Thrust of a thin plate starting impulsively

We studied on a vortex ring generated by a suddenly accelerated thin plate to understand a relation between the circulation and necessary force to accelerate the thin plate. The motion of thin plate is operated by trust force. We measured velocity fields around a circular disk, using a PIV system and high speed CMOS camera. We showed that the time derivative of the circulation related to the force to drive the disk because the disk gave energy impulsively to the vortex ring. This gives us the way to estimate thrust if we could measure the change in circulation of the starting vortex ring by the disk. We applied it to the estimation of thrust by an accelerated non-circular disk by introducing an equivalent circle that has the same area as the non-circular disk.