Dr. William Ko joined NASA’s Dryden Flight Research Center in 1977 after receiving a PhD in aeronautics from California Institute of Technology and conducting research at Southwest Research Institute in San Antonio, Texas. An accomplished scientist and inventor, he is credited with developing a number of mathematical theories critical to advancing the state-of-the-art in aerospace structural mechanics including the Blatz-Ko Constitutive Law for hyper-elastic materials, the Ko Flight Structure Aging Theory for fatigue life predictions, and the Ko Displacement Theory for structural shape predictions. The Ko Displacement Theory is currently being used at NASA Dryden to develop sophisticated fiber optic shape sensing technology that could one day give aircraft wings the ability to alter their shape in flight.

NASA Tech Briefs: After graduating from National Taiwan University with a degree in mechanical engineering, you began your professional career as a machine design engineer with the Taiwan Railroad Administration. How did you go from designing parts for railcars to analyzing structures for air and spacecraft?

Dr. William Ko: The steam locomotive era was over. After Russia launched Sputnik, I was impressed and became interested in new aerospace technologies, especially solid rocket motor technology. I applied to Caltech and was accepted, and earned a masters degree and PhD in aeronautics. During my PhD program I was partially supported by a NASA fellowship, which was $200 a month in 1962. During that time I invented the Blatz-Ko Constitutive Theory in 1962 for hyper-elastic materials such as solid rocket motor grains. It has been widely used by many researchers since 1962. As of November 4, 2009, international citations of Blatz-Ko reached 192,000.

NTB: You’ve been at NASA for 32 years now. Tell us a little bit about some of the more interesting projects you’ve worked on during that time.

Dr. Ko: During the space shuttle Columbia era, my group conducted the reentry heating analysis for predictions of the structural temperatures the Columbia would experience during reentry flights. This was the biggest job, and the most exciting. Later on, because the B-52 pylon hooks carrying the solid rocket booster drop test vehicle failed during taxiing, I developed the Ko Structural Aging Theory to predict how many times these hooks could be used to hoist the heavy drop test vehicle, which weighed 48,143 lb, into the sky for drop tests. Then I analyzed the thermal buckling of sandwich panels that are applied to the spacecraft structures, and during that time I invented superplastically formed, diffusion bonded, orthogonally corrugated structures. Recently I performed lunar reentry heating analysis of CEV (Crew Exploration Vehicle) wall structures to determine the optimum thicknesses of thermal protection needed for the CEV. And my latest invention is the Ko Displacement Theory with eight displacement transfer functions. At present, I have 157 technical publications.

NTB: Tell us about the Ko Displacement Theory. What, exactly, is the Ko Displacement Theory and how did you come up with it?

Dr. Ko: The Ko Displacement Theory was motivated in 2003 by the Helios flying wing project, which had a 247 foot wing span with wingtip deflections reaching 40 feet. The Helios flying wing failed in June 2003, creating a need to develop some kind of new technology to predict the in-flight deformed shapes of unmanned aircraft wings and display it for the ground-based pilots so they could maintain safe flights. The basic idea of the theory is to discretize the beam – or wing – structure into multiple small domains so that surface strain distribution may be represented with piece-wise linear – or piece-wise nonlinear – curves. This discretization approach enabled the integrations of the beam curvature equation to yield slope and deflection equations for each domain so one can plot the deformed shape of the structure. Fiber optic sensors, or conventional strain gauges, may be used to sense the surface strains for the Ko displacement transfer functions to convert into deflections and cross-sectional rotation for mapping out overall structure deformed shapes.

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