A computerized engineering handbook significantly reduced the time required to design and optimize a 42 meter windmill tower from three to two weeks by iterative determining of section properties. Section properties calculated with the computerized handbook were input to a finite element analysis program that allowed engineers to determine the strength and modal properties of the structure. Using conventional hand calculations, three to five minutes would have been required for each of the approximately 800 design alternatives that were evaluated in order to optimize the design.

Kenetech Windpower is the world's leading manufacturer of wind turbines. Its operations include a 420 Megawatt windplant in northern California and other development projects across the U.S., Canada, Europe and Central America. Kenetech windplants produce electricity at costs averaging between four and five cents per kilowatt hour which is competitive with new coal and natural gas fueled systems. Kenetech wind turbines average 95% availability and have generated over 5 billion kilowatt hours of electricity.

The new Model 33M-VS represents a breakthrough in wind turbine design. Conventional turbines operate at a constant speed so that changes in wind speed create high stress loads. A power electronics converter in the 33M-VS allows the rotor and generator to accelerate with higher wind speeds while assuring that a constant frequency alternating current is maintained. The result is reduced operating loads which increases efficiency and decreases the cost to build and maintain the turbine.

Recently, the author was assigned to design and optimize a tubular tower for a 33-meter blade diameter, 42 meter high version of this turbine for a major windplant. The tubes used to build the tower are created from sheet steel which is rolled into a conical section and welded longitudinally. Frequently, a special tower needs to be designed for wind turbine installation sites because different areas have better winds at different heights.

The basic process for designing a wind turbine tower consists of building a finite element model of the tower and applying wind and gravitational loads to determine whether the tower has sufficient buckling and fatigue strength. The modal frequencies of the tower are also analyzed in order to insure that the structure will not get excited by the turbine within its normal operating range. The Images 3-D finite element analysis program from Celestial Software, Berkeley, California, is used for structural and modal analyses of the structures.

Usually, each tower is designed with a specific taper to maintain the strength and fatigue resistance at a desirable level based on predicted loads. The role of the engineer is to interactively try different alternatives until the functional requirements are met with the minimum expenditure of material, welding and erection labor. Normally, the engineer, based on experience, selects certain shapes and thicknesses and uses the results of computations to progressively optimize the design. The final design for the 42 foot towers in this project require 62,000 pounds of structural steel.

Accurately representing each individual tubular element of the tower's structure by rate or solid FEA elements would take an enormous amount of time. Engineers typically simplify this task by modeling the tubes as beam elements. This makes it necessary to calculate the section properties of each tube used in the tower so it can be input to the FEA program. The traditional way to calculate these section properties is to use engineering handbook formulas to calculate area, moment of inertia, shear shape factor and shear stress factor. These calculations typically take three to five minutes per section.

This would not be a significant amount of time except that the calculations generally have to be repeated hundreds of times in order to optimize the design of a tower -- minimize the material and number of welds used. In order to optimize the tower design, it was necessary to evaluate 9 different tapers for the overall tower configuration. For each taper that was evaluated, the author tried three or four different thicknesses of tubing. For each taper-thickness combination, section properties had to be calculated for each of the 22 different tubing types of various diameters and thicknesses used in the tower. It should also be noted that design requirements changed several times during the tower design process which necessitated additional iterations. The total number of section property calculations for the project exceeded 1000.

In this project, the section properties for each of these alternatives were calculated in a matter of seconds with The Desktop Engineer, a computerized engineering handbook, from Desktop Engineering Int'l, Inc., Woodcliff Lake, New Jersey. The engineer selected the hollow circle module of the program and input the inner and outer diameter of the proposed cross-section. The program calculated the area, centroidal distances of the axis to remote fibers, moments and polar moments of inertia, shear shape factor and radius of gyration. The information was saved in a file and plotted for archival purposes.

An important advantage of the computerized engineering handbook is that it minimizes the possibility of computational errors. The author has been using the program for nearly a decade and has never encountered a serious deficiency in it. The output of the program includes all input parameters which makes it easy to check for the only possible source of error. The program provides a simple "fill in the blanks" type interface which makes it possible for even inexperienced engineers to solve difficult problems. The graphical user interface of the program makes it possible to use it after an extended absence without taking any time for refamiliarization.

The software package was used in several other areas of the design process. The thick plate cylindrical module was used to calculate shrink fits. The beam section of the program was used to analyze a simplified version of various structural components as a check on the finite element analysis. Stress concentration factors were verified. Fast computations of principal stresses for bi-axial/tri-axial states of stress were performed as well as iterrative computations of buckling stability of tower truss members and shells, etc. This provided a valuable assurance that a major error -- such as an input parameter or boundary condition -- was not made during detailed and more complex FEA.

The Desktop Engineer incorporates solutions to over 5000 structural/mechanical engineering equations found in over 100 reference books. It includes 37 modules grouped into the following categories: geometric and material properties; beams and columns; rings, arches and frames; plates, shells, and pressure vessels; cables and springs; natural frequencies and dynamics; stresses; user defined modules; and utilities. Modules are self-prompting to help the user find section properties, displacement, forces, stresses, etc. The Desktop Engineer also includes a material property database and a unit conversion utility. Once the problem is defined, the program will perform the necessary calculations and solutions to provide the required output. The program operates under MS-DOS or Microsoft Windows as well UNIX using the X-Window system and the Motif graphical user interface.