Inertial and Aerodynamic Torques on the Wings of Diptera in Flight

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Abstract
The magnitude and distribution of the torques caused by inertial and aerodynamic forces on the wings of Diptera in flight are calculated. The bending torque at stroke reversal due to the inertia of the virtual mass of air bound to the wing is only slightly less than the torque due to the inertia of the wing mass itself. The maximum inertial torque due to both wing mass and virtual mass is usually slightly greater than the maximum aerodynamic torque encountered by the wings. Bending torques decrease rapidly away from the wing base. Pitching torques are much smaller than bending torques at the wing base, but do not decrease much until near the tip. The pattern of loading affects the wing design. Wings are thicker nearer the base to resist bending, but thin and light near the tip to minimize inertial energy expenditure. Their open, corrugated structure resists bending, while allowing them to be twisted as a result of the weak pitching moments.