Methods for In-Flight Wing Shape Predictions of Highly Flexible Unmanned Aerial Vehicles: Formulation of Ko Displacement Theory

The Ko displacement theory is formulated for a cantilever tubular wing spar under bending, torsion, and combined bending and torsion loading. The Ko displacement equations are expressed in terms of strains measured at multiple sensing stations equally spaced on the surface of the wing spar. The bending and distortion strain data can then be input to the displacement equations to calculate slopes, deflections, and cross-sectional twist angles of the wing spar at the strain-sensing stations for generating the deformed shapes of flexible aircraft wing spars. The displacement equations have been successfully validated for accuracy by finite-element analysis. The Ko displacement theory that has been formulated could also be applied to calculate the deformed shape of simple and tapered beams, plates, and tapered cantilever wing boxes. The Ko displacement theory and associated strain-sensing system (such as fiber optic sensors) form a powerful tool for in-flight deformation monitoring of flexible wings and tails, such as those often employed on unmanned aerial vehicles. Ultimately, the calculated displacement data can be visually displayed in real time to the ground-based pilot for monitoring the deformed shape of unmanned aerial vehicles during flight.