Water droplets coalesce into larger ones in atmospheric clouds to form rain. But droplets on collision courses do not always coalesce due to the cushioning effects of the air between them. The extent to which these so-called hydrodynamic interactions reduce coalescence rates is embodied in the collision efficiency, which is often small and is not generally known. In order to characterize the mechanisms that determine the collision efficiency, we exploited new time-resolved three-dimensional droplet tracking techniques to measure the positions of cloud droplet pairs settling through quiescent air. We did so with an unprecedented precision that enabled us to calculate the relative positions, velocities, and accelerations of the droplets at droplet surface-to-surface separations as small as about one-tenth of a droplet diameter. We show that relative accelerations clearly distinguish coalescing from non-coalescing droplet trajectories, the former being associated with relative accelerations that exceeded a threshold value. We outline how relative accelerations relate to hydrodynamic interactions, and present scaling arguments that predict the threshold relative acceleration. We speculate that the relative acceleration distribution of droplets in turbulent clouds can parameterize the collision efficiency, and that this distribution together with the well-known relative position and velocity distributions can generate a physical description of both the collision and coalescence rates of cloud droplets. I. INTRODUCTIONIn warm atmospheric clouds, liquid water droplets are set onto collision courses by mechanisms that include differential sedimentation and turbulence [1][2][3]. The rate at which this happens can be explained by the way turbulence generates droplet relative position and velocity distributions [4,5]. In order for droplets on collision courses to coalescence into one larger droplet, however, they need to squeeze out the air between them, a process that couples the motions of droplets relative to one another through hydrodynamic interaction (HI) [e.g. 6, 7]. These interactions cause droplets to decelerate, which modifies the probability distributions of droplet relative positions and velocities in a way as yet unknown [e.g. 8-10]. The effect is most pronounced precisely where these distributions need to be evaluated, which is at the moment of contact between two droplets.Theoretical and empirical descriptions of the relative velocity distributions [e.g. 11-13] and radial distribution functions [e.g. 14-16] exist for droplets that are separated widely enough that they do not