On the Motion of Airplanes Fixing a Century-Old Error in Flight Dynamics N Ananthkrishnan & Nandan K Sinha Recently, a hundred-year-old error at the heart of flight dynamics was discovered and fixed. Following this, the basic theory of aircraft flight dynamics and its key results have undergone substantial change. The background and the aftermath of this development have been concisely described in this article. Keywords: Flight dynamics, error in Bryan’s model, corrected aerodynamic model, revised theo ry of aircraft flight Believe it or not, the modern equations for simulating the motion of an airplane in flight were presented over a century ago by Bryan 1 in 1911 (see Box A) less than a decade after the Wright brothers’ pioneering flight. These equations have been carried over virtually unchanged (but for minor notational differences) to the present. In the interim, these equations have been used to analyze and predict aircraft dynamic behavior, to simulate flight trajectories, and to design flight control laws – all quite successfully. Over the years, dozens of textbooks by experienced practitioners in the field have appeared, all of them more or less faithfully reproducing the equations by Bryan. If anything, Bryan’s equations can be claimed to have stood the test of time. Yet in an upcoming textbook 2 (Fig.1), the present authors have pointed out an error in the model put forward by Bryan – an error that has plagued flight dynamics for over a century but went unnoticed. In the rest of this article, we shall try to convey in simple terms the source of this error and speculate on how it may have arisen; we describe briefly how it has now been fixed; we explore the implications of this fix for flight dynamics education and practice, and conclude with an outlook for scientific research in the country. This article is written in as elementary and non-technical a manner as possible so as to appeal to a wider audience. The Crux of the Matter Consider the sketch in Fig. 2 which shows two different kinds of aircraft motion – the aircraft in sub- figure (a) is flying along a straight line (fixed velocity vector V) as it pitches nose-up (tail-down) as marked by the clockwise arrow. In contrast, the sketch in sub-figure (b) shows an aircraft that is also pitching nose-up (tail-down) but along a curved flight path such that the velocity vector V also pitches in sync with the aircraft. Effectively, in case (b), the velocity vector V is always aligned with the X B axis fixed to the aircraft whereas in case (a) the X B axis swings away from the velocity vector whose direction is fixed. From the point of view of an inertial observer (one on the ground), the X B -Z B axes (fixed to the aircraft) in either case (a) or (b) appear to rotate in the same manner, even at the same rate if the pitching 1 G. H. Bryan, Stability in Aviation, Macmillan, 1911. 2 N. K. Sinha and N. Ananthkrishnan, Elementary Flight Dynamics with an Introduction to Bifurcation and Continuation Methods, CRC Press, Taylor & Francis, 2013.