Helicopter collisions with obstacles are one of the most frequent and most devastating causes of accidents. To avoid these collisions in low-speed operations a “haptic ticker” cue in form of repetitive impulses as a force feedback was designed for an active sidestick. Various design questions were examined in pilot campaigns using a full flight simulator and four test scenarios. As a result, the pilots always knew which distance-based hazard area (green, yellow, red) they were in. Furthermore, the ticker is disruptive and roughly reduces the handling qualities from Level 1 to Level 2. It is therefore primarily activated as a hazard warning and not as a main input to control the distance. As a warning cue the ticker was evaluated as non-disturbing. The force threshold to detect the direction of a tick was determined. With tick strengths above this threshold, the direction is still not recognised at all in around 2% of the ticks. For the remaining ticks, the accuracy with which the direction is recognised is about 15°. In the fourth scenario, obstacles were moved towards the hovering helicopter, potentially forcing a collision. However, with the ticker a collision occurred in less than 4% of the cases, instead of 84% without the ticker. The ticker was rated as very intuitive and worth recommending. When asked how many accidents of this kind could be prevented with this ticker, all five pilots independently estimated 75%.

This paper presents the first analytical solutions for the three-dimensional motion of two idealized mobiles controlled by a particular guidance law designed to avoid a collision with minimal path deviation. The mobiles can be regarded as particles, and guidance can be interpreted as complex forces of interaction between the particles. The motion is then a generalized form of two-body Newtonian dynamics. If the mobiles have equal speeds, the relative motion is determined through various transformations of the differential equations. Solvability relies on congruence and symmetries of the paths, which is exploited to reduce the original twelve first-order differential equations to three first-order equations for the relative motion. The resulting state space is partitioned into five invariant subsets, with various symmetries and stabilities. One of these sets describes planar motion, where simple explicit solutions are given. In nonplanar motion, the solution is formally reduced to quadrature. A numerical calculation gives the separation at the closest point of approach, which provides control over minimum separation. The results should be of interest because of their application, which includes, most importantly, the prevention of midair collisions between aircraft, but also potential application to land, water and space vehicles. The solutions should be of interest to mathematical specialists in dynamical systems, because of some novel constants of the motion, novel symmetries, and the associated reducibility of the equations.