The tau of flight control

TLDR: In this paper, a new way of understanding of how pilots do what they do is proposed, based on the time to close on a goal, or close a gap, τ(t), and its derivatives.

Abstract: With this survey paper, the author proposes a new ‘tao’ – a new way of understanding – of how pilots do what they do. Research into the control of purposeful action in the natural world suggests that very rapid, efficient and ‘instinctive’ techniques have evolved based on the time to close on a goal, or close a gap, τ(t), and its derivatives. Purposeful actions involve the closure of one or more physical gaps, each with its own time to close, varying with time. Maintaining a constant rate of change of τ(t) with time ( 0·5), or a soft stop (gentle action with ṫ < 0·5). Synchronous coupling of two motions, x(t) and y(t), such that the times to close are coupled, τ x = kτ y , results in the motion gaps x(t) and y(t) being related through a power law, x = Cy 1/k, and closing smoothly together; examples of such coupling in the form of pursuit tracking in the natural world abound. Research has also shown that gaps can be closed by following ‘intrinsic’ guides, or self-generated mental models of desired motion, that have particular forms; for example, constant deceleration or constant acceleration. The gathering evidence from research into animal behaviour in the natural-world forms a background for the exploration of flight control in the man-made world. The implications for control theory, flight control developments and flight handling qualities, are considered to be profound. τ-theory suggests that natural control has a particular non-linear, albeit very simple, time varying form and that pilots learn control strategy skills by developing mental models, or internalised schemata, in the form of what are described as ‘τ guides’. In this context the author presents his perspective on flight control, briefly reviewing τ-theory and providing examples from research conducted at The University of Liverpool during the period 1999-2011, including the work of several PhD students. Concepts for guidance algorithms suitable for augmented manual or autonomous control are discussed and the implications for handling qualities developments, particularly relating to flight in degraded visual conditions, are presented. Some outstanding questions pointing directions for future research are raised.