The scaling of the drag force on an accelerating plate

The drag force on an accelerating object is usually described by a quasi-steady force that scales with the square of the instantaneous velocity and an added mass force due to the acceleration that scales directly proportional to the acceleration. This appears to underestimate the experimentally observed instantaneous drag force on an accelerating plate. We aim to find a better description of the drag force on a flat plate in an unsteady flow by measuring both the drag force and velocity field for a large range of constant accelerations and velocities. Our experiments show that the force due to acceleration scales with the square root of the acceleration, contrary to a linear scaling that is expected from added mass. This can be associated with a history force that describes the generation and advection of vorticity at the plate surface. We present a new scaling law for the drag force on accelerating plates. This avoids previous inconsistencies in using added mass forces in the description of forces on accelerating plates. This new scaling law has proven useful in predicting the drag force for different plate geometries and non-constant accelerations.