Prandtl's 1933 Bell-Shaped Lift Distribution - Translation and Commentary

In 1933, Ludwig Prandtl published a paper in the journal Zeitschrift für Flugtechnik und Motorluftschiffarht concerning minimum induced drag of straight wings. His publication showed that the elliptic lift distribution is not the optimum lift distribution to minimize induced drag in all cases. In fact, the elliptic lift distribution is only optimum for the special case of prescribed gross weight and wingspan. Because wing weight is a function of wingspan and lift distribution, there exists an optimum wingspan and lift distribution for a given net weight. Prandtl obtained an analytic solution for an alternate lift distribution that minimizes induced drag for prescribed gross lift and prescribed moment of inertia of the lift distribution. Unlike many of Prandtl’s other publications, his 1933 paper was never officially published in the English language. The present work includes an electronic typeset of the original German document, as well as a careful English translation. A commentary on the translation and typesetting is also included in an attempt to remove any confusion about the original document.

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