NTB: How long did it take you to develop the theory’s rather complicated equations, and how did you test them to verify the accuracy of your theory?
Dr. Ko: It took six years of tedious mathematical manipulations, including holidays and weekends. I developed eight different Ko Displacement Transfer Functions for non-uniform – or tapered – beams, slightly non-uniform beams, and uniform beams, including first and second order Ko Displacement Transfer Functions, as well as optimized and log-expanded Ko Displacement Transfer Functions.
The accuracy of the theory was verified by using finite element models of various structures, including the Ikhana [aircraft] wing model. The structures included tapered tubular beams, both cantilever and two-point supported; depth-tapered unswept and swept wing boxes; width-tapered wing boxes; doubly-tapered wing boxes; all under combined bending and torsional loads. Surface strains were generated from a SPAR finite-element computer program. Engineer Van Tran Fleischer then programmed in all eight Ko Displacement Transfer Functions to validate the accuracy of the predictions.
Accuracy of the Ko Displacement Theory was also experimentally validated by ground testing of the Ikhana’s wings by fiber optic team members, led by Dr. Lance Richards. Anthony Piazza installed the two-line fiber optic sensing system and gathered surface strains, Allan parker created a LabVIEW computer system for shape visualization, and Van Tran Fleischer programmed the Ko Displacement Transfer Functions to determine the optimum locations of the two-line sensing system on the Ikhana’s wing upper surface and also validated the prediction accuracy of the Ko Displacement Theory.
NTB: You recently co-authored a successful patent application for a fiber optic-based sensor technology that will make it possible to sense the shape of loaded structures such as aircraft wings and bridge supports in real time. What other potential commercial applications do you envision for this technology?
Dr. Ko: The majority of airlines; the space shuttle external tank; solid rocket booster cases; large, slender space structures; flat and curved structural panels; slender, curved structures; cylindrical walls, etc.
NTB: One question that comes to mind is, do wing structures act the same out in space as they do here on Earth?
Dr. Ko: Yes. The fiber optic sensor can only sense the structure’s surface strains, but not the deformed shapes. After the invention of the Ko Displacement Theory, a new revolutionary structure shape-sensing technology was created. Fiber optic sensors can be used to supply surface strain data so that the Ko Displacement process can convert the surface strain data into out-of-plane deflections and cross-sectional rotations for mapping out the structures overall deformed shapes for visual display.
In shape sensing, a fiber optic sensor system is like an airplane without wings. To fly the airplane, wings – in this case the Ko Displacement Theory – must be added.
NTB: When applied to a fiber optic sensor system, what does the Ko Displacement Theory do, and how does it work?
Dr. Ko: The Ko displacement transfer functions for each sensing line are written in terms of surface strains. By inputting the surface strain data, the Ko displacement transfer function can convert fiber optic measured surface strains into deflections and cross-sectional rotations using a two-line sensing system, enabling the mapping of the structure’s overall deformed shapes for visual display for the ground-based pilot.
NTB: Can your Displacement Theory be used with other types of sensor systems, or for other applications?
Dr. Ko: Yes. Surface strains can be generated from a finite-element model of the structure, or obtained using conventional strain gauges, but conventional strain gauges are too heavy for flight vehicles because of the lead wires. The most attractive candidate for surface strain sensing systems for flight vehicles is the fiber optic strain sensors because they’re lightweight and can be highly multiplexed using Bragg gratings to define the strain-sensing stations at desired sensing intervals. Another powerful characteristic of the fiber optic strain sensing system is that the strain sensing stations can be increased easily at will under a single command without the need to install additional strain sensors one-by-one, as in the case of conventional strain gauge systems.
NTB: What some people might not know about you is that you’re also an accomplished artist, so accomplished that in 1968 President Lyndon Johnson made you an honorary citizen of Texas, and one of your paintings now resides in the permanent collection of the Lyndon Baines Johnson Library in Austin, Texas. Tell us how that all came about.
Dr. Ko: I am a watercolor artist with invited articles published in the watercolor page of the October 1970 issue of American Artist magazine, and a special article published in the July/August 1976 issue of Southwest Art magazine. I lived in San Antonio, Texas while I was doing research work at Southwest Research Institute, and I was invited by the San Antonio City Library to hold regular one-man shows almost every year. During the HemisFair ’68 world’s fair, I was invited to demonstrate my advanced watercolor painting techniques for the President of the United States, Lyndon Baines Johnson; Texas Governor John Connolly; and numerous international dignitaries. I painted “L.B.J. Ranch in Springtime” that day, and that painting is now in the permanent collection of the Lyndon Baines Johnson Library in Austin, Texas. Because of my artistic contributions to the state of Texas, the governor bestowed upon me honorary citizenship in the Republic of Texas.