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The moments and torques acting on a deforming body determine its stability and maneuverability. For animals, robots, vehicles, and other deforming objects locomoting in liquid or gaseous fluids, these fluid moments are challenging to accurately measure during unconstrained motion. Particle image velocimetry and aerodynamic force platforms have the potential to resolve this challenge through the use of control surface integration. These measurement techniques have previously been used to recover fluid forces. Here, we show how control surface integration can similarly be used to recover the 3D fluid moments generated about a deforming body’s center of mass. We first derive a general formulation that can be applied to any body locomoting in a fluid. We then show when and how this formulation can be greatly simplified without loss of accuracy for conditions commonly encountered during fluid experiments, such as for tests done in wind or water channels. Finally, we provide detailed formulations to show how measurements from an aerodynamic force platform can be used to determine the net instantaneous moments generated by a freely flying body. These formulations also apply more generally to other fluid applications, such as underwater swimming or locomotion over water surfaces.

Fluid moment and force measurement based on control surface integration