums according to both explanations. The answers, of course, were identical. How come I had been flying for twelve years before learning of this? I'd been hoodwinked by a theorem. Of course, Bernoulli had developed his theorem while studying fluids, while Newton had not. Is this the reason why Bernoulli is the chosen explanation? Because it's part of the history of aviation? In four years simulator training, I have only come across two pilots who'd ever heard of this Newtonian explanation. Perhaps it's because it is too simple, too mundane: there's no magic with a law. A theorem keeps aviation in the realms of myth, with a lineage straight back to Icarus.

    I have since enquired of a number of newly qualified pilots whether Bernoulli is still the man, or whether Newton has assumed his rightful place in aeronautic lore. Bernoulli still holds sway, certainly here in the UK. Surely this Newtonian explanation should be part of the curriculum? I asked this question of a lecturer for ATPL exams based in Oxford. His answer shattered another illusion: that of the integrity of the taught word.

    “We don't want to confuse anyone”, he said. “As long as pilots think they know why it flies, then I've done my job.”

    He's right. Ignorance was bliss.

    by Captain Cargo

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