Identifiability of hydrodynamic forces inferred from instrumented-particle measurements at the threshold of motion

Abstract. Instrumented particles carrying inertial measurement units are increasingly used to infer the hydrodynamic drag and lift acting on a coarse grain at the threshold of motion. Because the grain is still in contact with its supporting grains at that instant, the measured response is produced jointly by the flow and by the bed–particle contact reactions, so the recovery of the hydrodynamic part is an inverse problem whose identifiability has not been examined. This study examines it, using an openly released dataset of 30 threshold conditions and two independent published analyses of a common subset of those runs. Three results follow. First, a recently proposed bounded inversion is degenerate in lift: for every contact angle and every friction coefficient the admissible interval collapses to [0,W'], and the inferred lift coefficient reduces to the exact identity C_L,eff = 2/3Fr_d^-2, so that its reported constancy is a restatement of a constant critical movability number and carries no information from the sensor. Second, because the two published analyses normalise the same rectified impulse by different durations, their ratio returns the fraction of the onset window during which the acceleration is positive; that fraction is 0.14–0.17, or two to three samples at 100 Hz. Third, taking moments about the contact point rather than the centre of mass annihilates both contact reactions exactly for a spherical grain and yields an identity linking the accelerometer and gyroscope channels; the identity requires a non-negative tangential reaction and is violated in all 30 conditions, the measured angular acceleration being 27–66 % of the value implied by the measured linear accelerations. Closing the inversion with the gyroscope channel alone returns C_D = 0.74–1.55, which brackets independent fixed-particle measurements, from the same published data. Instrumented particles measure the net response of a grain, and hydrodynamic coefficients are recoverable from them only when the rotational channel is referred to the contact point or when contact reactions are measured independently.